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LIBRARY
Michinan State
University

 

 

 

This is to certify that the

dissertation entitled

 

Computer—Assisted Optimization of Separations
in Capillary Zone Electrophoresis
presentedby

Marina Franco Maggi Tavares

has been accepted towards fulfillment

of the requirements for
Ph.D. degreein Analytical Chemistry
’U V ' . m A)
Major professor

Date September 9, 1993

MUN”... AMr-uln’u ‘ ‘ I" 'A

042771

 

 

 

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COMI

 

COMPUTER-ASSISTED OPTIMIZATION OF SEPARATIONS
IN CAPILLARY ZONE ELECTROPHORESIS

By

Marina Franco Maggi Tavares

A DISSERTATION

Submitted to
Michigan State University”
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

 

1 993

 

 

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ABSTRACT

COMPUTER-ASSISTED OPTIMIZATION OF SEPARATIONS
IN CAPILLARY ZONE ELECTROPHORESIS

By

Marina Franco Maggi Tavares

In this work, a systematic approach to separations has been established
for capillary zone electrophoresis with the development of a computer-assisted
optimization routine. This program incorporates theoretical models for both
electroosmotic and electrophoretic migration as well as a simple rationale for
zone dispersion. Variables related to the buffer composition (pH, ionic strength
and buffer concentration), capillary dimensions (diameter and length) and
instrumental parameters (applied voltage or current) are input to the optimization
routine. Resolution between adjacent zones is the primary criterion for
optimization. By methodically varying the input parameters and evaluating the
overall quality of the separation with an appropriate response function, this
computer program can be used to predict the experimental conditions required
for optimal separation of the solutes under consideration.

The mathematical model for electroosmotic migration describes the
response of the fused-silica capillary surface in analogy to an ion—selective
electrode. By studying the electroosmotic flow characteristics of solutions of
singly charged, strong electrolytes (NaCl, LiCl, KCI, NaBr, Nal, NaN03. and
NaClO4), as well as the phosphate buffer system, an equation that relates zeta
potential, and ultimately electroosmotic mobility, to the composition and pH of
the solution was derived. The model for electrophoretic migration is based on
classical equilibrium calculations and requires knowledge of the dissociation

constants and electrophoretic mobilities of the solutes under investigation. In

 

 

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the model for zone dispersion, the temporal width of each solute zone is derived
from contributions to variance resulting from longitudinal diffusion and finite
injection and detection volumes.

The experimental validation of the computer optimization program was
demonstrated for a mixture of the nucleotides adenosine, guanosine, cytidine,
and uridine 5'-mono- and di-phosphates in phosphate buffer solution. The
program predicted the correct elution order for all nucleotides, and provided a
reasonable estimate of the migration time, peak width and resolution within the
entire range of pH studied (from 6 to 11). The number of theoretical plates was
estimated as 1.4 x 105 plates per meter, which is representative of the efficiency
of the technique. The program was then applied to study the separation of
tetracycline antibiotics (tetracycline, chlortetracycline, demeclocycline,
oxytetracycline, doxycycline, methacycline, and minocycline) in phosphate buffer
solution. At the predicted optimum conditions, baseline resolution was not
completely achieved for all solutes, however, the separation can be performed
satisfactorily with 3 x 104 theoretical plates per meter (UV—absorbance
detection), under constant-current conditions of 20 uA, in a phosphate buffer
solution formulated at pH 7.5, with 15 mM total sodium concentration, 18.2 mM
ionic strength, and 4.29 mM buffer concentration. The analysis of tetracycline
pharmaceutical formulations was then performed under the optimized conditions,
with a detection limit of 10-5 M at a signal-to-noise of approximately 3, and a
linear range of two orders of magnitude. Capillary zone electrophoresis is
shown to be a suitable alternative method for the analysis of tetracycline,

tetracycline derivatives as well as common decomposition products.

 

 

 

 

Copyright by

Marina Franco Maggi Tavares

1 993

 

 

 

 

to my family

 

for the gu.
would like
Enke. Dr
discussior
fireful rel
IMlchigan
aCItnowled.
Clinllfico e

I wa
Evans, Dr. .
Che“, Dan
Ogasawaraj

You

ConsI‘Ielalio

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my advisor Dr. V. McGuffin
for the guidance and encouragement during the development of this work. I also
would like to express my appreciation to the members of my committee, Dr. C.
Enke, Dr. J. Watson, Dr. C. Chang, and Dr. J. Holland for the helpful
discussions. I am indebted to Dr. Faye Ogasawara, and Daniel Hopkins for their
careful revisions of this manuscript. I would like to thank Dr. Gerald Larson
(Michigan State University) for the pharmaceutical samples. I gratefully
acknowledge a fellowship from the Conselho Nacional de Desenvolvimento
Cientifico e Tecnologico (CNPq) of Brazil.

I was honored, throughout these years, with the friendship of Dr. Chris
Evans, Dr. Jon Wahl, John Judge, Dr. Jong Shin Yoo, Yiwen Wang, Dr. Shu-Hui
Chen, Daniel Hopkins, Patrick Lukulay, Jingpin Jia, Ying Wang, Dr. Faye
Ogasawara, and Chomin Lee.

You all, in many ways, touched my soul with your kindness and

consideration.

See you in Brazil.

vi

A“), I ‘_ '

 

 

LIST OF '
LIST OF I
lIST OF E

CHAPTEF

 

 

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

LIST OF SYMBOLS

CHAPTER 1

CHAPTER 2

CHAPTER 3

CAPILLARY ELECTROPHORESIS - FUNDAMENTAL
CONCEPTS AND HISTORICAL BACKGROUND

1.1 Modes of Electrophoresis
1.2 Rationale for Capillary Electrophoresis
1.3 Instrumental Considerations
Capillary Technology
1.4 Injection
Sample Concentration Strategies
1.5 Detection
Detector Cell Designs
Sample Collection Strategies
1.6 Conclusions
1.7 References

EXPERIMENTAL METHODS

2.1 Capillary Zone Electrophoresis System
2.2 Capillary Surface Treatment _ ‘
2.3 Electroomotic Flow Determination
2.4 Reagents and Solutions
Electrolyte Solutions
Phosphate Buffers
Nucleotides
Tetracyclines
2.5 Physical Measurements
2.6 Data Processing
2.7 References

THEORETICAL MODEL OF ELECTROOSMOTIC FLOW

3.1 Introduction

3.2 Theory
Ion-selective Membranes
Electrical Double Layer

xii

xix

42
45

46
48

Analogy between Ion-selective Membranes and Double-

layer Structure at Silica Surfaces
vii

CHAPTEI

CHAPTER

C”three

 

CHAPTER 4

CHAPTER 5

CHAPTER 6

 

3.3 Results and Discussion 56
Preliminary Studies of Electroosmotic Flow under
Constant-Voltage Conditions
Preliminary Studies of Electroosmotic Flow under
Constant-Current Conditions
Validation of the Ion-selective Model
3.4 Conclusions 88
3.5 References 89

OPTIMIZATION OF SEPARATIONS IN CAPILLARY ZONE
ELECTROPHORESIS

4.1 Introduction 92
4.2 Optimization Strategy 94

Model for Voltage

Model for Electroosmotic Mobility

Model for Effective Mobility

Model for Zone Variance

Chromatographic Resolution Statistic as a Response

Function
4. 3 Use of the Optimization Program as a Pedagogical Approach
to Capillary Zone Electrophoresis 142

4. 4 Conclusions 174
4.5 References 180

EXPERIMENTAL VALIDATION OF THE OPTIMIZATION
PROGRAM WITH NUCLEOTIDE MIXTURES

5.1 Introduction 183

5. 2 Results and Discussion 186
Study of the Electrophoretic Behavior of Nucleotides
Nucleotides as Model Solutes for the Optimization

Program ,
5 3 Conclusions 228
5.4 References 230

APPLICATION OF THE OPTIMIZATION PROGRAM TO THE
SEPARATION OF TETRACYCLINE ANTIBIOTICS

6.1 Introduction 232
6.2 Results and Discussion 238
Characterization of the Electrophoretic Behavior of

Tetracyclines
Optimization of the Separation of Tetracyclines
Decomposition of Tetracyclines
Analysis of Tetracyclines
6.3 Conclusions 263
6.4 References 264

VIII

 

CHAPTE

APPEND

APPENDI

CHAPTER 7

APPENDIX 1

APPENDIX 2

 

 

SUMMARY AND FUTURE WORK

7.1 Summary
7.2 Future Work
7.3 References

COMPUTER PROGRAM FOR BUFFER PREPARATION

A1.1 Introduction
Buffer H2A/ HA
Buffer HA / A
A1.2 References
A1.3 Buffer.Prp Program

COMPUTER OPTIMIZATION PROGRAM

A2.1 Introduction
A2.2 Nucleo.Opt and Tetra.0pt Programs

267
273

288
288

289
296

 

 

Table 1.1
Table 1.2

Table 2.1

Table 3.1
Table 3.2

Table 4.1

Table 4.2

Table 4. 3

IibIe 4.4

We 45
Table 4.6

IITIe 4.7

 

Table 1.1
Table 1.2

Table 2.1

Table 3.1
Table 3.2

Table 4.1

Table 4.2

Table 4.3

Table 4.4

Table 4.5

Table 4.6

Table 4.7

LIST OF TABLES

Capillary electrophoresis in a historical perspective.

Comparison between some of the detection schemes
available to capillary electrophoresis.

Comparison of the reproducibility of electroosmotic flow
measurements in sodium chloride solutions, using two
capillary conditioning methods. The electroosmotic flow was
determined under constant-voltage conditions of 30 W in a
capillary with 109.0 cm total length.

Parameters of the ion - selective model.

Comparison of the experimentally determined zeta potential
with values calculated from the ion-selective model.

Prediction of voltage in phosphate buffer solutions with total
sodium concentration of 10 mM under constant-current
conditions of 12.5 uA.

Prediction of the electroosmotic mobility in new and six-
month used capillaries, using phosphate buffer solutions
with total sodium concentration of 10 mM under constant-
current conditions of 12.5 uA.

Prediction of the effective electrophoretic mobility of
adenosine monophosphate in phosphate buffer solutions
with total sodium concentration of 10 mM under constant-
current conditions of 12.5 “A. . .

Prediction of the zone variance for adenosine
monophosphate in phosphate buffer solutions with total
sodium concentration of 10 mM under constant-current
conditions of 12.5 ILA.

Evaluation of the chromatographic resolution statistic (CRS)
as a response function using optimum resolution (Ropt) of
1.5 and minimum resolution (Rmin) of 0.

Evaluation of the chromatographic resolution statistic (CRS)
as a response function using optimum resolution (Rom) of
1.5 and minimum resolution (Rmin) of 0.75.

Evaluation of the chromatographic resolution statistic (CRS)
as a response function using optimum resolution (Rom) of
1.5 and minimum resolution (Rmin) of 1.0.

17

34
84

85

107

110

115

119

123

125

126

 

 

Table 5.

Table 5.:

Table 6.1

Table 6.2

Table 5.1

Table 5.2

Table 6.1

Table 6.2

 

 

Dissociation contants and electrophoretic mobilities of
nucleotides at 25° C and infinite dilution (the subscript b
denotes the constants associated with the nucleotide base).

Prediction of voltage, electroosmotic mobility, effective
mobility, and zone variance for nucleotide mono- and di-
phosphates in phosphate buffer solution, in the vicinity of
the optimum conditions (pH 10, ionic strength of 12.5 mM,
buffer concentration of 2.4 mM, and constant-current
conditions of 12.5 plA).

Dissociation constants and electrophoretic mobilities of
geltracyclines at 25° C, corrected to the conditions of infinite
iution.

Comparison of experimentally determined migration time
and base width of tetracyclines with computer-simulated
values in the vicinity of the optimum conditions (pH 7.5, ionic
strength of 18.2 mM, buffer concentration of 4.3 mM, and
constant-current conditions of 20 uA).

xi

190

227

240

257

 

Figure 1.
Figure 2.
mez;

figure 21

Filiure 3.1

FiQure 3.2

FIgure 3,3

FlgUre 3.4

FIIUTe 3,5

IIIIITe 3,5

 

Figure 1.1
Figure 2.1
Figure 2.2

Figure 2.3

Figure 3.1

Figure 3.2

Figure 3.3

Figure 3.4

Figure 3.5

Figure 3.6

 

LIST OF FIGURES

Schematic representation of the separation of two solutes by
the four modes of electrophoresis.

Schematic representation of the capillary zone
electrophoresis system.

Voltage divider used to interface the power supply remote
terminal and the recorder.

Schematic of typical recorder outputs during the
measurement of electroosmotic flow by the resistance—
monitoring method. (A) Constant-current conditions of
9 pA; pH 7 phosphate buffer solution with 12.5 mM sodium
concentration. (B) Constant-voltage conditions of 20 W;
3 mM sodium chloride solution.

Schematic diagram of an ion-selective glass membrane
(top) and the electrical double-layer structure at silica
surfaces (bottom).

Dependence of electroosmotic velocity on the applied
voltage for a ueous sodium chloride solutions of
concentration (a) 1 mM, (0)2mM, (D)3mM, (V)
4mM.

Evaluation of dielectric constant, viscosity, and zeta
potential of aqueous sodium chloride solutions at pH 9. The
zeta potential was evaluated under constant-voltage
conditions at (A) 10 kV, (0)20 kV, (EH30 kV.

Effect of cation type on the magnitude of the zeta potential
under constant—voltage conditions at 20 kV. Aqueous
solutions at pH 9 of (A) LiCl, (El) KCI, (0) NaCl.

Effect of anion type on the magnitude of the zeta potential
under constant-voltage conditions at 20 kV. Aqueous
solutions at pH90f (O)NaCI, (A)NaBr, (I)Nal, (fl)
NaNO3, (V)NaCIO4.

Effect of anion type on the electroosmotic velocity under
constant-current conditions. Aqueous solutions at pH 9 with
3 mM concentration of ( O ) NaCI, ( A) NaBr, ( Cl )
NaN03.

xii

32

38

40

51

60

63

65

68

73

 

 

Figure 3

Emmi

Figure 3.!

Fi9Ure3.1

Figure 4.1

FiIure 4.2

FIgure 4,3

FIQUTe 4,4
“We 4,5

IgIIIe 4.6

 

Figure 3.7

Figure 3.8

Figure 3.9

Figure 3.10

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

 

Effect of the ratio of Na(NaCI) to Na(buffer salts) on

electroosmotic velocity under constant-current conditions for

phosphate buffer solutions at pH 9 with 10 mM total sodium

cancentration. (V) 0: 10, (0)5: 5, (El ) 6.5: 3.5, (A)
: 0.

Effect of pH on electroosmotic velocity under constant-
current conditions for phosphate buffer solutions with 10 mM
total sodium concentration and 1:1 ratio of Na(NaCI) to
Na(buffersaltS)- (A)pH 4, (I)pH 5. (OlpH 6. (V)
pH7. (OlpHB. (EDPHQ. (AlpH10-

Effect of total sodium concentration on electroosmotic
velocity under constant-current conditions for phosphate
buffer solutions at pH 7 with 1:1 ratio of Na (NaCl) to Na
(buffer salts). (O) 5 mM, (A) 7.5 mM, (I ) 10 mM, (D)
12.5 mM, (v) 15 mM.

Comparison of experimental data with the ion-selective
model for zeta potential as a function of pH from 4 to 10 and
total sodium concentration from 5 to 15 mM (bottom to top
curves). Experimental conditions as given in Figures 3.8
and 3.9.

Schematic diagram of the computer optimization program for
capillary electrophoresis.

Comparison of the experimental resistance of phosphate
buffer solutions with theoretical calculations according to
Equations [4.7] and [4.8]. (A)pH 4, (I)pH 5, (0)
PH 6. (V) pH 7. (O)PH 8, (D)pH 9. and (A)pH 10-

Conductance of phosphate buffer solutions (A) and silica
capillary surface (8) as a function of pH and sodium
concentration (5, 7.5, 10, 12.5, and 15-mM from bottom to
top).

Distribution functions of guanosine 5'—monophosphate in
phosphate buffer solution, together With Individual and
effective electrophoretic mobilities.

Computer-simulated electropherograms of the nucleotides
(1)AMP, (2) CMP, (3) GMP, (4) UMP, (5) ADP, (6) CDP,
(7) GDP, and (8) UDP at different pH conditions.

Computer-simulated separation of nucleotides under

standard conditions. Solute identification as in Figure 4.5.
(a) Electropherogram. (b) Simulated data.

xiii

75

78

80

82

101

104

113

121

129

 

 

Figure I

Figure 4

Figure 4.

Figure 4,1

FIQUre 41

FIQUIe 4.12

 

Figure 4.7

Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.1 1

Figure 4.12

Figure 4.13

 

Effect of the capillary length (Ltot) on the separation of
nucleotides. Solute identification and standard conditions
as given in Figure 4.6. (a) Computer—simulated
electropherograms for 50, 75, and 100 cm capillary length.
(b) Separation characteristics for 50 cm capillary length. (0)
Separation characteristics for 75 cm capillary length.

Effect of the capillary diameter on the separation of
nucleotides. Solute identification and standard conditions
as given in Figure 4.6. (a) Computer-simulated
electropherograms for 75, 100, and 125 m capillary
diameter. (D) Separation characteristics or 100 um
capillary diameter. (0) Separation characteristics for
125 um capillary diameter.

Effect of the detector position (Ldet) on the separation of
nucleotides. Solute identification and standard conditions
as given in Figure 4.6. (a) Computer-simulated
electropherograms for 50, 75, and 100 cm detector position.
(b) Separation characteristics for 75 cm detector position.
(0) Separation characteristics for 100 cm detector position.

Effect of the detector window length (Eda) on the separation
of nucleotides. Solute identification and standard conditions
as given in Figure 4.6. (a) Computer-simulated
electropherograms for 0.50, 0.75, and 1.0 cm detector
window length. (b) Separation characteristics for 0.75 cm
detector window length. (0) Separation characteristics for
1.0 cm detector window length.

Effect of the height difference (AH) of hydrodynamic
injection with siphoning action on the separation of
nucleotides. Solute identification and standard conditions
as given in Figure 4.6. (a) Computer-simulated
electropherograms for 1, 2, and 5 cm height difference. (b)
Separation characteristics for 1cm height difference. (c)
Separation characteristics for 5 cm height difference.

Effect of the hydrodynamic injection time (tin) on the
separation of nucleotides. Solute identification and
standard conditions as given in Figure 4.6. (a) Computer-
simulated electropherograms for 60, 90, and 120 3 injection
time. (b) Separation characteristics for 90 5 injection time.
(0) Separation characteristics for 120 5 injection time.

Effect of the applied current (I) on the separation of
nucleotides. Solute identification and standard conditions
as given in Figure 4.6. (a) Computer-simulated
electropherograms for constant-current conditions of 10, 15,
and 17 uA. (b) Separation characteristics for constant-
current of 10 pA. (c) SeparatIon characteristics for
constant—current of 15 pA.

xiv

133

137

142

146

150

158

 

Figure I

Figure I

Figure 4.

Figure 4;

Flgum 5.1
FlQure 5,2

FIgllre 5,3

Flgllre 5'4

 

Figure 4.14

Figure 4.15

Figure 4.16

Figure 4.17

Figure 5.1
Figure 5.2

Figure 5.3

Figure 5.4

Effect of the buffer pH on the separation of nucleotides.
Solute identification and standard conditions as given in
Figure 4.6. (a) Computer—simulated electropherograms for
pH 6, 7, and 9.8. (b) Separation characteristics for pH 6.
(c) Separation characteristics for pH 7.

Effect of the buffer ionic strength (I) on the separation of
nucleotides. Solute identification and standard conditions
as given in Figure 4.6. (a) Computer-simulated
electropherograms for 10, 15, and 20 mM ionic strength. (b)
Separation characteristics for 15 mM ionic strength. (c)
Separation characteristics for 20 mM ionic strength.

Effect of the buffer concentration (CT) on the separation of
nucleotides. Solute identification and standard conditions
as given in Figure 4.6. (a) Computer—simulated
electropherograms for 1.5, 2.5, and 3.5 mM buffer
concentration. (b) Separation characteristics for 1.5 mM
buffer concentration. (c) Separation characteristics for 3.5
mM buffer concentration.

Effect of the electroosmotic mobility (tio m) on the
separation of nucleotides. Solute identification and
standard conditions as given in Figure 4.6. (a) Computer-
simulated electropherograms for 0.200, 0.235, and 0.260
cm2 V'1 5". (b) Separation characteristics for 0.200
cm2 V'1 s4. (c) Separation characteristics for 0.260

Chemical structures and ionization pattern of nucleotides.

Effective mobility of guanosine 5'-monophosphate as a
function of pH in phosphate buffer solutions formulated to
contain a total concentration of sodium of 10 mM. (Bottom)
Experimental values and calculated curve. (Top) Calculated
curve under conditions of infinite dilution.

Effective mobility curve of the nucleotides superimposed to
the electroosmotic mobility of phosphate buffer solutions.

Surface maps representing the separation of nucleotide
mono- and di—phosphates. (a) CRS as a function of pH and
applied current with constant ionic strength of 12.5 mM and
buffer concentration of 2.5 mM. (b) CRS as a function of pH
and ionic strength with constant buffer concentration of 2.5
mM and current of 12.5 pA. (0) CR8 as a function of pH and
buffer concentration with constant ionic strength of 12.5 mM
and current of 12.5 pA.

XV

163

167

171

176

.185

189

192

196

 

Figure I

met

FIgllre 5.7
Figure 5.3
Figure 5.9

FIIUIe 5,"

Figure 6,1
FIgllle 6,2

FIgIIIe 6'3

Figure 5.5

Figure 5.6

Figure 5.7
Figure 5.8
Figure 5.9

Figure 5.10

Figure 5.11

Figure 6.1
Figure 6.2

 

Figure 6.3

Contour maps representing the separation of nucleotide
mono- and di—phosphates. (a) CRS as a function of pH and
applied current with constant ionic strength of 12.5 mM and
buffer concentration of 2.5 mM. (a) CRS as a function of pH
and ionic strength with constant buffer concentration of 2.5
mM and current of 12.5 uA. (c) CRS as a function of pH and
buffer concentration with constant ionic strength of 12.5 mM
and current of 12.5 uA.

Separation of the nucleotides (1) AMP, (2) CMP, (3) GMP,
(4) UMP, (5) ADP, (6) GDP, (7) GDP, and (8) UDP in
phosphate buffer solution at pH 6, and 10 mM sodium
concentration, under constant-current conditions of 12.5 MA.
(3) Experimental electropherogram (top), computer-
simulated electropherogram (middle), computer-simulated
electropherogram with experimentally measured value of
electroosmotic mobility and voltage (bottom). (b) Separation
characteristics under the predicted conditions. (c)
Separation characteristics under the predicted conditions,
after input of the experimentally determined value of
electroosmotic mobility and voltage.

Separation of nucleotides in pH 7 phosphate buffer solution.
Solute identification and conditions as given in Figure 5.6.

Separation of nucleotides in pH 8 phosphate buffer solution.
Solute identification and conditions as given in Figure 5.6.

Separation of nucleotides in pH 9 phosphate buffer solution.
Solute identification and conditions as given in Figure 5.6.

Separation of nucleotides in the vicinity of the optimum
conditions: pH 10, ionic strength of 12.5 mM, buffer
concentration of 2.4 mM, and constant-current conditions of
12.5 uA. Solute identification and electropherogram
specification as given in Figure 5.6. ‘

Separation of nucleotides in pH 11 phosphate buffer
solution. Solute identification and conditions as given in
Figure 5.6.

Chemical structures of common tetracycline antibiotics.

Epimerization and dehydration pathways for the
decomposition of tetracycline.

Effective mobility curves as a function of pH for selected
mixtures of tetracyclines at 25° C and infinite dilution. (a)
CTC, DMCC, DOC, and OTC. (b) CTC, DMCC, MNC, MTC,
and TC. (0) CTC, DMCC, DOC, MNC, MTC, OTC, and TC.

200

204

208

212

216

220

224
234

237

242

 

Figure

Figure 6

Figure 6.

i"Isruree.

Figure 6.!
Figure .41
Figure A1.
”We A1.

Figure A1.

Figure 6.4

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8
Figure A1.1
Figure A1.2

Figure A1.3

Surface maps representing the separation of tetracyclines.
(a) CRS as a function of pH and applied current with
constant ionic strength of 18 mM and buffer concentration of
4.5 mM. (b) CRS as a function of pH and ionic strength with
constant buffer concentration of 4.5 mM and current of 20
. (c) CRS as a function of pH and buffer concentration
with constant ionic strength of 18 mM and current of 20 uA.

Contour maps representing the separation of tetracyclines.
(a) CRS as a function of pH and applied current with
constant ionic strength of 18 mM and buffer concentration of
4.5 mM. (8) CRS as a function of pH and ionic strength with
constant buffer concentration of 4.5 mM and current of 20
“A. (C) CRS as a function of pH and buffer concentration
with constant ionic strength of 18 mM and current of 20 uA.

Separation of mixtures of tetracyclines in the vicinity of the
optimum conditions (pH 7.5, with 15 mM total sodium
concentration, ionic strength of 18.2 mM, buffer
concentration of 4.3 mM, and applied current of 20 uA.

Identification of tetracycline decomposition products under
the optimized conditions given in Figre 6.6. (Top)
Tetracycline standard. (Middle) Tetracycline standard
previously treated with hydrochloric acid at pH 2, and
submitted to 70° C during 1 h. (Bottom) Hard filled capsule
of tetracycline 250 mg (Warner-Chillcott).

Electrophoretic behavior of chlortetracycline under the
optimized conditions of Figure 6.6.

Schematic representation of the BUFFER.PRP main
program.

Schematic representation of the BUFFER.PRP subroutine
for constant ionic strength buffer formulatIons.

Schematic representation of the BUFFER.PRP subroutine
for constant buffer concentration formulations.

Figure A1.4 Schematic representation of the BUFFER.PRP subroutine

for constant buffer capacity formulations.

xvii

247

251

255

259

262

278

280

282

284

 

Figure I

Figure l

 

 

Figure A2.1 Schematic representatio

n of the computer optimization main
program. 289
Figure A2.2 Typical output of the computer optimization program
representing a separation of (a) nucleotides, and (b)
tetracyclines. 296

xviii

LIST OF SYMBOLS

ROMAN ALPHABET

aH
ENa
CII'
CRS

hydrogen ion activity

sodium ion activity

equilibrium concentration of speciesj

total buffer concentration

chromatographic resolution statistic

effective diffusion coefficient of solute i
Faraday constant

gravitational acceleration constant

current

buffer ionic strength

potentiometric selectivity constant

detection zone length

capillary length to the detector

injection zone length

injection zone length for hydrodynamic injection
injection zone length for electrokinetic injection
total capillary length

number of solutes

negative logarithm of hydrogen ion activity
negative logarithm of the dissociation constants of the buffer species
negative logarithm of the dissociation constants of the solute species
capillary radius '
resistance

average resolution

resolution between adjacent solutes

minimum resolution

optimum resolution

solution resistance

surface resistance

migration time of solute i

injection time

migration time of the last eluting solute

applied voltage

electrophoretic velocity

velocity of solute i

electroosmotic velocity

base width of solute i, in time units

xix

f

2I'

ZR

ZsoI
GREEK
“I

AH

IF

e

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Ir

TI

K I
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Ilbur t
IIIeiIIi e
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02 .
I I "It
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rel

 

Zbur
Zi
ZR
Zsol

charge of buffer species
charge of species j

charge of the counterion
charge of solute species

GREEK ALPHABET

0‘1

distribution function of species j

height difference between solution levels at inlet and outlet reservoirs
pressure difference along the capillary length
dielectric constant of the solution
permittivity of vacuum

activity coefficient of species j

viscosity of the solution

conductivity of the solution

electrophoretic mobility at infinite dilution
electrophoretic mobility of buffer species
effective mobility of solute i

electrophoretic mobility

electrophoretic mobility of species j
electroosmotic mobility

electrophoretic mobility of solute species
standard deviation, in time units

density of the solution

total zone variance

detector contribution to the zone variance
diffusion contribution to the zone variance
injection contribution to the zone variance
individual contribution to the zone variance
zeta potential

reference potential in the double layer

 

El
different
early at
human sr
Tiselius \
held an U
the last I
elecgoph,
and gaine

Thi
mOdes, to
rationale I
adVances
seIISIIIVily
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persteeth.

1.1 M°II65

Trad

 

 

CHAPTER 1

CAPILLARY ELECTROPHORESIS - FUNDAMENTAL
CONCEPTS AND HISTORICAL BACKGROUND

Electrophoresis is the separation of charged molecules based on
differential migration in an electric field. Historically, it was introduced in the
early 19008 with the moving-boundary method of Tiselius, for the separation of
human serum into some of its constituent proteinsli2 For this pioneering work,
Tiselius was awarded a Nobel prize in 1948. Since then, electrophoresis has
held an unique position among the methodologies for biomolecules. But only in
the last decade, with the implementation of the capillary techniques?r5 has
electrophoresis evolved from a manually intensive to a fully automated format
and gained acceptance as a routine analytical technique. I

This introductory chapter gives a brief description of the electrophoretic
modes, followed by a more detailed discussion of zone electrophoresis and the
rationale for capillary techniques. This chapter also describes the most recent
advances in capillary technology and strategies for enhancement of the detector
sensitivity . Finally, the current capabilities and limitations of capillary zone
electrophoresis are discussed and the contribution of this work is brought into

perspective.

1.1 Modes of Electrophoresis

Traditionally, electrophoresis is performed by one of four basic modes:
1

 

monng
1.1 shc
elector
sample
electric
dictated
Instead,
the othe
analogue
Zc
which the
As the
character
lesult of I
dispersior
”0 locust

 

moving boundary, zone, isotachophoresis. and isoelectric focusing.€*3 Figure

1.1 shows schematically the progressive separation of two solutes by each
electrophoretic principle. In moving-boundary electrophoresis}2 a long band of
sample is placed between buffer solutions in a tube. Upon application of an
electric field, the sample components migrate in a direction and at a velocity
dictated by each component mobility. Complete separation is never achieved.
Instead, only the solutes with the highest mobility can be partially purified while
the other components overlap to different degrees. The chromatographic
analogue of zone electrophoresis is frontal chromatography.

Zone electrophoresis9 is, in principle, a moving-boundary technique in
which the sample is applied as a narrow band surrounded by the buffer solution.
As the electric field is applied, each zone migrates at a constant rate
characteristic of its own mobility. The separation is eventually achieved as a
result of maximizing the differential rate of migration while minimizing the zone
dispersion. In principle, each zone migrates independently from each other and
no focusing effects are operative. The chromatographic analogue of zone
electrophoresis is elution chromatography.

In isotachophoresis,1o a sample is inserted between two electrolyte
solutions, the leading and the terminating electrolytes. Both cations and anions
can be analysed by this mode, however in independent samples. In Figure 1.1,
the separation of a mixture of cations is represented. In this particular example,
the leading electrolyte contains a cation of higher mobility than any of the sample
components, whereas the terminating electrolyte contains a cation of lower
mobility. When the electric field is applied, different potential gradients evolve in
each band in such a way that all cations eventually migrate at constant velocity.
In regions where cations of lower mobility are present, the electric field is

tronger. These cations move at the same velocity as the most mobile cations,

 

 

 

 

Figure 1.1 Schematic representation of the separation of two solutes by the
four modes of electrophoresis.

 

Figure 1.1

 

In :9: In 33

 

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5

which are subjected to weaker electric fields. A characteristic of this mode is the
electrophoretic focusing that results at the boundaries of the bands. If a solute
diffuses forward into a subsequent band, which is a region of lower electric field,
its rate of migration is decreased and the solute rejoins the original band.
Likewise, if a solute diffuses backwards into a region of higher electric field, its
rate of migration is increased and the solute rejoins its former band. The
chromatographic analogue of isotachophoresis is displacement chromatography.

lsoelectric focusing11 involves the separation of amphoteric solutes in a
pH gradient. The key of this technique is the formation of a pH gradient. This
can be accomplished by a variety of methods, the most effective being the use of
a mixture of ampholytes, whose isoelectric points span the pH range desired for
the gradient. When an electric field is applied, the ampholytes migrate to their
respective isoelectric point, forming a relatively stable pH gradient.
Commercially available ampholyte mixtures allow the generation of gradients

from pH 2 to 11. The stability of the pH gradient can be greatly enhanced by

 
  
 
 
 
 
 
    
  

incorporating the ampholyte mixture into the molecular structure of a gel-forming
medium. Once the gradient is established, the gel is polymerized to yield a
permanently immobilized yet porous gradient. Figure 1.1 illustrates the analysis
of anions, in which the gradient is established from low pH at the anode to high
pH at the cathode. As the negatively charged solute migrates under the electric
field, it encounters regions of progressively lower pH and a greater fraction
becomes protonated. Eventually, the net charge of the solute is zero and it

ceases to migrate. Each sample component migrates to a position where the pH

 

is equal to the solute isoelectric point. If a solute molecule from a focused band
diffuses away, it immediately acquires charge by losing or gaining protons. In
his charged state, the solute migrates towards the electrode of opposite charge

nd rejoins the band. An important characteristic of this mode is the

 

establis

Iocuser

1.2 R3

T
separatI
oi elegy
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migratior
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establishment of a steady state in which the bands are stationary and sharply

focused. They will remain so while the electric field is maintained.

1.2 Rationale for Capillary Electrophoresis

The major limitation on the speed, efficiency, and scale of electrophoretic
separations is the ability to dissipate Joule heat, which is caused by the passage
of electric current through the conducting medium. Since heat is generated
uniformly throughout the medium and is dissipated only at the edges of the
migration channel, temperature gradients result. The temperature gradients
induce density gradients which, in turn, can cause natural convection. Any such
convection would serve to remix separated zones, severely reducing the

separation performance. A secondary outcome of Joule heating is the

   
 
 
 
 
 
 
 
 
  

introduction of a spatial dependence on the electrophoretic mobility of the
analytes. The molecules In the warmer central region of the separation medium
will move faster than those at the edges causing a deformation of the initially flat
velocity profile. Moreover, if the average temperature of the medium becomes
too high, the structural integrity of the sample analyte may be compromised.

The common approach to counteract the convective disturbances arising
from Joule heating is to use a solid support, such as paper, starch, agarose,
cellulose acetate, or polyacrylamide gels, as an integral part of the migration

channel],8 Although the use of a stabilizing medium effectively decreases

 

hermal convection. it increases the surface area available for solute adsorption,
hich can be detrimental. As an experimental method, manipulation of gels is
ime consuming and involves intensive preparative work that frequently leads to

reproducibility and poor quantitative results. Even when anticonvective

support
and is c
E
electrop
capillary
is effec
mechani
high fielc
zones a]
diffusion.
reported,
highest e
Th
electropm
u. by 36
lappfoxim
action of
Over COnVI
the Same

I50 ~ 20c

 

7
supports are used, the electric field strength can not be substantially increased,
and is commonly limited to the range of 10 to 50 V/cm.

Efficient heat dissipation is the primary reason for performing
electrophoretic separations in a capillary format.3-6 The microchannel of a
capillary (15 to 100 um) has such a high surface area-to-volume ratio that heat
is effectively transfered through the capillary walls. This heat removal
mechanism nearly eliminates convection, so that the application of unusually
high field strengths is possible (100 to 500 V/cm). Under these conditions, the
zones approach the theoretical limit of being broadened only by longitudinal
diffusion.4~6I12I13 In favorable cases, about 1 million theoretical plates has been
reported,14v15 making capillary electrophoresis the electrophoretic method of
highest efficiency.

The earliest demonstration of the use of high electric fields in zone
electrophoresis was published in 1967 by Hjertén,9 who employed a 300 um I.
D. by 36 cm length rotating quartz tube, with an applied voltage of 2.5 — 3 kV

 
  
  
 
 
 
    
  

(approximately 75 V/cm). In 1974, Pretorius et al.16 demonstrated the pump
action of electroosmotic flow and discussed the advantages of this technique
over conventional methods of driving solvent in chromatographic separations. At
the same time, Virtanen17 advocated the advantages of small diameter tubes
(50 - 200 pm) for electrophoretic separations. This tendency would soon
culminate with the first account of zone electrophoresis in narrow-bore teflon
tubes (200 um diameter), which is attributted to Everaerts3 and his research
group (Eindhoven University of Technology, The Netherlands, 1979). In his first
ork, the separation of a 16-component mixture of anions was peformed, with a
late height of less than 10 um and analysis time of ten minutes. During the
9803. Jorgenson and Lukacs,4-6 followed by several other research groupsw“24

ontributed significantly to the initial growth of the technique and investigated the

 

Ieasibil
to me
develor
techniq
separat
workers
micellar
formed
chromat
summar

capillary

1.3 Inst]

Diesenter

 

feasibility of capillary electrophoresis as an Instrumental technique. Worthwhile

to mention are the contributions of Karger and coworkers25:26 In the
development of capillary gel electrophoresis (CGE), which extends the use of the
technique to macromolecules, with the inclusion of a size dependence in the
separation mechanism. Also significant were the contributions of Terabe and co-
workers,27 who introduced a modified version of capillary zone electrophoresis,
micellar electrokinetic capillary chromatography (MECC). In MECC, surfactant-
formed micelles are included in the conducting buffer to provide a two-phase
chromatographic system for separating neutral molecules. Table 1.1
summarizes the achievements of the earliest workers in the field, and presents

capillary electrophoresis in a historical perspective.

1.3 Instrumental Considerations

 
   
 
 
  
 
 
 
   
  

A detailed description of the instrumental system used in this work is
presented in Chapter 2 (vide Figure 2.1). In this section, an overview of the
most commonly used methods of injection and detection are discussed as well

as the present status of the capillary surface technology.

Capillary Technology. Most capillaries used for electrophoresis are composed
of fused silica, which is a very pure form of amorphous silicon dioxide. This
material confers to the capillaries many convenient properties, such as precise
dimensions, a very high dielectric constant, low electrical conductance, high
hermal conductivity, mechanical strength, and high optical transmission to a
ide spectrum of light (190 to 900 nm).28 Chemically, the silica capillaries are

haracterized by the presence of several types of silanol groups (SIOH), which

 

 

 

 

 

 

 

 

 

 

 

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are we
silanol

silanol

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Opposit.
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Purpose
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as the 0

are weakly acidic in character. in contact with an aqueous medium, some of the
silanol groups are ionized causing the surface to be negatively charged. The
silanol groups are directly responsible for the phenomenon of eiectroosmosis,29
which is the induced flow of solution under an applied electric field. A more
elaborate discussion of electroosmotic flow is presented in Chapter 3. The
silanol groups also exist in abundant sites for coulombic interaction with
oppositely charged solute molecules, and thus can have both an adverse effect
on the quality of the separation as well as on the solute detectability. Several
approaches have been introduced as a means to control the charge density at
the capillary wall and prevent these undesirable effects. Neutralization of the
silanol groups by physical adsorption of small cationic molecules is one of the
earliest procedures employed. Several molecules have been used with this
purpose, including putrescine,14 cetyltrimethylammonium bromide,30
tetradecyltrimethylammonium bromide,31 and s-benzyithiouronium chloride?»2
By using multivalent ions, the direction of electroosmotic flow can even be
reversed.33 The use of cationic molecules has the disadvantage of potential
binding of the cations to the analyte molecules, which alters their electrophoretic
behavior. A second approach to controlling the surface charge density consists
of covalently blocking the silanol groups with polar organosiiane ligands. Some
of the most commonly used chemical derivatizing agents include
trimethylchlorosilane5 and (y-methacryloxypropyI)-trimethoxy silane,34 among
others.35 The bonded coating has proved to be effective for only limited periods
of time owing to the reversible hydrolysis of the silyl oxygen bond, particularly at
high pH. Recent advances in the technology of wall coating promises more
stable and longer lived coatings.35 The utilization of wail-coated capillaries, such
as the ones employed in gas chromatography, has also been attempted.

However, these materials have proven to be very hydrophobic, introducing the

 

 

phenOI
ddda
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revenx
pohani
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11
phenomenon of solute partitioning into the electrophoretic process, with causes
deleterious effects on resolution and efficiency. A more versatile approach to the
elimination of coulombic adsorption of solute analytes is to use a charge-
reversed polymeric coating. Recent work with high-molecular-weight
polyamines33 has demonstrated that the negative charge on the fused silica
surface, and hence, the electroosmotic flow can be carefully controlled by the
amount of polyamine adsorbed. This treatment has been shown to be very
effective in eliminating much of the charge-induced adsorption of multiply
charged bicpolymers, such as proteins and peptides. Furthermore, the
coulombic interactions of strongly basic analytes can be nearly eliminated by the
application of thicker polymer films and the formation of a positively charged
layer at the surface of the capillary. The most important benefit that covalent or
polymeric coatings provide is the ability to use buffers in the pH range from 4.5

to 8 without severe solute-wall interaction.

  
  
 
 
 
 
 
   

1.4 Injection

The manner by which the sample is introduced into the capillary has
dramatic implications on quantitative analysis.35 The peak area or height
reproducibility is a direct function of the precision of the injection technique.
Sample injection can be performed either eiectrokinetically or
hydrostaticallyfi19:3“H11 Electrokinetic injection is achieved by applying a
voltage gradient across the capillary length for a known period of time, whereas
hydrostatic injection uses a pressure gradient. The pressure gradient can be
established by different mechanisms: head-space pressurization injection

(Beckman Instruments, Inc., Fullerton, CA); vacuum injection, in which a

 

reduce
Divisior
inc. Se
the inle
introdu<
i
the ane
injectior
the cap
electrok
sample
SiQnifica
that is c
Preferret
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12
reduced pressure is applied to the outlet end of the capillary (Applied Biosystems
Division of The Perkin-Elmer Corporation, Foster City, CA and Spectraphysics,
lnc., San Jose, CA); and gravity injection (Dionex, lnc., Sunnyvale, CA), in which
the inlet reservoir is elevated with respect to outlet reservoir and the sample is
introduced by siphoning action.

Hydrodynamic injection provides a sample plug which is representative of
the analyte composition. The injection volume (nL range) depends on the
injection time, capillary dimensions, buffer viscosity, and pressure drop across
the capillary length.37 Hydrodynamic injection is usually more precise than
electrokinetic injection because it is based strictly on volume loading of the
sample (area reproducibility is approximately 3 % RSD).3‘5’37’41 However,
significant broadening of the zone can occur as a result of the parabolic profile
that is characteristic of pressure-driven flow.“2 Hydrodynamic injection is the
preferred injection method for CZE and MECC applications. particularly when the
sample concentration is within the sensitivity limits of the detector.

in electrokinetic injection, sample is introduced in the capillary as a
combination of electrophoretic and electroosmotic migration. Thus the amount
of material injected is a function of the solute electrophoretic mobility, the
electrical conductance of the sample and the conducting medium, and the
electroosmotic flow. An important consequence of this mode of injection is that
non-representative sampling may result from discrimination in the uptake of
sample components with different electrophoretic mobilities};0 This can be
particularly a problem when the sample is composed of low mobility solutes that
are near the concentration limit of detection. Electrokinetic injection finds its
major application with the use of gel-filled capillaries, where volumetric loading of
sample is impossible. A thorough examination of the impact of the injection

odes on separation efficiency is presented in Chapter 4.

 

 

Sample
zone w
increas.
techniqi
electron
detector
electroo
DGn‘ormi
strategie
extensiv.
the sari
concentr
field. Ur
9i€aler ti
interface
interfaCe,
Causingc
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convenfio
alter a s
iniECtion.
hmmezC
“Sample
i”jettion .
concerital

Stacking t

liiSilibutiOn

 

 

13
Sample Concentration Strategies. The small column dimensions and narrow
zone widths in capillary electrophoresis place a high demand on detection. An
increase in sensitivity is highly desirable for many applications. Several
techniques have been reported to enhance the detectability in capillary
electrophoresis.43 This is usually accomplished through improvement of the
detector (vide next section). However, the injection features of capillary
electrophoresis make it possible to obtain enhanced detection limits by
performing on-column sample concentration. Among the pre—concentration
strategies, sample stacking with discontinuous buffer systems has found
extensive use in many areas of electrophoresis.“47 When the conductivity of
the sample solution is lower than that of the electrophoretic buffer, a
concentration or stacking phenomenon occurs upon application of the electric
field. Under these conditions, the electric field in the sample medium is much
greater than that in the electrophoretic buffer, and the ions migrate rapidly to the
interface between the lower and higher conductivity zones. Upon reaching the
interface, the ions experience a lower electric field and slow down (stack),
causing contraction of the sample zone. The thin zone then moves through the
electrophoretic buffer and separates into individual zones according to
conventional zone electrophoresis principles. Sample stacking can be achieved
after a sample has been injected hydrodynamically or upon electrokinetic
injection. In this latter case, as the stacking proceeds, the concentration in the
sample zone increases. Consequently, the conductivity increases and the rate
of sample concentration falls off asymptotically during injection time. Thus, the
Snjection length can become larger than desired before a steady-state
concentration can be reached in the sample zone. Finally, the effectiveness of
tacking depends on the electroosmotic flow velocity. The non uniform

istribution of the electric field strength causes differences in the local

 

 

electrc
across
the sat
relative
electro
flow an
velocity
optimal
where t

i
overcon
high ele
ions will
migrate
the neg;
i0 migra
sample :
cteated,

Al
using a l
isoelecm
lower DH
charoeo
when th
direction I
Step, the

charged 3

 

14

electroosmotic velocities, which in turn generate an electroosmotic pressure
across the concentration boundary. When the electroosmotic flow velocity is in
the same direction as the analyte migration, the stacking efficiency is decreased
relative to the case where the flow is zero. The larger the magnitude of the
electroosmotic flow, the worse the stacking efficiency. When the electroosmotic
flow and the analyte migration are in opposite directions, with the electrophoretic
velocity much larger than the electroosmotic velocity. the stacking efficiency is
optimal. This situation is not commonly encountered, particularly at high pH,
where the electroosmotic flow can be quite high (vide Chapter 3).

The difficulties encountered in applying stacking at high pH can be
overcome by using polarity switching during electrokinetic injection.“3 With a
high electroosmotic flow and normal polarity (cathode end is grounded), positive
ions will stack at the sample-buffer interface, whereas negative ions will tend to

migrate out of the injection end of the capillary. Reversing the polarity will cause

  
    
  
 
 
 
    

the negative ions to migrate into the capillary and stack as the positive ions start
to migrate out. By appropriately controlling the injection time at each polarity, a
sample zone containing both positive and negative ions in a narrow zone can be
created.

Another way to achieve stacking, which is applicable to ampholytes, is by
using a pH gradient during injection.47 The injected zone has a pH above the
isoelectric point of the solutes, surrounded by an electrophoretic buffer with
lower pH. As a result, the solutes in the sample zone are initially negatively
charged and migrate towards the anode upon application of the electric field.
hen the solutes enter the acidic region, the charge reverses and so the
irection of migration. This results in a narrowing of the sample zone. in a final
tep. the pH gradient dissipates and the concentrated zone with positively

harged solutes migrates towards the cathode.

 

amptifi
iollowe
applica
altered
is hydr
using a
sample
electrot
is subs
indicate

Perform

1'5 Del

intense
articles
tleralu,e
10 the r
Deilonna
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be"ell n
varietlot

Se

15

An interesting approach to sample concentration is known as field
amplification,48‘51 in which a large fraction of the capillary is filled with sample,
followed by focusing of the solute zone prior to separation. This method is
applicable to the analysis of either cations (when the capillary surface charge is
altered) or anions, but not both simultaneously. For anions, a large sample plug
is hydrodynamically injected onto the column in a low-conductivity buffer. By
using a voltage polarity opposite to that employed for the electrophoresis, the
sample anions are focused at the interface between the sample zone and the
electrophoretic buffer, at the cathodic end of the capillary, and the sample zone
is substantially contracted. When the focusing step is completed, which is
indicated by a change in current, the polarity is reversed and the separation is

performed.

1.5 Detection

Detection development for capillary electrophoresis has been an area of
intense research since the inceptions of the technique. A series of review
articles covering a variety of detection schemes is found in the
literature.18,19,36-43’52 The rapid advance in detection technology is attributable
to the relative ease of adaptation of some detectors employed for high-
performance liquid chromatography (HPLC). With minor modification some of
these detectors have been adapted to accommodate the use of fused-silica
capillaries as the detector flow cell. Moreover, the diversity of molecules that
benefit from electrophoretic methods has contributed to the implementation of a
variety of detection principles.

Several criteria must be considered when choosing the appropriate

 

delect<
linear
reprodi
should
helpful
Ideally,
ot the l
and cor
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16

detector for a particular analysis. These criteria include sensitivity, selectivity,
linear range and noise. Detector response should produce a known and
reproducible relationship with the amount or concentration of the solute and
should have a wide linear-response range. In certain applications, it is more
helpful to use a detector that is universal and responds similarly to all solutes.
Ideally, the detector for capillary electrophoresis should respond independently
of the buffer, should not contribute to band broadening and should be reliable
and convenient to use. On-column detection is usually preferable because the
contributions to zone dispersion due to joints, fittings and connectors are
eliminated. Unfortunately no single detector provides all these properties.

There are two main types of detectors: bulk-property and specific-
property detectors. The bulk-property detectors measure the difference in some
physical property of the solute relative to that of the buffer alone. These include
refractive index,53r54 conductivity,'~"»31v5558 and indirect methods.22r59,50 These
detectors are generally more universal than the specific-property, however, they
usually have lower sensitivities and dynamic ranges. This is because the
detector signal depends not on the properties of the solutes but also on the
differences in properties of the solute and the buffer. Specific-property detectors
measure specific properties of solutes and include ultraviolet (UV)
absorbance,25’27:61-69 fluorescence,4‘2022-23'70'85 mass spectrometry,86
amperometric,37-90 radiometricfillv92 and Raman detectorsfi’3r94 These methods
limit detection only to those analytes that possess the required specific property.
The use of these selective detectors is very advantageous when the sample
matrix is complex and in situations where it is desirable to minimize background
interferences. This type of detector is normally more sensitive than the bulk-
Property detector, provides wider linear ranges and more acceptable signal-to-

noise ratios, and consequently, is used most often. Table 1.2 compares the

-aa,,.

2.4:; m '

 

 

Table

 

 

 

 

 

 

 

Table 1.2

 

17
Comparison between some of the detection schemes available to

capillary electrophoresis.

 

DETECTION MODE

TYPICAL DETECTION

 

 

 

 

 

 

 

 

 

 

LIMITS (M)

REFRACTIVE INDEX53:54 10'5 — 10'6
CONDUCTIVITY3v31:55'58 10'5 — 10‘6
ABSORBANCE

Direct“66 10-5 — 10‘6

Indirect67'69 10-4 — 10-5
FLUORESCENCE

Direct (lamp-based)4v7O 10'7 — 10‘8

Direct (laser-based)20:74‘8° 10'9 — 10‘12

Indirect22v23’84'85 10‘6 — 10'7
MASS SPECTROMETRYS'6 10‘4 -— 10'9
AMF’EROMETRICW‘Q0 10‘8 - 10'9
RADIOMETRIC91 .92 10'9 — 10'11
RAMAN93.94

 

 

10"5 - 10'7

 

 

 

limits
electrc
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18
limits of detection for some detection schemes available for capillary
electrophoresis. The section that follows describe in more detail the recent
advances for the capillary UV-absorbance detector, which is the detector
employed in this work.

UV-absorbance detection is by far the most widely used detection scheme
for capillary electrophoresis. In fact, all commercially available instruments for
capillary electrophoresis employ an ultraviolet-visible absorbance detector.
Additionally, there is a broad range of applicability for UV-absorbance detectors
among the compounds that can be analysed by electrophoretic methods.

Sensitivity of UV-absorbance detection depends on the pathtength of the
detection cell. Hence, detection limits tend to be lower than those of other
specific-property detectors. This limits the uselfulness of UV—absorbance to
capillaries having inner diameters greater than 25 pm. For UV-absorbance
detection, there is a compromise between the use of low cell volumes for high
performance and the use of large diameter capillaries for sensitivity. Increased
sample loading can overcome the sensitivity problems, but can also adversely
affect the electrophoretic separation process. The slit widths for the UV light
source should be sufficiently small that only the capillary is illuminated, thereby
reducing stray light levels that could result in excessive background noise.
Illumination volumes should be smaller than the analyte zones, which is best
accomplished by focusing the UV light on the capillary. Finally, many materials
absorb light in the UV region, so minimizing background interferences can be
difficult. In terms of selectivity, an UV-absorbance detector with continuous
variable wavelength is most desirable, even though there may be some loss in
sensitivity. With variable-wavelength operation, a monochromator is preferred

ver filters for wavelength selection since it is more versatile, can be used to

can wavelengths, and produces better resolution. The main disadvantage of

 

 

instrur

systen

compo
feature
is uset
gain ti
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are idenl
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Obiained

 

 

19
instruments utilizing a monochromator is that they are usually less sensitive than
systems utilizing filters, which provide more light throughout.

Direct ultraviolet-absorbance detection is useful for a large number of
compounds that contain a chromophore. Early work in capillary electrophoresis
featured the use of modified HPLC UV-absorbance detectors.27 Since no pump
is used, this detector is modified to obtain shorter response times and higher
gain than that needed for HPLC detection, where pump pulses can lead to
excessive noise. Another modification included the combination of a
commercially available instrument with optical fibers in direct contact with the
walls of the electrophoresis capillary.61 in this approach, the UV radiation of a
mercury lamp is filtered before entering the optical fiber, and the transmitted light
is collected opposite the incident light using another optical fiber. The advantage
of using optical fibers is that the capillary inner diameter and the light conducting
core can be matched for optimal sensitivity. The disadvantages of using optical
fibers include transmission losses in the fibers and reduced efficiency at low
wavelengths. Other approaches include the use of photodiode array
detectors.62 The advantage of this approach is that qualitative information about
unknown analytes can be obtained from the absorption spectra.

If the solutes do not contain a chromophore. an absorbance signal can be
obtained by indirect detection.”69 Optical systems used for indirect detection
are identical to those for direct UV-absorbance. The only difference is that the
electrophoretic buffer contains a chromophore. The best sensitivities are
obtained in low-concentration background electrolytes containing a co-ion with
high UV absorption at a given detection wavelength. Non-absorbing ionic
species are revealed by changes in light absorption due to charge displacement

fthe absorbing co-ion. It is desirable that the sample ions have effective

  

obilities similar to those of the absorbing co—ion. The useful dynamic range is

 

limited

the op
measu
spectrc
charao
perforn
capillar
capillar
liquid in
ion lase
“ml ser
the cap
solvent:
relractiu
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DUmp Ia
of 50 to

due I03

D°I90t0l
directly
measure
Sh0uld h
i”lerura
telling

system,“

 

 

2O
limited by the linearity and noise of the detector.

The use of high-intensity light sources offers an alternative to extending
the optimal path length to obtain greater sensitivity in an absorbance detection
measurement. The availability of UV lasers will have an impact on
spectroscopic-based instrumentation as costs decrease and optical
characteristics improve. Thermooptical detection is another detection technique
performed on-column by using two intersecting laser beams focused on the
capillary. A pump laser is focused at a right angle to the electrophoresis
capillary, and a second laser beam is used to probe the refractive index of the
liquid in the capillary. Either a 4 mW HeCd laser (442 nm)95 or a 130 mW argon
ion laser96 serves as the pump laser, whereas a 1 mW helium-neon laser (632.8
nm) serves as the probe laser. Absorbance of the pump beam by analytes in
the capillary produces a temperature rise. Since the refractive index of most
solvents change with temperature, absorbance of the pump beam produces
refractive index changes that are monitored by the probe laser. The absorbance
sensitivity for the thermooptical detection is proportional to the power of the
pump laser, and the signal is independent of the capillary diameter in the range
of 50 to 500 um. Unlike typical absorbance measurements, sensitivity is not lost

due to short detection path lengths.

Detector Cell Designs. According to Beer's law, the absorbance of a sample is
directly proportional to the path length through which the absorbance
measurement is performed. Therefore, extension of the optical path length
should lead to improved detection sensitivity. However, simply increasing the
inner diameter of the capillary is not always an attractive alternative because the
esulting Joule heating may lead to a loss of resolution. Bruin et al.97 have

ystematically investigated alternative flow cell designs and capillary diameters.

 

All flc
effect.
length
the ml

the ce

bendui
have r
optical
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With at
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21
All flow cell designs, including the standard cylindrical capillary, require an
effective means of coupling the excitation light into and through the capillary path
length. A ball lens made from saphire or quartz, placed closed to the capillary is
the most effective approach."'1 This configuration provides radial illumination of
the center of the capillary, optimizing light throughput and minimizing stray light.

The short optical path lengths in microcapillaries can be extended by
bending the capillary (Z-cell) and illuminating through the bend. Chervet et al.98
have manufactured Z-cells for capillary electrophoresis that provide a 3-mm
optical path length. However, in spite of the fact that the pathtength was
increased by 40—fold over a 75 turn inner-diameter capillary, only about a 5-fold
sensitivity enhancement occured. This was attributed to an increased
background noise level and poor efficiency in light throughput at the 3-mm bend.
With appropriate optics, the noise level can be reduced, while the signal gain is
maintained. The extended optical path length in the Z-cell contains an inherent
limitation: the contribution of the finite detector volume to the zone variance is
substantially increased.

An alternative to bending a cylindrical capillary to gain a longer optical
path length is to perform electrophoresis in flattened'channels. Several square
and rectangular capillaries of varying dimensions and materials have been
employed for this purpose.99-100 The advantage provided by flattened
geometries is that the narrow separation channel dimension is maintained for
efficient heat dissipation, while longer optical paths are obtained for enhanced
detection sensitivity.

The optical path length of the capillary can be effectively multiplied by
using mirrors (silver coated capillary) to reflect the incident light inside the
capillary prior to detection.101 In this approach, the optical path length increases

while the narrow separation dimension is maintained. A critical parameter in

 

 

such
interl
and

efficil
detec

width

isto

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22
such cell construction is the incident light angle, which controls the number of
internal reflections and the path length per reflection. The number of reflections,
and hence the ultimate sensitivity, must be restricted to minimize the loss in
efficiency caused by the flow cell size. The distance between incident light and
detection should be less than the standard deviation of the narrowest zone
width.

An interesting approach to increase sensitivity in capillary electrophoresis
is to select the entire capillary length as the light path rather than the radial
length.102v103 In this format, light is transmitted through the capillary by total
internal reflection. The absorbance indicates the sum of the absorbance signals
resulting from all analyte components. As components elute from the column,

the total absorbance decreases in a steplike manner.

Sample Collection Strategies. The most commonly used detectors in capillary
electrophoresis do not provide structural information. Therefore, there is a great
deal of interest, particularly in biotechnological applications, for sample collection
and identification, after the separation has occurred. The process of fraction
collection in capillary electrophoresis is fundamentally different from that
employed in other separation techniques, because the electric field must be
maintained during sampling, in order to transport the solutes out of the capillary.
Several strategies to perform sample collection in capillary electrophoresis have
been described.104107 Devices have been designed where the capillary moves
from one collection vessel to another in a programmable manner. Other
approaches include the use of a frit structure at the side wall of the capillary and
the use of multiple capillaries arranged in bundles. The amount of material that
can be collected by these schemes range from nanogram to tenth of microgram

with repetitive cycles. The shortcomings of sample collection for capillary

 

 

elect
more;

the s:

1.6 (

charai
applic.
Speed
descrii
injectic
over ll
fundan

Physic:

 

23
electrophoresis are loss of efficiency due to either mixing of the solute zones, or
increased capillary diameter. Moreover, there might be a substantial dilution of

the sample during the collection process.

1.6 Conclusions

Throughout this first chapter, capillary electrophoresis has been
characterized as a versatile technique for routine biomedical and industrial
applications, capable of achieving high efficiencies, superior resolution and high
speed separations. The present state-of-the-art of the technique has been
described in areas such as capillary technology, enhancement of sensitivity,
injection and detection schemes. However, despite the impressive advances
over the past ten years of capillary electrophoresis, there is still a scarcity of
fundamental studies that would lead to a greater understanding of the
physicochemical nature of the separation process. Without this knowledge, it is
not possible to model important parameters, and most importantly, to design
electrophoretic separations. '

In this work, a novel approach to capillary zone electrophoresis has been
devised through the development of a computer routine. The program
incorporates simple but reliable models for zone migration and dispersion, and
constitutes a comprehensive description of electrophoretic separations. The
program includes many versatile features, such as the choice of buffer
composition, capillary dimensions, and instrumental parameters related to
injection, detection, and power supply operation. This program serves as the
integral part of a systematic optimization strategy to search and identify the most

avorable conditions for a separation. Chapter 2 organizes the experimental

 

 

 

24
methods and instrumental details for the elaboration of the program constituent
models and validation of the overall optimization strategy. Chapter 3 describes
the development of a theoretical model for electroosmotic flow, and contrasts the
features of separations under constant-current and constant-voltage conditions.
Chapter 4 presents the mathematical background of the computer optimization
routine, and describes the usage of the computer program as a pedagogical tool
to examine the effect of a variety of parameters on electrophoretic separations.
Chapter 5 applies the methodology developed to determine dissociation
constants and electrophoretic mobilities to nucleotides and provides the
experimental validation of the optimization routine. Chapter 6 describes the use
of the optimization program to study the separation of tetracycline antibiotics and
explores the analytical capabilities of capillary zone electrophoresis as an
alternative method for the determination of tetracyclines. Chapter 7 summarizes
the overall accomplishments of the present work and introduces ideas for further
improvement of the optimization strategy. Finally, two appendices are
incorporated to detail the buffer preparation and the optimization computer

programs.

 

1.7 F

 

25

1.7 References

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meth
elect:
(Chat
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0080

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CHAPTER 2

EXPERIMENTAL METHODS

In this chapter, an overall view of the experimental apparatus and
methods used throughout this dissertation is provided. The capillary
electrophoresis system was basically the same for all developmental studies
(Chapters 3 and 4) and practical applications (Chapters 5 and 6). This chapter
includes a detailed description of the procedure used for capillary surface
conditioning, a process essential for migration time reproducibility. The method
developed for the electroosmotic flow determination and the measurements of
the viscosity and dielectric constant, needed in the model of electrosmotic flow
(Chapter 3), are also included. A descriptive list of all reagents and solutions is
presented. Finally, brief descriptions of data processing, computer hardware

and software are provided.

2.1 Capillary Zone Electrophoresis System

The capillary zone electrophoresis system used in this work is
represented schematically in Figure 2.1. A regulated high—voltage DC power
supply (Model EH50R0.19XM6, Glassman High Voltage lnc., Whitehouse
Station, NJ) is operated in either constant-current (O — 190 LlA) or constant-
voltage (0 — 50 kV) mode. The operator is protected from accidental exposure to
high voltage by enclosing the CZE system in a Plexiglas® box equipped with
safety interlocks. The power supply is connected via platinum rod electrodes to

30

 

 

31

Figure 2.1 Schematic representation of the capillary zone electrophoresis
system.

32
Figure 2.1

 

 

 

 

 

 

 

N=O>mwwmm
ammunm
_ . _ mOPOmeo _
wDOmHOme

 

>m<i_i=n_<0

 

>._n_n5m
mw>>0n_

 

 

 

w<._0_xw4n_

 

 

two:

capill

soluti
maint

water

diliere
min p
Sampl
Prelen
repres
Partict
"lactic
injecte.
lOwer i
quantit

l
Spectre
Wavelet

relliovir

 

33
two small reservoirs containing the solution under investigation. Fused-silica
capillary tubing (Polymicro Technologies, Phoenix, A2), with dimensions 75 um
id, 375 pm ed, and 110 cm total length, is immersed at each end in the
solution reservoirs. In order to minimize thermal effects, the capillary is
maintained at 250° C during operation by means of a thermostatically controlled
water bath (Model RTE 98, Neslab Instruments, Portsmouth, NH).

Injection was performed hydrodynamically, by maintaining a 2-cm
difference between the liquid levels at the inlet and outlet reservoirs, during a 1-
min period. Under typical operating conditions, this procedure introduces a
sample volume of approximately 9 nL. The hydrodynamic injection method was
preferred over electrokinetic injection because it provides a sample that is
representative of the analyte composition. The choice of injection method was
particularly critical in the studies with nucleotides. During electrokinetic
injection, the nucleotides of higher electrophoretic mobility were preferentially
injected into the capillary. As a result, the sample zone was depleted from the
lower mobility nucleotides, which compromised their apparent detectability and
quantitative determination.

Detection was performed by means of anon-column UV-absorbance
spectrophotometer (Model UVIDEC-100-V, Jasco, Tokyo, Japan), at a fixed
wavelength of 260 nm. A detection window of 0.5 cm length was created by

removing the polyimide coating from the capillary at a distance of 43.4 cm.

 

.2 Capillary Surface Treatment

The conditioning of the capillary surface is critical to assure reproducibility

fmigration time measurements. In the series of studies presented in Table 2.1,

 

Tab

CNat

 

 

 

 

 

 

 

 

 

34

 

 

 

 

 

 

 

 

 

 

Table 2.1 Comparison of the reproducibility of electroosmotic flow
measurements in sodium chloride solutions, using two capillary
conditioning methods. The electroosmotic flow was determined
under constant-voltage conditions of 30 W in a capillary with 109.0
cm total length.

CNac. (mM) MIGRATION TIME (min)

METHOD 1 METHOD 2
5 12.4 i 0.3 7.9 :t 0.3
10.7 :i: 0.6 7.7 :I: 0.4
8.1 t 0.3 8.1: 0.5
93:01 78:03
12 i 1 8.1 i 0.2
12.1 i 0.9
AVERAGE 108:1.7 7.9:018
R80 16 % 2.3 %
10 12.2:09 8.13:0.06
11 1 1 8.3 :l: 0.3
9.3101 8.3i0.2
9.2 :t 0.2 8.6 t 0.1
11 :l: 2
AVERAGE 10.5 i 1.3 8.3 i 0.20
__RSD 12 % 2.4 %

 

 

 

the

con:
infra
NaC
inve:
mea
repri
capil
solul
Unde
and I
six m
Condi
elect
06101
hydro.
Stand;
was c
and di

introdu
filledw

then re

 

35
the electroosmotic flow of sodium chloride solutions was measured under
constant—voltage conditions by means of the resistance-monitoring method (vide
infra). For the first conditioning method, the capillary was flushed with 0.1 M
NaOH solution (10 capillary volumes) followed by the solution under
investigation. Under these conditions, the electroosmotic flow could be
measured in the same day with approximately :10 % RSD and the day—to-day
reproducibility was $15 % RSD. For the second conditioning method, the
capillary was washed with 1 M NaOH solution, followed by flushing with the
solution under investigation, preferably overnight but at least for a 2-h period.
Under these conditions, the single-day reproducibility was better than :5 % RSD
and the day-to-day reproducibility was better than :3 % RSD, over a period of
six months. Therefore, this method was selected as the standard procedure to
condition the capillary surface. In the studies on the effect of cation type on
electroosmotic flow (Chapter 3), an acid wash with 10'2 M hydrochloric acid was
performed prior to the alkaline wash with a solution of the appropriate cation
hydroxide. In all the studies involving phosphate buffers (Chapters 3 to 6), the
standard conditioning procedure was performed only when the pH of the buffer
was changed. When not in use, the capillary was rinsed with deionized water

and dried under helium.

2.3 Electroosmotic Flow Determination

The electroosmotic flow was measured by a modification cf the procedure
introduced by Huang et al.1 Initially, the capillary and the outlet reservoir are
filed with an electrolyte solution of a certain concentration. The inlet reservoir is

hen replenished with a solution of the same composition but diluted by a factor

 

of i
mig
cor
sup
be 1
099
lollc
Plot
kVI
sub:
Hew
Powi
typic
cone
lime
Signs
moni
inflec
capill

the 9]

Elect,
NaNo

predis-

 

36
of 4% in volume. Under the applied electric field, the dilute solution continuously
migrates into the capillary and displaces an equivalent volume of the more
concentrated solution, thereby causing the resistance to change. If the power
supply is operated in the constant-voltage mode, the changes in resistance can
be followed by recording the changes in current. Conversely, if the instrument is
operated in the constant—current mode, the changes in resistance can be
followed by recording the changes in voltage. A 0 — 10 V DC signal, in direct
proportion to either the output current (0 — 190 pA) or the output voltage (0 — 50
W) is available at the remote terminal of the power supply. This signal is
subsequently divided to 0 — 1 V and displayed on a recorder (Model 3392A,
Hewlett-Packard Co., Avondale, PA). The voltage divider that interfaces the
power supply remote terminal and the recorder is displayed in Figure 2.2. A
typical output of the recorder is shown in Figure 2.3, under both operating
conditions. Note that when the current is monitored, the signal decreases with
time until the entire capillary is filled with the dilute solution, after which the
signal becomes constant. Under the same conditions, when the voltage is
monitored, the signal initially increases and then becomes constant. The
inflection point represents the time (T) required to complete the filling of the
capillary by electroosmosis. Thus, with knowledge of the capillary length (Ltot),

the electroosmotic velocity can be calculated (vosm = Ltot I T).

2.4 Reagents and Solutions

Electrolyte Solutions. All electrolyte solutions (LiCI, NaCI, KCI, NaBr, Nal,

NaNO3, and NaCIO4) were prepared from analytical-grade reagents and

predlstilled-deionized water (Corning Mega-PureTM System, Corning, NY),

 

37

Figure 2.2 Voltage divider used to interface the power supply remote terminal
and the recorder.

 

     
            

iilvViLseio >36
m

>e-o +

FDQHDO Gxoov

m0<HJO>

9||ll

szmmao Gxow

ivVieeio >26
0

H312.

 

 

 

39

Figure 2.3 Schematic of typical recorder outputs during the measurement of
electroosmotic flow by the resistance-monitoring method. (A)

Constant-current conditions of 9 uA; pH 7 phosphate buffer
solution with 12.5 mM sodium concentration. (B) Constant-voltage

conditions of 20 W; 3 mM sodium chloride solution.

4%-

/\--\

 

40
Figure 2.3

 

 

\/

m

 

L____

 

 

EDVIIOA

iNBHHnO

TIME

 

39

Figure 2.3 Schematic of typical recorder outputs during the measurement of
electroosmotic flow by the resistance-monitoring method. (A)
Constant-current conditions of 9 uA; pH 7 phosphate buffer
solution with 12.5 mM sodium concentration. (B) Constant-voltage
conditions of 20 W; 3 mM sodium chloride solution.

 

40
Figure 2.3

 

 

< an

\/

 

\____

 

 

 

BDVLWOA

.LNSHHHO

TIME

 

 

pie:

Phi
tea

bLl

 

41
preadjusted to pH 9 with 0.1 M NaOH solution.

Phosphate Buffers. The phosphate buffer solutions were prepared from
reagent-grade chemicals and predistilled-deionized water (Coming). The
buffers were formulated to contain apprOpriate amounts of sodium chloride in
addition to the sodium buffer salts and phosphoric acid. For the entire pH range
from 4 to 11, the total concentration of sodium was maintained constant (5 — 15
mM) and the ratio of sodium from each source, sodium chloride and buffer salts,
was equal to unity. Appendix 1 describes in greater detail the mathematical

basis of the computer program for buffer preparation.

Nucleotides. The nucleotides adenosine, guanosine, cytidine and uridine 5'-
mono and diphosphates (AMP, ADP, GMP, GDP, CMP, CDP, UMP and UDP)
were obtained as reagent-grade chemicals (Sigma, St. Louis, MO). Stock
aqueous solutions were prepared at 5 mM concentration. Analytical solutions of
0.1 mM concentration were prepared freshly as needed, by dilution of the stock

solutions with phosphate buffer of the appropriate pH.

Tetracyclines. The antibiotics tetracycline (TC), chlortetracycline (CTC),
demechlocycline (DMCC), oxytetracycline (OTC), doxycycline (DOC),
methacycline (MTC) and minocycline (MNC) were obtained as reagent-grade
chemicals (Sigma). Stock aqueous solutions were prepared at 25 mM nominal
concentration. At this concentration, TC, CTC and OTC solutions were
saturated. In order to provide a similar response from the UV-absorbance
detector, decanted aliquots of the stock solutions, in the ratio 2 TC : 3 CTC : 1
DMCC : 2 OTC : 1 DOC : 1 MTC : 1 MNC, were diluted with the phosphate

buffer solution of appropriate pH, to give approximately 5 mM standard solutions.

 

Individual letrar
combinations of '
mlibration curve
consecutively to
the dissolution 01
to prevent losses

Pharmace
and Warner Ch
obtained as harc
drug Was dissolv
nominal Concent
removed by car
SUPernatant solo
phosIthate buffer

A Common
is the control of it
order to Study the
by °°mp|ete dissi
acid at pH 2. Th
period, the Sampi

pH 75 phosphate

2'5 PhIlsical Me,

The absolt
measurements 01

 

42
Individual tetracycline standards and also mixtures containing different
combinations of the standards were prepared by the above procedure. For the
calibration curve, a 1 mM standard solution of tetracycline was diluted
consecutively to 0.5, 0.1, 0.05, and 0.01 mM with the same buffer employed in
the dissolution of the standard solution (pH 7.5), and was analysed immediately
to prevent losses by adsorption on the glassware.2

Pharmaceutical drugs, manufactured by Rugby (methacycline 500 mg)
and Warner Chilcott (tetracycline 250 mg and doxycycline 100 mg), were
obtained as hard-filled capsules. An appropriate weight of the pharmaceutical
drug was dissolved in pH 7.5 phosphate buffer to make a solution of 25 mM
nominal concentration. The undissolved filler and binder materials were
removed by centrifugation for approximately 15 min. An aliquot of the
supernatant solution was then diluted to 5 mM concentration with pH 7.5
phosphate buffer solution and analysed immediately.

A common concern in the manufacture industry of tetracycline antibiotics
is the control of toxic impurities that result from decomposition during storage. In
order to study the decomposition of tetracycline, a 25 mM solution was prepared
by complete dissolution of an appropriate weight of the standard in hydrochloric
acid at pH 2. This sample was submitted to heating at 70°C for 1 h. After this
period, the sample was cooled in an ice bath, diluted to 5 mM concentration with

pH 7.5 phosphate buffer solution and analysed immediately.

2.5 Physical Measurements

The absolute viscosity of sodium chloride solutions was determined by

easurements of kinematic viscosity and density.3 The kinematic viscosity

 

measurements v
25). The dens
constant absolut
for all solutions i

The dielei
heterodyne-beat
WISS. - Tech. -
frequency of a or
in a mixer resulti
Composed Of a fr;
Precision air cap
as detector, with
ray 6‘99 and the
Lissajous figure
capacitance can
3" caliacitor that
With the dieiii-chit
standard liquids c
accurate measur
“Dacitance (few
methoq Howeve
solutions of high ‘
of the Sodium cl

Greater than 0 1

appropriate! bUt ii‘

tiat25oCWas‘

 

 

43
measurements were performed in a Cannon-Ubbelhode viscometer (ASTM size
25). The density measurements utilized standard 10 mL pycnometers. A
constant absolute viscosity value of 0.8755 :t 0.0017 cP at 25° C was obtained
for all solutions in the concentration range from 1 to 10 mM.

The dielectric constant of sodium chloride solutions was evaluated by the
heterodyne-beat method3n4 using a beat-frequency oscillator (Model DM01,
Wiss. - Tech. - Werkstatten, Weilheim Obb., Germany). In this method, the
frequency of a crystal-controlled oscillator and a variable oscillator are combined
in a mixer resulting in a beat-frequency output signal. The variable oscillator is
composed of a fixed inductor and several capacitors including the cell, a variable
precision air capacitor, etc, combined in parallel. An oscilloscope can be used
as detector, with the beat-frequency applied to the vertical plates of the cathode-
ray tube and the 60-Hz line frequency applied to the horizontal plates. A simple
Lissajous figure serves as the indicator of balance. Changes in the cell
capacitance can be determined by noting the changes in the variable precision
air capacitor that are needed to restore balance. These readings are associated
with the dielectric constant by means of a calibration curve, determined using
standard liquids of known dielectric constant. For solutions of low conductance,
accurate measurements of beat-frequency (less than 1 Hz) or changes in
capacitance (few parts per million) can be performed by the beat-frequency
method. However, due to inherent limitations of this method when applied to
solutions of high electrical conductance, the determination of dielectric constant
of the sodium chloride solutions could not be performed at concentrations
greater than 0.1 mM. For such solutions, resonance methods and bridge
techniques for measuring capacitive reactance3 would have been more
appropriate, but this instrumentation was not available. A constant value of 78.5

i 1 at 25° C was obtained for all sodium chloride solutions in the concentration

 

range from 0.00

2.6 Data Proce

All data is
386 microproces
version 4.0, Mic
and the optimiz
'anguaee Asyst t
80-286 microoroi

The bufie
rSquired to p“
thermo‘ii’néltttic r

bufie’ sPecies.

capaCity, This F
incorliltrates ionic

matinitude of the

The Optimi
Chapter 4' in cit

prepare the bUffr

 

44

range from 0.001 to 0.1 mM.

2.6 Data Processing

All data processing and numerical calculations were performed on a 80-
386 microprocessor-based computer in a spreadsheet format (Microsoft Excel,
version 4.0, Microsoft Corp., Redmond, WA). The buffer formulation program
and the optimization program were written in the Forth-based programming
language Asyst (version 2.1, Keithley Asyst, Rochester, NY) to be executed on a
80-286 microprocessor-based computer.

The buffer formulation program (Appendix 1) performs the calculations
required to prepare phosphate buffers at a specified pH, given the
thermodynamic dissociation constants5 and the ionic charge of the individual
buffer species. Options are available to prepare buffers under conditions of
constant ionic strength, constant buffer concentration, and/or constant buffer
capacity. This program is based on classical equilibrium calculationsfi‘8 and
incorporates ionic strength corrections that are valid up to 0.5 M by means of the
Davies equation.7 No simplifying assumptions are made regarding the relative
magnitude of the equilibrium concentration of the buffer species.

The optimization program (Appendix 2), which is described in detail in
Chapter 4, includes a buffer calculation subroutine. In this subroutine,
phosphate buffers are formulated with both constant ionic strength and constant
buffer concentration, which requires the addition of an inert electrolyte. The
buffer formulation subroutine provides the analytical concentrations necessary to
Prepare the buffer solution correspondent to the optimal conditions for the

separation of the solutes under investigation.

 

2.7 References

1. Huang, X

2. Ciarlone,
255.

3. Weissber
Interscien

4. Shoemak.
Physical (

5- Hirokawa,

5- Butler, J,
Wesley Pi

7- Lambert, t
3- Rilbe, H_ t

 

45

2.7 References

1. Huang, X.; Gordon, M. J.; Zare, R. N. Anal. Chem. 1988, 60, 1837-1838.

2. Cia5rlone, A. E.; Fry, B. W.; Ziemer, D. M. Microchem. J. 1990, 42, 250-
25 .

3. Weissberger, A. Physical Methods of Organic Chemistry, 3rd ed.;
lnterscience Publishers Inc.: New York, 1959.

4. Shoemaker, D. P.; Garland, 0. W. and Steinfeld, J. I. Experiments in
Physical Chemistry, McGraw-Hill: New York, 1989.

5. Hirokawa, T.; Kobayashi, S.; Kiso, Y. J. Chromatogr. 1985, 318, 195-210.

6. Butler, J. N. Ionic Equilibrium - A Mathematical Approach; Addison-
Wesley Publishing Company, Inc.: Massachusetts, 1964.

7. Lambert, W. J. J. Chem. Ed. 1990, 67, 150-153.
8. Rilbe, H. Electrophoresis 1992, 13, 811-816.

 

 

 

THEORI

3.1 lntroductio

Over the
emerged as a v
biomolecules. l
resolving powe,
detection schen
leclmological Cit
has been direct
”“009 applicati
characterization
rundarItental Stu
nature of the Set:

'” capillar
buffering Proper
influence of a la
9°Cur.1.4,5 The
migrate With a C

Size, and shape.
as a

 

CHAPTER 3

THEORETICAL MODEL OF ELECTROOSMOTIC FLOW

3.1 Introduction

Over the past ten years, capillary zone electrophoresis (CZE) has
emerged as a very resourceful alternative method for the separation of charged
biomolecules. Relevant aspects of the technique such as high efficiency, high
resolving power, high speed, full automation, and a variety of injection and
detection schemes have been extensively investigated.1 In addition to these
technological developments, much research in capillary zone electrophoresis
has been directed towards demonstrating the versatility of the technique for
routine applications.2v3 However, despite the past considerable effort on the
characterization of the electrokinetic phenomena/'15 there is still a scarcity of
fundamental studies to provide greater understanding of the physicochemical
nature of the separation process at the capillary surface and in solution.

In capillary zone electrophoresis, a background electrolyte with adequate
buffering properties forms a continuum along the migration path. Under the
influence of a tangentially applied electric field, two mechanisms of migration
occur.1i4v5 The field exerts an electric force on charged molecules, which
migrate with a constant velocity that is characteristic of the molecular charge,
size, and shape. Concomitant to the electrophoretic migration, a flow of solution
as a bulk is induced by the electric field. This migration, regarded as

electroosmosis, is dependent on the characteristics of the capillary surface as

46

 

well as the com
The exi:
contributed sig
allowing for on
analysis of call-
has a substant
However, beg.
introduces no b
molecules, rega
efficiency benej
Compromised.
The und
implications in
several strateg
eleCtrOoSmotic f
and Physical prc
°°ncentration, a
an Inert electrol
09°80, dielec
demonstrated,
electroosmotic 1
capillary materia
and tefloh Capt“,
capillaries, the n
Coating and Cher

applicathn of ar

 

- j . . .mIEhmeig‘zz—EM an .m_..1

 

47
well as the composition of the conducting medium.

The existence of electroosmotic flow in fused-silica capillaries has
contributed significantly to the full automation of capillary electrophoresis,
allowing for on-line sample injection and detection as well as for simultaneous
analysis of cations and anions in favorable c:ases.1'3 The electroosmotic flow
has a substantial influence on the time the analytes reside in the capillary.
However, because of the flat velocity profile, electroosmotic flow theoretically
introduces no broadening. The same velocity component is added to all solute
molecules, regardless of their radial position. Consequently, analysis time and
efficiency benefit from a rapid electroosmotic flow, although resolution may be
compromised.

The understanding and control of electroosmotic flow have critical
implications in the design of electrophoretic separations. In recent years,
several strategies have been developed to exert proper control of the
electroosmotic flow. Perhaps the most effective means is to alter the chemical
and physical properties of the buffer solution. In this context, changes in the pH,
concentration, and ionic strength of the buffer,67 the type and concentration of
an Inert electrolyte or organic additive}11 as well as changes in the solvent
viscosity, dielectric constant,12 and temperature13 have all been successfully
demonstrated. Another simple approach to alter or ultimately inhibit the
electroosmotic flow consists of changing the chemical composition of the
capillary material and, hence, the surface charge density. Fused-silica, glass,
and teflon capillaries have been employed for this purpose.14 In fused-silica
capillaries, the nature of the capillary wall can be further modified by physical
coating and chemical derivatization methods.15'17 Other strategies, such as the

application of an external electric field across the capillary wall, can also be

 

used to influeni
At the p
been achieved
and chemical
parameters rel;
resulting equati
computationally
Practical means
In this I
capillaries is e:
PhYSiCally mear
surface to chant
iOil-selective ele
both constant-vi
‘3 °°nirmed usir

aControlled Cont

3'2 Theory

48
used to influence the electroosmotic flow”,19

At the present time, mathematical modelling of electroosmotic flow has
been achieved by solution of the fundamental laws describing mass transport
and chemical equilibria.20v21 Other approaches rely on the estimation of
parameters related to the electrical double layer.22 In most instances, the
resulting equations are not trivial and their solution can only be approached by
computationally intensive numerical methods. Therefore, a simpler and more
practical means of describing the migration process is highly desirable.

In this work, the nature of electroosmotic migration in fused-silica
capillaries is examined from a theoretical and experimental perspective. A
physically meaningful model is proposed, where the response of the capillary
surface to changes in buffer composition and pH is treated as an analogy to an
ion-selective electrode. The prediction of electroosmotic flow is evaluated under
both constant-voltage and constant-current conditions. The validity of the model
is confirmed using phosphate buffer solutions in the pH range from 4 to 10, with

a controlled concentration of sodium ions.

3.2 Theory

Ion-Selective Membranes. The ion—selective properties of glass membranes
have been exploited for the construction of a variety of chemical sensors.23'25
Among the many representative examples, the pH-sensing glass electrode is
one of the most common. A typical pH electrode consists of a thin glass
membrane sealed at the end of a tube containing an appropriate standard

solution and an internal reference electrode. During the measurements, the

 

complete asser
registered with r
of the glass mer
solution is show
Many of
membranes are
glasses are con
oxygen atoms v
Structure are oi
attraction to the
are 590090 bet:
the glass. How
lattice, are prim;
membrane,
EXposure
layer. At the 0
Chiced sites a
layer, there is a
increase in the I
are °°°Upied exi

The eXCh
soluli0n is lest

CharaCIeriatic of

Cation in the met

H+i9IHSs) '1‘ Na

 

49
complete assembly is immersed into a test solution and the potential is
registered with respect to an external reference electrode. A schematic diagram
of the glass membrane in contact with the internal reference solution and the test
solution is shown in the top part of Figure 3.1.

Many of the properties that confer selectivity and sensitivity to such
membranes are associated with the chemical structure of the glass.24 Silicate
glasses are composed of an irregular three-dimensional network of silicon and
oxygen atoms with nominal composition (Si02)x. The holes or defects in this
structure are occupied by cations, held more or less strongly by electrostatic
attraction to the neighboring oxygen atoms. Doubly and triply charged cations
are strongly held and do not contribute to the electrical conduction properties of
the glass. However, singly charged cations, which are quite mobile within the
lattice, are primarily responsible for charge transport in the interior of the glass
membrane.

Exposure of the glass to water causes the formation of a hydrated gel
layer. At the outer edge of this layer in contact with the solution, the singly
charged sites are predominantly occupied by hydrogen ions. Within the gel
layer, there is a continuous decrease of the number of hydrogen ions and an
increase in the number of other cations. In the interior of the glass, such sites
are occupied exclusively by cations.

The exchange of cations in the hydrated gel layer with cations in the
solution is responsible for the pH response and alkaline error that are
characteristic of glass membranes. If sodium is considered to be the only active

cation in the membrane, the ion-exchange reaction can be written as:

H+(glass) + Na+(soln) <—> H+(soln) + Na+(glass) [3.1]

 

 

 

Fig“re 3 1 0‘69 9'90”

ilad 8'39
Ca|do

uble lay; s

 

WI
iqtrucuetr eats

CtIV ve glas
smca

5 me
surfaCe

mbra
es(

INTERNAL
REFERENCE
SOLUTION
ane (tOPIa and
bottom SURFACE IHl

 

COMPAt

 

 

 

 

 

 

51
Figure 3.1
HYDRATED LAYER HYDRATED LAYER
INTERNAL TEST
REFERENCE<-> DRY GLASS <——> SOLUTION
SOLUTION
SURFACE IHP OHP PLANE OF SHEAR

<84

BULK SOLUTION

<8

 

 

COMPACT LAYER DIFFUSE LAYER

 

 

the contribution

I

2.;
Eb : E' + .—

where T is the a
and F is the Fe
the boundary pr
solution, as well
Equation [3.3] a
sodium ions in ft
magnitude of k9
of the determint

values that rang

 

 

 

52

with the associated equilibrium constant:

aH (soln) aNa (glass)

K _ [3.2]
aH (glass) aNa (soln)

 

where a... and am represent the activities of hydrogen and sodium ions,
respectively, in solution (soln) and in the interior of the glass membrane (glass).
The equilibrium constant for this reaction is quite small, favoring the
incorporation of hydrogen rather than sodium ions into the silicate lattice in close
contact with the solution.26

When a difference in pH exists between the test and the internal
reference solutions, a boundary potential develops across the glass membrane.
This boundary potential (Eb) is given by the Nernst equation, modified to include

the contribution of the sodium ions to the pH response223

2.303 R T
Eb = E' + log [aH(soln)+ kPOT aNa(soIn)] [3.3]
2 F

 

where T is the absolute temperature, 2 is the ionic charge, R is the gas constant
and F is the Faraday constant. The constant term (E') includes contributions to
the boundary potential from hydrogen and sodium ions in the internal reference
solution, as well as the reference electrode, junction, and asymmetry potentials.
Equation [3.3] shows that the membrane is responsive to both hydrogen and
sodium ions in the test solution, where the degree of selectivity is dictated by the
magnitude of kPOT. The quantity kPOT is defined as the potentiometric constant
of the determinand H+ with respect to the interferent Na+ and may assume

values that range from zero (no interference) to greater than unity, depending

1 l

 

 

 

masses 8”,

sodium-selective

 

Electrical double
presence of seven
character?7 In cor
ionized and cause
homogeneous spa
immediate proximil
Much theoretical
between the surfac
concentration profit
accepted features .
bottom part of Figur
The region

chanted water mole

 

 

 

53
upon the composition of the membrane2425 The potentiometric constant is
comprised of the ratio of ionic mobilities (u) in the membrane as well the
exchange equilibrium constant defined by Equation [3.2]:

lass
kPOT = K ————”Na(g ) [3.4]

IlH (glass)

Equation [3.3] leads to interesting predictions concerning the glass membrane
response. If the product of kPOT and aNa is sufficiently small compared to aH,
the membrane is primarily responsive to hydrogen ions, constituting a pH-
selective glass electrode. Conversely, when the product of kPOT and aNa
surpasses aH, the membrane responds primarily to sodium ions, constituting a

sodium-selective glass electrode.

Electrical double-layer structure. Silica surfaces are characterized by the
presence of several types of silanol groups (SIOH), which are weakly acidic in
character.27 In contact with an aqueous medium, some of the silanol groups are
ionized and cause the surface to be negatively charged.28 As a result, a non-
homogeneous spatial distribution of charge originates within the solution in
immediate proximity to the surface, designated as the electrical double layer.
Much theoretical work has been concerned with describing the interface
between the surface and the solution, including evaluation of the potential and
concentration profiles as a function of distance.4i5i23 Some of the presently
accepted features of the electrical double-layer structure are illustrated in the
bottom part of Figure 3.1.

The region adjacent to the surface is occupied by layers of strongly

oriented water molecules and some ions, presumably dehydrated, tightly held to

 

    

docble layer.

motion, some

approaches
double layer.
When an
forces act upon
a unilateral mc
During their mit
inducing the ovr
differences in tt
layer, a velocity
increases insidi
certain, very sn
solution migrate
portion of the
characterized a:
shear is known

important impl

 

 

 

54

the surface by electrostatic and other cohesive forces (specific adsorption). The
center of these ions defines a plane known as the inner Helmholtz plane (IHP).
Hydrated ions approach the surface by a distance corresponding to their
hydration radius. These ions are loosely bound and their interaction with the
surface is independent of their chemical properties (non-Specific adsorption).
The plane defined by the center of the hydrated ions is known as the outer
Helmholtz plane (OHP), or Stern layer, and delimits the compact region of the
double layer. Due to the finite temperature and associated random thermal
motion, some of the ions diffuse farther into solution. As the distance from the
surface increases, the counterion concentration decreases and ultimately
approaches the bulk value. This region is referred to as the diffuse part of the
double layer.

When an electric field is imposed tangentially to the surface, the electrical
forces act upon the spatial distribution of charge within the diffuse layer, causing
a unilateral movement of ions towards the oppositely charged electrode.4v5
During their migration, these ions transport the surrounding solvent molecules,
inducing the overall movement of solution known as electroosmotic flow. Due to
differences in the magnitude of electrical and frictional forces within the double
layer, a velocity gradient originates. The flow velocity is zero at the surface,
increases inside the double-layer region and reaches a maximum value at a
certain, very small distance from the charged surface. The remainder of the
solution migrates with this maximum velocity. The location at which the mobile
portion of the diffuse layer can slip or flow past the charged surface is
characterized as the plane of shear. The potential developed at the plane of
shear is known as the electrokinetic or zeta potential. lts magnitude has

important implications on the development and characterization of

 

 

 

 

 

where 2i is the
constant of the
is Boltzmann's
known as the I

double layer.

Analogy betwe
Silica Surface:
behavioral anal
structure at the
analogy to the ?

compact region

 

 

 

 

55
electroosmotic flow (vide infra).
The potential distribution in the double layer can be derived by solving the
Poisson-Boltzmann equation for limiting cases. If the surface potential (9’0) is
sufficiently low (< 50 mV), the potential profile with distance (x) can be

approximated by the Debye-Huckel theoryz4v23

‘I’=‘I‘o exp(—I(x) [3.5]

One of the most important quantities to emerge from the Debye-Huckel theory is
the parameter K, which correlates properties of the solution with the double-layer

dimensions:

1000 52 NA
K2 = 2 Ziz Mi [3.6]
8 6 T

 

where zi is the charge and M is the molarity of the ith ion, 8 is the dielectric
constant of the medium, a is the elemental charge, NA is Avogadro's number, é
is Boltzmann's constant, and T is the absolute temperature. The quantity K'I,
known as the Debye length, is often used to characterize the thickness of the

double layer.

Analogy between Ion-Selective Membranes and Double-Layer Structure at
Silica Surfaces. The proposed model for electroosmotic flow is based on
behavioral analogies between an ion-selective membrane and the double-layer
structure at the fused-silica capillary surface, as illustrated in Figure 3.1. In
analogy to the internal reference solution of a pH-sensing glass electrode, the

compact region of the double layer is modelled as a reference layer for the bulk

 

 

 

 

 

solution. Thl
extent of mm:
the ionic cha
within the con
the plane of
mobile parts

sodium ions I
potential, is re
a mechanism
membranes.

manipulate 811
Choice of pH 1

cortcentration

3'3 ROSUIts a

The Che

effect of a g“
PTOpet selectic
eXIIemeiy impc

. most commenh
0pr on the e)
the Complexity
can be f°lmula
as pH, from or

 

 

56
solution. The establishment of the compact layer is dictated primarily by the
extent of ionization of the silica surface, which is affected by the pH but not by
the ionic character and content of the bulk solution. Therefore, the potential
within the compact layer responds only to changes in pH of the bulk solution. At
the plane of shear, which is a physical boundary between the immobile and
mobile parts of the solution, an exchange equilibrium between hydrogen and
sodium ions occurs. Therefore, the potential at the plane of shear, the zeta
potential, is responsive to both hydrogen and sodium ions in the bulk solution, in
a mechanism analogous to that which accounts for the alkaline error in glass
membranes. The proposed model thus comprises two fundamental ways to
manipulate electroosmotic flow in capillary zone electrophoresis: the judicious
choice of pH (a coarseadjustment) and the selection of an appropriate sodium

concentration (a fine adjustment).

3.3 Results and Discussion

The characterization of electroosmotic flow depends on how distinctly the
effect of a given variable can be isolated from others. For this reason, the
proper selection of the conducting medium and the control of its composition is
extremely important. Conducting media with buffering properties are among the
' most commonly used in capillary zone electrophoresis because of the dual effect
of pH on the extent of ionization of the solutes and the silanol groups. However,
the complexity of buffer systems and the diversity with which a buffer solution
can be formulated make it difficult to isolate the effect of a single variable, such

as pH, from other changes that may occur concomitantly when pH is varied,

 

such as ionic
Therefore, in
system seem
studies were I
later studies,
system and
magnitude uni
The are
and accuracy
accepted7,12,2
manner in whi
Slistematic pr:
Wmmw
i20 % RSD (.
described prei
and the day-tc
six months,
The reli
"‘6 method 39
most Common
the Weighing '
large range of
continuing in
m°difi°ations d
melhOd to bOtl'

the direct cm

 

 

 

 

57

such as ionic strength, buffer concentration and capacity, cation and anion type.
Therefore, in order to characterize the electroosmotic flow, a simpler electrolyte
system seems to be a more appropriate choice. In this work, the preliminary
studies were performed using solutions of singly-charged, strong electrolytes. In
later studies, the electroosmotic flow was characterized in the phosphate buffer
system and a comprehensive model was developed to predict the flow
magnitude under a variety of operational conditions.

The experimental validation of the proposed model relies on the precision
and accuracy with which the electroosmotic flow can be determined. It is well
accepted7i1229i3° that the electroosmotic flow is strongly dependent on the
manner in which the capillary surface has been conditioned. In the absence of a
systematic procedure, the electroosmotic flow could be measured in the same
day with approximately i 10 % RSD and the day-to-day reproducibility was
:t: 20 % RSD (vide Chapter 2). By conditioning properly the capillary surface, as
described previously, the single-day reproducibility was better than :t: 1 % RSD
and the day-to-day reproducibility was better than :t: 3 % RSD, over a period of
six months.

The reliability of the model for the electroosmotic flow also depends on
the method selected to evalute the flow magnitude. In this work, several of the
most common methods were compared, including the neutral-marker method,14
the weighing procedure,31 and the resistance-monitoring method.32 When a
large range of pH was inspected, the monitoring of resistance changes in the
conducting medium was found to be the most reliable method. The
modifications described in Chapter 2 extend the use of the resistance-monitoring
method to both constant-voltage and constant-current conditions. This enables

the direct comparison of results obtained under both conditions for the

 

 

 

development a

Preliminary .
Conditions.

electroosmotic
equation“:5 wt

(5) according l

Vosm=-~

where V is U
PVOPOrtionality
c{imprised of
viscosity (ll) c
Potential (Q), ~
the capillary (r
[35]), or Wher
theoretical deri
structUre of the
implied, how 6v
are applicable
Velocity and eh
zeta potential is

A°°0rdin
between the el

 

58

development and evaluation of the proposed model of electroosmotic flow.

Preliminary Studies of Electroosmotic Flow under Constant-Voltage
Conditions. In the constant-voltage operation of the power supply, the
electroosmotic flow is evaluated by means of the Helmholtz-Smoluchowski

equation,“'r5 which relates the linear velocity (vosm) and the electric field strength

(E) according to:

8 80 C V
Vosm = ' ——— E = “osm _ [3-7]

11

where V is the applied voltage and L is the total capillary length. The
proportionality term, which represents the electroosmotic mobility (uosm), is
comprised of several constants such as the dielectric constant (8) and the
viscosity (1]) of the medium, the permittivity of a vacuum (80), and the zeta
potential (C). The Helmholtz-Smoluchowski equation is valid when the radius of
the capillary (r) is large compared to the double-layer thickness (1C1, Equation
[3.6]), or when the product (K r) is much larger than one hundred. In the
theoretical derivation of Equation [3.7], no assumptions are made regarding the
structure of the double layer except for the existence of a plane of shear. It is
implied, however, that the dielectric constant and viscosity of the bulk solution
are applicable within the double layer. It is interesting to note that when the
velocity and electric field vectors are in the same direction, a negative value for
zeta potential is required.

According to the Helmholtz-Smoluchowski equation, a linear relationship
between the electroosmotic velocity and field strength is expected. However,

when the velocity is displayed as a function of the applied voltage (Figure 3.2),

 

 

 

 

59

Figure 3.2 Dependence of electroosmotic velocity on the applied voltage for
aqueous sodium chloride solutions of concentration (A) 1 mM.

(0)2mM, (D)3mM, (v)4mM.

4O

ed voltage for

.n (A) 1 “‘M‘

 

 

 

 

 

 

 

0.40

 

60
Figure 3.2
O
<-
l.
0
“no
_ 0
<1 01
_o
r
r T F T r r O
O O O O
”'3 (‘4 “‘ O,
O O O O

(S/w) ALDO—GA

 

 

 

 

 

 

VOLTAGE (kV)

 

 

 

the slope sh
aqueous solu
of concentrati
equation. lnc
results are p
properties of
be dependen'
concentration
be fairly cons
was calculate
electroosmotic
measured vali
the zeta poter
and the surfai
marked depen
results identify
deveIODmenl r
resPonds lo
dependence 0.
Characterrzres ,
With the
CaFilllary Surfer
electrolyre Syst
maQnitude of t
DotasstUm Chlo

varied “”eélrly ‘

 

61

the slope shows a dependence on the concentration of sodium chloride in
aqueous solutions. Therefore, it is important to examine in more detail the effect
of concentration on each constant in the sl0pe of the Helmholtz-Smoluchowski
equation. In order to accommodate the large range of concentration studied, the
results are plotted in a semi-logarithmic manner in Figure 3.3. As intrinsic
properties ofthe solution, the dielectric constant and viscosity are expected to
be dependent on the solution composition.33 However, within the range of
concentration studied, both the dielectric constant and the viscosity are shown to
be fairly constant and approach the values for pure water. The zeta potential
was calculated from Equation [3.7], where the slope of the graph of
electroosmotic velocity versus applied voltage was used, together with the
measured values of viscosity and dielectric constant. As an interface potential,
the zeta potential is expected to be influenced by both the solution composition
and the surface characteristics as well. Indeed, the zeta potential shows a
marked dependence on the concentration of the solution in Figure 3.3. These
results identify the zeta potential as the most significant parameter in the
development of electroosmotic flow and the mechanism by which the surface
responds to changes in the electrolyte composition. Furthermore, the
dependence of the zeta potential on the logarithm of the sodium concentration
characterizes an ion-selective type of response.

With the intent of exploring in more detail the ion-selective behavior of the
capillary surface, the zeta potential was determined in other singly charged
electrolyte systems. Figure 3.4 presents the influence of the cation type on the
magnitude of the zeta potential for aqueous solutions of lithium, sodium, and
potassium chloride. Within the range of concentration studied, the zeta potential

varied linearly with the logarithm of the cation concentration, which verifies that

 

 

Figure 3.3

62

. . . _ . . f
Evaluation of dielectric constant, vuscosrty, and zeta potential 0
aqueous sodium chloride solutions at pH 9. The zeta potential was
evaluated under constant-voltage conditions at (A) 10 kV. ( O)

20 W, (n) 30 kV.

\I‘C‘f ‘AF‘IT\/

/M\/\

7F‘TA DflTL‘IxITI/H

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

63
Figure3.3
k..—
Z 100
<
P—
‘2
O 80-
C.) i" 0 ~o
Q ‘1
E 60—
C.)
Lu
__J
Lu
5 40 i I L _l 1 I g
1.0
6; e—e—e-eep
v 0.8—
>—
i“ .
a otentialoi U7
otentlal was 0 O. 5 _
y10kV,(O) ,3
>
0.4 A L . a . L 4
g —75
E,
_J —iOO— 9
<1
:
E] —125'i
l— .
E
< 450- O
l—- T
[Li], —175 T— | ‘— i T l '
—3.0 -2.0 -1.0 0.0 1.0

log CONCENTRATION (mM)

 

 

 

 

 

 

 

64

Figure 3.4 Effectt of cation type (is? the magnitude of the zeta potential under
ons an -vo age con i ions at 20 kV. Aqueous solutions at H 9 of
(A) chi,(l:l) KCl. (0) NaCl. p

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_75/

 

65
Figure 3.4

 

O.—

 

EEV zorZEzmozoo mo.
ma 90 so No
» L

b _ F _

0.0

 

 

mm—l

romil

imN_l

TOOPI

 

 

tential under
ns at P“ 9 °f

mml

'lVLLNlLOd ViEZ

(Aw)

 

 

 

the capillary
at any given
of the zeta p
not distingui
These result
the complete
This conclus
radiometric r
ions only in
studies in c
from those re
increased w
observed in.
conditioning
altered, Ana
0f the diffuse
cation during
comPosition
the reliability
Figure
the zeta pcti
nitrate, and p
panicu'ar'l’ ir
i8 inVOIVed‘ ii
The em 0r

°°”9|ation 0.

 

 

66

the capillary surface respOnds to each cation in a Nernstian fashion. However,
at any given concentration, no statistically significant variation in the magnitude
of the zeta potential was observed. This behavior implies that the surface does
not distinguish between cation types, regardless of their chemical diversity.
These results preclude the possibility of specific adsorption and, in fact, suggest
the complete absence of cations other than hydrogen ion in the compact layer.
This conclusion is supported by the previous work of Li and Bruyn,34 where
radiometric measurements at quartz surfaces revealed the presence of sodium
ions only in the diffuse region of the double layer. However, several recent
studies in capillary zone electrOphoresis have reached conclusions different
from those reported here. Salomon et al.22 reported that electroosmotic velocity
increased with the hydrated radius of the cation, whereas Atamna et al.8
observed the opposite behavior. Based on our experience, the method of
conditioning the capillary surface is particularly important when the cation type is
altered. An acid wash is necessary to remove the cations in the immobile region
of the diffuse layer, so that they can be replaced completely with the appropriate
cation during the alkaline wash. In the absence of this treatment, a mixed
composition of cations is obtained at the capillary surface which compromises
the reliability and long-term reproducibility of the electroosmotic flow.

Figure 3.5 presents the influence of the anion type on the magnitude of
the zeta potential for aqueous solutions of sodium chloride, bromide, iodide,
nitrate, and perchlorate. The zeta potential varied markedly with the anion type,
particularly in the low concentration range. These results suggest that the anion
is involved, in some manner, in the development of the double-layer structure.
The exact origin of this effect is not known, however, as there is no apparent

correlation of the zeta potential with either the hydrated radius35r35 or the

 

 

 

67

Figure 3.5 Effect of anion type on the magnitude of the zeta potential under

constant-volta e conditions at 20 kV. Aqueous solutions at pH 9 of

(O)NaCI, ( )NaBr, (.)Nal, (a) NaNO3, (v) NaClO4.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_.5/

 

68
Figure 3.5

 

1.0

I

0.8

log CONCENTRATION (mM)

 

 

iotential under
ions at PH 9 0
') NaClO4-

 

 

 

 

 

L“!

. CD

O

T— I T ] VIV ‘ {—1 T ’

LO Q LO 0 L00
l\ O N to r\
I r— 1— 1— r—
t l l l

(Aw) TyitNaiOa V132

   

 

mobility23 of
literature to i
electroosmot
electroosmot
found that b
electroosmot
Green and
unimportant
higher than
observations
controlled to
electroosmot
In con
of predicting
the logarithm
surface reSpi
0f the electrc
toWards the
anion identit
eleCthOsmot
sllSlem.

Preliminary
c0nditidns_
conditiOnS, C

equation (Eq

 

 

 

 

 

69

mobility?!3 of the anion. There appears to be a great deal of controversy in the
literature to date regarding the effect of anion type on the development of the
electroosmotic flow. Atamna et 31.9 observed strong differences in the
electroosmotic flow using common sodium buffer solutions. VanOrman ef al.7
found that buffers with several different anion types can produce the same
electroosmotic velocity provided that the ionic strength is carefully controlled.
Green and Jorgenson10 concluded that differences in anion type are
unimportant if the concentration of an inert electrolyte is at least three-fold
higher than the concentration of the operating buffer. Despite these prior
observations, our data suggest that even solutions of inert electrolytes with well-
controlled ionic strength exhibit a distinct influence of the anion type on the
electroosmotic flow.

In conclusion, the results presented herein clearly sustain the possibility
of predicting electroosmotic flow by modelling the‘zeta potential as a function of
the logarithm of the cation concentration. It has been shown that the capillary
surface responds to the solution concentration in a Nernstian fashion, regardless
of the electrolyte type employed. There is no apparent selectivity of the surface
towards the cation, however, the zeta potential magnitude is affected by the
anion identity. Therefore, under constant-voltage conditions, the prediction of
electroosmotic flow is determined by the ionic character of the electrolyte

system.

Preliminary Studies of Electroosmotic Flow under Constant-Current
Conditions. In order to describe electroosmotic flow under constant-current
conditions, Ohm's law must be incorporated into the Helmholtz-Smoluchowski

equation (Equation [3.7])1

 

 

 

 

Vosm :

where R is tl

variables are

where A is ti
the solution,

individual ior

k = F 2 '2
By combining

E
vosm : ‘ \

Equation [3;
and the 8pol
meeltieS, a
deriVaticn of l

ACCorc
intrinsic Cha
electhSmoti

velocities of

 

 

 

seoCRl

 

Vosm [3.8]

n L
where R is the resistance of the medium and l is the applied current. All other
variables are as previously defined. The resistance is given by:

1 A
__ = k __ [39]
R L

where A is the cross-sectional area of the capillary and k is the conductivity of
the solution. The conductivity is related to the electrophoretic mobility ([1,) of the

individual ionic species as follows:

k=F2lZilui Mi - [3.10]

By combining Equations [3.8], [3.9], and [3.10], the following expression results:

8
60 Q ___ “05m l [3.11]

I
n X? Aquan.

 

 

Vosm = ‘

Equation [3.11] predicts a linear relationship between electroosmotic velocity
and the applied current. The influence of the capillary dimensions, solution
properties, as well as the surface characteristics are clearly evident in the
derivation of Equation [3.11].

According to Equation [3.11], the electrophoretic mobility is one of the
intrinsic characteristics of the electrolyte that is expected to affect the
electroosmotic velocity. To examine the extent of this effect, the electroosmotic

velocities of sodium nitrate and sodium bromide solutions were measured in

 

 

 

 

reference to
whose soluti
the previous
velocity undi
with the apt
Therefore, it
sufficiently if
conditions er

As sh
flow is by at
when studyir
buffer syster
likely to be ‘
charged elei
controlled. l
bullersolutio
With iltcreasii
Chloride exce
approaches!

The s
Selfictive bet
30|Uticns as
differences it
adClitiOn Of a
°areiuiiy cc

electroos,“0t

 

 

 

71

reference to sodium chloride solutions. Nitrate and bromide are the anions
whose solutions presented the greatest difference in electroosmotic behavior in
the previous study under constant-voltage conditions. The electroosmotic
velocity under constant-current conditions, shown in Figure 3.6, varied linearly
with the applied current and seems to be independent of the type of anion.
Therefore, it is valid to conclude that the differences in anion mobility23 were not
sufficiently large to affect the electroosmotic velocity under the experimental
conditions employed in this work.

As shown in Equation [3.11], another means to affect the electroosmotic
flow is by altering the charge of the electrolyte. This is particularly important
when studying the electroosmotic behavior of more complex electrolytes such as
buffer systems, where several species with different charge and mobility are
likely to be present. However, by addition of a substantial amount of a singly
charged electrolyte, the electroosmotic velocity of the buffer solution can be
controlled. Figure 3.7 shows the results of flow measurements in phosphate
buffer solutions at pH 9 (where the highly charged PO43' species predominates),
with increasing amounts of sodium chloride. When the concentration of sodium
chloride exceeds the concentration of the buffer salts, the electroosmotic velocity
approaches that of a sodium chloride solution.

The studies under constant-current conditions have shown that the ion-
selective behavior of the capillary surface applies to singly charged electrolyte
solutions as well as to buffer systems. In buffer solutions, however, the
differences in charge and mobility of the individual species must be masked by
addition of an excess of a singly charged strong electrolyte. Therefore, under
carefully controlled experimental conditions, the proposed model of

electroosmotic flow can be explored in more detail to represent the behavior of

 

 

 

 

 

72

Figure 3.6 Effect of anion type on the electroosmotic velocity under constant-
current conditions. Aqueous solutions at pH 9 with 3 mM
concentration of (0) NaCl, (A) NaBr, (El) NaNO3.

 

 

 

 

 

40

O.

ider constant-
I With 3 m

 

 

’12.." '.__.-. t-P- -. 7

 

 

 

0.40

 

73
Figure 3.6
O.
LO
-0.
<-
O
l— .
rt)
._0.
(\I
-0.
O
i i T T T ‘
O O O O O
“’3. b! F. O.
CD C) O O
(“S/w) MIOO'IEIA

CURRENT (MA)

 

Figure 3.7

74

Effect of the ratio of Na(NaCI) to Na(buffer salts) on electroosmotic
velocity under constant-current conditions for phosphate buffer
solutions at pH 9 with 10 mM total sodium concentration.

(V)0:10, (0)5:5, (El)6.5:3.5, (A)10:O.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.20/

electroosmotic
sphate bu er
on.

 

75
Figure 3.7

 

 

15 20

10
CURRENT (MA)

 

0.20~

O.IO—i

0.15—~
0.05—

(S/ws) ALDO—BA

 

0.00

 

 

 

complex bu

Validation .
phosphate l
conditions.
sodium from
and equal '
representati'
nonlinearly
influencingt
potential. \
extensive pr
density in th.
eleittroosmoi
Produced thi
39- FOra o
eteetrcosmot
conCentratior
increases, Cc
decrees“.
The (x
magflittide of
data were fly

behavior of gl

l=§

0+SL

 

 

76

complex buffer systems.

Validation of the Ion-Selective Model. The effects of pH and composition of
phosphate buffer solutions were examined separately under constant-current
conditions. These solutions were prepared in such a way that the ratio of
sodium from sodium chloride and the sodium buffer salt was maintained constant
and equal to unity. For a constant concentration of sodium, shown for a
representative case in Figure 3.8, the electroosmotic velocity increased
nonlinearly from pH 4 to 10. The pH affects the electroosmotic flow by
influencing the extent of ionization of the silica surface, thus altering the surface
potential. When the pH is much lower than the pKa of the silica surface,
extensive protonation of the silanol groups occurs, which reduces the charge
density in the double layer. Consequently, the zeta potential is lowered and the
electroosmotic flow decreases. A change in the electrolyte concentration
produced the Opposite effect, as illustrated for a representative case in Figure
3.9. For a constant value of pH, which defines a constant surface potential, the
electroosmotic velocity decreased proportionately with the total sodium
concentration from 5 to 15 mM. As the concentration of the bulk solution
increases, compression of the double layer occurs and the electroosmotic flow
decreases.

The combined effect of pH and composition of the buffer solution on the
magnitude of the zeta potential is illustrated in Figure 3.10. These experimental

data were fit to an equation analogous to that describing the ion-selective

behavior of glass membranes (Equation [3.3])3

C = C0 + SLOPE log( aH + kl"OT am) [312]

 

 

 

77

Figure 3.8 Effect of pH on electroosmotic velocity under constant-current
conditions for phosphate buffer solutions with 10 mM total sodium
concentration and 1:1 ratio of Na(NaCI to Na(buffer salts). (A)

pH4. (lipH5. (inHG. (le 7. (inHB. (DipH9.
(A)pH10-

 

 

 

 

 

 

 

 

 

0.20/

instant-current
if total sodium
salts).

3’ (0) H9.

 

 

 

 

 

0.20—-

 

78
Figure 3.8
O
(\I
[_ LO
_ O
r- LO
t.
I T T‘ r 1* 0
if) 0 LO O
._I P. O. O
o o o 0'

(S/wa) AllOO’lElA

CURRENT (,uA)

 

 

 

 

79

Figure 3.9 Effect of total sodium concentration on electroosmotic velocity
under constant-current conditions for phosphate buffer solutions at
pH 7 with 1:1 ratio of Na (NaCl) to Na (buffer salts). ( O) 5 mM.
(A) 7.5 mM. (I) 10 mM, (u)12.5 mM, (V) 15 mM.

 

 

 

 

 

 

 

 

 

0.20/

 

 

 

 

 

 

,, E- »Wr
80
Figure 3.9
O
(\l
_m
A
~ <
:3.
V
O t—
__ leJ
. 0:
mode velOCIi)’ 0:
fer solutions at . D
(0) 5m. 0
.mM.
-LO
T r I I I I I O
0 LO 0 LO Q
9! "T '7 O. O
O O O O O
(S/w) ALIOO‘IEIA

 

 

 

 

 

81

Figure 3.10 Comparison of experimental data with the ion-selective model. for
zeta potential as a function of pH from 4 to 10 and total sodium
concentration from 5 to 15 mM (bottom to top curves).
Experimental conditions as given in Figures 3.8 and 3.9.

Im‘A

DnTEMTlA l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

82
Figure 3.10
100
50 -
S‘ o -
E,
2'
ctive modeliol I— J
Id total sodium 5 .
I[op CUIVeS- I—
3.9. 8 -50 -
C '.
“100 - .
O
-150 T I f I 1 I I l ' l ‘ I
0 2 4 6 8 10 12 14
pH

 

 

Co is mat

function (E

to = lERl

The pararr
distributior
parameter
unknown l
and the b
magnitude
(SSE) are
ion-selectl
interpretin
The
surface, it
Detential I
the pH in
dramatica
part to th
Primarily
Preposed
SOdiUm 3'
higher th:
Which is t
significan

 

 

 

83
Co is mathematically described by a Gaussian probability integral or error

function (ERF), which is sigmoidal in shape:37

Co = [ERF(AOPH + Boll Co + Do [313]

The parameters A0 and Bo are related to the mean and standard deviation “of the
distribution. The parameter Co confers the height to the sigmoidal curve and the
parameter Do is needed for displacement in the zeta potential axis. The
unknown parameters of Equation [3.12] and [3.13] were searched numerically
and the best fit was determined by means of the least-square method.38 The
magnitude of these parameters as well as the sum of the squared residuals
(SSE) are presented in Table 3.1. In Table 3.2, an statistical evaluation of the
ion-selective model is presented. These results can be understood by
interpreting separately the contribution of each term in Equation [3.12].

The logarithm term, which represents the ion-selective behavior of the
surface, is shown in the bottom part of Figure 3.10. At very low pH, the zeta
potential responds exclusively to the logarithm of the hydrogen ion activity. As
the pH increases, the contribution of sodium to the-overall potential increases
dramatically and predominates shortly after pH 4. This behavior is attributed in
part to the relative magnitude of the hydrogen and sodium ions activity, but
primarily to the magnitude of the potentiometric constant. According to the
proposed model, kPOT carries information on the exchange equilibrium between
sodium and hydrogen ions at the plane of shear. The value 0.22 is appreciably
higher than the potentiometric constant of a pH-sensing glass electrode,25v26
which is on the order of 1042. This result suggests that sodium ions contribute

significantly to the transport of charge across the plane of shear.

 

 

Table 3.1 P

 

 

 

84

Table 3.1 Parameters of the ion - selective model.

 

 

 

 

 

 

PARAMETERS VALUES

A0 —0.86
30 5.11

C0 33.2 '
00 59.7
SLOPE 44.4
W” 0.22
SSE 247

 

 

 

 

 

 

Table 3.2 C
V

 

pH

 

 

 

 

 

 

 

 

L...

Equation
" % ERRC

 

85

Table 3.2 Comparison of the experimentally determined zeta potential with
values calculated from the ion-selective model.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

pH aNa+ ZETA ROJENTIAL % ERROR"
m )
EXPERIMENTAL CALCULATED”
4 4. 63 X 10'3 -35. 7 + 1. 2 -38.5 —7.8
6. 84 x 10'3 —30. 6- 1. 1 —31.6 —3.3
9.00 x 10’3 -—27.3 i 0.75 —26.6 2.6
1.11 x10“2 —25.7 i 0.68 —22.7 12
1 3.2 X 10'2 —23.3 i- 0 42 —-19.5 16
5 4. 63 x10'3 —46.3 i1.3 -47.9 —3.5
6. 84 x10'3 —36.8 $1.5 —40.7 —11
9. 00 x 10'3 —32.8 i 0.94 —35.2 -7.3
1.11 x10'2 —31.1i 0.77 —31.1 0.0
1. 32 x 10'2 —28.5 i- 0.85 -27.8 2.5
6 4. 63 x10‘3 --78. 7 i- 2. 3 —74.8 5.0
6. 83 x 10’3 -—70.5 i 1.8 —67.3 4.5
8. 99 x10‘3 —64. 2 i 2.1 —62.0 3.4
1.11 x 10‘2 ~56. 3 i 2. 3 -57.9 -2.8
1.32 x 10‘2 —53. 6 i 2. 9 -54.6 —1.9
7 4. 61 x10'3 —100. 3 1'1. 6 —99.6 7.0
6.80 x 10'3 -89.7 i 1.5 -92.1 -2.7
8.94 x 10'3 —85.0 $1.5 —86.8 -2.1
1.10x10'2 —81.6i1.5 —82.7 —1.3
1. 31 x 10'2 -77.3 i 1.8 —79.4 —2.7
8 4.60 x 10‘3 —107.5 :1 6 —105.8 1.6
6.78 x 10’3 —99.9 i 1.4 —98.3 1.6
8.91 x 10‘3 -93.7 :L' 1.3 —93.0 0.75
1.10 x10“2 —87.6 1'12 —88.9 —1.5
1.31 x 10'2 —81.0 $1.2 -85.6 —5.7
9 4.60 x 10‘3 —100.8 i 2. 8 -106.2 -5.4
6.78 x 10'3 —96. 7 i 1.5 —98.7 -2.1
8.91 x 10'3 —91.6 i 1 6 -93.4 -—2.0
1.10 x10’2 —87.8 i- 2.0 —89.3 —1.7
1.31 x 10‘2 —83.7 i 2.4 -86.0 -2.7
10 4.60x10’3 —110..4i21 —106.2 3.8
6.78 x 10‘3 —102.3 i 2.1 —98.7 3.5
8.91 x 10'3 -96. 8 i: 1.9 -93.4 3.5
1.10x10'2 —93.4i2.0 —89.3 4.4
1.31 x10'2 -89 4 $1.7 —86.0 3.8
* Equation [3.12]

“ % ERROR = 100 (EXP — CALC) / EXP

 

 

 

The io
phosphate bu
change in cor
observed in th
of electrolyte c
subject of mar
departure of th
Several model:
rate of chang
idC/diiog C» i
explanation pn
surface alters
describing the
applicable. ‘I
Lyklema,28 wh
surface in whit
cations.

The ion
second term of
of the experim
zeta potential I
many possible
was chosen be
potential curve

curve of the

characterized l

 

86

The ion-selective model in Equation [3.12], when applied to the
phosphate buffer system, gives a value for SLOPE of 44.4 mV per tenfold
change in concentration. It is noteworthy that a slope of 43.7 mV was also
observed in the studies with pure electrolyte systems (Figure 3.3). The influence
of electrolyte concentration on the zeta potential of silica surfaces has been the
subject of many studies,39'43 and there is substantial evidence to support the
departure of the slope from the value of 59 mV expected for Nernstian behavior.
Several models have been proposed to account for this phenomenon, where the
rate of change of the zeta potential with the logarithm of concentration
(dC/d(log C)) is correlated with important parameters of the double layer. An
explanation proposed by Hunter and Wright“2 is that conductance at the silica
surface alters the surface charge density, such that the classical equationsz:5
describing the potential profile in the double layer are no longer strictly
applicable. This concept is further supported by the theoretical model of
Lyklema,28 who postulated the existence of an amorphous gel layer at the silica
surface in which the potential is affected by the degree of penetration of certain
cations.

The ion-selective behavior of the surface alone, as represented by the
second term of Equation [3.12], is not sufficient to explain the sigmoidal contour
of the experimental data. It is the first term, Co, that imparts this feature to the
zeta potential curve, as demonstrated in the top part of Figure 3.10. Among the
many possible mathematical functions with sigmoidal shape,37 the error function
was chosen because of its physical meaning. Another way to interpret the zeta
potential curve as a function of pH is to recognize that it represents a titration
curve of the acidic sites at the Silica surface. These acidic sites are

characterized by different types of silanol groups, whose abundance is assumed

 

 

 

to be normally
overall pKa wli
experimentally
reported valui
spectroscopic,‘
found a pKa I
Likewise, Luka
versus pH with
provided a pKa
groups by com
oxides.45 Prev
values betweei
used as titrant.
The mor
membrane teat
3.10 reveals l
approaches 24
inflnitesimally I
corresponding
point of zero c
approximately
from this mod
should be exe
predicts positiv

Practice, for tht

the surface, rei

 

 

87

to be normally distributed. The inflection point of the titration curve gives an
overall pKa which is representative of the average acidity of the surface. The
experimentally determined pKa of 5.9 is in good agreement with previously
reported values for silica materials determined by electrophoretic,12~14
spectroscopic,45 and potentiometric methods.39v46 Schwer and Kenndler12
found a pKa of 5.3 by electrophoretic measurements in aqueous solutions.
Likewise, Lukacs and Jorgenson14 presented a curve of electroosmotic mobility
versus pH with an inflection point around pH 6. Spectroscopic measurements
provided a pKa of 7.1, which was attributted to the various silica surface hydroxyl
groups by comparing the hydroxyl band frequency shifts of alcohols and silica
oxides.45 Previous reports on titration curves of silica gels and sols have given
values between 5.2 and 5.739 and 6.5 to 7.7,“6 depending on the type of base
used as titrant.

The modelling of the response of the capillary surface as an ion-selective
membrane leads to interesting observations. For instance, inspection of Figure
3.10 reveals that all curves tend to the same point as the zeta potential
approaches zero. At this point, the double layer has collapsed to an
infinitesimally thin layer of ions and the electroosmotic flow ceases. The pH
corresponding to the point where the zeta potential reaches zero is known as the
point of zero charge (PZC). For colloidal silica, the PZC is believed to occur
approximately at pH 2,5,39,43 which is in good agreement with that predicted
from this model. It is necessary to emphasize that beyond the PZC caution
should be exercized in the physical interpretation of the model. The model
predicts positive values for the zeta potential at pH values less than the PZC. In
practice, for that to occur, a layer of cations would have to adsorb specifically at

the surface, reversing its charge.

 

 

L

 

 

 

3.4 Conclusir

The det
under both i
successfully a
meaningful mc
potential as a
which describ
potential toget
can then be L
Smoluchawski
data in the p

electrophoresi

potential.

 

88

3.4 Conclusions

The determination of electroosmotic flow in capillary zone electrophoresis
under both constant-voltage and constant-current conditions has been
successfully achieved through the development of a simple but physically
meaningful model. The proposed model is based on the evaluation of the zeta
potential as a function of the buffer composition in a manner analogous to that
which describes the ion-selective behavior of glass membranes. The zeta
potential together with the dielectric constant and viscosity of the buffer solution
can then be used to calculate the electroosmotic velocity from the Helmholtz-
Smoluchowski equation. The model has been fully supported by experimental
data in the pH range from 4 to 10, which is most useful in capillary zone
electrophoresis, resulting in approximately 5 % error in the prediction of the zeta

potential.

 

 

 

3.5 Referencr

Grossm
and Pra

Kuhr, Vl
McLaug
K W.; l
1992, 1

Hiemen
Marcel

Bier, ll
Acaden

Vindevr

VanOrn
Ewing,

Atamna
Chrome

Atamna
Chroma

Green .
Fujiwar
Sshwer

Kurosu
1991,1

Lukacs
SChom
Hierten
McCon

Lee, c
1519.1

Hayes,

Dose, 1

 

 

 

89

3.5 References

10.
11.
12.
13.

14.
15.
16.

17.
18.

19.
20.

Grossman, P. D.; Colburn, J. C., Eds; Capillary Electrophoresis - Theory
and Practice; Academic Press Inc.: San Diego, CA, 1992.

Kuhr, W. G.; Monnig, C. A. Anal. Chem. 1992, 64, 389R-407R.

McLaughlin, G. M.; Nolan, J. A.; Lindahl, J. L.; Paimieri, R. H.; Anderson,
K. W.; Morris, S. C.; Morrison, J. A.; Bronzert, T. J. J. Liq. Chromatogr.

1992, 15, 961-1021.

Hiemenz, P. C. Principles of Colloid and Surface Chemistry, 2nd ed;
Marcel Dekker: New York, 1986. ‘

Bier, M., Ed; Electrophoresis - Theory, Methods and Applications;
Academic Press Inc.: New York, 1959.

Vindevogel, J.; Sandra, P. J. Chromatogr. 1991, 541, 483-488.

VanOrman, B. B.; Liversidge, G. G.; McIntire, G. L.; Olefirowicz, T. M.;
Ewing, A. G. J. Microcol. Sep. 1990, 2, 176-180.

Atamna, I. Z.; Metral, C. J.; Muschik, G. M.; lssaq, H. J. J. Liq.
Chromatogr. 1990, 13, 2517-2527.

Atamna, I. Z.; Metral, C. J.; Muschik, G. M.; lssaq, H. J. J. Liq.
Chromatogr. 1990, 13, 3201-3210.

Green J. S.; Jorgenson, J. W. J. Chromatogr. 1989, 478, 63-70.
Fujiwara, 8.; Honda, S. Anal. Chem. 1987, 59, 487-490.
Schwer, C.; Kenndler, E. Anal. Chem. 1991, 63, 1801 -1807.

Kurosu, Y.; Hibi, K.; Sasaki, T.; Saito, M. J. High Resol. Chromatogr.
1991 , 14, 200-203.

Lukacs, K. D.; Jorgenson, J. W. J. Chromatogr. 1985, 8, 407-411.
Schomburg, G. Trends Anal. Chem. 1991, 10, 163-169.

Hjerten, S. J. Chromatogr. 1985, 347, 191-198.

McCormick, R. Anal. Chem. 1988, 60, 2322-2328.

Lee, C. S.,' McManigiIl, 0.; Wu, C. T.; Patel, B. Anal. Chem. 1991, 63,
1519-1523.

Hayes, M. A. ; Ewing, A. G. Anal. Chem. 1992, 64, 512-516.
Dose, E. V.; Guiochon, G. A. Anal. Chem. 1991, 63, 1063-1072.

 

 

 

21.

23.

24.

25.

26.

27.

28.

29.
30.

32.
33.

35.

36.

37.

38.

39.
40.

Bier, M.
219, 12:

Salomo

Bard, A
Applical

Koryta .
London

Freiser,
York, 1!

Buck, F
46, 255

Ungen
Pubhsh

Lyklem:
Lamber

Smith,
57-68.

Altria, .J
Huang,

Weisst
lntersci

Li, H, c

McCon
Dugge,

Melchir

A08 3.
1990. ‘

SDanie
aShir

DBVOre
2nd ed

Parks,

 

 

 

21.

22.
23.

24.

25.

26.

27.

28.
29.
30.

31.
32.
33.

34.
35.

36.

37.

38.

39.
40.

90
Bier, M.; Palusinski, *0. A.; Mosher, R. A.; Saville, D. A. Science 1983,
219, 1281-1287.

Salomon, K.; Burgi, D. S.; Helmer, J. C. J. Chromatogr. 1991, 559, 69-80.

Bard, A. J.; Faulkner, L. R. Electrochemical Methods - Fundamentals and
Applications; John Wiley & Sons: New York, 1980.

Koryta J. Ion-Selective Electrodes, 2nd ed.; Cambridge University Press:
London,1975.

Freiser, H. Ion-Selective in Analytical Chemistry, Plenum Press: New
York, 1978.

Buck, R. F.; Boles, J. H.; Porter, R. D.; Margolis, J. A. Anal. Chem. 1974,
46, 255-261.

Unger, K. K. Porous Silica, J. Chromatogr. Lib., Vol. 16, Elsevier Scientific
Publishing Company: New York, 1979.

Lyklema, J. J. Electroanal. Chem. 1968, 18, 341 -348.
Lambert, W. J. ; Middleton, D. L. Anal. Chem. 1990, 62, 1585-1587.

32%? S. C.; Strasters, J. K.; Khaledi, M. G. J. Chromatogr. 1991, 559,

Altria, J. D.; Simpson, C. F. Anal. Proc. 1986, 23, 453-454.
Huang, X.; Gordon, M. J.; Zare, R. N. Anal. Chem. 1988, 60, 1837-1838.

Weissberger, A. Physical Methods of Organic Chemistry, 3rd ed.;
lnterscience Publishers Inc.: New York, 1959.

Li, H. C.; Bruyn, P. L. Surface Sci. 1966, 5, 203-220.

McConnell, B. L.; Williams, K. 0; Daniel, J. L.; Stanton, J. H.; lrby, B. N.;
Dugger, D. L.; Maatman, R. W. J. Phys. Chem. 1964, 68, 2941-2946.

Melchior, D. C.; Bassett, R. L. Chemical Modeling of Aqueous Systems ll,
ACS Symp. Sen, Vol. 416, American Chemical Society: Washington, DC,

1990.

Spanier, J.; Oldham, K. An Atlas of Functions; Hemisphere Pub. Corp.:
Washington, DC, 1987.

Devore, J. L. Probability and Statistics for Engineering and the Sciences,
2nd ed.; Brooks/Cole Publishing Company: Monterey, CA, 1987.

Parks, G. A. Chem. Rev. 1965, 65, 177-198.

Wiese, G. R.; James, R. 0.; Healy, T. W. Faraday Discuss. Chem. Soc.
1971, 52, 302-311.

 

 

 

 

41.
42.
43.

45.

Rutgers
Hunter,

Churae
lnten‘ac

Tadros,
Hair, M

Strazhe
Chroma

 

41.
42.
43.

44.
45.
46.

 

91
Rutgers, A. J.; De Smet, M. Trans. Faraday Soc. 1945, 41, 758-771.

Hunter, R. J.; Wright, H. J. L. J. Colloid Interface Sci. 1971, 37, 564-580.

Churaev, N. V.; Sergeeva, l. P.; Sobolev, V.D.; Derjaguin, B. V. J. Colloid
Interface Sci. 1981, 84, 451-460.

Tadros, T. F.; Lyklema, J.; J. Electroanal. Chem. 1968, 17, 267-275.
Hair, M. L.; Hertl, W. J. Phys. Chem. 1970, 74, 91-94.

Strazhesko, D. N.; Strelko, V. B.; Belyakov, V. N.; Rubanik, S. C. J.
Chromatogr. 1974, 102, 191-195.

 

 

 

 

 

4.1. Introduct

The ca
resolution set
industrial and
Of separation
strategy utiliz
Parameter is
constant,3,4
misleading in
methods Whe
diversity and
complexity of
approaches
procedures, 1
Variab|es of
ProcedUreS'
experimental
the Optimized.
aSSiSted 0pm

regarding the

 

CHAPTER 4

OPTIMIZATION OF SEPARATIONS IN
CAPILLARY ZONE ELECTROPHORESIS

4.1. Introduction

The capability of capillary zone electrophoresis (CZE) to achieve high-
resolution separations has been demonstrated for a variety of substances of
industrial and biomedical importance}.2 However, to a large extent, optimization
of separations has been approached in an empirical manner. A common
strategy utilizes univariate sequential methods, where the effect of each
parameter is assessed individually while all other parameters are held
constant.314 Such procedures are inherently time consuming and often
misleading in the search for the global optimum. The reliability of univariate
methods when applied to CZE separations is further compromised by the
diversity and interactive nature of the system variables as well as by the
complexity of typical CZE samples. In the literature to date, several systematic
approaches to optimization have been proposed.5'10 Some of these
procedures, however, are rather simplistic and do not consider all important
variables of the system.58 Other approaches utilize resolution mapping
procedures, which may demand the initial inspection of a large set of
experimental conditions.6’9v10 Therefore, a more comprehensive approach to
the optimization of electrophoretic separations is highly desirable. A computer-
assisted optimization routine fulfills this need in many respects, especially

regarding the speed and accuracy with which a variety of conditions can be
92

 

 

 

 

evaluated. F
our understa
develop such
for zone migr:
During
electrophores
mathematical
incorporates '
This approac
computationa
rigorous and
Simplified att.
inherent asst
applications.5
In can
have receive
CZE. longitu.
brOadeningfl
broadening,
expeeled. i,
because add
the most cor
finite VoIUmi
brofldeningn
profile Cause
Contributions

 

 

 

 

evaluated. Furthermore, the resulting simulation data can add substantially to
our understanding of fundamental electrokinetic phenomena. In order to
develop such an optimization procedure, however, proper and reliable models
for zone migration and dispersion processes are required.

During the past decades, the simulation of migration processes in
electrophoresis has been a subject of considerable interest.”18 The
mathematical description of the temporal evolution of the zone profile
incorporates the fundamental laws of chemical equilibrium and mass transport.
This approach generates complex equations, whose solution often demands
computationally intensive numerical methods. Although these models are
rigorous and exact, they may not be practical for routine implementation. Other
simplified attempts to describe zone migration have been proposed, but the
inherent assumptions and limitations of these models restrict their use to specific
applications.5’8-16

In comparison to zone migration, dispersive processes in electrophoresis
have received significantly less attention. Since the initial implementation of
CZE, longitudinal diffusion has been considered as the major cause of zone
broadening.2 If the technique truly approached the theoretical limit of diffusional
broadening, a number of theoretical plates on the order of 105 would be
expected. In practice, however, such high plate numbers are rarely achieved
because additional factors contribute to the loss of separation efficiency. Among
the most common sources of broadening are instrumental contributions due to
finite volumes for injection and detection”,20 In addition, detrimental
broadening may result from deviation from the theoretically expected flat velocity
profile caused by either laminar flow or thermal effects.2,20v21 Sample-specific
contributions may arise from differences in conductivity between the sample

zone and the conducting medium2 as well as from solute adsorption to the

 

 

 

 

 

capillary wall}
In this
through the «
incorporates
migration as r
the buffer on
judiciously of
solute zones
assessed by
varying the
optimum cor
Program mo

Phosphate bl

4-2 optimiz;

The c
separations
Separation is
Chmmatogra

Statistic (CR!

CR8: "1

Where RI i+1

 

 

 

94

capillary wall.2:20’21

In this work, a systematic approach to CZE separations has been devised
through the development of a computer optimization routine. The program
incorporates theoretical models for both electroosmotic and electrophoretic
migration as well as a simple rationale for zone dispersion. Variables related to
the buffer composition, capillary dimensions, and instrumental parameters are
judiciously chosen as input to the program. The resolution between adjacent
solute zones is then calculated and the overall quality of the separation is
assessed by means of an appropriate response function. By systematically
varying the input parameters and evaluating the resultant separation, the
optimum conditions may be identified. The experimental validation of the
program models has been demonstrated for a mixture of nucleotides in

phosphate buffer solutions.

4.2 Optimization Strategy

The computer routine developed for the optimization of electrophoretic
separations is presented schematically in Figure 4.1. The quality of the entire
separation is assessed by means of a response function developed originally for
chromatographic separations,22 designated the chromatographic resolution

statistic (CRS):

"-1 R.. — R )2 n-1 R2. T
CRS ={ 2 [ ( "”1 0;" + Z ———'—-':21—— -—f- [4.1]
i=1 (R — R ) Ru+1 i=1 (n-1) R avg n

 

i,i+1 min

where Rim is the resolution between adjacent solute pairs, Ravg is the average

 

 

 

 

 

95

Figure 4.1 Schematic diagram of the computer optimization program for
capillary electrophoresis.

 

 

 

 

1 program for

96
Figure 4.1

o

 

 

 

 

 

 

 

 

 

 

p‘buf
, 7i

 

 

@ is
U
pKabuf
'1 Hi
CONCENTRATION]
Zbut
Area

Total
I Length

 

 

SURFACE SOLUTION
RESISTANCE RESISTANCE

 

I____I

@TT ,

VOLTAGE

 

 

 

IV

 

 

 

 

 
   

 

RESOLUTION

 

 

+— Length to Detector

 

 

 

—

resolution of a
minimum acce
is the number
considers the
resolved pair,
first term in El
between all a
optimum and
approaches R
equal to R0‘
improvement
maintained at
rapidly as R”,
equal to Rmin.
considers the
approaches a
equal to the a
spaced. The
analysis time a
In capil
zones is defini

by their averar

2 I
Rim = —-—
W

The migration

1-

 

97

resolution of all solute pairs, Rom is the optimum desired resolution, Rmin is the
minimum acceptable resolution, Tf is the migration time of the last solute, and n
is the number of solutes in the sample. The chromatographic resolution statistic
considers the resolution of all solutes in the sample. rather than solely the least-
resolved pair, and incorporates three important aspects of the separation. The
first term in Equation [4.1], named the resolution term, evaluates the resolution
between all adjacent solute pairs In comparison to the defined values for
optimum and minimum resolution. The resolution term decreases as Ri,i+1
approaches Rom and reaches the minimum value of zero when RLM is exactly
equal to Ropt. Any further increase in resolution offers no additional
improvement in the quality of the separation, hence the resolution term is
maintained at a constant value close to zero. The resolution term increases
rapidly as Ri.i+1 approaches Rmin and becomes undefined when Ri,i+1 is exactly
equal to Rmin. The second term of Equation [4.1], named the distribution term,
considers the relative spacing of the solute zones. The distribution term
approaches a minimum value of one when the resolution of each solute pair is
equal to the average resolution, which is the case when all zones are uniformly
spaced. The final multiplier term in Equation [4.1] takes into consideration the
analysis time and the complexity of the sample.

In capillary zone electrophoresis, the resolution between adjacent solute
zones is defined as the difference between their mean migration time (t) divided
by their average temporal base width (w):

2 “H1 — ti)

Ri,i+1 = —— [42]
Wt + Wr+1

The migration time of each zone to the detector position (Ldet) is determined by

 

—

the net rate

electroosmotir

et
ti=_:
Vi

where posm
respectively, \
For a n

deviation of th

Wi=4T

where r is ex;

the spatial dis

The variance
phenomena tI

these process

02 = 2 02,,

where 02,, re;
An OVI

appropriately

"‘6 compute

"I I

 

 

98

the net rate of zone migration (vi), which is a vectorial summation of the

electroosmotic (Vosm) and electrophoretic (vep) velocities:

Ldet Luet Ldet I-tot

Vi Vosm + Vep (Vosm "' Ilep) V

 

[4.3]

 

ti:

 

where uosm and uep are the electroosmotic and electrophoretic mobilities,
respectively, V is the applied voltage, and Ltot is the total capillary length.

For a normally distributed zone, the base width is related to the standard

 

deviation of the temporal distribution (13):

wi = 4 r [4.4]

 

where ’C is expressed in'units of time, and is related to the standard deviation of

the spatial distribution (0') by means of the zone velocity:

 

[4.5]

The variance of the spatial distribution (62) arises from several dispersive
phenomena that occur during the migration of the solute zone in the capillary. If

these processes are independent, then the variances are statistically additive: 23

0'2 = 202,, [4.6]

where 02,, represents the individual contributions to the total variance.
An overall expression for resolution can be derived by combining
appropriately Equations [4.2] to [4.6]. In order to incorporate these equations in

the computer optimization routine, independent models for voltage,

 

 

—

electroosmotii
These mode

described in 9

Model for V0
conditions, thi
constant-cum
means of Ohn

the conducting

=K

.—I=i

1
Rsoln
where r is thr

conductivity is

all ionic specir

IC=FEIZJ

where F is the

Figure
solutions at 0‘
determined v:
and [4.8], usir
of the system
Ohm's law on
resulting volts

resistance is r

#4

 

 

 

 

 

99

electroosmotic mobility, electroohoretic mobility, and zone variance are required.
These models and their correlation with the experimental variables are

described in greater detail in the following sections.

Model for Voltage. When the power supply is operated under constant-voltage
conditions, the system voltage is an experimentally available parameter. Under
constant-current conditions, however, the voltage must be predicted indirectly by
means of Ohm's law. This may be accomplished by evaluating the resistance of
the conducting medium (Rsoln), which is given by:24

1 1tr2

.__:K

Rsoln l-tot

 

[4.7]

where r is the capillary radius and K is the conductivity of the solution. The
conductivity is related to the charge (2]), mobility (uj), and concentration (Ci) of

all ionic species in solution by:

K=F2|Zj|uj Cj [4-8]

where F is the Faraday constant.

Figure 4.2 presents the resistance calculated for phosphate buffer
solutions at different pH and concentration, in comparison with experimentally
determined values. The calculated resistance was derived from Equations [4.7]
and [4.8], using literature values of ionic mobility25 and other known parameters
of the system. The experimental resistance was obtained from the slope of an
Ohm's law curve (not shown), by applying a constant current and measuring the
resulting voltage. The results shown in Figure 4.2 indicate that the prediction of

resistance is satisfactory for acidic solutions. However, as the pH increases, the

_ __ __J

 

Figure 4.2

100

Comparison of experimental resistance of phosphate buffer
solutions with theoretical calculations according to Equations [4.7]
andI4-8l- (AlpH4. (IlpHS. (.IPHG. (leH7, (0)
pH 8. (Cl)pH 9. anth) pH 10-

(10‘9 ohm)

EXPERIMENTAL RESISTANCE

(Tl

C»:

 

101
Figure 4.2

 

 

 

 

 

E
g 6
O
b
.— 5-
LLJ
C)
Z 4-
<
I?)
rsphate buffer (7)
: {new}
ri‘fiiiirm BE 3-
—‘ I
<
E
LLI 2‘
2
DC
LLI
% I r r r r r r . r '
LLJ I 2 3 4 5 6
CALCULATED RESISTANCE (10’9 Ohm)

 

 

 

 

Figure 4.2

100

Comparison of experimental resistance of phosphate buffer
solutions with theoretical calculations according to Equations [4.7]
andl4.81. (A)pH4. (IlpHS. (OlpHe. (leH7, (0)
pH 8. (mpH 9. and(A) pH 10.

(IO—9 ohm)

EXPERIMENTAL RESISTANCE

(D

(N

 

101
Figure 4.2

 

 

as hate buffer
Eriuations I4];

7)pH7, IO

 

 

 

 

 

EXPERIMENTAL RESISTANCE (Io-9 ohm)
I
J
'1
I
i

CALCULATED RESISTANCE (Io-9 ohm)

 

 

 

 

 

 

experimental
by the model
the current,
magnitude 01
but may becr
area to volur
an equivaler
resistors con

(R) can be e:

1
R R

where RS,"f

therefore de
System and
The curve ‘
solution (a

h
manner:

1
Rd ‘1

Where A. a
data preser

525 x 10s.

Figur
8"“ Capri:

 

102

experimental resistance gradually becomes lower than the resistance predicted
by the model. This observation suggests the existence of a secondary path for
the current, other than the solution, possibly the capillary surface. The
magnitude of surface conductance in silica capillaries is usually negligible.2‘5v27
but may become significant for capillaries because of their high ration of surface
area to volume. The mathematical description of surface conductance invokes
an equivalent electric circuit, where the solution and surface are treated as
resistors combined in parallel. Therefore, the overall resistance of the system

(R) can be evaluated according to:

 

 

[4.9]

where Rsurf represents the surface resistance. The surface resistance is
therefore derived from experimental measurements of the total resistance of the
system and the evaluation of the solution resistance by Equations [4.7] and [4.8].
The curve 1/Rsurf versus pH and the activity of the sodium ion in the buffer
solution (am) can be numerically fit to an error function28 in the following

manner:

1
Rsurf

 

={[ERF(ApH+B)]C+D}aNa [4.10]

where A, B, C, and D are fitting parameters. Typical values obtained from the
data presented in Figure 4.2 are: A = 1.16, B = —7.75, C = 3.00 x 109, and D =
5.25 x 109.

Figure 4.3 presents the estimate of the surface conductance of fused-

silica capillaries in comparison to the solution conductance for phosphate buffer

 

 

 

103

Figure 4.3 Conductance of phosphate buffer solutions (a) and silica capillary
surface (b) as a function of pH and sodium concentration (5, 7.5.

10, 12.5, and 15 mM from bottom to top).

I . O/‘EHRW 44 weak

 

 

 

 

 

 

 

 

 

 

 

 

104
Figure 3a
61
T T 1’ I“ f “9
CD CD C) C) C) e
C C C C CD - (I)
I
. l <1 i
silica capillary _
ration (517- .
— Lo
— <1-
T I T I T T r I —r N
O 00. ‘0. V. 9t O
*- 0 o o o O

 

 

 

 

 

 

 

 

105
Figure 3b
0 O 0 ID I —
O 0 CD CD -

 

 

 

 

 

 

 

 

 

 

 

 

 

IS7 ~-

1.0-—

(twtlo OIOI)

D: 0.5-—

0.0

12

10

 

 

 

solutions. Tl
buffer solutic
consequence
concentratior
increases, thI
compensatec
buffer solutic
conductance.
dependence
mechanism I
subject to Spi
of ionized 3
increase with
lilpUps on tr
providing few
conductance
be transpone
solution imm.
mitlht occur II
gel layer at I
for conductic
considerably

In Tab
Which incarpc
[4.7] to [4.10,
coneentration

106

solutions. The solution conductance increases with the sodium content of the
buffer solution, but does not vary significantly with pH. This result is a
consequence of the manner in which the buffers are prepared, with a constant
concentration of sodium ion regardless of the pH. Therefore, as the pH
increases, the decrease in the concentration of the highly mobile hydrogen ion is
compensated by an increase in the ionic strength of the buffer. As a result, all
buffer solutions with the same total sodium concentration possess a similar
conductance. In contrast, the surface conductance shows a marked
dependence not only on pH, but also on the sodium concentration. The
mechanism by which the current is conducted along the capillary. surface is
subject to speculation. If the mechanism of conduction is related to the presence
of ionized silanol groups, the surface conductance would be expected to
increase with pH, as observed in Figure 4.3. At low pH, protonation of the silanol
groups on the capillary surface occurs to a greater extent (vide Chapter 3),
providing fewer sites for conduction. However, the dependence of the surface
conductance on the sodium concentration suggests that charge might actually
be transported by the ions in the electrical double layer. Although the layer of
solution immediately adjacent to the surface is immobile, transport of charge
might occur in a manner similar to a semi-conductor. Alternatively, the hydrated
gel layer at the capillary surface would constitute another apprOpriate medium
for conduction of charge, given that the mobility of ions in this layer is
considerably greater than that in the dry silica.29

In Table 4.1, the prediction of voltage under constant-current conditions,
which incorporates the solution and surface resistance according to Equations
[4.7] to [4.10], is evaluated for phosphate buffer solutions at different pH and
concentration. A good agreement is observed between the proposed model for

voltage and the experimental results, with a typical error of approximately 1.2 %.

 

 

Table 4.1

pH

 

10
11

 

* % ERROR -.-

 

 

107

Table 4-1 Prediction 0f voltage in phosphate buffer solutions with total
sodium concentration of 10 mM under constant-current conditions

 

 

 

of 12.5 “A.
pH VOLTAGE % ERROR"
(le
EXPERIMENTAL CALCULATED
6 29.6 29.9 1.0
7 27.4 26.9 -1.8
8 25.8 25.5 —1.2
9 25.6 25.4 -0.78
10 25.3 25.2 —o.39
11 22.9 23.3 17

 

 

 

 

 

 

* % ERROR = (CALC — EXP) x 100/ EXP

 

 

 

Model for El
electroosmot
has been es
4.1. The re
composition:
mathematica:
composition l

ion-selective

h‘Co‘tSl

where aH an
solution, res;
reference p.
mathematical

(ERF) accord

Co=IERFI

Where A0 B,
mathematical
because of it
Versus pH at
acidic Sites

abundance is
are reI‘clted

parameter C(

needed for di

 

108
Model for Electroosmotic Mobility. A systematic approach to the prediction of
electroosmotic flow under both constant-voltage and constant-current conditions
has been established in Chapter 3 and is represented schematically in Figure
4.1. The response of the fused-silica capillary surface to changes in buffer
composition and pH is modelled in analogy to an ion-selective electrode.24 The
mathematical model predicts the zeta potential (C) as a function of the
composition of the solution with the corresponding modified Nernst equation for

ion-selective electrodes:

I; = C0 + SLOPE log(aH + kPOT am) [4.11]

where a... and am are the activities of hydrogen and sodium ions in the buffer
solution, respectively, kPOT is the potentiometric selectivity constant, and C0 is a
reference potential in the double layer. The potential Co has been
mathematically described by a Gaussian probability integral or error function

(ERF) according to:

Co = IERF(AopH + 80)] C0 + Do [4.12]

where A0, B0, C0, and D0 are fitting parameters. Among the many possible
mathematical functions with sigmoidal shape,28 the error function was chosen
because of its physical meaning. It is possible to interpret the zeta potential
versus pH as a titration curve of the acidic sites at the silica surface. These
acidic sites are characterized by different types of silanol groups, whose
abundance is assumed to be normally distributed. The parameters A0 and BO
are related to the mean and standard deviation of the distribution. The
parameter C0 confers the height to the sigmoidal curve and the parameter Do is

needed for displacement in the zeta potential axis.

 

 

 

The u
by regressior
for fused-silk
= 44.4 mle
With knowle

accurately pr

where I] m
respectively,

The pl
mobility in pl
increasing ar
model deper
buffer solutic
mobility from
phosphate b
heme” pTeI
However, err
Used for six
irreversible ;

during Ihe a"

Model for E

SGVeral iOnit

 

 

 

109
The unknown parameters in Equation [4.11] and [4.12] were determined
by regression analysis using the least-square method. Typical values obtained
for fused-silica capillaries with phosphate buffer solutions are as follows: SLOPE
= 44.4 mV/pH, kPOT = 0.22, A0 = —0.86, B0 = 5.11, C0 = 33.2, and D0 = 59.7.
With knowledge of the zeta potential, the electroosmotic mobility can be

accurately predicted by means of the Helmholtz—Smoluchowski equation:26

6 e C
nos", =- ——n°—— [4.13]

where n and 8 are the viscosity and the dielectric constant of the medium,
respectively, and so is the permittivity of the vacuum.

The proposed model has been applied to the prediction of electroosmotic
mobility in phosphate buffer solutions in the pH range from 4 to 10, containing
increasing amounts of sodium chloride from 5 to 15 mM. The success of the
model depends on the rigorous control of the sodium content and pH of the
buffer solution. Table 4.2 compares the predicted values of electroosmotic
mobility from Equations [4.11] to [4.13] with experimental measurements using
phosphate buffer solutions in both new and used capillaries. The agreement
between predicted and experimental values for new capillaries is typically 2.3 %.
However, errors as large as 9.6 % are obtained with capillaries that have been
used for six months. The observed loss of accuracy may be attributed to
irreversible alteration of the capillary surface caused by continuous etching

during the alkaline solution rinses.

Model for Effective Electrophoretic Mobility. For a solute (i) that consists of

several ionic and neutral species (j) interacting by a dynamic acid-base

 

 

 

 

 

Table 4.2

pH

10
11

 

* % ERROR :

 

 

 

 

 

110

 

 

 

Table 4.2 Prediction of the electroosmotic mobility in new and six-month used
capillaries, usin phosphate buffer solutions with total sodium
concentration 0 10 mM under constant-current conditions of
12.5 uA.

pH ELECTROOSMOTIC MOBILITY % ERROR*
(x 105 cm2 V'1 3'1)

EXPERIMENTAL CALCULATED

NEW USED NEW USED
6 50.9 54.4 49.2 —3.3 —9.6
7 67.4 70.1 69.0 2.4 —1.6
8 74.5 75.8 73.9 —0.81 -2.5
9 72.8 81.0 74.3 2.1 —8.3
10 76.7 82.0 74.3 —3.1 —9.4
11 —— 81.1 74.2 —— —8.5

 

 

 

 

 

 

 

* % ERROR = (CALC — EXP) x 100 / EXP

 

 

 

 

 

equilibrium, ti
(pert I1 = 2

where or,- re
dissociation I
each individu
The r
dissociation .
experimental
advantageoL
constants a
composed ol
experimenta
more comp
conceptual
distribution I
function ofp
of each die
Individua| Sp
clWe that a.
0’ two distri
Sp9cies, Whr
point in the
the effectivI
repleSsion’ ,

the individu;

 

 

 

111

equilibrium, the effective electrophoretic mobility (uefi) is defined as:
(lien )1 = 2 (09- ll;) [4-14]

where Otj represents the distribution functions,30 which are related to the
dissociation constants (Ka) of the solutes, and [ti is the electrophoretic mobility of
each individual species.

The prediction of effective mobility relies on accurate values of the
dissociation constants and electrophoretic mobilities. Although there are many
experimental methods for the determination of these parameters,31:32 it is
advantageous to use electrophoretic methods because both dissociation
constants and mobilities can be derived simultaneously.33 For solutes
composed of less than three species, these parameters may be determined from
experimental data by direct solution of the equations of mass balance;3134'35 for
more complex solutes, a numerical procedure may be employed. The
conceptual basis of this procedure is illustrated in Figure 4.4, where the
distribution functions for guanosine 5'-monophosphate are represented as a
function of pH (mobility and pKa data from Table 5.1, Chapter 5). The maximum
of each distribution function defines the pH region of predominance for an
individual species. In this region, a plateau is observed in the effective mobility
curve that approximates the mobility of that individual species. The intersection
of two distribution functions defines the point of equal concentration for two
species, where the pH is equal to the pKa. This point coincides with an inflection
point in the effective mobility curve. Therefore, experimental measurements of
the effective mobility as a function of pH can be analyzed by numerical
regression, where the plateaus and inflection points serve as initial estimates of

the individual mobilities and dissociation constants (pKa). respectively. The best

 

 

 

 

112

Figure 4.4 Distribution functions of guanosine 5'-monophosphate in phosphate

buffer solution, together with individual and effective
electrophoretic mobilities.

/\

 

100

 

 

in hospitale
hand p effective

 

 

 

113
Figure 4.4
VHdTV
LO 10
N to N
O O O O
/ _
\

 

 

 

 

 

 

 

:1,

pH

1.

fl

I

 

 

100 —

(SA/3W3) 90L X AlITIBOW aArLoaaaa-

0

14

12

10

 

 

 

 

values for '
method.“ '
number of
determine If
the dissocia‘
data in thee
values Is mr
mobilities is
likely to be e
The
and IIICIIVIdl
Therefore, I
thermodyna

OI activity cc
‘Iogh = 0

Where I is

m0bilitycan
II = [10 2 ‘

Where “0 II

COUIIIelion.

Table

 

 

114

values for these parameters can then be determined by the least-square
method.314 This procedure, in principle, is applicable to solutes consisting of any
number of species. However, the ability to differentiate and accurately
determine the parameters for all species depends on the relative magnitude of
the dissociati0n constants and mobilities, as well as the number of experimental
data in the appropriate pH region. In general, if the difference between the pKa
values is more than two pH units and the difference between the electrophoretic
mobilities is more than 10‘4 cm2 V-1 s", the numerical regression procedure is
likely to be successful.

The optimization program uses thermodynamic dissociation constants
and individual electrophoretic mobilities at the condition of infinite dilution.
Therefore, both parameters must be corrected for ionic strength effects. The
thermodynamic constants are related to the stoichiometric constants by means

of activity coefficients (7,), which are calculated by the Davies equation:24v36

—log y, = 0.509 2,2 I — 0.15 I I [4.15]

1+1}?

where I is the ionic strength and zi is the charge of the individual species. The

mobility can be corrected by means of the Onsager equation:25

lf
u=u0_(o,23po [2,le +31.3x10'9IziI)-1————

4.16
+ If I l

where [Jo is the mobility at zero ionic strength and 2,5 is the charge of the
counterion.
Table 4.3 compares the experimentally determined effective mobility of

adenosine monophosphate with predicted values. The predicted values of the

 

 

 

 

 

Table 4.3

 

pH

10
11

 

* % ERROR :

 

 

Table 4.3 Prediction of the effective electrophoretic-mobility of adenosine
monophosphate in phosphate buffer solutions with total sodium
concentration of 10 mM under constant-current conditions of

 

 

 

12.5 [1A.
pH EFFECTIVE MOBILITY % ERROR*
(x 105 cm2 V'1 5")
EXPERIMENTAL CALCULATED

6 —22.4 —23.1 3.1

7 -—30.0 -—28.9 -3.7

8 —31.0 —31.5 1.6

9 —33.0 -31.8 —3.6

10 —32.7 —31.9 —2.4

11 -31.1 —32.0 2.9

 

 

 

 

 

* % ERROR = (CALC — EXP) x 100 / EXP

 

 

 

 

 

 

effective mc
mobility of r
entire pH rar

experimenta

Model for 2
considered:
volumes ((52

The \

equation:23
021111 = 2 E

where Di is l
the resident
exclusively r
and other in
EQuation {4,

2

Uzdif = \

(I1:

 

 

116
effective mobility were calculated from the pKa and individual electrophoretic
mobility of nucleotides determined in Chapter 5 (vide Table 5.1). Within the
entire pH range, the prediction of effective mobility is in good agreement with the

experimental results, with an average relative error of 2.9 %.

Model for Zone Variance. In this work, three sources of broadening were
considered: longitudinal diffusion (62“), and finite injection and detection
volumes (62,,“- and ozdet, respectively).

The variance resulting from longitudinal diffusion is given by the Einstein

equation223
62d" = 2 Di ti ' [4.17]

where D, is the diffusion coefficient of the solute i. The variance is a function of
the residence time of the solute in the capillary and, hence, does not depend
exclusively on the solute characteristics but also on the electroosmotic mobility
and other instrumental parameters. By substituting the migration time given by
Equation [4.3] into Equation [4.17], this influence becomes explicitly clear:

2 Di |-det Ltot

62.111 = —— [4.181
(Hosm + Hep) V

The contribution to variance caused by a finite injection volume is
approximated by the expression developed by Sternberg37 for a rectangular

zone profile:

 

[4.19]

 

 

 

 

In order to a
must be cor
establishing
Under the or

by means of

AI
hnjllr = —

81

where tinj is
difference al
by applying

pressure difl

achieved by

AP:pg‘

Where AH it
outlet reser
acceleration
which is oh:
[4'19] and [4

In eIe
“393 grad
i"potion 20

mobIIIIIeS an

 

117
In order to evaluate the length of the Injection zone (Kim), the mode of injection
must be considered. In hydrodynamic injection, the sample is introduced by
establishing a pressme gradient along the capillary for a brief period of time.
Under the condition of laminar flow, the length of the injection zone is determined

by means of the Hagen-Poiseuille equation223

AP r2
4,, =—— t- - [4.20]
I.” III]
8 TI Ltot

where tinj is the injection time, n is the fluid viscosity, and AP is the pressure
difference along the capillary length. When hydrodynamic injection is performed
by applying pressure at the capillary inlet or vacuum at the capillary outlet, the
pressure difference along the capillary is a known parameter. When injection is

achieved by siphoning action, the pressure difference can be calculated as:

AP = p 9 AH [4.21]

where AH is the height difference between the solution level at the inlet and
outlet reservoirs, p is the density of the solution, 9 is the gravitational
acceleration constant. The dispersion caused by a parabolic velocity profile,
which is characteristic of pressure-driven flow, was disregarded in Equations
[4.19] and [4.20].

In electrokinetic injection, the sample is introduced by establishing a
voltage gradient along the capillary for a brief period of time. The length of the
injection zone is determined from the electroosmotic and electrophoretic

mobilities and the injection time:

 

 

 

IInlet = (I

In an
transducer
transducerl
the zone (I
approximate
lzd

ozdet ‘—
12

Where Idet i:
The
therefore, th
Spatial distri
appear to b.

Chromatogi
various res]
Separations
advantagem
resOIution, d
fUoction eva
0f the nucle
qualitative in

 

 

 

118

V
[injek = (Hosm T Pep) — tinj I422]
Ltot

In any detector device, a finite volume of solution is in contact with the
transducer and the output signal represents an average response. If the
transducer has distinct spatial boundaries and uniform response along its length,
the zone distribution is rectangular in profile, so that the variance can be

approximated by the Sternberg equation:37

6 2(let

12

 

62061 = [4.23]

where goat is the length of the detector window.

The processes of diffusion, injection, and detection are independent;
therefore, their variances can be added to represent the overall variance of the
spatial distribution, as expressed by Equation [4.6]. These sources of variance
appear to be sufficient to describe the experimental results, as shown in Table

4.4, with an average relative error of 9.4 %.

Chromatographic Resolution Statistic as a Response Function. Among the
various response functions used to numerically assess the quality of a
separation,”40 the chromatographic resolution statistic (CRS)22 is
advantageous because it comprises three important features of the separation:
resolution, distribution, and analysis time. In order to understand how the CRS
function evaluates a separation, several computer-simulated electropherograms
of the nucleotide mono- and di-phosphates are displayed in Figure 4.5. By
qualitative inspection, the electropherogram at pH 10 may be easily identified as

the best separation, whereas that at pH 11 is the second best. In both of these

 

 

 

 

 

Table 4.4

 

10
11

 

' % ERROR:

 

 

119

Table 4.4 Prediction of the zone variance for adenosine monophosphate in
phosphate buffer solutions with total sodium concentration of
10 mM under constant-current conditions of 12.5 pA.

 

 

 

 

 

 

 

pH ZONE VARIANCE % ERROR*
(cm2)
EXPERIMENTAL CALCULATED

6 0.0372 0.0353 —5.1

7 0.0276 0.0335 21

8 0.0295 0.0331 12

9 0.0314 0.0327 4.1

10 0.0292 0.0325 11
11 0.0344 0.0334 —2.9

 

 

 

' % ERROR = (CALC — EXP) x 100 I EXP

 

 

 

 

 

120

Figure 4.5 Computer-simulated electropherograms of the nucleotides (1)
AMP, (2)CMP, (3) GMP, (4) UMP, (5) ADP, (6) CDP, (7) GDP,
and (8) UDP at different pH conditions.

 

nucleotides III
I CDP (7 I GDP

 

 

 

 

 

 

 

 

 

121
Figure 4.5
pH 11
M EM 7 8
pH 10
MAM; ‘6 a
pH9
7s 5
pH8
pHT
31 42
7 5 6A8
pH6
3.1.2 4
II It”
5 7 9 11 13 15

TIME (min)

 

 

 

 

 

 

electrophen
remaining .
unresolved
would be or
unambiguor
be conside
accurate de
in principle,
mathematic

For
correspondi
[4.1] are su
CRS value,
distinctly su
Still conside
term and th
Optimum on
Of DEak Spa
Value pace]
in 900d 8ch

Upon
function are
Iange of v;
Separations!
Separatinn i
separation,

ppals that

 

 

122

electrOpherograms, a single pair of solutes is overlapped (Rr,l+1 .<_ 1.5). In the
remaining electropherograms from pH 6 to 9, three pairs of solutes are
unresolved to different degrees. Among these latter electropherograms, pH 9
would be considered the most desirable if qualitative analysis is the goal, since
unambiguous identification of all eight solutes is possible. However, pH 6 would
be considered the most desirable if quantitative analysis is the goal, since
accurate determination of five solutes is possible. The response function should,
in principle, be able to represent these subjective evaluations in an objective
mathematical manner.

For each of the electropherograms shown in Figure 4.5, the
corresponding values of the CRS function and its individual terms from Equation
[4.1] are summarized in Table 4.5 (Root = 1.5, Rmin = 0). According to the total
CRS value, the overall. quality of the separations at pH 9 to 11 is ranked as
distinctly superior. The separation at pH 6, while significantly less desirable, is
still considered to be of higher quality than those at pH 7 and 8. The resolution
term and the distribution term correctly identify the separation at pH 10 as the
optimum condition, because of the high degree of resolution and the uniformity
of peak spacing. The multiplier term assigns the separation at pH 9 the smallest
value because of the comparatively short analysis time. These conclusions are
in good accord with the subjective evaluation of the separation.

Upon inspection of Table 4.5, several important features of the CRS
function are apparent. First, the resolution term has the greatest magnitude and
range of values and, hence, generally controls the relative ranking of the
separations. This is intuitively desirable, since the primary goal of any
separation is to achieve resolution of all solutes. The other aspects of the
separation, spatial distribution of the zones and analysis time, are secondary

goals that become important only when all solutes have been adequately

 

 

 

Table 4.5

 

pH

10
11

 

 

 

123

Table 4.5 Evaluation of the chromatographic resolution statistic (CRS) as a
response function using Optimum resolution (Rom) of 1.5 and
minimum resolution (Rmin) of 0.

 

 

 

 

pH CHROMATOGRAPHIC RESOLUTION STATISTIC
RESOLUTION DISTRIBUTION MULTIPLIER TOTAL
TERM TERM TERM CR8
6 228 3.5 1.8 420
7 4478 2.8 1.3 5612
8 2745 2.7 1.2 3304
9 19 2.5 1.1 23
10 0.89 1.4 1.2 2.8
11 48 1.8 1.5 74

 

 

 

 

 

 

 

 

 

 

selected val
in Table 4.!
Table 4.6 (F
resolution t1
passes thrr
becomes 1
separation

example, It
and 0.73 81
in Table 4.

whether hi]

the judicior

the separa

The
Separatior
eVilanted
learning I
Critical pal
”def to it

and Ultdin

124

selected values of Ropt and Rmin. The relative ranking of the separations shown
in Table 4.5 (Ropt '= 1.5, Rmin = O) is completely different from that shown in
Table 4.6 (Rom = 1.5, Rm," = 0.75). Because of the mathematical features of the
resolution term, (Rpm — Rom)2 passes through a minimum and 1/(Ri,i+1 - Rmin)?!
passes through‘a maximum as Rim increases. As a result, the CRS value
becomes extremely high and is no longer representative of the overall
separation quality when any individual value of Rim approaches Rmin. For
example, the separation at pH 9 contains individual resolution elements of 0.70
and 0.73 and, therefore, is ranked as the second best in Table 4.5 but the worst
in Table 4.6. More importantly, values of Rim that are equidistant from Rmin,
whether higher or lower in magnitude, are ranked equally. As shown in Table
4.7 (Rom = 1.5, Rmin = 1.0), the resolution term becomes relatively constant and
the CRS function provides little discrimination of the separation quality. Hence,
the judicious choice of these parameters is critical to the objective assessment of

the separation and the correct identification of the optimum conditions.

4.3 Use of the Optimization Program as a Pedagogical Approach to

Capillary Zone Electrophoresis

The optimization program developed to assess electrophoretic
separations can be operated in such a way that one single set of conditions is
evaluated at a time. With this approach, the program becomes a powerful

learning tool that can be used advantageously to examine the influence of

critical parameters on the separation efficiency, resolution, and analysis time. In ,

order to illustrated this concept, the nucleotides adenosine, guanosine, cytidine,

and uridine 5'-mono- and di-phosphates were chosen as model solutes and their

 

 

 

 

Table 4.6

 

pH

10
11

 

 

 

 

 

125
Table 4.6 Evaluation of the chromatographic resolution statistic (CRS) as a
response function using optimum resolution (Root) of 1.5 and
minimum resolution (Rmin) of 0.75.
pH CHROMATOGRAPHIC RESOLUTION STATISTIC
RESOLUTION DISTRIBUTION MULTIPLIER TOTAL
TERM TERM TERM CRS
6 136 3.5 1.8 252
7 91 2.8 1.3 117
8 102 2.7 1.2 126
9 2422 2.5 1.1 2600
10 16 1.4 1.2 21
11 24 1.8 1.5 39

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.7

 

pH

 

10
11

 

 

 

 

 

 

 

126
Table 4.7 Evaluation of the chromatographic resolution statistic (CRS) as a
response function using optimum resolution (Root) of 1.5 and
minimum resolution (ijn) of 1.0.
pH CHROMATOGRAPHIC RESOLUTION STATISTIC
RESOLUTION DISTRIBUTION MULTIPLIER TOTAL
TERM TERM TERM CR8
6 42 3.5 1.8 82
7 48 2.8 1.3 64
8 66 2.7 1.2 82
9 31 2.5 1.1 36
10 48 1.4 1.2 61
11 10 1.8 1.5 18

 

 

 

 

 

 

 

 

 

 

 

separation
4.6a, a typ
initial stanr
This outpu
under the
electrophOI
electroosm
resistance)
dimensions
necessary
the comp
ConeSponc
completed
plates per
the least-re

Ase
CZE syster
and length
are include
will be eva
Outlet rese
next Studie
ionic stren
Capillah, SI

magnhude

 

 

127

separation is simulated and compared under a variety of conditions. In Figure
4.6a, a typical output of the program illustrates the set of parameters chosen as
initial standard conditions (current, buffer pH, ionic strength and concentration).
This output also gives the complete characterization of the separation achieved
under the stated conditions (resolution, variances, and efficiency), the solute
electrophoretic behavior (migration time and effective mobility), the
electroosmotic flow properties (zeta potential, electroosmotic mobility,
resistance) as well as other instrumental related parameters (voltage, capillary
dimensions, injection characteristics). Finally, the analytical concentrations
necessary to prepare the phosphate buffer solution is provided. In Figure 4.6b,
the computer-generated electropherogram of the mixture of nucleotides
corresponding to the standard conditions is presented. The separation is
completed in about 10 min, with an average efficiency of 1.4 x 105 theoretical
plates per meter. Also, all solutes have been completely resolved (resolution of
the least-resolved pair is 1.88).

As an initial comparative study, the effect of the parameters related to the
CZE system is evaluated. In this category, the capillary dimensions of diameter
and length, as well as the detection position and window length exposed to light
are included. Next, some characteristics of the hydrodynamic injection method
will be evaluated, such as the height difference between the capillary inlet and
outlet reservoirs and also the injection time. The effect of the applied current is
next studied. Then the buffer properties of the buffer solutions, including the pH,
ionic strength and concentration, are examined. Finally, the effect of the
capillary surface charge density as a means to control the electroosmotic flow

magnitude is explored.

 

 

 

128

Figure 4.6 Computer-simulated separation of nucleotides under standard
conditions. Solute identification as in Figure 4.5. (a)
Electropherogram. (b) Simulated data.

 

 

 

129
Figure 4.6a

; under standard

Figure 4.5. (a)

 

 

 

15

10

 

TIME (min)

 

 

 

 

 

PREDICT]
CURRENT.
pH = !
IONIC s:
surm l

cmmu
Tom. 0
pmcror
I. 9., ,

ELUTION
in m;

AMP
CHP
6MP
UMP
ADP
CDP
GDP
UDP = .
INJECTII
DETECTOI

FLOW CHI
2m PO’.
ZETAZERI
kPOTNa :
ELECTROI
ELECTROI
comer:
RESISTA}

 

 

130
Figure 4.6b

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes - 17.000

pH = 9.800 Correction Factor, in pH units = .0000
IONIC STRENGTH, in moles/liter - 1.25008 -2

BUFFER CONCENTRATION, in moles/liter = 2.50008 -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAHIC
TOTAL LENGTH, in cm I 100.00 HEIGHT DIFFERENCE, in em = 2.00
DETECTOR LENGTH, in em = 50.00 INJECTION TIME, in sec = 60.00
I. D., in micrometers = 75.00 HYDRODYNAHIC VELOCITY, in cm/s = 3.938 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cmZ/Vs in cmz
AMP = 6.20 .090 -.31858 -3 7.448 '3 7.568 4 1.88
CMP = 6.37 .093 -.33008 -3 7.648 -3 7.528 4 9.06
GNP = 7.28 .108 -.38168 -3 8.738 -3 7.288 4 4.48
UMP = 7.78 .116 -.40498 -3 9.348 -3 7.158 4 2.69
ADP = 8.10 .122 -.41838 -3 9.728 -3 7.078 4 3.31
CD? = 8.52 .129 -.434lE -3 1.028 -2 6.978 4 5.61
GDP = 9.28 .142 -.45948 -3 1.118 -2 6.808 4 7.22
UDP = 10.37 .162 -.48958 -3 1.248 -2 6.568 4 CR5 = 2.67_
INJECTION ZONE, in cm = .24 INJ VARIANCE, in cm2 = 4.638 -3
DETECTOR WINDOW, in cm s .50 DET VARIANCE, in cm2 = 2.088 -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV = -93.54

ZETAZERO, in mV = 26.44

kPOTNa = 2.23478 -1

ELECTROOSMOTIC MOBILITY, in cmZ/Vs = 7.43008 -4
ELECTROOSMOTIC VELOCITY, in cm/s = .2349
VOLTAGE, in RV = 31.610

RESISTANCE, in Ohm ' 1.85948 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH = 9.800

IONIC STRENGTH = 1.25008 -2
BUFFER CONCENTRATION = 2.50008 -3
BUFFER CAPACITY = 2.03808 -4
CHARGE CONC = 1.99568 -2
[M]butfer = 5.07968 -3

[Mjelectr = 4.89858 -3

BUFFER FORMULATION:

CONC M-HBA = 0.00008 -1

CONC N-HZA = 0.00008 -1

CONC H-HA = 2.42048 -3

CONC M-A - 7.95678 -5

CONC M-X = 4.89858 -3

OK

 

 

 

 

 

 

 

In F
quality is
conditions
increases;
differences
conductanl
capillary Sl
this work,
approxima‘
thMa
thus, is re
simulated
significantl
its initial ve

FigL
nucleotide:
constant, it
cQmPared
anall'sis tir
the mixture
are also a;
time due t<
Capillaries
diameter c
thesolutior

In c

resolution,

 

 

 

131

In Figure 4.7, the effect of the capillary total length on the separation
quality is studied by comparison with the results obtained for the standard
conditions of Figure 4.6. Under constant-current conditions, the resistance
increases linearly with the capillary length and so does the voltage. The minor
differences observed in migration time result from the overestimation of surface
conductance in the shorter capillaries. Surface conductance is a function of the
capillary surface area, which is the capillary perimeter multiplied by its length. In
this work, surface conductance was characterized for a 75 um diameter,
approximately 100 cm long capillary. The model developed voltage considers
the surface conductance as a function of the characteristics of the solution and
thus, is restricted to the above cited capillary dimensions. However, the
simulated data suggest that the surface conductance may not be affected
significantly by the capillary length. By decreasing the capillary lenght to half of
its initial value, the calculated voltage is higher than expected by only 1%.

Figure 4.8 presents the effect of the capillary diameter in the separation of
nucleotides. In spite of the fact that the applied current and capillary length are
constant, there is a much higher field strength in the 75 um capillary (316 V/cm)
_ compared to the 125 um (124 V/cm). As a result, an appreciable gain in
analysis time and efficiency is achieved without compromise of the resolution of
the mixture. The restrictions discussed above regarding surface conductance
are also applicable here. However, the ultimate error introduced in the migration
time due to false estimation of surface conductance may be critical only when
capillaries with diameters much smaller than 75 um are considered. For wider
diameter capillaries, the surface conductance becomes negligible compared to
the solution conductance which varies inversely with the square of the radius.

In capillary zone electrophoresis, there is a spatial dependence on

resolution. Therefore, the placement of the detector along the capillary length

 

 

 

132

Figure 4.7 Effect of the capillary length (Lt t) on the separation of nucleotides.
Solute identification and stan ard conditions as given In Figure
4.6. (a) Computer-simulated electropherograms for 50, 75, and
100 cm capillary length. (b) Separation characteristics for 50 cm

capillary length. (c) Separation characteristics for 75 cm capillary
length.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

133
FiQure4.7;,1
50 cm
12
3
4 5 6
7 8
l l L
12 75 cm
3
4 5 s
7 8
on of nucleotides.
5 given ianigautre m
sfor 50, ,
bristics forSQcm l l l l l
r75 cm capillary
12 100 cm
3
4 5 5 . ,
7
8
5 ‘. M i i l L : l
o 5 10 15
“ME (min)

 

 

 

 

134
Figure 4.7b

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT in microamperes = 1

H = 9.800 Correction Factor, in pH units = .0000
IONIC STRENGTH, in moles/liter = 1.25008

BUFFER CONCENTRATION, in moles/liter = 2.50008 -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm I 50.00 HEIGHT DIFFERENCE, cm .00
DETECTOR LENGTH, in cm = 50.00 INJECTION TIME, in sec = 60 .00
I. D., in micrometers = 75.00 HYDRODYNAMIC VELOCITY, in cm/s = 7.858 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cmZ/Vs in cm2
AMP = 5.77 .100 -.31858 -3 6.928 -3 5.358 4 1.58
CMP = 5.93 .103 -.33008 -3 7.128 -3 5.338 4 7.65
GMP = 6.78 .119 -.38168 -3 8.138 -3 5.228 4 3.80
UMP = 7.24 128 -.40498 -3 8.698 -3 5.168 4 2.28
ADP = 7.54 .133 -.41838 -3 9.058 -3 5.128 4 2.82
CDP = 7.93 .141 -.43418 -3 9.528 -3 5.078 4 4.79
GDP = 8.64 .155 -.45948 -3 1.048 -2 4.988 4 6 20
UDP = . .175 —.48958 -3 1.168 -2 4.868 4 CR5 = 2.43
INJECTION ZONE, in cm .47 INJ VARIANCE, in cm2 1.858 -2

DETECTOR WINDOW, in cm = .50 DET VARIANCE, in cmz 2.088 -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV = -93.54

ZETAZERO, in mV = 26.44

kPOTNa = 2.23478 -1

ELECTROOSMOTIC MOBILITY, in cm2/Vs = 7.43008 -4
ELECTROOSMOTIC VELOCITY, in cm/s = .2516
VOLTAGE, in kV = 16.93

RESISTANCE, in ohm = 9. 96038 8

BUFFER CHARACTERISTICS (cone in moles/liter):
p = . 0

IONIC STRENGTH = 1.25008 —2

BUFFER CONCENTRATION = 2.50008 —3

BUFFER CAPACITY = 2.03808 -4

CHARGE CONC = 1.99568 -2

[Hlbuffer = 5.07968 -3

[M]electr = 4.89858 -3

BUFFER FORMULATION:

CONC M-H3A 0.00008 -1

CONC M-HZA 0.00008 -1

CONC M-HA = 2.42048 -3

CONC M-A = 7.95678 -5

CONC M-X 8 4.89858 -3

OK

 

 

 

 

 

 

““35
3’ .K
sagas

FLOW c
ZETA r
ZETAZE
kPOTNa
ELECTF
ELECTF
Vomc
RESIS1

BUFFE}
PH =
IONIC
BUFPE;
Burrs;
CHARGE
[H]but
[Hialr
BUFFE}
CONC )
CONC t
CONC y
CONC )
CONC )
0K

K

 

135
Figure 4.70

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT in microamperes - 1

H = 9.800 Correction Factor, in pH units - .0000
IONIC STRENGTH, in moles/liter = 1. 25008 -2

BUFFER CONCENTRATION, in moles/liter = 2.50008 -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm = 75.00 HEIGHT DIFFERENCE, in on = 2.00
DETECTOR LENGTH, in cm = 50.00 INJECTION TIME, in sec = .00
I. D., in micrometers = 75.00 HYDRODYNAMIC VELOCITY, in cm/s = 5.248 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cmZ/Vs in cm2
AMP = 5.98 .091 -.31858 -3 7.188 -3 6.868 4 1.79
CMP = 6.15 .094 -.33008 -3 7.388 -3 6.828 4 8.64
GMP = 7.03 .109 -.38168 -3 8.448 -3 6.638 4 4.28
UMP = 7.52 118 -.40498 -3 9.028 -3 6.528 4 2.57
ADP = 7.82 .123 -.41838 -3 9.398 -3 6.468 4 3.16
CDP = 8.23 .130 -.43418 -3 9.878 -3 6.388 4 5.37
GDP = 8.96 .143 -.45948 -3 1.088 -2 6.248 4 6.93
= .02 .163 -.48958 -3 1.208 -2 4 CRS = 2.56
INJECTION ZONE, in Cm = .31 INJ VARIANCE, in cm2 = 8 228 -3
DETECTOR WINDOW, in on = .50 DET VARIANCE, in cm2 = 2.088 -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV = -93.54

ZETAZERO, in mV = 26.44

kPOTNa = 2.23478 -1

ELECTROOSMOTIC MOBILITY, in cmZ/Vs = 7.43008 -4
ELECTROOSMOTIC VELOCITY, in cm/s = .2429
VOLTAGE, in RV = 24.524

RESISTANCE, in ohm = 1.44268 9

BUFFER CHARACTERISTICS (cone in moles/liter):
p 9.800

IONIC STRENGTH = 1.25008 -2
BUFFER CONCENTRATION = 2.50008 -3
BUFFER CAPACITY = 2.03808 -4
CHARGE CONC = 1.99568 -2
[M]buffer = 5.07968 -3

[M]e1ectr = 4.89858 -3

BUFFER FORMULATION:

CONC M-H3A = 0.00008 -1

CONC M-HZA = 0.00008 -1

CONC M-HA = 2.42048 -3

CONC M-A = 7.95678 -5

CONC M-X = 4.89858 -3

OK

 

 

 

 

136

Figure 4. 8 Effect of the capillary diameter on the separation of nucleotides.
Solute identification and standard conditions as given in Figure
4. 6. (a) Computer-simulated electropherograms for 75, 100, and
125 um capillary diameter. (b) Separation characteristics for

100 um capillary diameter (c) Separation characteristics for
125 um capillary diameter.

 

on of nucleotides
is given in Figure
5 f0 r75 100, and
characteristics for
characteristics for

 

137

 

1 2 75pm

 

ill

 

 

 

 

lll’l

TIME (min)

 

 

 

 

 

emtc
mam
PH =

IONIC :
BUFFER

CAPIIJ.
TOTAL 1
DETECTi
I. D.,

ELUTIOl
in l

5

ll
llllllllllll

CHP
GMP
UHP
ADP
CDP
GDP
UDP -
INJEC‘I‘f
DETECTi

FLOW c1
ZETA Pi
2mm
kPOTNa
ELECTRI
ELECTRi
VOLTAGI
RESIST,

BUFFER
PH =
IONIC 1
BUFFER
BUFFER
CHARGE
[Hibuf1
[Mielei
BUFFER
CONC H.
CONC n.
CONC H«
CONC H'
CONC a.
0K

\

 

 

138

Figure 4.8b

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes
pH = 9.800

CAPILLARY DIMENSIONS:

' 17.000

TOTAL LENGTH, in cm 3 100.00

DETECTOR LENGTH, in cm =

I. D., in micrometers =
ELUTION TIME WIDTH
in min in min
AMP = 10.35 .182
CMP = 10.64 .188
GMP = 12.16 .219
UMP = 13.00 .236
ADP = 13.54 .247
CDP = 14.23 .262
GDP = 15.50 .290
UDP = 17.34 .330

INJECTION ZONE, in on =
DETECTOR WINDOW, in cm s

FLOW CHARACTERISTICS:
ZETA POTENTIAL, in mV =

ZETAZERO, in mV = 26.44

kPOTNa = 2.23478 -1

ELECTROOSMOTIC MOBILITY,
ELECTROOSMOTIC VELOCITY,
VOLTAGE, in kV = 18.881

50.00
100.00

EFFECTIVE
MOBILITY
in cmZ/Vs
-.31858
-.33008
-.38168
.40498
.41838
-.43418
-.45948
.48958
.42
.50

-93.54

in cmZ/Vs
in cm/s =

RESISTANCE, in ohm = 1.11068 9

Correction Factor, in pH units = .0000
IONIC STRENGTH, in moles/liter = 1.25008 -2
BUFFER CONCENTRATION, in moles/liter = 2.50008 -3

TYPE OF INJECTION: HYDRODYNAMIC

HEIGHT DIFFERENCE, in on = 2.00
INJECTION TIME, in sec = 60.00
HYDRODYNAMIC VELOCITY, in cm/s = 6.988 -3

-3
-3
-3
-3
'3
-3
-3
-3

DIFFUSION EFFICIENCY RESOLUTION

VARIANCE
in cmz

1.248 -2 5.188 4 1.55
1.288 -2 5.148 4 7.48
1.468 -2 4.958 4 3.70
1.568 -2 4.868 4 2.21
1.628 -2 4.808 4 2.72
1.718 -2 4.728 4 4.61
1.868 -2 4.598 4 5.93
2.088 -2 4.418 4 CR5 = 4.36_
INJ VARIANCE, in cm2 = 1.468 -2
DET VARIANCE, in cm2 = 2.088 -2

7.43008 -4
.1403

BUFFER CHARACTERISTICS (cone in moles/liter):

pH = 9.800
IONIC STRENGTH = 1.25008

BUFFER CONCENTRATION = 2.
BUFFER CAPACITY = 2.03808
CHARGE CONC = 1.99568 -2

[Mjbuffer = 5.07968 -3
[M]e1ectr = 4.89858 -3
BUFFER FORMULATION:

CONC M-H3A = 0.00008 -1
CONC M-HZA = 0.00008 -1
CONC M-HA = 2.42048 -3
CONC M-A = 7.95678 -5
CONC M-X 8 4.89858 -3
OK

-2
50008 -3
-4

 

 

 

 

 

 

 

 

”

ELECTR
VOLTAG
RESIST

BUFFER
PH =
IONIC
BUFFER
BUFFER
CHARGE
[Hibuf
[Male
BUFFER
CONC M
cone M
CONC H
CONC H
CONC n
0K

 

\

 

 

139
Figure 4.8c

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes - 17.000

pH = 9.800 Correction Factor, in pH units = .0000
IONIC STRENGTH, in moles/liter - 1.25008 -2

BUFFER CONCENTRATION, in moles/liter - 2.50008 -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC

TOTAL LENGTH, in cm t 100.00 HEIGHT DIFFERENCE, in cm - 2.00
DETECTOR LENGTH, in cm = 50.00 INJECTION TIME, in sec 8 60.00

I. D., in micrometers = 125.00 HYDRODYNAMIC VELOCITY, in cm/s = 1.098 -2

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2

AMP = 15.68 .347 -.31858 -3 1.888 -2 3.288 4 1.24
CMP = 16.11 .357 -.33008 -3 1.938 -2 3.258 4 5.95
GMP = 18.41 .416 -.38168 -3 2.218 -2 3.148 4 2.94
UMP = 19.69 .449 -.40498 -3 2.368 -2 3.088 4 1.76
ADP = 20.50 .470 -.41838 -3 2.468 -2 3.048 4 2.17
CDP = 21.55 .498 -.43418 -3 2.598 -2 3.008 4 3.67
GDP = 23.47 .550 -.45948 -3 2.828 -2 2.918 4 4.72
UDP = 26.25 .627 -.48958 -3 3.158 -2 2.808 4 CR5 = 7.16_
INJECTION ZONE, in on = .65 INJ VARIANCE, in cm2 = 3.578 -2
DETECTOR WINDOW, in on = .50 DET VARIANCE, in cm2 = 2.088 -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV = -93.54

ZETAZERO, in mV = 26.44

kPOTNa = 2.23478 -1

ELECTROOSMOTIC MOBILITY, in cm2/Vs = 7.43008 -4
ELECTROOSMOTIC VELOCITY, in cm/S = .0924
VOLTAGE, in RV = 12.440

RESISTANCE, in Ohm = 7.31768 8

BUFFER CHARACTERISTICS (cone in moles/liter):
pH = 9.800

IONIC STRENGTH = 1.25008 -2
BUFFER CONCENTRATION = 2.50008 -3
BUFFER CAPACITY = 2.03808 -4
CHARGE CONC = 1.99568 -2
[M]buffer = 5.07968 -3

[M]e1ectr = 4.89858 -3

BUFFER FORMULATION:

CONC M-H3A = 0.00008 -1

CONC M-HZA = 0.00008 -1

CONC M-HA = 2.42048 -3

CONC M-A - 7.95678 -5

CONC M-X 3 4.89858 '3

OK

 

 

 

 

 

 

 

can affecl
several d
from the i
sample h
unnecess
time. If t
further av
separatio
capillary
might age
As
tranducer
Figure 4
character
migration
Observed
Th
lGChnique
HYdrodyn
inlBCtion 1
Figure 4‘.
reservoir
The effec
that regul.
Un
presents

Figure 4;

 

 

140

can affect substantially the separation characteristics. In Figure 4.9, the effect of
several detector positions is examined. With the detector positioned at 50 cm
from the inlet end of the capillary, complete resolution of the components in the
sample has already been achieved. Therefore, by increasing this distance, an
unnecessary increase in resolution is obtained at the expense of the analysis
time. If the resolution of the mixture is of concern, the position of the detector
further away from the inlet may be beneficial because it allows more time for the

separation to occur. However, as the residence time of the solutes in the

 

capillary increases, diffusional broadening also increases and the resolution
might again be compromised.

As discussed in section 4.2, the length of capillary exposed to the
tranducer has a direct influence on the observed profile of the solute zone. In
Figure 4.10, the effect of the detector window length on the separation

characteristics is inspected. By increasing the detector window length, the

 

migration time of each zone is unaffected. However, a substantial broadening is
observed with a concomitant deterioration of the overall resolution.

The initial length of the solute zone, which is dependent on the injection
technique, is another parameter of the system that can affect the zone profile.
Hydrodynamic injection is based strictly on volume transfer and depends on the
injection time, capillary dimensions, buffer viscosity, and pressure gradient. In
Figure 4.11, the effect of the height difference between the inlet and outlet liquid
reservoir is demonstrated, when the sample is introduced by siphoning action.
The effect of injection time is presented by Figure 4.12. The loss of of efficiency
that results from larger injection volumes is evident.

Under constant-current conditions, the magnitude of the applied current
presents a marked effect on the separation characteristics as illustrated by

Figure 4.13. A larger current, which imposes an increase in the electroosmotic

—J.L_

 

 

141

Figure 4.9 Effect of the detector position (Ldet) on the separation of
nucleotides. Solute identification and standard conditions as given
in Figure 4.6. (a) Computer-simulated electropherograms for 50.
75, and 100 cm detector position. (b) Separation characteristics
for 75 cm detector position. (0) Separation characteristics for
100 cm detector position.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

142
Figure 4.9a
12 50 cm
3
4
56
7
a
L
75 cm
12
3
4 5 s
7
8
iii l l l
100 cm
12
3 4 _-
5 6
7
a
5 10 15 20 25
TIME (min)

 

 

 

 

 

 

 

 

 

5§§§SS$§
Tl," II II II I M

:35
mm
£3 £3

FLOW i
ZETA i
ZETAZI
kPOTNa
ELECT)

VOLTAC
RESIST

BUFFE}
PH =
IONIC
BUFFE}
BUFFE}
CHARGI
[Ml but
[Hleli
BUFFm
CONC p
CONC )
CONC j
CONC }
CONC 3
OK

143
Figure 4%

 

 

PREDICTED OPTIMUM CONDITIONS FOR oTHE SEPARATION:
C ENT, in microamperes - 17.
800 Correction Factor, in pH units = .0000
IONIC STRENGTH, in moles/liter = 1. 2500B
BUFFER CONCENTRATION, in moles/liter a 2. 50008 -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm = 100.00 HEIGHT DIFFERENC CE, in em = 2.00
DETECTOR LENGTH, in cm = 75.00 INJECTION TIME, in sec = 60 .00
I. D., in micrometers = 75.00 HYDRODYNAMIC VELOCITY, in cm/s = 3.938 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
AMP = 9.30 .095 - .31858 -3 1.128 -2 1.538 5 2.67
CMP = 9.56 .098 -.33008 -3 1.158 -2 1.528 5 12.84
GMP = 10.92 .115 -.38168 -3 1.318 -2 1.458 5 6.33
UMP = 11.68 .124 -.40498 -3 1.408 -2 1.428 5 3.79
ADP = 12.16 .130 -.41838 -3 1.468 -2 1.408 5 4.65
CDP = 12.78 .138 -.43418 -3 1.538 -2 1.378 5 7.86
GDP = 13.92 .153 -.45948 -3 1.678 -2 1.338 5 10.07
UDP =15. .175 -.48958 -3 1.878 -2 1.278 5 CR5 = 3.97
INJECTION ZONE, in cm = .24 INJ VARIANCE, in cm2 = 4 638 —3
DETECTOR WINDOW, in cm = .50 DET VARIANCE, in cm2 = 2.088 -2
FLOW CHARACTERISTICS:
ZETA POTENTIAL, in mV = -93.54

ZETAZERO, in mV = 26.44

kPOTNa = 2.23478 -1

ELECTROOSMOTIC MOBILITY, in Cm2/Vs = 7.43008 -4
ELECTROOSMOTIC VELOCITY, in Cm/s = .2349
VOLTAGE, in kV = 31.610

RESISTANCE, in ohm = 1.85948 9

BUFFER CHARACTERISTICS (cone in moles/liter):

p .
IONIC STRENGTH = 1.2500E -2
BUFFER CONCENTRATION = 2.50008 -3
BUFFER CAPACITY = 2.03808 -4
CHARGE CONC = 1.99568 -2
[Mjbuffer = 5.07968 —3
[M]electr = 4.89858 -3

BUFFER FORMULATION:

CONC M-HJA = 0.00008 -1

CONC M-HZA = 0.00008 -1

CONC M-HA = 2.42048 -3

CONC M-A - 7.95678 -5

CONC M-X = 4.89858 -3

OK

 

 

 

144
Figure 4.9c

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:
CURRENT, in microanperes - 17.000

pH - 9.800 Correction Factor,
IONIC STRENGTH, in moles/liter - 1.2500E -2

BUFFER CONCENTRATION, in moles/liter = 2.50008 -3

in pH units a .0000

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm = 100.00 HEIGHT DIFFERENCE, in cm - 2.00
DETECTOR LENGTH, in cm = 100.00 INJECTION TIME, in sec = 60.00

I. D., in micrometers = 75.00 HYDRODYNAMIC VELOCITY, in cm/s a 3.938 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
AMP = 12.41 .100 -.31858 -3 1.498 -2 2.478 5 3.39
CMP = 12.75 .103 -.33008 -3 1.538 -2 2.458 5 16.26
GMP = 14.57 .121 -.38168 -3 1.758 -2 2.328 5 7.99
UMP = 15.58 .131 -.40498 -3 1.878 -2 2.268 5 4.77
ADP = 16.22 .138 -.41838 -3 1.958 -2 2.228 5 5.85
CDP = 17.05 .146 -.43418 -3 2.058 -2 2.178 5 9.86
GDP = 18.57 .163 -.4S94E -3 2.238 -2 2.098 5 12.60
UDP = 20.77 .187 -.48958 -3 2.498 -2 1.988 5 CR5 = 5.10_
INJECTION ZONE, in em = .24 INJ VARIANCE, in cm2 = 4.638 -3
DETECTOR WINDOW, in cm = .50 DET VARIANCE, in cm2 = 2.088 -2
FLOW CHARACTERISTICS:
ZETA POTENTIAL, in mV = -93.54
ZETAZERO, in mV = 26.44

kPOTNa = 2.23478 '1

ELECTROOSMOTIC MOBILITY, in cm2/Vs = 7.43008 -4

ELECTROOSMOTIC VELOCITY, in cm/s = .2349
VOLTAGE, in kV = 31.610
RESISTANCE, in Ohm = 1.85948 9

BUFFER CHARACTERISTICS (conc in moles/liter):
pH = 9.800

IONIC STRENGTH = 1.25008 -2

BUFFER CONCENTRATION = 2.50008 -3

BUFFER CAPACITY = 2.03808 -4

CHARGE CONC = 1.99568 -2

[M]buffer - 5.07968 -3

[Mjelectr = 4.89858 -3
BUFFER FORMULATION:
CONC M-H3A = 0.00008 '1

CONC M-HZA = 0.00008 -1
CONC M-HA = 2.42048 -3
CONC M-A - 7.95678 -5
CONC M-X = 4.89858 -3
OK

 

 

 

 

 

 

145

Figure 4.10 Effect of the detector window length (Ida) on the separation of
nucleotides. Solute identification and standard conditions as given
in Figure 4.6. (a) Computer-simulated electropherograms for 0.50.
0.75, and 1.0 cm detector window length. (b) Separatlon
characteristics for 0.75 cm detector window length. (0) Separation
characteristics for 1.0 cm detector window length.

 

 

 

 

 

 

 

 

146
Figure 4.10a
12 0.50 cm
3
4 5 6
AA 7
a
0.75 cm
12
3 4 5 s
7 s
1.0 cm
12
3
4
MA; 7 8
0 5 10 15
TIME (min)

 

 

 

 

147
Figure 4.10b

 

 

PREDICTED OPTIMUM CONDITIONS 1FOR oTHE SEPARATION:
WENT, in microamperes -
cH = 9.800 Correction Factor, in pH units = .0000
IONIC STRENGTH, in moles/liter = 1.25008 -2
BUFFER CONCENTRATION, in moles/liter - 2.50008 -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm - 100.00 HEIGHT DIFFERENCE, in cm = 2.00
DETECTOR LENGTH, in cm = 50.00 INJECTION TIME, in sec = 60.00
I. D., in micrometers = 75.00 HYDRODYNAMIC VELOCITY, in cm/s - 3.938 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
AMP = 6.20 .121 -.31858 -3 7.448 -3 4.228 4 1.40
CMP = 6.37 .124 r.33008 -3 7.648 -3 4.218 4 6.80
GMP = 7.28 .143 -.38168 -3 8.738 -3 4.138 4 3.38
UMP = 7.78 .154 -.40498 -3 9.348 -3 4.098 4 2.04
ADP = 8.10 .161 -.41838 -3 9.728 -3 4.068 4 2.51
CDP = 8.52 .170 -.43418 -3 1.028 -2 4.038 4 4.28
GDP = 9.28 .186 -.45948 -3 1.118 -2 3.978 4 5 54
UDP = 10.37 .210 -.48958 -3 1.248 -2 3.898 4 CR5 = 2.60_
INJECTION ZONE, in em = .24 INJ VARIANCE, in cm2 = 4.638 -3
DETECTOR WINDOW, in cm - .75 DET VARIANCE, in cm2 = 4.698 -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV = -93.54

ZETAZERO, in mV = 26.

kPOTNa = 2.23478 -1

ELECTROOSMOTIC MOBILITY, in cm2/Vs = 7.43008 —4
ELECTROOSMOTIC VELOCITY, in cm/s = .2349
VOLTAGE, in kV = 31.610

RESISTANCE, in ohm = 1.85948 9

BUFFER CHARACTERISTICS (cone in moles/liter):

p 9.3
IONIC STRENGTH = 1.25008 -2
BUFFER CONCENTRATION = 2.50008 -3
BUFFER CAPACITY = 2.03808 -4
CHARGE CONC = 1.99568 —2
[Mjbuffer = 5.0796E -3

[M]e1ectr = 4.89858 —3

BUFFER FORMULATION:

CONC M-H3A = 0.00008 -1

CONC M—HZA = 0.00008 -1

CONC M-HA = 2.42048 -3

CONC M-A - 7.95672 -5

CONC M-X = 4.89858 -3

OK

 

 

 

 

 

 

 

 

148
Figure 4100

 

 

 

 

 

 

PREDICTED OPTIMUM CONDITIONS FORO THE SEPARATION:
ENT, in microamperes - 17.
pH = 9. 800 Correction Factor, in pH units = .0000
IONIC STRENGTH, in moles/liter = 1. 250008 -2
BUFFER CONCENTRATION, in moles/liter = 2.50008 -3

CAPILLARY DIMENSIONS: _ TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm I 100.00 HEIGHT DIFFERENCE, .00
DETECTOR LENGTH, in cm = 50.00 INJECTION TIME, in s: ecc = 00
I. D., in micrometers = 75.00 HYDRODYNAMIC VELOCITY, in cm/s = 3.938 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIM
in cm2/Vs in cm2E
AMP = 6.20 .153 -.31858 -3 7.448 -3 2.618 4 1.10
CMP = 6.37 .158 -.33008 -3 7.648 -3 2.608 4 5.36
GMP = 7.28 .181 -.38168 -3 8.738 -3 2.578 4 2.67
UMP = 7.78 .195 -.40498 -3 9.348 -3 2.568 4 1.61
ADP = 8.10 .203 -.41838 -3 9.728 -3 2.558 4 1.99
CDP = 8.52 .214 -.43418 -3 1.028 -2 2.538 4 3.39
GDP = 9.28 .234 -.45948 -3 1.118 -2 2.518 4 4.42
UDP = 0.37 .264 -.48958 -3 1.248 -2 2.488 4 CRS = 3.93_
INJECTION ZONE, in cm = .24 INJ VARIANCE, in cm2 = 4.638 -3
DETECTOR WINDOW, in cm = 1.00 DET VARIANCE, in cm2 = 8.338 -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV = ~93.54

ZETAZERO, in mV = 26.44

kPOTNa = 2.23478 -1

ELECTROOSMOTIC MOBILITY, in cm2/Vs = 7.43008 -4
ELECTROOSMOTIC VELOCITY, in cm/s = .2349
VOLTAGE, in kV = 31. 610

RESISTANCE, in ohm = 1. 85948 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH - 9.8000

IONIC STRENGTH=1.ZSOOE -2

BUFFER CONCENTRATION = 2.50008 -3

BUFFER CAPACITY = 2.03808 ‘4

CHARGE CONC - 1.99568 -2

[Mjbuffer = 5.07968 -3

[Mjelectr = 4.8985E ‘3

CONC M-A = 7.95678 -5
CONC M-X I 4.89858 -3
OK

 

 

 

 

 

 

 

149

Figure 4.11 Effect of the height difference (AH) of hydrodynamic injection With
siphoning action on the separation of nucleotides. Solute
identification and standard conditions as given in Figure 4.6. _(a)
Computer-simulated electropherograms for 1, 2, and 5 cm height
difference. (b) Separation characteristics for 1cm height

difference. (c) Separation characteristics for 5 cm height
difference.

 

 

 

 

 

 

 

 

 

 

 

 

 

150

 

 

 

 

 

Figure4.11a
1cm
1
2 3456 7 3
2cm
12
3
M ‘456 1
”AA ii
1
2 Sam
34
5
s 7 _
'3

TIME (min)

 

 

 

 

 

 

 

 

151
Figure 4.11b

 

 

PREDICTED OPTIMUM CONDITIONS FOR oTHE SEPARATION:

CURRENT, in microamperes - 17.

pH = 9. 800 Correction Factor, in pH units = .0000
IONIC STRENGTH, in moles/liter = 1. 25008 -2

BUFFER CONCENTRATION, in moles/liter = 2. 50008 -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm - 100.00 HEIGHT DIFFERENCE, in cm - 1.00
DETECTOR LENGTH, in cm = 50.00 INJECTION TIME, in sec = 60.00
I. D., in micrometers = 75.00 HYDRODYNAMIC VELOCITY, in cm/s = 1.968 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
AMP = 6.20 .085 -.31858 -3 7.448 -3 8.478 4 1.99
CMP = 6.38 .088 -.33008 -3 7.658 -3 8.418 4 9.57
GMP = 7.29 .102 -.38168 -3 8.748 -3 8.128 4 4.73
UMP = 7.79 .110 -.40498 -3 9.358 -3 7.968 4 2.83
ADP = 8.11 .116 -.41838 -3 9.738 -3 7.868 4 3.49
CDP = 8.53 .123 -.43418 -3 1.028 -2 7.748 4 5.90
GDP = 9.29 .135 -.45948 -3 1.118 -2 7.538 4 7 59
= 1 .39 .154 -.48958 -3 1.258 -2 7.248 4 CR5 = 2.68_
INJECTION ZONE, in c = .12 INJ VARIANCE, in cm2 = 1.168 -3
DETECTOR WINDOW, in cm = .50 DET VARIANCE, in cm2 = 2.088 -2
FLOW CHARACTERISTICS:
ZETA POTENTIAL, in mV = -93.54

ZETAZERO, in mV = 26. 44

kPOTNa = 2.23478 -1

ELECTROOSMOTIC MOBILITY, in cm2/Vs = 7.43008 -4
ELECTROOSMOTIC VELOCITY, in cm/s = .2349
VOLTAGE, in kV = 31.610

RESISTANCE, in Ohm = 1.85948 9

BUFFER CHARACTERISTICS (conc in moles/liter):
pH = 9.8 0

IONIC STRENGTH = 1.25008 -2
BUFFER CONCENTRATION = 2.50008 -3
BUFFER CAPACITY = 2.03808 -4
CHARGE CONC = 1.99568 -2
[Mjbuffer = 5.07968 —3

[Mjelectr = 4.89858 -3

BUFFER FORMULATION:

CONC M-H3A = 0.00008 -1

CONC M-H2A = 0.00008 -1

CONC M-HA = 2.42048 -3

CONC M-A = 7.95678 -5

CONC M-X = 4.89858 -3

OK

 

 

 

 

 

152
Figure 4.11c

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes - 17 00 00

pH = 9. 800 Correction Factor, in pH units = .0000
IONIC STRENGTH, in moles/liter = 1. 25008 -2

BUFFER CONCENTRATION, in moles/liter - 2. 50008 -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC

TOTAL LENGTH, in cm = 100.00 HEIGHT DIFFERENCE, in cm - 5.00
DETECTOR LENGTH, in cm I 50.00 INJECTION TIME, in sec = 60.00

I. D., in micrometers = 75.00 HYDRODYNAMIC VELOCITY, in cm/s = 9.828 -3

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION

in min in min MOBILITY VARIANCE

in cm2/Vs in cm2

AMP = 6.17 .119 -.318 858 -3 7.418 -3 4.328 4 1.42
CMP = 6.35 .122 -.33008 -3 7.618 -3 4.318 4 6.88
GMP = 7.25 .141 -.38168 -3 8.708 -3 4.238 4 3.42
UMP = 7.75 .152 -.40498 -3 9.308 -3 4.188 4 2.06
ADP = 8.07 .158 -.41838 -3 9.698 -3 4.168 4 2.54
CDP = 8.48 .167 -.43418 -3 1.028 -2 4.128 4 4.32
GDP = 9.24 .183 -.45948 -3 1.118 -2 4.068 4 5.60

= . .207 -.48958 -3 1.248 -2 4 CRS = 2.59_
INJECTION ZONE, in cm - .59 INJ VARIANCE, in cm2 = 2.898 -2
DETECTOR WINDOW, in Cm = .50 DET VARIANCE, in cm2 = 2.088 -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV = -93.54

ZETAZERO, in mV = 26.44

kPOTNa = 2.23478 -1

ELECTROOSMOTIC MOBILITY, in cm2/Vs = 7.43008 -4
ELECTROOSMOTIC VELOCITY, in Cm/s = .2349
VOLTAGE, in RV = 31.610

RESISTANCE, in ohm = 1. 85948 9

BUFFER CHARACTERISTICS (cone in moles/liter):
p 00

IONIC STRENGTH = 1.25008 -2
BUFFER CONCENTRATION = 2.50008 -3
BUFFER CAPACITY = 2.03808 -4
CHARGE CONC = 1.99568 -2
[M]buffer = 5.07968 -3
[Mjelectr = 4.89858 -3
BUFFER FORMULATION:

CONC M-H3A = 0.00008 -1

CONC M-HZA = 0.00008 —1

CONC M-HA = 2.42048 -3

CONC M-A - 7.95678 -5

CONC M-x - 4.89858 -3

OK

 

 

 

 

 

 

 

 

153

Figure 4.12 Effect of the hydrodynamic injection time (t-n-) on the separation of
nucleotides. Solute identification and standérd conditions as given
in Figure 4.6. (a) Computer-simulated electropherograms for 60,
90, and 120 3 injection time. (b) Separation characteristics for 90 5
injection time. (c) Separation characteristics for 120 3 injection
ime.

L._ _._ I- .

 

 

 

 

 

 

 

 

 

 

 

 

 

INJ!
DET!

FLOW
ZETA

kPOT
ELEC
ELEC
VOLT
RESI

BUPF

IONL
BUFF
BUFF
CHAN
[film
We
BUFP]
couc
cone
CONC
CONC
cone
0K

155
Figure 4.12b

 

 

PREDICTED OPTIMUM CONDITIONS FOR OTHE SEPARATION:

CURRENT, in omicroamperes - 17

pH - 9.80 Correction Factor, in pH units = .0000
IONIC STRENGTH, in moles/liter = L 25008 2

BUFFER CONCENTRATIO ON in moles/liter = 2. 50008 -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm = 100.00 HEIGHT DIFFERENCE, in cm = 2.00
DETECTOR LENGTH, in cm = 50.00 INJECTION TIME, in sec = 90.00
I. D., in micrometers = 75.00 HYDRODYNAMIC VELOCITY, in Cm/s = 3.938 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
AMP = 6.19 .098 -.31858 -3 7.438 ‘3 6.428 4 1.73
CMP = 6.36 .101 -.33008 -3 7.638 —3 6.398 4 8.36
GMP = 7.27 .117 -.38168 -3 8.728 -3 6.218 4 4.14
UMP = 7.77 .126 -.40498 -3 9.328 -3 6.128 4 2.49
ADP = 8.09 .131 -.41838 -3 9.718 -3 6.068 4 3.07
CDP = 8.51 .139 -.43418 -3 1.028 -2 5.998 4 5.20
GDP =19.26 .153 -.45948 -3 1.118 -2 5.868 4 6.71
= .36 .174 -.48958 -3 1.248 -2 . 4 CRS = 2.64_
INJECTION ZONE, in cm a .35 INJ VARIANCE, in cm2 = 1.048 -2
DETECTOR WINDOW, in cm = .50 DET VARIANCE, in cm2 = 2.088 -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV = -93.54

ZETAZERO, in mV = 26.44

kPOTNa = 2.23478 -1

ELECTROOSMOTIC MOBILITY, in CmZ/Vs = 7.43008 -4
ELECTROOSMOTIC VELOCITY, in cm/s = .2349
VOLTAGE, in kV = 31.610

RESISTANCE, in ohm = 1.85948 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH = 9.

IONIC STRENGTH = 1.25008 -2
BUFFER CONCENTRATION = 2.50008 -3
BUFFER CAPACITY = 2.03808 —4
CHARGE CONC = 1.99568 -2
[M]buffer = 5.07968 -3

[Mjelectr = 4.89858 -3

BUFFER FORMULATION:

CONC M-H3A = 0.00008 —1

CONC M-H2A = 0.00008 —1

CONC M-HA = 2.42048 -3

CONC M-A = 7.95678 -5

CONC M-X = 4.89858 -3

OK

 

 

 

fl

 

 

 

INJE

156
Figure 4.12c

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:
CURRENT, in nicroanperee I 17.000
pH - 9.800

IONIC STRENGTH, in males/liter I 1.25008 -2
BUFFER CONCENTRATION, in moles/liter I 2.50008

Correction Factor, in pH units -

.0000

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm I 100.00 HEIGHT DIFFERENCE, in cm I 2.00
DETECTOR LENGTH, in cm I 50.00 INJECTION TIME, in sec I 120.00
I. D., in micrometers I 75.00 HYDRODYNAMIC VELOCITY, in cn/s - 3.93E -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
AMP I 6.18 .107 -.31858 -3 7.428 -3 5.308 4 1.57
CMP I 6.35 .111 -.33008 -3 7.628 -3 5.278 4 7.61
GMP I 7.26 .128 -.38168 -3 8.718 -3 5.158 4 3.78
UMP I 7.76 .138 -.40498 -3 9.318 -3 5.098 4 2.27
ADP I 8.08 .144 -.41838 -3 9.708 -3 5.058 4 2.80
CDP I 8.49 .152 -.43418 -3 1.028 -2 5.008 4 4.76
GDP I 9.25 .167 -.45948 '3 1.118 -2 4.918 4 6.15
UDP I 10.35 .189 -.48958 -3 1.248 -2 4.798 4 CRS = 2.60
INJECTION ZONE, in cm I .47 INJ VARIANCE, in cm2 I 1.858 -2
DETECTOR WINDOW, in cm I .50 DET VARIANCE, in cm2 I 2.088 -2
FLOW CHARACTERISTICS:
ZETA POTENTIAL, in mV = -93.54

ZETAZERO, in mV I 26.44
kPOTNa I 2.23478 -1
ELECTROOSMOTIC MOBILITY, in cm2/Vs = 7.43008 -4
ELECTROOSMOTIC VELOCITY, in cm/s I .2349
VOLTAGE, in kV = 31.610

RESISTANCE, in Ohm I 1.85948 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH I 9.800

IONIC STRENGTH I 1.25008 -2

BUFFER CONCENTRATION I 2.50008 -3

BUFFER CAPACITY I 2.03808 -4

CHARGE CONC I 1.99568 -2

[Hlbufter I 5.07968 -3

 

[MJelectr = 4.89858 -3

BUFFER FORMULATION:
CONC M-HJA I 0.00008
CONC M-HZA I 0.00008
CONC M-HA I 2.42048

CONC M-A I 7.95678
CONC M-X I 4.89858

OK

-5
-3

 

 

 

 

 

157

Figure 4.13 Effect of the applied current (I) on the separation of nucleotides.
Solute identification and standard conditions as given In Figure
4.6. (a) Computer-simulated electropherograms for constant-
current conditions of 10, 15, and 17 uA. (b) Separation
characteristics for constant-current of 10 uA. (c) Separatlon
characteristics for constant-current of 15 11A.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

158
Figure 4.13a
10uA
12
AAAA A 8
1511A
12
3
u A 45 6
7
M 8
17uA
3
l 456
7
s
10 15 20
TIME (min)

 

 

' “9.517;!

159
Figure 4.13b

 

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:
CURRENT, in microamperee - 10.000
pH . 9.800

IONIC STRENGTH, in moles/liter I 1.25008 -2
BUFFER CONCENTRATION, in moles/liter I 2.50008

Correction Factor,

in pH units I

.0000

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm I 100.00 HEIGHT DIFFERENCE, in cm I 2.00
DETECTOR LENGTH, in cm I 50.00 INJECTION TIME, in see I 60.00
I. D., in micrometers I 75.00 HYDRODYNAMIC VELOCITY, in cm/s I 3.938 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
AMP I 10.53 .165 -.31858 -3 1.268 -2 6.538 4 1.74
CMP I 10.83 .170 -.33008 -3 1.308 -2 6.478 4 8.37
GMP I 12.37 .199 -.38168 -3 1.488 -2 6.178 4 4.12
UMP I 13.23 .216 -.40498 -3 1.598 I2 6.028 4 2.46
ADP I 13.77 .226 I.41838 -3 1.658 -2 5.938 4 3.02
CDP I 14.48 .240 -.43418 -3 1.748 -2 5.818 4 5.10
GDP I 15.77 .266 -.45948 -3 1.898 -2 5.618 4 6.54
UDP I 17.64 .305 -.48958 -3 2.128 -2 5.348 4 CR5 I 4.51
INJECTION ZONE, in cm I .24 INJ VARIANCE, in cm2 I 4.638 -3

DETECTOR WINDOW, in cm I .50

FLOW CHARACTERISTICS:
ZETA POTENTIAL, in mV I
ZETAZERO, in mV I 26.44
kPOTNa I 2.23478 -1
ELECTROOSMOTIC MOBILITY, in cm2/Vs I 7.43008 -4
ELECTROOSMOTIC VELOCITY, in cm/s I .1382
VOLTAGE, in RV I 18.594

RESISTANCE, in ohm I 1.85948 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH I 9.800

IONIC STRENGTH I 1.25008 -2
BUFFER CONCENTRATION I 2.50008 -3
BUFFER CAPACITY I 2.03808 -4
CHARGE CONC = 1.99568 -2
[MJBuffer I 5.0796E -3

[M]e1ectr I 4.89858 -3

BUFFER FORMULATION:

CONC M-H3A I 0.00008 -1

CONC H-HZA I 0.0000E -1

CONC N-HA I 2.42048 -3

CONC M-A I 7.9567E IS

CONC M-X I 4.89858 -3

OK

DET VARIANCE,

in cm2 I 2.088 -2

 

 

 

 

 

160
Figure 4.130

 

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes I 15.000

pH . 9.800 Correction Factor, in pH units = .0000
IONIC STRENGTH, in moles/liter I 1.25008 -2

BUFFER CONCENTRATION, in moles/liter I 2.50008 -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm I 100.00 HEIGHT DIFFERENCE. in cm I 2.00
DETECTOR LENGTH, in cm I 50.00 INJECTION TIME, in sec I 60.00
I. D., in micrometers = 75.00 HYDRODYNAMIC VELOCITY, in cm/s I 3.938 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
AMP I 7.02 .104 -.31858 I3 8.438 I3 7.348 4 1.85
CMP I 7.22 .107 -.33008 I3 8.668 I3 7.298 4 8.91
GMP I 8.25 .124 -.38168 I3 9.908 I3 7.048 4 4.41
UMP I 8.82 .134 -.40498 I3 1.068 I2 6.908 4 2.64
ADP = 9.18 .141 -.41838 -3 1.108 -2 6.828 4 3.25
CDP I 9.65 .149 I.43418 I3 1.168 I2 6.728 4 5.50
GDP I 10.51 .164 -.45948 I3 1.268 I2 6.548 4 7.08
UDP I 11.76 .188 I.48958 I3 1.418 I2 6.298 4 CRS I 3.02_
INJECTION ZONE, in cm I .24 INJ VARIANCE, in cm2 I 4.638 I3
DETECTOR WINDOW, in cm I .50 DET VARIANCE, in cm2 I 2.088 -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV I ~93.54

ZETAZERO, in mV I 26.44

kPOTNa I 2.2347E I1

ELECTROOSMOTIC MOBILITY, in cm2/Vs I 7.43008 I4
ELECTROOSMOTIC VELOCITY, in cm/s I .2072
VOLTAGE, in RV I 27.891

RESISTANCE, in ohm I 1.85948 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH I 9.800

IONIC STRENGTH I 1.25008 -2
BUFFER CONCENTRATION = 2.50008 -3
BUFFER CAPACITY = 2.03808 -4
CHARGE CONC I 1.99568 -2
[MJBuffer I 5.07968 -3

[M)e1ectr I 4.89858 -3

BUFFER FORMULATION:

CONC M-HJA I 0.00008 -1

CONC M-HZA I 0.00008 -1

CONC M-HA I 2.42048 -3

CONC M-A I 7.95678 -5

CONC MIX I 4.89858 I3

OK

 

 

 

 

 

 

flow ve
decreas

F
separati
marked
as well
silanols
ionic st
electropl
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flow by
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also can

Th
Interestin
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161
flow velocity, can decrease substantially the analysis time with a resulting
decrease in diffusional variance.

Perhaps the most effective means to influence an electrophoretic
separation is by altering the buffer properties. The buffer pH (Figure 4.14) has a
marked effect on the effective mobility and dissociation equilibrium of the solutes
as well as on the electroosmotic flow characteristics through protonation of
silanol sites at the capillary surface (Equations [4.14] and [4.11]). Likewise, the
ionic strength of the buffer solution (Figure 4.15) influences the solute
electrophoretic behavior by decreasing the solute mobility and retarding its
migration (Equation [416]). The ionic strength also alters the electroosmotic
flow by compression of the double layer structure at the silica surface (vide
Chapter 3). In traditional paper and slab gel electrophoresis, the effect of ionic
strength is to contribute to the sharpening of the band boundaries. That does
not seem to be the case in capillary zone electrophoresis. The loss of efficiency
is evident as the ionic strength of the solution increases. In conclusion, the
overall effect of pH is more dramatic than that of the ionic strength because pH
is capable of altering not only the order of solute elution and analysis time but
also can cause a distinct change in the resolution pattern.

The effect of the buffer concentration is presented in Figure 4.16.
Interestingly, the increase in concentration of the buffer contributes to shorter
analysis time. This is a consequence of the manner in which the buffer solutions
are formulated. For a constant ionic strength and high pH, an increase in buffer
concentration is achieved by an increase in the amount of the doubly and triply
charged phosphate species and a corresponding decrease in the amount of
sodium chloride. As a result, the resistance of the solution is substantially
increased, and so the voltage. The field strength varied from 275 Vlcm to 372

Vlcm with a small increase in the buffer concentration from 1.5 to 3.5 mM.

 

 

162

Figure 4.14 Effect of the buffer pH on the separation of nucleotides. Solute
identification and standard conditions as given in Figure 4.6. (a)
Computer-simulated electropherograms for pH 6, 7, and 9.8. (b)

fSepara7tion characteristics for pH 6. (c) Separation characteristics
orpH .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

163
Figure 4.14s
12 pH 9.8
3
4
56
7
a
pH 7
31
2,4
7
5 8.5
pH 6
3 1 2 ‘
A Ii 5 6 a
0 10 15 20 25 30 35

TIME (min)

 

 

 

 

 

 

164
Figure 4.14b

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperea I 17.000

pH I 7.000 Correction Factor, in pH units I .0000
IONIC STRENGTH, in moles/liter I 1.25008 -2

BUFFER CONCENTRATION, in moles/liter I 2.50008 I3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC

TOTAL LENGTH, in cm I 100.00 HEIGHT DIFFERENCE, in cm I 2.00
DETECTOR LENGTH, in cm I 50.00 INJECTION TIME, in sec I 60.00

I. D., in micrometers I 75.00 HYDRODYNAMIC VELOCITY, in cm/s I 3.938 I3

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2

GMP I 7.76 .116 I.29218 I3 9.318 I3 7.168 4 1.30
AMP I 7.91 .119 I.2994E I3 9.508 I3 7.128 4 2.60
CMP I 8.23 .124 I.31378 I3 9.888 I3 7.048 4 .22
UMP I 8.26 .125 I.3149E I3 9.918 I3 7.048 4 14.69
GDP I 10.36 .162 I.38728 I3 1.248 I2 6.578 4 2.26
ADP I 10.73 .169 I.39718 I3 1.298 I2 6.498 4 4.02
UDP I 11.44 .182 I.41398 I3 1.378 I2 6.358 4 .11
CDP I 11.46 .182 I.41448 I3 1.378 I2 6.358 4 CRS I 105.31_
INJECTION ZONE, in cm I .24 INJ VARIANCE, in cm2 I 4.638 I3
DETECTOR WINDOW, in cm I .50 DET VARIANCE, in cm2 I 2.088 -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV I I84.50

ZETAZERO, in mV I 33.02

kPOTNa I 2.2347E I1

ELECTROOSMOTIC MOBILITY, in cm2/Vs I 6.71218 I4
ELECTROOSMOTIC VELOCITY, in cm/s I .1896
VOLTAGE, in kV I 28.251

RESISTANCE, in Ohm I 1.66188 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH I 7.000

IONIC STRENGTH I 1.25008 -2
BUFFER CONCENTRATION = 2.50008 -3
BUFFER CAPACITY I 1.43408 -3
CHARGE CONC I 2.26628 -2
[H]buffer I 3.66918 -3

[H]e1ectr I 7.66178 -3

BUFFER FORMULATION:

CONC H-H3A I 0.00008 -1

CONC H-HZA I 1.33098 -3

CONC H-HA I 1.16918 -3

CONC H-A I 0.00008 -1

CONC H-x I 7.66178 -3

OK

 

 

 

 

 

 

   

 

 

165
Figure 4140

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

C ENT, in microamperes I 17.00 0

pH I 6.000 Correction Factor, in pH units - .0000
IONIC STRENGTH, in moles/liter I 1. 25008 -2

BUFFER CONCENTRATION, in moles/liter I 2.50008 -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm I 100.00 HEIGHT DIFFERENCE, in cm I 2.00
DETECTOR LENGTH, in cm I 50.00 INJECTION TIME, in sec I 60.00
I. D., in micrometers I 75.00 HYDRODYNAMIC VELOCITY, in cm/s I 3.938 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
GMP I 13.55 .222 -.237OE -3 1.638 -2 5.968 4 1.17
AMP I 13.81 .227 I.24138 I3 1.668 I2 5.928 4 2.17
CMP = 14.31 .237 -.24908 I3 1.728 I2 5.848 4 2.26
UMP I 14.86 .248 I.25698 I3 1.788 I2 5.758 4 27.96
GDP I 24.89 .470 I.33958 I3 2.998 I2 4.508 4 2.03
ADP = 25.87 .493 -.34418 -3 3.108 -2 4.408 4 5.40
CDP = 28.72 .564 -.35588 I3 3.458 -2 4.158 4 2.77
UDP = . .605 -.36148 I3 3.648 I2 4.028 4 CRS I 15.88_
INJECTION ZONE, in cm I .24 INJ VARIANCE, in cm2 I 4. 638 -3
DETECTOR WINDOW, in cm I .50 DET VARIANCE, in cm2 = 2. 088 -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV = I58.14

ZETAZERO, in mV = 57.80

kPOTNa = 2.23478 I1

ELECTROOSMOTIC MOBILITY, in cm2/Vs I 4.61798 I4
ELECTROOSMOTIC VELOCITY, in cm/s I .1261
VOLTAGE, in RV = 27.307

RESISTANCE, in Ohm I 1.60638 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH = 6.0 0

IONIC STRENGTH = 1.25008 I2
BUFFER CONCENTRATION = 2.50008 I3
BUFFER CAPACITY I 4.30728 I4
CHARGE CONC I 2.45968 I2
[HJbuffer I 2.70048 -3

[M)electr I 9.59668 I3

BUFFER FORMULATION:

CONC M-H3A = 0.00008 I1

CONC MIH2A I 2.29968 I3

CONC MIHA I 2.00448 I4

CONC MIA I 0.00008 I1

CONC MIX I 9.59668 I3

OK

 

 

 

 

 

 

 

Figure 4.15

166

Effect of the buffer ionic strength (I) on the separation of

nucleotides. Solute identification an

d standard conditions as given

in Figure 4.6. (a) Computer-simulated electropherograms for 10,

15, and 20 mM ionic strength. (b)

Separation characteristics for

15 mM ionic strength. (c) Separation characteristics for 20 mM

ionic strength.

 

 

167

 

 

 

 

 

 

 

 

Figure 4.15a
12 12.5 mM
3
4
56
7
M 8
15 mM
12
3
456
7 s
20 mM
12
3
A M I] 7 8
1o 15 20 25
TIME (min)

 

 

 

 

168
Figure 4.15b

 

 

PREDICTED OPTIMUM CONDITIONS FOR oTHE SEPARATION:

CURRENT, in microamperes - 17

pH I 9. 800 Correction Factor, in pH units I .0000
IONIC STRENGTH, in moles/liter = 1. 500008

BUFFER CONCENTRATION, in moles/liter I 2. 50008 I3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm I 100.00 HEIGHT DIFFERENCE, in cm - 2.00
DETECTOR LENGTH, in cm I 50.00 INJECTION TIME, in see I 60.00
I. D., in micrometers I 75.00 HYDRODYNAMIC VELOCITY, in cm/s I 3.938 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
AMP I 8.33 .126 I.3116E I3 1.008 I2 7.028 4 1.92
CMP = 8.58 .130 I.32308 I3 1.038 I2 6.968 4 9.05
GMP I 9.86 .153 I.37328 I3 1.188 I2 6.678 4 4.59
UMP I 10.59 .166 I.39658 I3 1.278 I2 6.528 4 2.17
ADP = 10.96 .173 I.40708 I3 1.318 I2 6.448 4 3.36
CDP = 11.56 .184 -.42278 I3 1.398 I2 6.338 4 5.29
GDP = 12.58 .203 I.44618 I3 1.518 I2 6.148 4 7.28
DP I .17 .234 I.47588 I3 1.708 -2 5.868 4 CR3 = 3.63_
INJECTION ZONE, in cm I .24 INJ VARIANCE, in cm2 = 4. 638 I3
DETECTOR WINDOW, in cm I .50 DET VARIANCE, in cm2 I 2. 088 I2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV I I89.42

ZETAZERO, in mV = 26.44

kPOTNa I 2.2347E I1

ELECTROOSMOTIC MOBILITY, in cm2/Vs I 7.10248 I4
ELECTROOSMOTIC VELOCITY, in cm/s = .1777
VOLTAGE, in kV I 25.022

RESISTANCE, in ohm = 1.47198 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH = 9.80

IONIC STRENGTH I 1.50008 -2

BUFFER CONCENTRATION I 2.50008 -3

BUFFER CAPACITY = 2.06558 -4

CHARGE CONC I 2.49538 -2

[MJbuffer = 5.08108 —3

[MJelectr I 7.39568 -3

BUFFER FORMULATION:

CONC M-HJA 0.00008 -1

CONC M-HZA
CONC M-HA = 2.41908 -3
CONC M-A I 8.10228 -5
CONC MIX I 7.39568 -3
OK

 

 

 

 

169
Figure 4.15c

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperee I 17.000

pH I 9.800 Correction Factor, in pH units I .0000
IONIC STRENGTH, in moles/liter I 2.00008 I2

BUFFER CONCENTRATION, in moles/liter I 2.50008 -3

 

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC

TOTAL LENGTH, in cm I 100.00 HEIGHT DIFFERENCE, in cm I 2.00
DETECTOR LENGTH, in cm I 50.00 INJECTION TIME, in sec I 60.00

I. D., in micrometers I 75.00 HYDRODYNAMIC VELOCITY, in cm/s I 3.938 -3

 

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2

AMP I 12.97 .211 I.29968 I3 1.568 I2 6.078 4 1.95
CMP I 13.39 .219 I.3109E I3 1.618 I2 5.998 4 8.78
GMP I 15.49 .261 I.35858 I3 1.868 I2 5.658 4 4.68
UMP I 16.77 .287 I.38168 I3 2.018 I2 5.468 4 1.24
ADP I 17.13 .295 I.38758 I3 2.068 I2 5.418 4 3.38
CDP I 18.17 .317 I.40318 I3 2.188 I2 5.278 4 4.49
GDP I 19.66 .349 I.4227E I3 2.368 I2 5.078 4 7.18
UDP I 22.39 .411 I.45188 I3 2.698 I2 4.768 4 CR8 I 6.29_
INJECTION ZONE, in cm I .24 INJ VARIANCE, in cm2 I 4.638 I3
DETECTOR WINDOW, in cm I .50 DET VARIANCE, in cm2 I 2.088 I2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV I I83.24

ZETAZERO, in mV I 26.44

kPOTNa I 2.23478 I1

ELECTROOSMOTIC MOBILITY, in cm2/Vs = 6.61168 I4
ELECTROOSMOTIC VELOCITY, in cm/s I .1172
VOLTAGE, in kV I 17.732

RESISTANCE, in ohm I 1.04308 9

 

BUFFER CHARACTERISTICS (cone in moles/liter):
pH I 9.800

IONIC STRENGTH I 2.00008 I2
BUFFER CONCENTRATION I 2.50008 I3
BUFFER CAPACITY I 2.11498 I4
CHARGE CONC I 3.49488 I2
[M]buffer - 5.08368 —3

[M]e1ectr I 1.23908 -2

BUFFER FORMULATION:

CONC MIH3A I 0.00008 I1

CONC MIHZA I 0.00008 I1

CONC MIHA I 2.41648 I3

CONC MIA I 8.36028 I5

CONC MIX I 1.23908 I2

OK

 

 

170

Figure 4.16 Effect of' the buffer concentration (CT) on the separation of
nucleotides. Solute identification and standard conditions as given
In Figure 4.6. (a) Computer-simulated electropherograms for 1.5,
2.5, and 3.5 mM buffer concentration. (b) Separation
characteristics for 1.5 mM buffer concentration. (0) Separation
characteristics for 3.5 mM buffer concentration.

 

 

 

 

 

171

 

 

 

 

 

 

Figure 4.16a
1.5 mM
12
3
4
AJAG 7 8
2.5 mM
12
45 s 7
s
12 3.5 mM
3
45s
7 8
TIME (min)

 

 

 

 

172
Figure 4.160

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes I 17.000

pH I 9.800 Correction Factor, in pH units I .0000
IONIC STRENGTH, in moles/liter I 1.25008 I2

BUFFER CONCENTRATION, in moles/liter I 1.50008 I3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC

TOTAL LENGTH, in cm I 100.00 HEIGHT DIFFERENCE, in cm I 2.00
DETECTOR LENGTH, in cm I 50.00 INJECTION TIME, in sec I 60.00

I. D., in micrometers I 75.00 HYDRODYNAMIC VELOCITY, in cm/s I 3.938 I3

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
AMP I 7.39 .110 I.31858 I3 8.878 I3 7.258 4 1.90
CMP I 7.60 .113 I.33008 I3 9.128 I3 7.208 4 9.20
GMP I 8.73 .133 I.38168 I3 1.058 I2 6.928 4 4.56
UMP I 9.36 .144 I.40498 I3 1.128 I2 6.788 4 2.74
ADP I 9.77 .151 I.41838 I3 1.178 I2 6.698 4 3.37
CDP I 10.29 .160 I.43418 I3 1.238 I2 6.588 4 5.73
GDP I 11.26 .178 I.45948 I3 1.358 I2 6.388 4 7.39
UDP I 12.68 .205 I.48958 I3 1.528 I2 6.128 4 CRS I 3.26
INJECTION ZONE, in cm I .24 INJ VARIANCE, in cm2 I 4.638 I3 -
DETECTOR WINDOW, in cm I .50 DET VARIANCE, in cm2 I 2.088 I2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV I I91.68

ZETAZERO, in mv I 26.44

kPOTNa I 2.2347E I1

ELECTROOSMOTIC MOBILITY, in cm2/Vs I 7.28258 I4
ELECTROOSMOTIC VELOCITY, in cm/s I .2000
VOLTAGE, in kV I 27.466

RESISTANCE, in ohm I 1.61568 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH = 9.800

IONIC STRENGTH - 1.25008 -2
BUFFER CONCENTRATION = 1.50002 -3
BUFFER CAPACITY - 1.87538 -4
CHARGE CONC - 2.19748 -2
[MJbuffer - 3.07618 -3

[Mjelectr - 7.91088 -3

BUFFER FORMULATION:

CONC MIH3A - 0.00008 -1

CONC MIH2A - 0.0000: -1

CONC MIHA - 1.42398 -3

CONC n-A - 7.60738 -5

CONC N-x - 7.91088 -3

0x

 

 

 

 

 

173
Figure 4.160

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes I 17.000

pH I 9.800 Correction Factor, in pH units I .0000
IONIC STRENGTH, in moles/liter I 1.25008 I2

BUFFER CONCENTRATION, in moles/liter I 3.50008 I3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC

TOTAL LENGTH, in cm I 100.00 HEIGHT DIFFERENCE, in cm I 2.00
DETECTOR LENGTH, in cm I 50.00 INJECTION TIME, in sec I 60.00

I. D., in micrometers I 75.00 HYDRODYNAMIC VELOCITY, in cm/s I 3.938 I3

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2

AMP I 5.07 .072 I.31858 I3 6.088 I3 7.898 4 1.85
CMP I 5.20 .074 I.33OOE I3 6.248 I3 7.858 4 8.90
GMP I 5.91 .086 I.3816E I3 7.098 I3 7.648 4 4.39
UMP I 6.30 .092 I.4049E I3 7.568 I3 7.548 4 2.63
ADP I 6.55 .096 I.41838 I3 7.868 I3 7.478 4 3.24
CDP I 6.87 .101 I.43418 I3 8.248 I3 7.388 4 5.48
GDP I 7.45 .111 I.45948 I3 8.948 I3 7.238 4 7.04
UDP I 8.28 .125 I.48958 I3 9.938 I3 7.038 4 CR8 I 2.13
INJECTION ZONE, in cm I .24 INJ VARIANCE, in cm2 I 4.638 I3
DETECTOR WINDOW, in cm I .50 DET VARIANCE, in cm2 I 2.088 I2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV I I95.60

ZETAZERO, in mV I 26.44

kPOTNa I 2.2347E I1

ELECTROOSMOTIC MOBILITY, in cm2/Vs I 7.59328 I4
ELECTROOSMOTIC VELOCITY, in cm/s I .2827
VOLTAGE, in RV I 37.227

RESISTANCE, in ohm I 2.18988 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH I 9.800

IONIC STRENGTH I 1.25008 I2
BUFFER CONCENTRATION I 3.50008 I3
BUFFER CAPACITY I 2.20078 I4
CHARGE CONC I 1.79398 I2
[M]buffer I 7.08318 I3

[Mlelectr I 1.88628 I3

BUFFER FORMULATION:

CONC MIH3A I 0.0000E I1

CONC MIHZA I 0.00008 I1

CONC MIHA I 3.41698 I3

CONC MIA I 8.30608 I5

CONC MIX I 1.88628 I3

OK

 

 

 

 

 

 

 

 

 

 

 

 

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174

The double-layer structure at the capillary surface can be affected by the
solution characteristics and the surface charge density (Chapter 3). In any case,
the result is a change in the electroosmotic flow magnitude and even direction.
Capillary coating is a versatile means to manipulate the surface charge density.
The program can simulate this effect by accepting values of the electroosmotic
flow as an input parameter rather than by calculating the flow from the buffer
characteristics. Figure 4.17 illustrates the effect of the electroosmotic mobility
on the separation characteristics. The electroosmotic flow does not contribute to
achieve any separation, because it affects the migration of all solutes to the
same extent. However, since the electroosmotic flow influences the residence
time of the solutes in the capillary, a dramatic change in efficiency and resolution

may occur.

4.4 Conclusions

The computer routine developed in this work constitutes a resourceful
approach to the optimization of electrophoretic separations. The program is
based on theoretical models for ' zone migration and dispersion and
encompasses versatile features, such as the choice of different injection and
detection conditions as well as a particular power-supply operation mode. The
applicability of the program model for voltage is restricted to capillaries of 75 um
diameter and approximately 100 cm long because of the surface conductance.
Also, in this program, temperature effects that result from Joule heating are not
considered. Possible consequences of the temperature increase during
instrument operation are changes in the electrophoretic mobility of the solutes,

and changes in the viscosity of the buffer solution, which directly alter the

 

_ _._ ._._....Ir ._

 

 

175

Figure 4.17 Effect of the electroosmotic mobility (005m) on the separation of
nucleotides. Solute identification and standard conditions as given
in Figure 4.6. (a) Computer-simulated electropherograms for
0.200, 0.235, and 0.260 cm2 V'1 3'1. (b) Separation characteristics

for 0.200 cm2 V'1 3'1. c Se aration characteristics for
0.260 cm2 V'1 3'1. ( ) p

 

 

 

 

 

 

 

 

 

 

 

176
Figure 4.17a

 

0.200 cm 2i V s

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12
3
4 5 5
AAJ 7 8
0.235 cmZIVs
12
fl 3
45s
7
3
ii i
,2 0.260 cm2/Vs
34
5s
7 8
, ill , , .
5 10 15 20

TIME (min)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

177
Figure 4.17b

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes = 1700

pH = 9. 800 Correction Factor, in pH units = .0000
IONIC STRENGTH, in moles/liter I 1.25008 I2

BUFFER CONCENTRATION, in moles/liter I 2.50008 I3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm I 100.00 HEIGHT DIFFERENCE, in cm I 2.00
DETECTOR LENGTH, in cm I 50.00 INJECTION TIME, in sec I 60.00
I. D., in micrometers I 75.00 HYDRODYNAMIC VELOCITY, in cm/s = 3.938 I3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
AMP I 8.37 .126 -.31858 I3 1.008 I2 7.018 4 2.45
CMP = 8.69 .132 -.33008 I3 1.048 I2 6.938 4 12.08
GMP I 10.47 .164 I.38168 I3 1.268 I2 6.548 4 6.18
UMP I 11.55 .184 -.40498 -3 1.398 -2 6.338 4 3.78
ADP = 12.27 .197 I.4183E I3 1.478 I2 6.198 4 4.73
CDP I 13.24 .216 -.43418 I3 1.598 I2 6.028 4 8.23
GDP I 15.18 .254 -.45948 I3 1.828 I2 5.708 4 11.07
UDP I 18.36 .321 -.48958 I3 2.208 -2 5.248 4 CRS = 4.65
INJECTION ZONE, in cm I .24 INJ VARIANCE, in cm2 = 4.638 I3
DETECTOR WINDOW, in cm I .50 DET VARIANCE, in cm2 = 2.088 -2

FLOW CHARACTERISTICS (experimental values):
ELECTROOSMOTIC MOBILITY, in cm2/Vs I 6. 32718 I4
ELECTROOSMOTIC VELOCITY, in cm/s = .2000
VOLTAGE, in RV I 31.610

RESISTANCE, in ohm = 1.85948 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH = 9.800

IONIC STRENGTH = 1.25008 I2
BUFFER CONCENTRATION = 2.50008 I3
BUFFER CAPACITY = 2.03808 -4
CHARGE CONC = 1.99568 -2
[MJbutfer = 5.07968 -3

[Mjelectr I 4.89858 -3

BUFFER FORMULATION:

CONC M-H3A = 0.00008 I1

CONC M-HZA = 0.00008 -1

CONC MIHA I 2.42048 I3

CONC MIA I 7.95678 I5

CONC MIX I 4.89858 I3

OK

 

 

 

 

178
Figure 4.170

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in nicroanperee I 17.000

pg . 9.800 Correction Factor, in pH units = .0000
IONIC STRENGTH, in moles/liter I 1.2500E -2

BUFFER CONCENTRATION, in moles/liter I 2.5000E I3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC

TOTAL LENGTH, in cm I 100.00 HEIGHT DIFFERENCE, in cm I 2.00
DETECTOR LENGTH, in cm I 50.00 INJECTION TIME, in sec I 60.00

I. D., in micrometers I 75.00 HYDRODYNAMIC VELOCITY, in cm]: I 3.93E I3

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in an/Vs in cmz
AMP I 5.22 .075 I.3185E I3 6.26E I3 7.84E 4 1.61
CMP I 5.34 .076 I.3300E I3 6.41E I3 7.81E 4 7.68
GMP I 5.96 .086 I.3816E I3 7.16E I3 7.63E 4 3.75
UMP I 6.30 .092 I.4049E I3 7.56E I3 7.54E 4 2.23
ADP I 6.51 .095 I.4183E I3 7.81E I3 7.48E 4 2.72
CDP = 6.77 .100 -.43412 -3 8.13E -3 7.412 4 4.57
GDP I 7.24 .107 I.4594E I3 8.69E I3 7.29E 4 5.79
UDP . 7.90 .118- -.4895E -3 9.482 -3 7.122 4 CRS = 1.99
INJECTION ZONE, in cm I .24 INJ VARIANCE, in cm2 I 4.63E I3 -
DETECTOR WINDOW, in cm I .50 DET VARIANCE, in cm2 I 2.08E I2

FLOW CHARACTERISTICS (experimental values):
ELECTROOSMOTIC MOBILITY, in cm2/Vs I 8.2252E I4
ELECTROOSMOTIC VELOCITY, in cm/s I .2600
VOLTAGE, in RV I 31.610

RESISTANCE, in Ohm I 1.8594E 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH - 9.800

IONIC STRENGTH I 1.2500E I2
BUFFER CONCENTRATION I 2.5000E I3
BUFFER CAPACITY I 2.0380E I4
CHARGE CONC I 1.9956E I2
[M1buffer - 5.0796E —3

[Hlelectr = 4.89852 -3

BUFFER FORMULATION:

CONC MIH3A I 0.0000E I1

CONC MIHZA I 0.0000E I1

CONC MIHA I 2.4204E I3

CONC HIA I 7.9567E I5

CONC HIX I 4.8985E I3

OK

 

 

 

 

 

 

 

179
electroomotic flow. Moreover, temperature gradients in the capillary cause
convective flow which may be detrimental to the separation performance.
Experimentally, temperature effects can be minimized by limiting the field
strength of the system to less than 350 Vlcm. Another aspect that is neglected
by the program is the differences in conductivity between the sample zone and
the buffer solution, which can cause either fronting or tailing of the zone profile.
This effect can also be controlled experimentally, by the judicious choice of the
solute concentration in the buffer solution. This program can be used
advantageously as a pedagogical tool to examine the effect of buffer
composition and instrumental parameters on the separation performance.
Furthermore, this optimization routine can be easily implemented on personal

computers.

 

 

 

180

4.5 References

10.

11.

12.

13.
14.
15.

16.

17.

18.

19.

Kuhr, W. G.; Monnig, C. A. Anal. Chem. 1992, 64, 389R-407R.

Grossman, P. D.; Colburn, J. C., Eds; Capillary Electrophoresis- Theory
and Practice; Academic Press Inc.: San Diego, CA, 1992.

Massart, D. L.; Dijkstra, A.; Kaufman, L. Evaluation and Optimization of
Laboratory Methods and Analytical Procedures; Elsevier: New York,
1978.

Massart, D. L. Vandeginste, B. G. M.; Deming, S. N.; Michotte, Y.;
Kaufman, L. Chemometrics: a textbook, Elsevier: New York, 1988

Kuhr, W. G.; Yeung, E. 8. Anal. Chem. 1988, 60, 2642-2646.
Vindevogel, J.; Sandra, P. Anal. Chem. 1991, 63, 1530-1536.

Kggbedi, M. G.; Smith, S. C.; Strasters, J. K. Anal. Chem. 1991, 63, 1820-

Smith, S. C.; Khaledi, M. G. Anal. Chem. 1993, 65, 193-198.
Friedl, W.; Kenndler, E. Anal. Chem. 1993, 65, 2003-2009.

N991, C139 L.; Ong, C. F.; Lee, H. K.; Li, S. F. Y. J. Microcol. Sep. 1993, 5,
- 7.

Bier, M., Ed.; Electrophoresis - Theory, Methods and Applications;
Academic Press Inc.: New York, 1959.

Bier, M.; Palusinski, O. A. Mosher, R. A.; Saville, D. A. Science 1983,
219, 1281- 1287.

Gas, B.; Vacik, J.; Zelensky, l. J. Chromatogr. 1991, 545, 225-237.
Dose, E. V.; Guiochon, G. A. Anal. Chem. 1991, 63. 1063-1072.

Giannovario, J. A.; Griffin, R. N.; Gray, E. L. J. Chromatogr. 1978, 153,
329-352.

Mosher, R. A.; Dewey, D.; Thormann, W.; Saville, D. A.; Bier, M. Anal.
Chem. 1989, 61, 362-366.

Mikkers, .F. E. P.; Everaerts, F. M.; Verheggen, Th. P. E. M. J.
Chromatogr. 1979, 169, 1-10.

Ermakov, S. V.; Mazhorova, O. S.; Zhukov, M. Y. Electrophoresis 1991,
13, 838-848.

Jones, H. K.; Nguyen, N. T.; Smith, R. D. J. Chromatogr. 1990, 504, 1-19.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_T—W"

20.

21.

22.
23.

24.

25.

26.

27.

28.

29.
30.

31.

 

32.

33.
34.

35.

36.
37.

181
Huang, X.; Coleman, W. F.; Zare, R. N. J. Chromatogr. 1989, 480, 95-
110.

Roberts, G. 0.; Rhodes, P. H.; Snyder, R. S. J. Chromatogr. 1989, 480,
35-67.
Schlabach, T. D.; Excoffier, J. L. J. Chromatogr. 1988, 439, 173-184.

Giddings, J. C. Unified Separation Science; Wiley-lnterscience Pulication:
New York, 1991.

Bard, A. J.; Faulkner, L. R. Electrochemical Methods - Fundamentals and
Applications; John Wiley & Sons: New York, 1980.

Robinson, R. A.; Stokes, R. H. Electrolyte Solutions - The Measurement
and Interpretation of Conductance, Chemical Potential and Diffusion in
Solutions of Simple Electrolytes; Butterworths Scientific Publications:
London,1959.

Hiemenz, P. C. Principles of Colloid and Surface Chemistry, 2nd ed.;
Marcel Dekker: New York, 1986.

Haygs, M. A.; Kheterpal, l.; Ewing, A. G. Anal. Chem. 1993, 65, 2010-
201 .

Spanier,.J; Oldham, K. An Atlas of Functions; Hemisphere Pub. Corp:
Washington, DC, 1987.

Lyklema, J. J. Electroanal. Chem. 1968, 18, 341-348.

Butler, J. N. Ionic Equilibrium - A Mathematical Approach; Addison-
Wesley Publishing Company, Inc: Massachusetts, 1964.

Rossotti, F. J. C. Rossotti, H. The Determination of Stability Constants
and other Equilibrium Constants in Solution; McGraw Hill Book Company,
lnc.: New York, 1961

Rossotti, H. The Study of Ionic Equilibria - An Introduction; Longman:
New York, 1978.

Hirokawa, T.; Kobayashi, S.; Kiso, Y. J. Chromatogr. 1985, 318, 195-210.

Beckers, J. L.; Everaerts, F. M.; Ackermans, M. T. J. Chromatogr. 1991,
537, 407-428.

ggiéJ; Smith, J. T.; El Rassi, Z. J. High. Resol. Chromatogr. 1992, 15,
- 2.

Lambert, W. J. J. Chem. Ed. 1990, 67, 150-153.

Sternberg, J. C. in Advances in Chromatography, Vol. 2, pp. 205- 270;
Giddings, J. C.; Keller, R. A. Eds. Marcel Dekker lnc.: New York, 1966.

 

 

 

182
38. Glajch, J. L.; Snyder, L. R., Eds; _ Computer-Assisted Method
Development for HIgh-Performance LIqUId Chromatography, Elsevier
Science Publishing Company Inc: New York, 1990.

39. Schoenmakers, P. J. Optimization of Chromatographic Selectivity - a
guide to method development, J. Chromatogr. Lib., Vol. 35; Elsevier
Science Publishing Company Inc: New York, 1986.

40. Berridge, J. C. Techniques for the Automated Optimization Of HPLC
Separations, John Wiley and Sons: New York, 1986.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHAPTER 5

EXPERIMENTAL VALIDATION OF THE OPTIMIZATION
PROGRAM WITH NUCLEOTIDE MIXTURES

5.1 Introduction

In order to validate experimentally the computer optimization program
described in Chapter 4, the nucleotides 5'-mono- and di—phosphates were
chosen as model solutes. Nucleotides constitute an important class of
biomolecules that function as intermediates in nearly all biochemical processes.1
As building blocks, they are the precursors of nucleic acids (DNA and RNA) and
the components of three major coenzymes (NAD+, FAD and CoA). Nucleotides
act as metabolic regulators, mediating the action of many hormones and as
storage of chemical energy for biological reactions. Inhibitors of the nucleotide
biosynthesis2 (methotrexate and fluorouracil) have been employed in cancer
chemotherapy, and the metabolism of nucleotide'analogs3 (azidothymidine,
AZT) has been exploited in the treatment of acquired immune deficiency
syndrome (AIDS).

Nucleotides contain characteristic structural features:4-6 a nitrogenous
heterocyclic base, which is a derivative of either pyrimidine or purine, and a
pentose sugar ring, esterified by phosphoric acid at the 5' position. The
structures and ionization patterns of the nucleotides studied in this work are
displayed in Figure 5.1. The base and the sugar rings are nearly planar and in
the most stable conformation, they are positioned almost at right angles to each

other. Although the heterocyclic bases can exist in several tautomeric forms, the
1 83

 

 

184

Figure 5.1 Chemical structures and ionization pattern of nucleotides.

 

 

185
Figure 5.1

6H OH
I
Ho--I=-—o-—I=—o-cI-I2 o BASE

twang

 

 

 

 

 

 

 

 

 

 

HO OH
NH2 .NHZ
HN/ N : N/ N
KG) l\ J \——— K |\ J
R R
ADENOSINE
O H O Q
”/r '1‘ H N N 9 I N
H2NJ§N N) H2NJ§ N) HZNK N/1
#2 I . I,
GUANOSINE
HN/
:0 LL 3,335
CYTIDINE URIDINE

 

 

 

 

 

 

 

 

 

 

 

 

 

186

enol-imino structure is usually regarded as a minor form. Thus, for uridine the
corresponding base occurs predominantly as the diketo tautomer. The keto-
amino tautomeric forms prevail in cytidine and guanosine, and the amino form
prevails in adenosine. The phosphate chain is acidic in character, but the
heterocyclic bases can actually have prOperties of weak acids, bases or
both.5-7'9

The presence of multiple ionization sites makes the nucleotides suitable
molecules for electrophoretic analysis. Nucleotides have been chosen as model
compounds in a variety of applicationsf’ts10 to demonstrate different modes of
electrophoretic methods,9.11'13 detection schemes,14'18 and optimization
strategies.914 In this work, the electrophoretic behavior of nucleotides in
phosphate buffer solutions is characterized. The computational method
developed in section 4.2 (Chapter 4) to determine dissociation constants and
individual electrophoretic mobility is applied here. A new set of dissociation
constants and individual electrophoretic mobility of nucleotide molecules is
derived, which complements the available literature data.7‘9 The characteristics
of the separation of these compounds are then thoroughly examined in the pH
range from 6 to 11, and contrasted with those predicted by the computer

optimization routine.

5.2 Results and Discussion

Study of the Electrophoretic Behavior of Nucleotides. The model for
effective mobility and the computational method developed to determine
dissociation constants and electrophoretic mobilities (section 4.2) were applied

to evaluate the electrophoretic behavior of nucleotides in phosphate buffer

 

 

 

 

 

 

 

 

 

 

 

187
solutions. The experimental determination of the effective electrophoretic
mobility is based on measurements of migration time and electroosmotic velocity
(Equation [43]), under a variety of pH conditions. The experimental curve of
effective mobility versus pH of each nucleotide is then analyzed by numerical
procedures, where the plateaus and inflection points serve as initial estimates of
the individual mobilities and dissociation constants (pKa), respectively (Equation
[4.141). The best values for these parameters are determined by the least-
squares method.19 The experimentally measured effective mobility of guanosine
5'-monophosphate and the curve calculated from the procedure described above
are shown in Figure 5.2 as a function of pH. Additionally, Figure 5.2 shows the
curve derived from dissociation constants and electrophoretic mobilities
corrected to the condition of infinite dilution (Equations [4.15] and [416]).20 The

decrease in mobility, imposed by the ionic strength of the medium, is a

 

phenomenon known as the retardation effect.21

 

‘The experimentally determined pKa and individual electrophoretic
mobilities of the nucleotides studied in this work are given in Table 5.1. All
constants and mobilities were corrected to the condition of infinite dilution.20 In
the table, the marked values were obtained from “determinations of pKéI and
mobility performed in other buffer systems."-9 These parameters could not be
evaluated in phosphate buffer solutions because, the region below pH 5 is
experimentally inaccessible for both nucleotide mono- and di-phosphates,
concomitantly. This is clear from inspection of Figure 5.3, where the
electroosmotic mobility curve of the phosphate buffer is superimposed to the
effective mobility curves of the nucleotides. In fused-silica capillaries, the
electroosmotic flow is directed towards the cathode.21 Thus, according with the
convention adopted in this work, the electroosmotic mobility has a positive sign.

Conversely, above pH 4, all nucleotides are negatively charged and thus, their

—2_4

188

Figure 5.2 Effective mobility of guanosine 5'-monophosphate as a function of
pH in phosphate buffer solutions formulated to contaIn a total
concentration of sodium of 10 mM. (Bottom) ExperImental values

and calculated curve. (Top) Calculated curve under conditions of
infinite dilution.

 

 

all“

 

 

 

189
Figure 5.2

 

 

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191

Figure 5.3 Effective mobility curve of the nucleotides superimposed to the
electroosmotic mobility of phosphate buffer solutions.

 

 

 

192
Figure 5.3

 

UDP
GDP
CMP
AMP

 

 

 

 

 

GMP

 

 

 

 

 

“osm
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193

mobility is negative in sign. When the magnitude of the electroosmotic flow is
larger compared to the electrophoretic migration, all nucleotides are directed
towards the cathode. However, near pH 5, the electroosmotic mobility has
decreased to a value in between the electrophoretic mobility of the nucleotide
mono- and di-phosphates. Therefore, at this pH condition, only the
monophosphates are able to migrate towards the cathode, and the analysis of
both groups of solutes in the same mixture is no longer possible.

The effective mobility as a function of pH curve constitutes a valuable tool
for the preliminary assessment of an electrophoretic separation. As Figure 5.3
illustrates, in phosphate buffers, it would be very difficult to accomplish the
separation of nucleotides in the range of pH between 5 and 9, due to the
similarities in electrophoretic behavior. The region above pH 9 is promising.
However, the differences in the magnitude of the electrophoretic mobility are

small, and operational conditions must be optimized to enhance efficiency.

Nucleotides as Model Solutes for the Optimization Program. In order to
utilize the optimization program described in Chapter 4 to the separation of
nucleotides, appropriate boundary conditions must'be established. Some of
these boundary conditions are necessary to define the domains of the input
parameters and, hence, are chosen explicitly by the user for a specific
application. Minimum and maximum values together with a suitable interval
must be chosen for the applied current or voltage as well as the buffer pH,
concentration, and ionic strength. Other boundary conditions are invoked
implicitly by the program whenever the specified input parameters lead to an
undesirable situation. For example, high voltage may cause temperature effects
that are not considered in the program models. Therefore, combinations of the

experimental parameters that lead to a predicted voltage in excess of 35 W are

 

 

 

 

 

194

rejected. Other constraints considered by the program are related to the buffer
formulation. Not all combinations of the buffer pH, concentration, and ionic
strength are experimentally feasible. In addition, when solutes possess an
effective mobility that is opposite in sign and larger in magnitude than the
electroosmotic mobility, they will not migrate toward the cathode. Appropriate
constraints have been incorporated in the program to avoid these unacceptable
conditions.

By methodically varying the input parameters within the defined boundary
conditions and evaluating the CRS response function, the computer program can
predict the experimental conditions required for optimal separation of the
solutes. This simulation has been applied to assess the separation of the
nucleotide mono- and di-phosphates in phosphate buffer solutions, under
constant-current conditions. Figures 5.4 and 5.5 present surface maps and
contour plots, which allow for visual inspection of the CRS response function
within the defined range of parameters. This system is characterized by the
presence of multiple minima.

Appropriate sets of conditions were chosen, including the vicinity of the
optimum conditions (pH 10, ionic strength 12.5 mM, buffer concentration 2.4
mM, current 12.5 uA), to study the separation of nucleotides. The resulting
electropherograms are shown - in Figures 5.6 to 5.10 together with those
predicted by the program, followed by outputs of the simulated conditions. The
program predicts the correct elution order for all nucleotides, and provides a
reasonable estimate of the peak width and resolution. However, the predicted
migration times are considerably longer than those observed experimentally. In
order to understand this discrepancy, the errors associated with each constituent
model of the program must be examined separately. As shown in Table 5.2, the

voltage and electrophoretic mobility are predicted with average relative errors of

 

-

- nul-

 

195

Figure 5.4 Surface maps representing the separation of nucleotide mono- and
dI-phosphatesl. (a) CRS as a function of pH and applied current
WIth constant IonIc strength of 12.5 mM and buffer concentration of
2.5 mM. (b CRS as a function of pH and ionic strength with
constant bu er concentration of 2.5 mM and current of 12.5 [AA
(0) CR8 as a functIon of pH and buffer concentration with constant
Ionic strength of 12.5 mM and current of 12.5 11A.

 

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196
Figure 5.4a

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199

Figure 5.5 Contour maps representing the separation of nucleotide mono- and
dI-phosphates. (a) CRS as a function of pH and applied current
wrth constant ionic strength of 12.5 mM and buffer concentration of
2.5 mM. (a CRS as a function of pH and ionic strength with
constant bu er concentration of 2.5 mM and current of 12.5 0A.
(0) CR8 as a function of pH and buffer concentration with constant
IonIc strength of 12.5 mM and current of 12.5 uA.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 5.5a

 

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Figure 5.5c

 

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203

Fi ure 5.6 Se aration of the nucleotides (1) AMP, (2) CMP, (a) GMP. (4)
g UNLP, (5) ADP, (6) CDP, (7) GDP, and (8) UDP In phosphgte
buffer solution at pH 6, and 10 mM sodIum concentratIon, un te:
constant-current conditions of 12.5 “A. (a) Experrmen a
electropherogram (top), computer-SImulated electropherogralrn

(middle), computer-simulated electropherogram WIth expenmenta y

measured value of electroosmotic mommy and voltage (bottom).

(b) Separation characteristics under the predIcted condItIons. (0)

Separation characteristics under the predIcted condItIons, after

input of the experimentally determined value of electroosmotic
mobility and voltage.

 

 

204

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5.6a
pH 6
3,1
2 7 5
4 8
6
10 15 20
3.1.2 ‘
7 5 A5 8
10 15 20
3.1.2 4
75 6 8
1o 15 20
TIME (min)

 

 

205
Figure 5.6b

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes - 12.500

pH - 6.000 Correction Factor, in pH units a .2550
IONIC STRENGTH, in moles/liter = 1.0366E -2

BUFFER CONCENTRATION, in moles/liter - 4.6367E -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm - 112.15 HEIGHT DIFFERENCE, in cm I 2.00
DETECTOR LENGTH, in cm 8 43.40 INJECTION TIHE, in sec = 60.00
I. D., in micrometers = 75.50 HYDRODYNAMIC VELOCITY, in cm/s - 3.55E
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION

in min in min MOBILITY VARIANCE

in cm2/Vs in cm2

GMP = 10.33 .184 -.2298E -3 1.24E -2 5.06E 4 .24
AMP = 10.38 .185 -.2309E -3 1.25E -2 5.06E 4 .36
CMP = 10.44 .186 -.2326E -3 1.25E -2 5.05E 4 3.38
UMP = 11.10 .200 -.2479E -3 1.33E -2 4.94E 4 23.37
GDP = 17.45 .344 -.3368E -3 2.09E -2 4.11E 4 1.05
ADP = 17.82 .353 -.3400E -3 2.14E -2 4.08E 4 2.85
CDP = 18.86 .379 -.3484E -3 2.26E -2 3.97E 4 2.72
UDP = 19.93 .406 -.3561E -3 2.39E -2 3.86E 4 CRS = 137.58_
INJECTION ZONE, in cm = .21 INJ VARIANCE, in cm2 = 3.78E -3
DETECTOR WINDOW, in cm = .50 DET VARIANCE, in cm2 = 2.08E -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV = *61.95

ZETAZERO, in mV 8 57.80

kPOTNa = 2.2347E -1

ELECTROOSMOTIC MOBILITY, in cm2/Vs = 4.9204E -4
ELECTROOSMOTIC VELOCITY, in cm/s = .1310
VOLTAGE, in RV = 29.863

RESISTANCE, in ohm = 2.3891E 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH = 6.000

IONIC STRENGTH = 1.0366E -2
BUFFER CONCENTRATION = 4.6367E -3
BUFFER CAPACITY a 7.7847E -4
CHARGE CONC = 2.0002E -2
[M]buffer - 5.0000E -3

[H]e1ectr = 4.9999E -3

BUFFER FORMULATION:

CONC M-H3A = 0.0000E -1

CONC H-HZA - 4.2734E -3

CONC N-HA - 3.6333E -4

CONC H-A - 0.0000E -1

CONC H-X I 4.9999E -3

OK

 

 

,.,. _.g.

 

 

206
Figure 5.6c

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes - 12.500

pH = 6.000 Correction Factor, in pH units = .2550
IONIC STRENGTH, in moles/liter - 1.0366E -2

BUFFER CONCENTRATION, in moles/liter = 4.6367E -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC

TOTAL LENGTH, in cm - 112.15 HEIGHT DIFFERENCE, in cm - 2.00
DETECTOR LENGTH, in cm - 43.40 INJECTION TIME, in sec - 60.00

I. D., in micrometers = 75.50 HYDRODYNAMIC VELOCITY, in cm/s - 3.55E -3

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2

GMP = 8.69 .150 -.2298E -3 1.04E -2 5.35E 4 .21
AMP = 8.72 .151 -.2309E -3 1.05E -2 5.34E 4 .31
CMP = 8.76 .152 -.2326E -3 1.05E -2 5.34E 4 2.89
UMP = 9.21 .161 -.2479E -3 1.11E -2 5.26E 4 19.49
GDP = 13.16 .244 -.3368E -3 1.58E -2 4.64E 4 .83
ADP = 13.37 .249 -.3400E -3 1.60E -2 4.61E 4 2.25
CDP = 13.94 .262 -.3484E -3 1.67E -2 4.53E 4 2.13
UDP = 14.51 .275 -.3561E -3 1.74E -2 4.46E 4 CRS = 243.18_
INJECTION ZONE, in-cm = .21 INJ VARIANCE, in cm2 = 3.78E -3
DETECTOR WINDOW, in cm = .50 DET VARIANCE, in cm2 = 2.08E -2

FLOW CHARACTERISTICS (experimental values):
ELECTROOSMOTIC MOBILITY, in cm2/Vs = 5.4421E -4
ELECTROOSMOTIC VELOCITY, in cm/s = .1438
VOLTAGE, in RV = 29.634

RESISTANCE, in Ohm = 2.3707E 9

BUFFER CHARACTERISTICS (conc in moles/liter):
pH = 6.000

IONIC STRENGTH - 1.0366E -2
BUFFER CONCENTRATION = 4.6367E -3
BUFFER CAPACITY = 7.7847E -4
CHARGE CONC = 2.0002E -2
[M]buffer = 5.00002 -3

[Mjelectr - 4.9999E -3

BUFFER FORMULATION:

CONC M-H3A = 0.0000E -1

CONC M-HZA = 4.2734E -3

CONC M-HA = 3.6333E -4

CONC M-A = 0.0000E -1

CONC M-X - 4.9999E -3

OK

 

 

 

 

 

 

 

207

Figure 5.7 Separation of nucleotide '
. .. _ s In pH 7 hos hate buffer solution.
Solute IdentIfIcatIon and conditions pas Fgiven in Figure 5.6.

 

 

 

 

208

 

 

 

 

 

 

 

 

 

 

Figure 5.78
pH?
3
1 5
, 4'2 6,8
' 7
10 15 20
31*2
M1 75 6,8
10 15 20
31
4,2
m 75 6,8
10 15 20
TIME (min)

 

 

 

 

 

 

209

Figure 5.7b

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes - 12.500
pH - 7.000 Correction Factor, in pH units = .2800
IONIC STRENGTH, in moles/liter - 1.1587E -2
BUFFER CONCENTRATION, in moles/liter - 3.4135E -3
CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm 8 112.15 HEIGHT DIFFERENCE, in cm - 2.00
DETECTOR LENGTH, in cm a 43.40 INJECTION TIME, in sec - 60.00
I. D., in micrometers = 75.50 HYDRODYNAMIC VELOCITY, in cm/s = 3.55E -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION

in min in min MOBILITY VARIANCE

in cm2/Vs in cm2

GMP I 7.35 .124 -.2803E -3 8.82E -3 5.61E 4 1.24
AMP = 7.51 .127 -.2889E -3 9.01E -3 5.57E 4 2.18
UMP = 7.79 .133 -.3035E -3 9.35E -3 5.52E 4 .08
CMP = 7.81 .133 -.3040E -3 9.37E -3 5.52E 4 12.41
GDP = 9.69 .170 -.3789E -3 1.16E -2 5.17E 4 1.62
ADP = 9.97 .176 -.3877E -3 1.20E -2 5.13E 4 3.33
CDP = 10.57 .189 -.4050E -3 1.27E -2 5.03E 4 .16
UDP = 10.60 .189 -.4058E -3 1.27E -2 5.02E 4 CRS = 121.65_
INJECTION ZONE, in cm a .21 INJ VARIANCE, in cm2 = 3.78E -3
DETECTOR WINDOW, in on = .50 DET VARIANCE, in cm2 = 2.08E -2
FLOW CHARACTERISTICS:
ZETA POTENTIAL, in mV = -86.84
ZETAZERO, in mV = 33.02
kPOTNa = 2.2347E -1
ELECTROOSMOTIC MOBILITY, in cm2/Vs = 6.8976E -4
ELECTROOSMOTIC VELOCITY, in cm/s = .1653

VOLTAGE, in RV = 26.876

RESISTANCE,

in ohm a 2.1500E 9

BUFFER CHARACTERISTICS (cone in moles/liter):

pH = 7.000
IONIC STRENGTH = 1.1587E

-2

BUFFER CONCENTRATION = 3.4135E

BUFFER CAPACITY = 1.95638
CHARGE CONC = 2.0001E -2
[M]buffer - 5.0001E -3
[MJelectr - 5.0002E -3
BUFFER FORMULATION:

CONC M-H3A - 0.0000E -1
CONC M-HZA - 1.8269E -3
CONC M-HA - 1.5866E -3
CONC M-A - 0.00008 -1
CONC M-X - 5.0002E -3

OK

-3

-3

 

 

 

 

 

 

210
Figure 5.7c

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes - 12.500

pH = 7.000 Correction Factor, in pH units = .2800
IONIC STRENGTH, in moleSIIiter = 1.1587E -2

BUFFER CONCENTRATION, in moles/liter = 3.4135E -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC

TOTAL LENGTH, in cm - 112.15 HEIGHT DIFFERENCE, in cm - 2.00
DETECTOR LENGTH, in on = 43.40 INJECTION TIME, in sec - 60.00

I. D., in micrometers = 75.50 HYDRODYNAMIC VELOCITY, in cm/s = 3.55E -3

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2

GMP = 7.03 .118 -.2803E -3 8.43E -3 5.67E 4 1.22
AMP = 7.17 .121 -.2889E -3 8.61E -3 5.64E 4 2.14
UMP = 7.43 .126 -.3035E -3 8.92E -3 5.59E 4 .08
CMP = 7.44 .126 -.304OE -3 8.93E -3 5.59E 4 12.13
GDP = 9.18 .160 -.3789E -3 1.10E -2 5.26E 4 1.58
ADP = 9.44 .165 -.3877E -3 1.13E -2 5.22E 4 3.24
CDP = 9.99 .177 -.4050E -3 1.20E -2 5.12E 4 .15
UDP = 10.02 .177 -.4058E -3 1.20E -2 5.12E 4 CRS = 117.13_

INJ VARIANCE, in cm2 = 3.78E -3

INJECTION ZONE, in on = .21
DET VARIANCE, in cm2 = 2.08E -2

DETECTOR WINDOW, in cm = .50

FLOW CHARACTERISTICS (experimental values):
ELECTROOSMOTIC MOBILITY, in cm2/Vs a 7.0066E -4
ELECTROOSMOTIC VELOCITY, in cm/s = .1712
VOLTAGE, in kv = 27.403

RESISTANCE, in ohm = 2.1922E 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH = 7.000

IONIC STRENGTH = 1.1587E -2
BUFFER CONCENTRATION = 3.4135E -3
BUFFER CAPACITY = 1.9563E -3
CHARGE CONC = 2.0001E -2
[M1buffer = 5.0001E -3

[M]electr = 5.0002E -3

BUFFER FORMULATION:

CONC M-H3A = 0.0000E -1

CONC M-HZA = 1.8269E -3

CONC M-HA = 1.5866E -3

CONC M-A - 0.0000E -1

CONC M-X = 5.0002E -3

OK

 

 

 

.- —_-_._..

 

 

 

211

Figure 5.8 Separation of nu ' '
_ .. .cleotIdes In pH 8 hos hate buff '
Solute IdentIfIcatIon and conditions pas Fgiven in Pigjgmgg.

 

 

212
Figure 5.8a

 

 

 

 

 

 

 

 

 

 

 

pH 8
10 15 20
3
758,6
10 15 20
31
75 8,6
10 15 20

 

TIME (min)

 

 

 

 

 

213
Figure 5.8b

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:
, in microamperes - 12 500
pH = 8.000 Correction Factor, in pH units = .2000
IONIC STRENGTH, in moles/liter = 1.2365E 2
BUFFER CONCENTRATION, in moles/liter - 2.6342E -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC

TOTAL LENGTH, in cm - 112.15 HEIGHT DIFFERENCE, in cm - 2.00
DETECTOR LENGTH, in cm = 43.40 INJECTION TIME, in sec = 60.00

I. D., in micrometers - 75.50 HYDRODYNAMIC VELOCITY, in cm/s = 3.55E -3

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2

GMP = 7.42 .126 -.3123E -3 8.91E -3 5.59E 4 .43
AMP = 7.48 .127 -.3154E -3 8.97E -3 5.58E 4 1.71
CMP = 7.70 .131 -.3275E -3 9.24E -3 5.54E 4 .91
UMP = 7.82 133 -.3338E -3 9.38E -3 5.51E 4 11.07
GDP = 9.47 .166 -.4047E -3 1.14E -2 5.21E 4 1.75
ADP = 9.77 .172 -.4149E -3 1.17E -2 5.16E 4 2.81
UDP = 10.27 .182 -.4306E -3 1.23E -2 5.08E 4 .10
CDP = .29 .183 -.4311E -3 1.23E -2 5.07E 4 CR8 = 118.83_
INJECTION ZONE, in cm = .21 INJ VARIANCE, in cm2 = 3.78E -3
DETECTOR WINDOW, in on = .50 DET VARIANCE, in cm2 = 2.08E -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV = -93.08

ZETAZERO, in mV = 26.8

kPOTNa = 2.2347E -1

ELECTROOSMOTIC MOBILITY, in cm2/Vs = 7.3933E -4
ELECTROOSMOTIC VELOCITY, in cm/s = .1683
VOLTAGE, in RV = 25.528

RESISTANCE, in ohm = 2.0423E 9

BUFFER CHARACTERISTICS (cone in moles/liter):

pH = 8.0
IONIC STRENGTH = 1.2365E -2
BUFFER CONCENTRATION = 2.6342E -3
BUFFER CAPACITY s 5.6053E -4
CHARGE CONC = 2.00005 -2
[MJbuffer = 5.00012 -3

[Mlelectr - 4.9999E -3

CONC M-H3A = 0.0000E -1
CONC M-HZA = 2.6831E -4
CONC M-HA = 2.3659E -3
CONC M-A = 0.0000E -1
CONC M-X I 4.9999E -3
OK

 

 

 

 

 

 

214
Figure 5.8c

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:
T, in microamperes - 12 500
CH = 8. 000 Correction Factor, in pH units = .2000
IONIC STRENGTH, in moles/liter = 1. 2365B -2
BUFFER CONCENTRATION, in moles/liter a 2. 6342E -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm = 112.15 HEIGHT DIFFERENCE, inc em = 2.00
DETECTOR LENGTH, in cm = 43.40 INJECTION TIME, in se - 60.00
I. D., in micrometers = 75.50 HYDRODYNAMIC VELOCITY, in cm/s = 3.55E -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
GMP = 7.06 .119 -.3123E -3 8.47E -3 5.67E 4 .41
AMP = 7.10 .119 -.3154E -3 8.53E -3 5.66E 4 1.65
CMP = 7.30 .123 -.3275E -3 8.77E -3 5.62E 4 .88
UMP = 7.41 .125 -.3338E -3 8.90E -3 5.59E 4 10.64
GDP = 8.90 .155 -.4047E -3 1.07E -2 5.31E 4 1.68
ADP = 9.17 .160 -.4149E -3 1.10E -2 5.26E 4 2.68
UDP = 9.61 .169 -.4306E -3 1.15E -2 5.19E 4 .09
CDP = 9.62 .169 -.4311E -3 1.15E -2 5.1BE 4 CR5 = 128.28_
INJECTION ZONE, in Cm - .21 INJ VARIANCE, in cm2 = 3.78E -3
DETECTOR WINDOW, in cm a .50 DET VARIANCE, in cm2 = 2.08E -2
FLOW CHARACTERISTICS (experimentalv Mes)
ELECTROOSMOTIC MOBILITY, in CmZ/Vs = a7. 5763B -4
ELECTROOSMOTIC VELOCITY, in cm/s = .1740

VOLTAGE, in RV = 25.755
RESISTANCE, in ohm = 2.0604E 9

BUFFER CHARACTERISTICS (cone in moles/liter):
000

IONIC STRENGTH = 1. 2365B -2
BUFFER CONCENTRATION = 2. 6342E -3
BUFFER CAPACITY = 5.6053E -4
CHARGE CONC = 2.0000E -2
[M]buffer = 5.0001E -3
[M]electr = 4.9999E -3
BUFFER FORMULATION:

CONC M-HJA = 0.0000E '1

CONC M-HZA = 2.6831E -4

CONC M—HA = 2.3659E -3

CONC M-A = 0.0000E '1

CONC M-X - 4.9999E -3

OK

 

 

 

 

 

 

 

215

Figure 5.9 Separation of nucleotides in pH 9 phosphate buffer solution.
Solute IdentIfIcatIon and conditions as given in Figure 5.6.

 

 

 

216
Figure 5.9a

 

 

 

 

 

 

 

 

pH 9
0 5 10 15 20
1,3,2
4
l' 7553
0 5 10 15 20
1,3,2 4
5
7 63
0 5 10 15 20

 

TIME (min)

 

 

217
Figure 5.9b

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes a 12.500

pH = 9.000 Correction Factor, in pH units a .3900
IONIC STRENGTH, in moles/liter - 1.2484E -2

BUFFER CONCENTRATION, in moles/liter - 2.507SE -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC

TOTAL LENGTH, in cm I 112.15 HEIGHT DIFFERENCE, in cm - 2.00
DETECTOR LENGTH, in cm = 43.40 INJECTION TIME, in sec - 60.00

I. D., in micrometers - 75.50 HYDRODYNAMIC VELOCITY, in cm/s = 3.55E -3

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2

AMP - 7.51 .127 -.3180E -3 9.01E -3 5.58E 4 .83
GMP 8 7.61 .129 -.324OE -3 9.14E -3 5.55E 4 .80
CMP - 7.72 .131 -.3296E -3 9.26E -3 5.53E 4 2.28
UMP 8 8.02 .137 -.3453E -3 9.63E -3 5.47E 4 11.05
GDP = 9.73 .171 -.4149E -3 1.17E -2 5.17E 4 .49
ADP = 9.81 .173 -.4178E -3 1.18E -2 5.15E 4 2.83
CDP = 10.32 .183 -.4337E -3 1.24E -2 5.07E 4 1.49
UDP = 10.59 .189 -.4417E -3 1.27E -2 5.02E 4 CR8 = 531.98_
INJECTION ZONE, in c6 = .21 INJ VARIANCE, in cm2 = 3.78E -3
DETECTOR WINDOW, in cm a .50 DET VARIANCE, in cm2 - 2.08E -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV = -93.49

ZETAZERO, in mV = 26.44

kPOTNa = 2.2347E -1

ELECTROOSMOTIC MOBILITY, in cm2/Vs = 7.4259E -4
ELECTROOSMOTIC VELOCITY, in cm/s = .1681
VOLTAGE, in RV = 25.390

RESISTANCE, in ohm 8 2.0312E 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH - 9.000

IONIC STRENGTH = 1.2484E -2
BUFFER CONCENTRATION = 2.5075E -3
BUFFER CAPACITY - 9.5000E -5
CHARGE CONC - 2.00018 -2
[MJbufter - 5.0001E -3

[M]electr = 5.0004E -3

BUFFER FORMULATION:

CONC M-H3A = 0.0000E -1

CONC M-HZA a 1.4893E -5

CONC M-HA - 2.4926E -3

CONC M-A - 0.0000E -1

CONC M-x - 5.0004E -3

OK

 

 

 

 

 

 

218
Figure 5.9c

i....~—.g———~—-

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes - 12.500

pH - 9.000 Correction Factor, in pH units = .3900
IONIC STRENGTH, in m0138/liter I 1.2484E -2

BUFFER CONCENTRATION, in moles/liter I 2.5075E -3

TYPE OF INJECTION: HYDRODYNAMIC

HEIGHT DIFFERENCE, in cm I 2.00
INJECTION TIME, in sec I 60.00
HYDRODYNAMIC VELOCITY, in cm/s I 3.55E -3

CAPILLARY DIMENSIONS:

TOTAL LENGTH, in cm I 112.15
DETECTOR LENGTH, in cm I 43.40
I. D., in micrometers I 75.50

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2

AMP I 6.42 .107 I.318OE -3 7.70E -3 5.80E 4 .73
GMP = 6.50 .108 -.3240E -3 7.80E -3 5.78E 4 .70
CMP = 6.57 .110 -.3296E -3 7.89E -3 5.77E 4 2.00
UMP I 6.80 .114 -.3453E -3 8.16E -3 5.72E 4 9.56
GDP = 7.99 .137 -.4149E -3 9.598 -3 5.48E 4 .42
ADP I 8.05 .138 -.4178E -3 9.66E -3 5.47E 4 2.41
CDP = 8.39 .144 -.4337E -3 1.01E -2 5.40E 4 1.26
UDP = 8.58 .148 -.4417E -3 1.03E -2 5.37E 4 CR5 = 2318.49_
INJECTION ZONE, in cm I .21 INJ VARIANCE, in cm2 I 3.78E -3

DETECTOR WINDOW, in cm I .50 DET VARIANCE, in cm2 I 2.08E -2

FLOW CHARACTERISTICS (experimental values):
ELECTROOSMOTIC MOBILITY, in cm2/Vs I 8.1027E -4
ELECTROOSMOTIC VELOCITY, in cm/s I .1850
VOLTAGE, in RV = 25.606

RESISTANCE, in ohm = 2.0485E 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH I 9.000

IONIC STRENGTH I 1.2484E -2
BUFFER CONCENTRATION = 2.5075E -3
BUFFER CAPACITY I 9.5000E -5
CHARGE CONC I 2.0001E -2
[Mjbuffer I 5.0001E -3

[M]electr I 5.0004E -3

BUFFER FORMULATION:

CONC M-H3A I 0.0000E -1

CONC M-HZA I 1.4893E -5

CONC M-HA I 2.4926E -3

CONC M-A I 0.0000E -1

CONC MIX I 5.0004E -3

ox

 

 

 

219

Figure 5.10 Separation of nucleotides in the vicinit of the optimum conditions:
pH 10, Ionic strength of 12.5 mM, bu er concentration of 2.4 mM.
and constant-current conditions of 12.5 uA. Solute identification
and electropherogram specification as given in Figure 5.6.

 

 

 

220
Figure 5.10a

 

 

 

 

 

 

 

 

 

 

pH 10

5 10 15 20

12

3 ‘53
7
5 10 15 20
12
456 7
a

5 10 15 20

 

TIME (min)

 

 

 

 

 

221
Figure 5.10b

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:
, in microamperes - 100
pH = 10.000 Correction Factor, in pH units - .0850
IONIC STRENGTH, in moles/liter - 1. 2475B -2
BUFFER CONCENTRATION, in moles/liter - 2. 4355E -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in Cm = 112.15 HEIGHT DIFFERENCE, in cm I 2. 00
DETECTOR LENGTH, in cm I 43.40 INJECTION TIME, in sec = 60 .00
I. D., in micrometers = 75.50 HYDRODYNAMIC VELOCITY, in cm/s = 3. 55E -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
AMP = 7.58 .129 -.3186E -3 9.10E -3 5.56E 4 1.61
CMP = 7.79 .133 -.3300E -3 9.35E -3 5.52E 4 8.85
GMP = 9.08 .158 -.3885E -3 1.09E -2 5.28E 4 3.94
UMP = 9.73 .171 -.4121E -3 1.17E -2 5.17E 4 1.09
ADP = 9.92 .175 -.4184E -3 1.19E -2 5.13E 4 2.82
CDP = 10.43 .186 -.4343E -3 1.25E ‘2 5.05E 4 5.65
GDP = 11.54 .209 -.4640E -3 1.38E -2 4.87E 4 6.21
UDP = . .239 -.4940E -3 1.55E -2 4.67E 4 CRS = 5.31
INJECTION ZONE, in cm = .21 INJ VARIANCE, in cm2 = 3.78E -3
DETECTOR WINDOW, in on = .50 DET VARIANCE, in Cm2 = 2.08E -2

FLOW CHARACTERISTICS:

ZETA POTENTIAL, in mV = -93.49

ZETAZERO, in mV = 26.44

kPOTNa = 2.2347E -1

ELECTROOSMOTIC MOBILITY, in cm2/Vs = 7.4262E -4
ELECTROOSMOTIC VELOCITY, in cm/s = . 667
VOLTAGE, in RV = 25.170

RESISTANCE, in ohm = 2.0136E 9

BUFFER CHARACTERISTICS (cone in moles/liter):
H = 10. 000

IONIC STRENGTH = 1. 2475B -2
BUFFER CONCENTRATION— 2.4355E -3
BUFFER CAPACITY = 3.1139E -4
CHARGE CONC = 2.0003E —2
[M)buffer = 5.0008E —3

[MJeleCtr = 5.0007E -3

BUFFER FORMULATION:

CONC M-H3A = 0.0000E -1

CONC M-HZA = 0.0000E -1

CONC M-HA = 2.3057E —3

CONC M-A = 1.2984E -4

CONC M-x = 5.0007E -3

OK

 

 

 

222
Figure 5.10c

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microamperes - 12.500

pH - 10.000 Correction Factor, in pH units - .0850
IONIC STRENGTH, in moles/liter - 1.2475E -2

BUFFER CONCENTRATION, in moles/liter - 2.4355E -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC

TOTAL LENGTH, in cm - 112.15 HEIGHT DIFFERENCE, in cm 8 2.00
DETECTOR LENGTH, in cm 3 43.40 INJECTION TIME, in sec - 60.00

I. D., in micrometers = 75.50 HYDRODYNAMIC VELOCITY, in cm/s a 3.55E -3

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2

AMP I 6.38 .106 -.3186E -3 7.65E -3 5.81E 4 1.39
CMP c 6.53 .109 -.3300E -3 7.83E -3 5.78E 4 7.57
GMP - 7.41 .125 -.3885E -3 8.89E -3 5.59E 4 3.32
UMP a 7.84 .134 -.4121E -3 9.41E -3 5.51E 4 .91
ADP = 7.96 .136 -.4184E -3 9.56E -3 5.49E 4 2.35
CDP = 8.29 .142 -.4343E -3 9.95E -3 5.42E 4 4.65
GDP = 8.99 .156 -.464OE -3 1.08E -2 5.3OE 4 5.03
UDP = 9.82 .173 -.4940E -3 1.18E -2 5.15E 4 CR8 = 19.52_
INJECTION ZONE, in cm = .21 INJ VARIANCE, in cm2 8 3.78E -3
DETECTOR WINDOW, in cm - .50 DET VARIANCE, in cm2 = 2.08E -2

FLOW CHARACTERISTICS (experimental values):
ELECTROOSMOTIC MOBILITY, in cm2/Vs = 8.1954E -4
ELECTROOSMOTIC VELOCITY, in cm/s = .1851
VOLTAGE, in RV = 25.330

RESISTANCE, in ohm = 2.0264E 9

BUFFER CHARACTERISTICS (cone in moles/liter):
pH 8 10.000

IONIC STRENGTH = 1.2475E -2
BUFFER CONCENTRATION - 2.4355E -3
BUFFER CAPACITY = 3.1139E -4
CHARGE CONC = 2.0003E -2
[M]buffer = 5.0008E -3

[M]e1ectr = 5.00078 -3

BUFFER FORMULATION:

CONC M-H3A - 0.0000E -1

CONC M-HZA = 0.0000E -1

CONC M-HA = 2.3057E -3

CONC H-A 8 1.2984E -4

CONC M-X - 5.0007E -3

OK

 

 

 

 

 

223

Figure 5.11 Separation of nucleotides in pH 11 phosphate buffer solution.
Solute identification and conditions as given in Figure 5.6.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

224
Figure 5.11a
‘ H 1
1 5:3 p 1
7
1o 15 20
12
136‘
a
10 15 20
12
5554
8
1o 15 20
TIME (min)

 

 

225
Figure 5.11b

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in omicroamperes - 12. 50 0

pH - 11.00 Correction Factor, in pH units - .0775
IONIC STRENGTH, in moles/liter - 1. 2156B -2

BUFFER CONCENTRATION, in moles/liter - 1. 3674E -3

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in cm = 112.15 HEIGHT DIFFERENCE, in cm = 2.00
DETECTOR LENGTH, in on = 43.40 INJECTION TIME, in sec = 60.00
I. D., in micrometers = 75.50 HYDRODYNAMIC VELOCITY, in cm/s = 3.55E -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2
AMP - 8.22 .141 -.3196E -3 9.87E -3 5.44E 4 1.60
CMP = 8.45 .146 -.3310E -3 1.01E -2 5.39E 4 13.77
ADP = 10.78 .193 -.4200E -3 1.29E -2 4.99E 4 .37
GMP = 10.85 .195 -.42215 '3 1.30E -2 4.98E 4 2.43
CDP = 11.34 .205 -.4358E -3 1.36E ‘2 4.90E 4 2.05
UMP = 11.77 .214 -.4470E -3 1.41E -2 4.84E 4 7.48
GDP = 13.52 .252 -.4852E -3 1.62E -2 4.59E 4 6.38
= 15. .292 -.5145E -3 1.83E -2 4.37E 4 CR5 = 49.90_
INJECTION ZONE, in cm = .21 INJ VARIANCE, in cm2 = 3.78E -3
DETECTOR WINDOW, in cm = .50 DET VARIANCE, in cm2 = 2.082 -2
FLOW CHARACTERISTICS:
ZETA POTENTIAL, in mV = -93.47

ZETAZERO, in mV = 26.44

kPOTNa = 2.2347E -1

ELECTROOSMOTIC MOBILITY, in cm2/Vs = 7.4244E -4
ELECTROOSMOTIC VELOCITY, in cm/s = .1541
VOLTAGE, in kV = 23.273

RESISTANCE, in ohm = 1.8618E 9

BUFFER CHARACTERISTICS (conc in moles/liter):
pH = 11.000

IONIC STRENGTH = 1.2156E -2
BUFFER CONCENTRATION = 1.8674E -3
BUFFER CAPACITY = 2.889OE -3
CHARGE CONC = 2.0000E -2
[M]buffer - 5.0000E -3

[M]electr = 5.00023 -3

BUFFER FORMULATION:

CONC M-H3A = 0.0000E -1

CONC M-HZA a 0.0000E -1

CONC M-HA = 6.0224E -4

CONC M-A I 1.2652E -3

CONC M-X - 5.0002E -3

OK

 

 

 

 

 

226
Figure 5.11c

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:

CURRENT, in microampores - 12.500

pH - 11.000 Correction Factor, in pH units - .0775
IONIC STRENGTH, in moles/liter I 1.2156E -2

BUFFER CONCENTRATION, in moles/liter - 1.86748 -3

CAPILLARY DIMENSIONS: - TYPE OF INJECTION: HYDRODYNAMIC

TOTAL LENGTH, in cm I 112.15 HEIGHT DIFFERENCE, in cm I 2.00
DETECTOR LENGTH, in cm I 43.40 INJECTION TIME, in sec - 60.00

I. D., in micrometers I 75.50 HYDRODYNAMIC VELOCITY, in cm/s I 3.55E -3

ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
in cm2/Vs in cm2

AMP I 7.18 .121 -.3196E -3 8.62E -3 5.64E 4 1.40
CMP I 7.35 .124 -.3310E -3 8.82E -3 5.61E 4 11.90
ADP I 9.03 .157 -.4200E -3 1.088 -2 5.29E 4 .31
GMP = 9.08 .158 -.4221E -3 1.09E -2 5.28E 4 2.06
CDP = 9.41 .165 -.4358E -3 1.13E -2 5.22E 4 1.73
UMP I 9.70 .171 -.4470E -3 1.16E -2 5.17E 4 6.23
GDP = 10.83 .194 -.4852E -3 1.30E -2 4.98E 4 5.21
UDP = 11.91 .217 -.5145E -3 1.43E -2 4.82E 4 CR5 I 38.49_
INJECTION ZONE, in cm I .21 INJ VARIANCE, in cm2 I 3.78E -3

DETECTOR WINDOW, in cm I .50 DET VARIANCE, in cm2 I 2.08E -2

FLOW CHARACTERISTICS (experimental values):
ELECTROOSMOTIC MOBILITY, in cm2/Vs I 8.1089E -4
ELECTROOSMOTIC VELOCITY, in cm/s I .1658
VOLTAGE, in RV I 22.931

RESISTANCE, in ohm I 1.8345E 9

BUFFER CHARACTERISTICS (can; in moles/liter):
pH = 11.000

IONIC STRENGTH I 1.2156E -2
BUFFER CONCENTRATION I 1.8674E -3
BUFFER CAPACITY I 2.8890E -3
CHARGE CONC I 2.0000E -2
[M]buffer = 5.00002 -3

[M1electr I 5.0002E -3

BUFFER FORMULATION:

CONC M-H3A I 0.0000E -1

CONC M-HZA I 0.0000E ~1

CONC M-HA I 6.0224E -4

CONC M-A I 1.2652E -3

CONC M-X I 5.0002E -3

OK

 

 

 

 

 

 

 

 

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228
0.6 and 1.7 %, respectively, which are comparable to those obtained previously
in the validation studies (Chapter 4, Tables 4.1 to 4.4). Although the zone
variance is less accurately predicted, it has no influence on the migration time.
The electroosmotic. mobility, which affects the migration time of all solutes in a
similar manner (Equation [43]), is significantly lower than the experimentally
measured value (9.4%). Changes in the electroosmotic flow may arise from
alteration in either the buffer composition or the capillary surface. If the prepared
buffer differed appreciably from the recommended formulation, the resulting
solution conductance would also differ and a larger discrepancy in the predicted
voltage would be expected. Therefore, it seems more likely that the capillary
surface has been altered, possibly due to the wash with alkaline solution over an
extended period of time (vide Chapter 3). However, the error introduced by
changes in the electroosmotic mobility is not sufficiently large to compromise the
search for the optimum conditions. When the experimentally measured value of
the electroosmotic mobility is used as an input parameter, the predicted
electropherogram is in very good agreement with the experimental results in all

respects (Figures 5.6 to 5.11, bottom).

5.3 Conclusions

The electrophoretic behavior of 5'-mono and diphosphate nucleotides was
characterized in phosphate buffer solutions, in the range of pH from 5 to 11. A
new set of dissociation constants and individual electrophoretic mobilites,
complementary to the literature data, was generated based on a computer
methodology developed in Chapter 4. The separation of nucleotide mixtures

was studied as a means to validate the computer routine developed to optimize

 

.—

 

 

 

 

 

229
separations in capillary zone electrOphoresis. The program provided accurate
predictions of the separation characteristics in the entire pH range studied, from

6 to 11 as well as a good estimate of the optimum conditions.

 

 

 

230

5.4 References

10.

11.

12.

13.

14.
15.
16.
17.

18.

Lehninger, A. L. Principles of Biochemistry; Worth Publishers, lnc.: New
York, 1993.

De, B. E. A.; Pattyn, G.; David, F.; Sandra, P. J. High Resolut.Chromatogr.
1991, 14, 627—629.

Ng, M.; Blaschke, T. F.; Arias, A. A.; Zare, R. N. Anal. Chem. 1992, 64
1682-1684.

Saenger, W. Principles of Nucleic Acid Structure; Springer-Verlag: New
York, 1984.

Bloomfield, V. A.; Crothers, D. M.; Tinoco, l., Jr. Physical Chemistry of
Nucleic Acids; Harper & Row: New York, 1974.

Towsend, L. B. Chemistry of Nucleosides and Nucleotides; Plenum Press:
New York, 1988.

Chargaff, Es, Davidson, J. N. The Nucleic Acids - Chemistry and Biology;
Academic Press Inc, Publishers: New York, 1955.

Dawson, R. M. C.; Elliott, D. C.; Elliott, W. H.; Jones, K. M. Data for
Biochemical Research; Clarendon Press: Oxford, 1986.

Hirokawa, T.; Kobayashi, 8.; Kiso, Y. J. Chromatogr. 1985, 318, 195-210.
ngrdlow, H.; Wu, 8.; Harke, H.; Dovichi, N. J. J. Chromatogr. 1990, 516
- 7.

Tsuda, T.; Nakagawa, G.; Sato, M.; Yagi, K. J. Appl. Biochem. 1983, 5,
330-336.

Cohen, A. 8.; Terabe, 8.; Smith, J. A.; Karger, B. L. Anal. Chem. 1987, 59,
1021-1027.

RowéKé H.; Griest, W. H.; Maskarinec, M. P. J. Chromatogr. 1987, 409,
93- 0 .

Kuhr, W. G.; Yeung, E. 8. Anal. Chem. 1988, 60, 2642-2646.
Gross, L.; Yeung, E. 8. J. Chromatogr. 1989, 480, 169-178,

Pentoney, 8. L.; Zare, R. N.; Quint, J. F. Anal. Chem. 1989, 61, 1642-1647.

Wang, T.; Hartwick, R. A.; Champlin, J. J. Chromatogr. 1989, 462, 147-
54

Milofsky, R. E.; Yeung, E. 8. Anal. Chem. 1993, 65, 153-157.

 

 

 

 

 

 

19.

20.

21.

231
Devore, J. L. Probability and Statistics for E

. ncgineering and the Sciences;
Brooks/Cole Publishing Company: Monterey, A, 1987.

Robinson, R. A.; Stokes, R. H. Electrolyte Solutions - The Measurement
and Interpretation of Conductance, Chemical Potential and Diffusion in

Solutions of Simple Electrolytes, Butterworths Scientific Publications:
London,1959.

Bier, M., Ed.; Electrophoresis - Theory, Methods and Applications;
Academic Press lnc.: New York, 1959.

 

 

 

 

 

CHAPTER 6

APPLICATION OF THE OPTIMIZATION PROGRAM TO THE
SEPARATION OF TETRACYCLINE ANTIBIOTICS

6.1 Introduction

Tetracyclines are a group of clinically important natural products and
semi-synthetic derivatives, characterized by a broad-spectrum activity against
pathogenic microorganisms}:2 In addition to their extensive therapeutical use,
these drugs have found application in the preservation of harvested fruits and
vegetables, extermination of insect pests, and as animal feed supplement3'5
All members of the group possess closely related chemical structures,
derived from a common hydronaphthacene nucleus containing four fused
rings}.5 as shown schematically in Figure 6.1. The presence of multiple
functional groups with acid-base properties confers an amphoteric character to
the tetracyclines, most of which exhibit an lsoelectric point between 4 and 6.5
The same structural features account for their appreciably high solubility in polar
organic solvents and water, which is enhanced at low pH. These compounds
undergo complex formation and precipitation reactions with a variety of metallic
cations, among which the complexes with calcium, magnesium, and aluminum
have been particularly well characterized.5
Commercially available tetracycline and tetracycline derivatives may
contain significant amounts of degradation productsfi’8 These contaminants are
often isomers with only minor structural differences from the original precursor,

The most important impurities of tetracycline (TC) are the products of
232

 

 

 

 

 

 

Figure 6.1

233

Chemical structures of common tetracycline antibiotics.

 

234

Figure 6.1

 

 

 

 

 

 

 

 

 

 

R2 R3 R4 H N ( CH3)2
009001 ,,
N
H / \H
NAME SYMBOL R1 R2 R3 R4
TETRACYCLINE TC H OH CH3 H
CHLORTETRACYCLINE CTC Cl OH CH3 H
DEMECLOCYCLINE DMCC Cl OH H H
OXYTETRACYCLINE OTC H OH CH3 OH
DOXYCYCLINE DOC H H CH3 OH
METHACYCLINE MTC H = CH2 OH
MINOCYCLINE MNC N(CH3)2 H H H

 

 

 

 

 

 

 

 

 

 

 

 

 

235

epimerization (epiTC), dehydration (anhydroTC), and combined epimerization-
dehydration (epianhydroTC) reactions, as shown schematically in Figure 6.2.
EpianhydroTC has been implicated in several toxic manifestations such as renal
dysfunction caused by ingestion of degraded tetracycline products.1

The analytical methodology applied to tetracyclines has supported
microbiological production, synthetic and pharmacological studies, and clinical
practice. Several techniques have been employed,2v5v9 including microbiological
assays,5 spectrophotometry,1°'12 phosphorimetry,13 chemiluminescence,“ as
well as flow injection methods.15 Many of these methods do not provide a
precise and accurate means to determine the tetracycline content in the
presence of known degradation products. In particular, the microbiological
methods lack specificity, since the total drug activity is estimated without
correlation to the chemical structure. Also, the presence of metabolites with no
antimicrobial activity is disregarded. Among the chromatographic techniques,
thin-layer, paper, and column chromatography followed by UV spectrometric
assay have been used extensively.16'22 However, even these methods have
proven to be laborious, often requiring extensive sample pretreatment, and
generally exhibit poor sensitivity and precision. Gas chromatographic methods,
although fast and specific, require derivatization of the polar functional groups
under carefully controlled conditions. This limits its application to antibiotics
which are termally stable after derivatization. Liquid chromatography, specially
the reversed-phase and ion-exchange modes, has been the method of choice for
tetracyclinesfii'323'30 Some of these procedures, however, use solvent systems
at relatively low pH at which the tetracyclines are known to epimerize and many
silica-based stationary phases are unstable. Other methods employ mobile
phases containing high salt concentration which, in combination with the low pH,

can be deleterious to the life of the column. Moreover, because of the structural

 

 

 

 

 

 

236

Figure 6.2 Epimerization and dehydration pathways for the decomPosmon Of

tetracycline.

 

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Figure 6.2

 

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238
similarities of the tetracyclines and their potential contaminants, complete
resolution of the compounds is not usually achieved.

The physicochemical properties of tetracyclines, particularly their ionic
nature, multiple ionization sites and water solubility, make them suitable for
electrophoretic analysis. Capillary zone electrophoresis (CZE) has gained
increased acceptance for the analysis of pharmaceuticals,9:31'33 as a result of
relevant features such as high efficiency, high speed, full automation, and
compatibility with a variety of detection schemes. This chapter explores CZE as
an attractive alternative to the available analytical methodologies for
tetracyclines. The computer optimization routine developed in Chapter 4 is used
here to assess theseparation of seven naturally occuring and synthetically
produced tetracyclines. Based on this program, an optimized analytical
procedure is developed and applied to the quantitation of tetracyclines in

comercially available pharmaceutical drugs.

6.2 Results and Discussion

Characterization of the Electrophoretic Behavior of Tetracyclines. In order
to characterize the electrophoretic behavior of tetracyclines knowledge of the
dissociation constants and individual species electrophoretic mobility is required.
Dissociation constants of very few tetracyclines are available in the literature.5
After an initial misassigment,34 the attribution of pKa values to specific functional
groups in the molecule was reevaluated35 and is now generally accepted. The
most acidic group of tetracycline, with a typical pKa value of about 3.3,
corresponds to the tricarbonyl system in ring A (Figure 6.1). The second

dissociation constant, with a pKa value of about 7.6, is assigned to the

 

 

 

239

dicarbonyl system between rings B and C. The third constant, with a pKa value
of about 9.7, is attributed to the dimethylamino functionality in ring A. The
highest dissociation constant, with a pKa of 10.7, was recently related to the
phenolic group in ring D35 I

The electrophoretic determination of dissociation constants and
electrophoretic mobilities is based on experimental measurements of migration
time as a function of pH, as described in section 4.2. Table 6.1 presents the
constants corrected to the condition of infinite dilution, for seven members of the
tetracycline group. The agreement between these values and those previously
reported in the literature (vide supra) is very good. The data of Table 6.1 were
used to calculate the effective mobility as a function of pH (Equation [414]),
which is displayed in Figure 6.3, for selected mixtures of tetracyclines containing
four, five, and seven compounds. An effective mobility curve versus pH is a
valuable tool for the preliminary assessment of a separation, because it can
' indicate regions of pH where the mobilities differ and the separation is likely to
be achieved. As observed from Figure 6.3, the electrophoretic behavior of
tetracyclines is quite similar in the entire pH range studied and the separation
appears to be very difficult. Even for the selected mixtures containing fewer
tetracyclines, differences in effective mobility occur at very narrow pH regions
and a procedure able to optimize the conditions for the separation is highly

desirable.

Optimization of the Separation of Tetracyclines. The separation of
tetracyclines was approached by the computer optimization routine described in
Chapter 4. The separation was optimized under constant-current conditions,
with hydrodynamic injection, for a capillary of fixed dimensions, and the detector

positioned at a known distance from the capillary inlet. In the search of optimum

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Figure 6.3 Effective mobility curves as a function of pH for selected mixtures
of tetracyclines at 25° C and infinite dilution. (a) CTC, DMCC.
DOC, and OTC. (b) CTC, DMCC, MNC, MTC, and TC. (0) CTC,
DMCC, DOC, MNC, MTC, OTC, and TC.

 

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242
Figure 6.3a

 

 

 

 

 

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conditions, the current was varied from 5.00 to 22.50 uA with 0.25 increments,
the pH was varied from 4.0 to 11.0 with increments of 0.10, the ionic strength
from 5.00 to 22.50 mM with 0.25 mM increments, and the buffer concentration
from 0.50 to 11.00 mM with 0.15 mM increments. The surface maps and
correspondent contour plots presented in Figures 6.4 and 6.5 allow the visual
inspection of the CRS response function within the defined range of parameters.
A minimum value of CR8 occurs between pH 7 and 8. In this region, the CRS
function decreases rapidly as the current approaches 20 NA. The function
behaves similarly when the buffer concentration approaches 4 mM. In contrast,
the ionic strength surface map is composed of several very sharp minima in the
region between 15 and 20 mM, which indicates that this variable must be
controlled carefully.

The separation of seven tetracyclines in the vicinity of the optimal
conditions, is demonstrated in Figure 6.6. Even though it is possible to identify
unequivocally all components of the mixture, complete separation of the seven
tetracyclines is not accomplished. For comparison, other mixtures containing
fewer tetracyclines are also presented in Figure 6.6. Regardless of the partial
resolution of these mixtures, the analysis of tetracyclines by capillary
electrophoresis represents an improvement over the available methodology for
tetracycline, since there is a gain in efficiency (about 3 x 104 theoretical plates
per meter) and analysis time (analysis is performed in less than 6 min).
Reversed-phase liquid chromatographic methods, which are among the most
commonly employed methods for tetracyclines, provide efficiencies in the order
of thOUSands of plates and analysis time as long as 30 min for typical mixtures.2

The program predicts the correct elution order for all tetracyclines, and
provides a reasonable estimate of migration time and peak width. The

agreement between predicted and experimental values for migration time and

 

 

246

Fi ure 6.4 Surface ma s re resentin the separation of tetracyclrnes._ (a)
9 CR8 as a fanctith of pH and applied current w1th constant Ionic
strength of 18 mM and buffer concentration of 4.5 mM. (b) CRSfiaS
a function of pH and ionic strength wrth constant bu er
concentration of 4.5 mM and current of 20 HA. (0) CR8 as t:
function of pH and buffer concentration with constant IOI'llC streng
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C

RS as a function of H and applied current with constant ionic
strength of 18 mM and gutter concentration of 4.5 mM. (B) CRS as
a function of pH and ionic strength With constant buffer
concentration of 4.5 mM and current of 20 pA. C _CRS as a
function of pH and buffer concentration with constant ionic strength
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255
Figure 6.6

 

 

 

 

 

 

 

 

 

 

 

 

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256

peak width .is typically 1.7 % and 23 %, respectively, as demonstrated in Table

6.2.

Decomposition of Tetracyclines. A common concern in the manufacture
industry of tetracycline antibiotics is the control of impurities. Tetracyclines can
degrade through at least four different pathways (epimerization, dehydration,
hydrolysis and oxidation), where epimerization and dehydration are the most
important processes.5 The epimerization of the dimethylamine group in ring A of
tetracycline produces the inactive and non-toxic epitetracycline (Figure 6.2).
Dehydration followed by aromatization of the C-ring give anhydrotetracycline,
which is also inactive and nontoxic. Both epimerization of the
anhydrotetracycline and dehydration of the epitetracycline lead to the formation
of the inactive, but rather toxic epianhydrotetracycline. The kinetics of the
epimerization and dehydration reactions have been extensively studied,5-36‘37
indicating that these processes can be accelerated at very low pH and under
thermal conditions. In Figure 6.7, the electropherogram of a tetracycline sample,
which was previously decomposed by heating under acidic conditions, is
displayed together with the intact standard. The presence of new zones is
clearly visualized in the electropherogram of the decomposed sample,
suggesting the formation of the dehydration and epimerization products.
However, the unequivocal identification of these zones was not possible due to
unavailability of standards. The analysis of a commercially available formulation
of tetracycline is also illustrated in Figure 6.7, for comparison purposes. The
electropherograms indicate the presence of the epitetracycline in the
pharmaceutical formulation, and of anhydrotetracycline in the tetracycline

standard.

 

 

 

257

 

 

 

Table 6.2. Comparison of experimentally determined migration time and base
width of tetracyclines with computer-simulated values in the vicinity
of the optimum conditions (pH 7.5, ionic strength of 18.2 mM, buffer
concentration of 4.3 mM, and constant-current conditions of
20 0A).

SOLUTE MIGRATION TIME (min) WIDTH (min)
EXP CALC" % ERROR* EXP CALC % ERROR+

MNC 5.05 5.03 0.40 0.085 0.098 -15
DOC 5.16 5.14 0.39 0.0679 0.100 —47
TC 5.25 5.24 0.19 0.0807 0.102 -26
OTC 5.41 5.30 2.0 0.0807 0.104 -29
MTC 5.48 5.32 2.9 0.0849 0.104 -22
CTC 5.59 5.46 2.3 0.115 0.107 +7.0
DMCC 5.71 5.49 3.9 0.123 0.108 +12

 

 

 

 

 

 

 

 

*

 

 

calculated from Equation [1] with an experimentally determined
electroosmotic mobility of 6.40 x 10'4 cm2 V'1 3'1.

+ °/o ERROR = 100 (EXP - CALC) / EXP

 

Figure 6.7

258

Identification of tetracycline decomposition products under the
optimized conditions given in Figre 6.6. (Top) TetracyC“?1e
standard. (Middle) Tetracycline standard preViously treated WIth
hydrochloric acid at pH 2, and submitted to 70° C during 1 “-
(Bottom) Hard filled capsule of tetracycline 250 mg (Warner-
Chillcott®).

 

259
Figure 6.7

 

 

TC (standard)

 

TC (after decomposition)

 

 

TC (phannaceutical formulation)

 

 

 

TIME (min)

 

 

 

 

 

 

 

 

 

260

Analysis of Tetracyclines. The analysis of hard filled capsules of tetracycline
was performed with a minimum of 95% recovery in the dissolution process. A
calibration curve of peak height versus concentration with slope of 6.15 x 10‘4
cm M'1, intercept of —1.18 x 10'5 and coefficient of determination equal to
0.9989. A linear range of two orders of magnitude, with a detection limit of 10'5
M at a signal-to-noise ratio?”8 of approximately 3 were obtained. In addition to
tetracycline, other commercially available pharmaceutical counter drugs were
examined, such as' minocycline and doxycycline (expired lot), presenting
comparable degrees of purity.

Among all tetracyclines characterized in this work, chlortetracycline
exhibited the most unusual electrophoretic behavior, as demonstrated in Figure
6.8. The chlortetracycline zone exhibits a marked asymmetry towards a minor
zone which possesses a migration time coincident with that of tetracycline.
Chlortetracycline is known to decompose to tetracycline under mild
conditions.39"‘*1 However, the behavior of chlortetracycline upon the influence of
the electric field suggests that the convertion of chlortetracycline to tetracycline
may be enhanced during the electrophoretic migration. These results indicate
that the use of capillary zone electrophoresis may be impaired as a means to
detect the presence of tetracycline in chlortetracycline pharmaceutical
formulations as well as to monitor the decomposition of chlortetracycline during
storage. It is interesting to observe from the electropherograms of Figure 6.6
that a shift in the baseline occurred during the passage of the solute zones
through the detector. This phenomenon, which deteriorated the resolution of all
solutes to certain extent, can be associated to the presence of chlortetracycline

in these mixtures.

 

 

261

Figure 6.8 Electrophoretic behavior of chlortetracycline under the optimized

conditions of Figure 6.6.

 

 

 

tiled

 

 

 

 

 

 

TIME (min)

262
Figure 6.8
TC
5: -_ fig)
CTC
l I I I I fl
0 3 4 5 6 7

 

 

 

 

 

 

263

6.3 Conclusions

This work characterized CZE as a very resourceful alternative method for
the separation and quantitative analysis of tetracycline, its analogs and common
impurities originated from decomposition. The electrophoretic behavior of seven
members of the group was studied and a complete set of dissociation constants
and individual electrophoretic mobilities derived. The separation of all seven
antibiotics was approached by a computer optimization program which indicated
that the separation can be performed satisfactorily under mild conditions. The
analysis of tetracycline in commercially available pharmaceutical counter drugs
gave a linear range of two orders of magnitude, with a detection limit of 10'5 M

(UV detection) and a signal-to-noise ratio of approximately 3.

 

 

 

 

 

264

6.4 References

15.

16.

17.

18.

19.

Lambert, H. P.; O'Grady, F. W. Antibiotic and Chemotherapy, 6th edition;
Churchill Livingstone: London, 1992.

Aszalos, A. Modern Analysis of Antibiotics, Drugs andthe Pharmaceutical
Sciences, Vol. 27; Marcel Dekker: New York, 1986.

De Leenheer, A. P.; Nelis, H. J. C. F. J. Pharm. Sci. 1979, 68, 999-1002.

Sharma, J. P.; Perkins, E. G.; Bevill, R. F. J. Chromatogr. 1977, 134, 441-
450.

Mitscher, L. A. The Chemistry of the Tetracycline Antibiotics, Medicinal
Research Series, Vol. 9; Marcel Dekker: New York, 1978.

Hermansson, J.; Andersson, M. J. Pharm. Sci. 1982, 71, 222-229.
Mack, G. D.; Ashworth, R. B. J. Chromatogr. Sci. 1978, 16, 93-101.
Tsuji, K.; Robertson, J. H. J. Pharm. Sci. 1976, 65, 400-404.

Gilpin, R. K.; Pachla, L. A. Anal. Chem. 1993, 65, 117R-132R.
Ping-Kay, H.; Wai-Kwong, F. Analyst 1991, 116, 751-752.

Emara, K. M.; Askal, H. F.; Saleh, G. A. Talanta 1991, 38, 1219-1221.

1Saha, U.; Sen, A. K.; Das, T. K.; Bhowal, S. K. Talanta 1990, 37, 1193-
196.

Duggan, J. X. J. Liq. Chromatogr. 1991, 14, 2499-2525.

Eygopoulos, A. 8.; Calokerinos, A. C. Anal. Chim. Acta 1991, 255, 403-

Alggarthan, A. A.; AI-Tamrah, S. A.; Sultan, S. M. Analyst 1991, 116, 183-

Naidong, W.; Hua, S.; Roets, E.; Hoogmartens, J. J. Planar Chromatogr. -
Mod. TLC 1992, 5, 92-98.

Naidong, W.; Hauglustaine, C.; Roets, E.; Hoogmartens, J. J. Planar
Chromatogr. - Mod. TLC 1991, 4, 63-68.

Naidong, W.; Hua, 8.; Verresen, K.; Roets, E.; Hoogmartens, J. J. Pharm.
Biomed. Anal. 1991, 9, 717-723.

Egg/écs-Hadady, K. J. J. Planar Chromatogr. - Mod. TLC 1991, 4, 456-

 

 

 

 

 

20.

21.

22.

23.

24.

25.

26.
27.
28.
29.

30.

31.

32.

33.

34.

35.

36.
37.

38.

265

Naidong, W.; Geelen, S.; Roets, E.; Hoogmartens, J. J. Pharm. Biomed.
Anal. 1990, 8, 891-898.

Naidong, W.; Cachet, T.; Roets, E.; Hoogmartens, J. J. Planar
Chromatogr. - Mod. TLC 1989, 2, 424-429.

Kahg, J. S.; Ebel, S. J. J. Planar Chromatogr. - Mod. TLC 1989, 2, 434-
43 . -

Khan, N. H.; Wera, P.; Roets, E.; Hoogmartens, J. J. Liq. Chromatogr.
1990, 13, 1351-1374.

Naidong, W.; Roets, E.; Hoogmartens, J. J. Pharm. Biomed. Anal. 1989,
7, 1691 -1703.

Aszalos, A.; Haneke, 0.; Hayden, M. J.; Crawford, J. Chromatographia
1982, 15, 367-373.

Knox, J. H.; Jurand, J. J. Chromatogr. 1979, 186, 763-782.
De Leenheer, A. P.; Nelis, H. J. C. F. J. Chromatogr. 1977, 140, 293-299.
Knox, J. H.; Jurand, J. J. Chromatogr. 1975, 110, 103-115.

White, E. R.; Carrol, M. A.; Zarembo, J. E.; Bender, A. D. J. Antibiotics
1975, 28, 205-214.

Butterfield, A. G.; Hughes, D. W.; Pound, N. J.; Wilson, W. L. Antimicrob.
Ag. Chemother. 1973, 4, 1 1-15.

Grossman, P. D.; Colburn, J. 0., Ed; Capillary Electrophoresis - Theory
and Practice; Academic Press lnc.: San Diego, CA, 1992.

Ackermans, M. T.; Beckers, J. L.; Everaerts, F. M.; Seelen, I. G. J. A. J.
Chromatogr. 1992, 590, 341-353.

Eggkabaugh, M.; Biswas, M.; Krull, I. S. J. Chromatogr.-1991, 549, 357-

Leeson, L. J.; Krueger, J. E.; Nash, R. A. Tetrahedron Letters 1963, 18,
1155-1160. .

Rigler, N. E.; Bag, S. P.; Leyden, D. E.; Sudmeier, J. L.; Reilley, C. N.
Anal. Chem. 1965, 37, 872-875.

Schlecht, K. 0.; Frank, C. W. J. Pharm. Sci. 1975, 64, 352-354.

Hoener, B. A.; Sokoloski, T. D.; Mitscher, L. A.; Malspeis, L. J. Pharm.
Sci. 1974, 63, 1901 -1904.

St. John, P. A.; McCathy, W. J.; Winefordner, J. D. Anal. Chem. 1967, 39,
1495-1497.

 

 

 

 

39.

40.
41.

 

266

Naidong, W.; Roets, E.; Busson, R.; Hoogmartens, J. J. Pharm. Biomed.
Anal. 1990, 8, 881-889.

Sokolic, M.; Filipovic, B.; Pokorny, M. J. Chromatogr. 1990, 509, 189-193.

Ngédong, W.; Roets, E.; Hoogmartens, J. Chromatographia 1990, 30, 105-

 

 

 

CHAPTER 7

SUMMARY AND FUTURE WORK

7.1 Summary

In this work, a systematic approach to the optimization of capillary zone
electrophoresis separations has been devised with the development,
experimental validation, and application of a computer routine. This optimization
program is structured on theoretical models for both electroosmotic and
electrophoretic migration and incorporates a simple rationale for zone
dispersion. The program is able to accommodate different injection methods
and can be used to optimize separations under constant-current or constant-
voltage conditions. In addition to the solute characteristics, variables related to
the buffer composition (pH, ionic strength and concentration), capillary
dimensions (diameter and length) and instrumental parameters (applied voltage
or current) are also utilized by the program. For any given set of conditions, the
solute zone is characterized by its migration time and temporal width. The
migration time of each solute zone is derived from the sum of the solute effective
mobility and the electroosmotic mobility. The temporal width is derived from
contributions to variance resulting from longitudinal diffusion and finite injection
and detection volumes. Resolution between adjacent zones is then estimated
and the overall quality of the separation is assessed by means of an appropriate
response function, such as the chromatographic resolution statistic.1 By
methodically varying the input parameters and evaluating the quality of the

resulting separation, this computer program can be used to predict the

267

 

 

 

 

 

268
experimental conditions required for optimal separation of the solutes.

The mathematical model for electroosmotic migration (Chapter 3) was
developed by taking into consideration the ion-selective properties of silica
surfaces. A study of electroosmotic flow characteristics in solutions of singly
charged, strong electrolytes (NaCI, LiCl, KCI, NaBr, Nal, NaNO3, and NaClO4),
as well as the phosphate buffer system, revealed a linear correlation between
the zeta potential and the logarithm of the cation activity. These results
suggested that the capillary surface behaves as an ion-selective electrode.
Consequently, the zeta potential can be calculated as a function of the
composition and pH of the solution with the corresponding modified Nernst
equation for ion-selective electrodes.2 If the viscosity and dielectric constant of
the solution are known, the electroosmotic velocity can then be accurately
predicted by means of the Helmholtz-Smoluchowski equation.3 The proposed
model for electroosmotic flow has been succcessfully applied to phosphate
buffer solutions in the pH range from 4 to 10, containing sodium chloride from 5
to 15 mM, resulting in approximately 5 % error in the prediction of the zeta
potential. The model for the electrophoretic migration (Chapter 4) is based on
classical equilibrium calculations and requires the knowledge of the dissociation
constants and electrOphoretic mobilities of the solutes under investigation.
When these constants are not available, a numerical evaluation of pKa and
electrophoretic mobilities may be attempted. The conceptual basis of this
procedure was presented in Chapter 4 and verified in Chapters 5 and 6 for the
determination of constants for nucleotides and tetracyclines, respectively.

The overall optimization routine has been experimentally validated with a
mixture of nucleotides in phosphate buffer solutions (Chapter 5). In preliminary
studies, the electrophoretic behavior of the nucleotides adenosine, guanosine,

cytidine and uridine 5'-mono- and di-phosphates was studied in the pH range

 

 

 

 

 

269
from 5 to 11. In final studies, the separation of mixtures of nucleotides was
characterized by the program and contrasted with experimental results. A good
agreement between migration time, order of elution, zone profile and resolution
pattern was obtained for the entire pH range studied.

The optimization program was then applied to study the separation of
tetracycline antibiotics (Chapter 6). The electrophoretic behavior of tetracycline,
chlortetracycline, demeclocycline, oxytetracycline, doxycycline, methacycline,
and minocycline was characterized by measurements of migration time in
phosphate buffer solutions, in the range of pH from 4 to 11. A complete set of
dissociation constants and individual electrophoretic mobilities was derived
numerically for the'optimization program. The computer routine was then
employed to determine the experimental conditions for the optimal separation of
all seven antibiotics. In the vicinity of the optimum, baseline resolution was not
achieved for separation of all solutes, however, the separation can be performed
satisfactorily under the following experimental conditions: pH 7.5 phosphate
buffer solution, with 18.2 mM ionic strength, and 4.3 mM concentration, under
constant-current conditions of 20 uA. A common concern in the manufacture of
tetracyclines is the control of impurities resulting from decomposition. The
treatment of a tetracycline standard solution, under acidic conditions and
prolonged heating, generated dehydration and epimerization products, which
were easily distinguished from the standard zone. The analysis of tetracycline,
minocycline, and doxycycline was performed in commercially available
pharmaceutical drugs with a minimum of 95 % recovery. A calibration curve of
peak height versus concentration with slope of 6.15 x 10‘4 M/cm, intercept of
-1.18 x 10'5 M, and coefficient of determination equal to 0.9989 gave a linear
range of two orders of magnitude for tetracycline, with a detection limit of 10‘5 M

(UV detection at 260 nm) and a signal-to-noise ratio of approximately 3. Among

 

 

 

 

f “ fim‘z‘f ’

 

270
all the antibiotics studied, chlortetracycline presented the most unusual
behavior. The asymmetry of the zone suggested its conversion to tetracycline
during the electrophoretic measurement. This result may impair the
identification of tetracycline as an impurity in chlortetracycline formulations.

The computer optimization routine has proven to be a valuable tool to
study the separation of complex mixtures. It represents a simple but reliable
approach to electrophoretic separations, based on physically meaningful models
and thorough consideration of the variables that influence the migration
processes. Furthermore, this optimization routine is easily implemented on

personal computers and is instructive from a pedagogical point of view.

7.2 Future Work

According to Braun and Nagydiosi-Rozsa,4 who evaluated the growth of
capillary electrophoresis from the Science Citation lndex® database, the
technique seems to have reached a stage of maturity. Yet, a rich variety of
separation mechanisms and detection schemes have presently been under
development5'7 Capillary zone electrophoresis differs from the other modes of
electrophoresis (vide Chapter 1) in an important respect: there is no secondary
mechanism, such as partition into micelles or sieving through a gel framework,
contributing to the separation selectivity. Indeed, selectivity in capillary zone
electrophoresis separations relies exclusively on intrinsic differences in the
solute mobility. Perhaps the only means to manipulate the solute mobility,
without introducing a secondary phase to the separation, is to alter the chemical
and physical properties of the solution. In this context, changes in the buffer pH,

concentration, and ionic strength}.9 type and concentration of an inert

 

 

 

271
electrolyte or organic additive,1°'13 as well as changes in temperature7»14 have
all been demonstrated to affect direct or indirectly the solute mobility.

An alternative approach to influence the solute mobility is by
complexation with an appropriate chelating agent. _By incorporating a chelating
agent in the buffer solution, not only the solute mobility can be altered but also
the detectability may be enhanced due to the fact that many of these complexes
are chromophores. Many solutes of biomedical importance are known to form
stable complexes with a variety of metallic cations. The very analytes used in
this work can serve as examples: magnesium-nucleotide complexes15 and
calcium-tetracycline complexes16 are well characterized in the literature. In fact,
the separation of nucleotides in the presence of magnesium salts has been
attempted.17 However, this approach was based on trial-and-error
experimentation and resulted in a complicated procedure for the separation.
Therefore, a systematic approach to the electrophoretic separation of solutes
that include complexation equilibrium in parallel to the acid-base equilibrium
could find many applications in biotechnology.

With this purpose, minor modifications of the computer optimization
program developed in this work would be required. The electrophoretic mobility
subroutine must be expanded to include the new equilibrium stages. Preliminary
evaluation of the solute equilibria is required with the determination of both
dissociation and complexation constants. Then, the electrophoretic behavior of
the analyte in buffer solutions containing the chelating agent must be
characterized as a means to determine the solute individual mobility. The
number of species to be analysed may increase considerably, depending on the
number of protonation sites of the solute and the number of complexes formed
with the chelating agent. With knowledge of the dissociation constants,

complex-formation constants, and the electrophoretic mobility of individual

 

 

 

 

 

272

species, the effective mobility of the solute can then be calculated. The content
of chelating agent in the buffer solution is now an additional variable that can be
optimized.

Another complement of this work would be a more thorough
understanding of the surface conductance phenomenon. In the past few years,
the tendency towards performing separations in small-diameter capillaries (5 —
10 um has increased significantly as a means to enhance separation efficiency
and to accommodate sample availability?”7 Surface conductance may be
critical in such small-diameter capillaries.3 In this work, surface conductance
has been evaluated for 75 um capillaries, 100 cm long and the corrections to the
prediction of voltage resulting from this study are restricted to capillaries of these
dimensions. Therefore, with the characterization of the surface conductance in
other bore capillaries, the capillary diameter and lengthcould be used as
variables for optimization purposes.

Temperature is another interesting parameter to study because of its
effect on electrophoretic separations. The detrimental effect of temperature
gradients arising from Joule heating on the separation efficiency is well
characterized.5'7 The description of the intracapillary temperature profile is also
relatively well stated.5 However, in spite of previous efforts,7'14 the effect of
temperature on the solute mobility and how resolution, efficiency, and analysis
time can benefit from this effect is a subject that needs better understanding.

In conclusion, the optimization program developed in this work is a
valuable tool for the assessment of electrophoretic separations and clearly can

be expanded to serve many applications based on free solution as well as gel

and micellar capillary electrophoresis.

 

 

 

273

7.3 References

10.

11.

12.
13.
14.

 

15.

16.

17.

Schlabach, T. D.; Excoffier, J. L. J. Chromatogr. 1988, 439, 173-184.

Bard, A. J.; Faulkner, L. R. Electrochemical Methods - Fundamentals and
Applications; John Wiley & Sons: New York, .1980.

Hiemenz, P. C. Principles of Colloid and Surface Chemistry, 2nd ed.;
Marcel Dekker: New York, 1986.

Braun, T.; Nagydiési-Rozsa, S. Trends Anal. Chem. 1991, 9, 266-268.

Grossman, P. D.; Colburn, J. C., Ed; Capillary Electrophoresis - Theory
and Practice; Academic Press lnc.: San Diego, CA, 1992.

Kuhr, W. G.; Monnig, C. A. Anal. Chem. 1992, 64, 389R-407R.
McLaughlin, G. M.; Nolan, J. A.; Lindahl, J. L.; Paimieri, R. H.; Anderson,
K. W.; Morris, S. C.; Morrison, J. A.; Bronzert, T. J. J. Liq. Chromatogr.
1992, 15, 961-1021.

Vindevogel, J.; Sandra, P. J. Chromatogr. 1991, 541 , 483-488.

VanOrman, B. B.; Liversidge, G. G.; McIntire, G. L.; Olefirowicz, T. M.;
Ewing, A. G. J. Microcol.,Sep. 1990, 2, 176-180.

Atamna, l. 2.; Metral, C. J.; Muschik, G. M.; lssaq, H. J. J. Liq.
Chromatogr. 1990, 13, 2517-2527.

Atamna, I. Z.; Metral, C. J.; Muschik, G. M.; lssaq, H. J. J. Liq.
Chromatogr. 1990, 13, 3201 -3210.

Green J. 6.; Jorgenson, J. W. J. Chromatogr. 1989, 478, 63-70.
Fujiwara, 8.; Honda, S. Anal. Chem. 1987, 59, 487-490.

Kurosu, Y.; Hibi, K.; Sasaki, T.; Saito, M. J. High Resol. Chromatogr.
1991, 14, 200-203.

Lehninger, A. L. Principles of Biochemistry; Worth Publishers, lnc.: New
York, 1993.

Mitscher, L. A. The Chemistry of the Tetracycline Antibiotics, Medicinal
Research Series, Vol. 9; Marcel Dekker: New York, 1978.

Nukatsuka, |.; Yoshida, H. J. Chromatogr. 1982, 237, 506.

 

 

 

 

 

 

APPENDIX 1

COMPUTER PROGRAM FOR BUFFER PREPARATION

In this appendix, the mathematical basis of the program used for buffer
preparation is discussed. The program BUFFER.PRP, whose copy is attached,
was written in the Forth-based programming language Asyst (version 2.1,
Keithley Asyst, Rochester, NY) to be executed on a 80-286 microprocessor-
based computer. This program performs the calculations required to prepare
buffers at a specified pH given the thermodynamic dissociation constants and
the ionic charge of the individual buffer species. Options are available to
prepare buffers under conditions of constant ionic strength, constant buffer
concentration, and/or constant buffer capacity. This program is based on
classical equilibrium calculations,1'3 with no simplifying assumptions regarding
the relative magnitude of the equilibrium concentration of the buffer species.
The following equilibria define the thermodynamic formation constants (K7), in
successive steps, for a triprotic weak acid system. The numerical values

correspond to the phosphate buffer system.4 Charges are omitted for

 

 

 

 

simplification.
1 [HA]

H + A 9 HA, K1f = = VHA = 2.11 x1012 [A1.1]
Ka3 [A] [HI IA 'YH
1 [H A]

H + HA 9 HZA, K21 = = 2 YHZA = 1.61x107 [A1.2]
Kaz [HA] [H] 'YHA TH
1 [HaAWHsA

 

 

H + “2" <—> “3". K3‘ = 1.45x102 [A13]

Ka1 [“21“] [H] 'YHZA 1H

274

 

 

 

275

where K8 are the dissociation constants and 7, are the activity coefficients of

individual species. The overall formation constants (6“) can be written as:

H + A (—> HA, [31“ = K1f = 2.11X1012 [A1.4]
2 H + A <—-> H2A, [321‘ = K1fo2f =13.40x1019 [A15]
3 H + A <——> H3A, [53f = K1fo2fo3f = 4.93x1021 [A1.6]

The activity coefficients are determined by means of the Davies equation, which

incorporates ionic strength corrections valid up to 0.5 M:1'3

«I'I'

—— — 0.15 I [A17]
1 + ‘5

-109 Y] = 0.509 Ziz [

where Zi is the species charge, and I is the ionic strength. The distribution

function (oq) of each species is defined as:

 

 

 

 

0‘0 = f: (1 + 51f [H] + 32‘ [H12 + 33f [1113f1 [AI-8]
a = [HA] f
1 CT B1 [H] 010 [A19]
a2 — [HZA] [32f [H]2 a0 [A1.10]
CT
013 = [HaA] [33f [H]3 a0 [A1.11]
CT

where CT is the sum of the equilibrium concentrations of all the species of the

buffer system:

CT = [A] + [HA] + [H2A] + [H3A] [A1.12]

 

 

 

 

276
The buffer capacity (BUFCAP) can be calculated by:23

CT [H] KAPPA

(Kai Kaz Kas + [H] K31 K32 "’ [H12 Kai ‘* [H]3)2

 

BUFCAP=2.303 [ +[H]+[OH] ] [A1.13]

where KAPPA is a cluster of constants given by the term:

KAPPA =Ka12 Ka22 Ka3 + 4 [H] Ka12 Ka2 Ka3 + 9 [H12 Ka1 Ka2 Ka3 + [A1-14]
[H12 Ka12 Ka2 1" 4 [H13 Ka1 Ka2 1‘ [H14 Ka1

Equations [A1.1] to [A1.14] convene the basic concepts for the calculation of
buffer formulations. Depending on the pH region and the pKa of the buffer
system, a different combination of the buffer salts must be used to prepare the
buffer solution, such as H3A/H2A, H2AIHA or HAIA. Once the pH is chosen,
BUFFER.PRP solves an appropriate system of equations based on the user
specification of ionic strength, buffer concentration, and/or buffer capacity. This
system of equations is comprised of three out of four distribution functions
(Equations [A18] to [A1.11]), a mass balance equation, an equation for the
hydrogen ion concentration, and an equation for the ionic strength. The sections
that follow define in more detail these equations for any given pH region. A
schematic diagram of the main program (defined as BUF.PREP), and the three
most important subroutines of BUFFER.PRP is shown in Figures A1.1 to A1 .4.
The subroutine BUF.PLOT is designed to output graphically the distribution
functions, buffer concentration, buffer capacity, and cation Concentration (as
p[M]) as a function of pH. The subroutine BUF.LIB is a library of pKa and pr

values for the most commonly used buffer systems.

4%

 

277

Figure A1.1 Schematic representation of the BUFFER.PRP main program.

 

 

 

 

mn:0< O_._.Omn_<m._.m._. ii
ii >t0<¢<0 mun—”_Dm Ome

 

ii_ ._.Oi_n_i_<._.ms_ _

 

mnzo< O_._.Omn:m._. ii

1— 5.E¢<on5m; l 20.252328 mmtam omxi

 

 

w 8.2 0.555 I

1.— 5._n_.ozoou_:m _ I 15235 0.20. omxi

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

«.92 0.5262021 4 5.22152 _
m MA... 895 ofiomaozos 1 :a .N .33
2 m. Fonz-<20
F . .
TE _ _ 945:. _ i 5.526 _ .— ofiomgme _
, _ . p . _ . -

 

ifi ofiomaa _

1+ 0.52.6202 _

r mwmamDm 1—

 

 

 

 

 

 

 

 

 

 

279

Figure A1.2 Schematic representation of the BUFFER.PRP subroutine for
constant ionic strength buffer formulations.

 

 

 

 

. II.— OZOOFZEQ _ilil
_ X§._Dwx_m.<\<In_Dm _i ,

 

 

_ XE._OmX_m.<I\<NIqu _i

 

 

_X§._Dm_x_u_.<NI\<quDm—i

 

 

 

 

 

 

_>._._O<n_<0.u3m _

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_ _ I_XEOZ._DwX_n_.<\<In._Dm _
_ozoomDm _ _ Eo<n_<o.u5m _ ‘ .
. _ , _ , i— XEOZ._OwX_u_.<I\<NIu_Dm _
m Qomamo cozmbcoocoo - w
m M Lotsm Sac. Cram Sac. i— x202._0wx_u_.<~I\<qu5m _
mo _ _ _ , ,
F mg _ , _ o:
_ 6 XS. mm: _
. _ ,
_ 0.._<O.<In_i_< _

 

_

_ HwZOO.IO_O._.m4

_

_ ”_mOo. >._._>_._.o< _
_

_. £9.26 25. Sac. _

 

 

 

 

 

 

[ell

 

281

Figure A1.3 Schematic representation of the BUFFER.PRP subroutine for

constant buffer concentration formulations.

 

[111

282
Figure A1.3

Input Buffer
Concentration

I = 0|
_ I
I ACTIVITY.COEF I

 

 

 

 

 

 

i
I STOICH.CONST I

* , I
I ALPHA.CALC I

 

 

 

—I BUFH3A/H2A.FIXEDCONC I

 

 

—I BUFH2A/HA.FIXEDCONCI

 

 

—I BUFHA/A.F|XEDCONC I

 

 

 

I Calculate II

 

 

 

no ' f I o
——IABS(IZ- I1)< 0.01 I1.

 

yes

 

I BUF.CAPACITY I
‘ I .

 

 

I PRINT.CONC I

 

 

 

283

Figure A1.4 Schematic representation of the BUFFER.PRP subroutine for

constant buffer capacity formulations.

 

 

[91

284
Figure A1.4

 

Input Buffer
Capacity

I=0I

 

 

 

 

I ACTIVITY.COEF I
i

I STOICH.CONST I

 

 

 

i
I ALPHA.CALC I

 

 

—I BUFH3A/H2A.F|XEDCAP I

 

_I BUFH2A/HA.FIXEDCAP I

 

 

-I BUFHA/A.FIXEDCAP I

 

 

 

 

 

 

 

 

 

 

r Calculate II
no i ,
——IABS(Iz- I1)< 0.01 I1fl
. ‘ lye.
I BUF.CONC I
i l
I PRINT.CONC I

 

 

 

 

285
Buffer H3A I H2A. Valid approximately for pH 0 — 4.5 for the phosphate buffer

system. Ci represents the analytical concentration of the buffer species; MX
represents sodium chloride; N represents sodium from the buffer salts; the
subscripts 0 to 3 refers to the buffer species charge.

EQUILIBRIA:

+

H3A (—) H2A
-X X

H2A <—> HA +
-y y

HA<—->A+
—z 2

H20 H OH +
-W W

EQUILIBRIUM CONCENTRATIONS:
[H3A] = CH3A lzN l L x

[H2A] = CHZA lzN I + x — y

[HA] = Y - Z

[A] = z

21 NI ~<I xI

[H] = x + y + z + w
[OH] = W = K«iv/[H]
[N] = CH3A |z3l + CHZA Izzl

[M] = CMX 'le
[X] = CMX Izml
MASS BALANCE:

CT = CH3A IZNI T CH2A IZNI

I = 1/2 [H + OH + (CH3A Izal + CHZA |22|)ZN2 *
(CMX IZx|)ZM2 + (CMX IZMIIZXZ +
(Z3.2 03 + Z22 0‘2 1" Z12 0‘1 + 202 0‘0) CT]

 

286
Buffer HZAI HA. Valid approximately for pH 4.5 — 9.5 for the phosphate buffer

system.

EQUILIBRIA:

H2A (—) HA + H
'Y V y
HA 9 A + H
—z z z
H2A 4' H (—) H3A
—x —x x

H20 (—> OH + H
-W W W

EQUILIBRIUM CONCENTRATIONS:
IHsA] = X

[H2A1= CHzA IZN I - X - Y
[HA]=CHAIZNI +y-z

[A] = z

[H]=—x+y+z+w

[OH] = W = Kw/[H]

IN] = CH2A I22I + CHA IZ1I

[M] = ch lle
[X] = CMX IZMI
MASS BALANCE:

CT = cHZA [le + CHA lle

I = 112 [H + OH + (CHZA IzzI + CHA IZ1IIZN2 +
(CMX lle)zM2 + (CMx IZMIIZXZ +
(232013 + 222 a2 + Z12 011 + Z02 0‘0)(31'1

 

287
Buffer HA / A. Valid approximately for pH 9.5 — 14 for the phosphate buffer

system.

EQUI Ll BRIA:

HA <—) A + H
z —z —2
HA + H <—> HZA
TY "Y Y
H 2A 4' H (—) H 3A
—x —x x

H20<—> OH + H
—w w w

EQUILIBRIUM CONCENTRATIONS:
[H3A] = X

[H2A] = -X + y

[HA]=CHAIZNI —y+z
IAI=CAIZNI —z
[H]=—x—y—z+w

[OH] = w = Kw/H

[N] = CHA lzil + CA IZoI

[M] = CMX szI
[X] = CMx IZMI
MASS BALANCE:

CT = cHA lle + cA lle

I = 1/2 [H + OH + (cHA lz1l + CA Izo|)zN2 +
(CMX IZXIIZMZ + (CMX IZii/iIIZx2 +
(232 013 + 222 012 + 212 011 + 202 010) CT]

 

 

 

 

288

A12 References

1. Butler, J. N.; Ionic Equilibrium - A Mathematical Approach; Addison-
Wesley Publishing Company, Inc: Massachusetts, 1964.

2. Lambert, W. J. J. Chem. Ed. 1990, 67, 150-153.
3. Rilbe, H. Electrophoresis 1992, 13, 81 1-816.
4. Hirokawa, S. Kobayashi and Y. Kiso, J. Chromatogr. 1985, 318, 195-210.

A1.3 BUFFER.PRP Program
A typical buffer formulation provided by the program BUFFER.PRP is

attached. A copy of the program is available upon request.

 

 

 

 

 

288a

CONDITIONS

paH = 7.50008 0
ch = 7.44098 0
IONIC STRENGTH =_

1.82078 -2
BUFFER CONCENTRATION =
4.29278 -3

BUFFER CAPACITY =
1.86938 -3

THERMODYNAMIC CONSTANTS
pKal = 2.16108 0

pKa2 = 7.20708 0

pKa3 = 1.23258 1

Kw = 1.00008 -14

ACTIVITY COEFFICIENTS
actcoef 83A = 1.00008 0
actcoef HZA - 8.72728 -1
actcoef HA = 5.80098 -1
actcoef A = 2.93688 -1
actcoef H = 8.72728 -1

STOICHIOHETRIC CONSTANTS
Kal = 9.06268 -3
K32 = 1.07038 -7
Ka3 = 1.07098 -12
Kw = 1.31308 '14

DISTRIBUTION FUNCTIONS
ALPHA 0 = 2.20798 -5
ALPHA 1 ' 7.47068 -1
ALPHA 2 8 2.52928 -1
ALPHA 3 = 1.01128 -6

ANALYTICAL CONCENTRATIONS
CONC N-H3A = 0.00008 -1
CONC H-HZA = 1.08538 -3
CONC H-HA 3 3.20748 -3
CONC H-A 8 0.00008 -1
CONC H-X = 7.49978 -3

EQUILIBRIUM CONCENTRATIONS
[H3A] = 4.34098 -9

[HZA] = 1.08578 -3

[HA] = 3.20698 -3

[A] = 9.47798 -8

[H] = 3.62358 -8

[OH] = 3.62358 -7
[Hjbuffer = 7.50018 -3
[N]electr = 7.49978 -3
[x1e1ectr = 7.49978 -3

CHARGE CONC = 3.00008 -2

 

 

 

 

 

APPENDIX 2

COMPUTER OPTIMIZATION PROGRAM

A2.1 Introduction

In this appendix, the computer program developed to optimize
electrophoretic separations is discussed. The mathematical rationale of the
program has been described previously in Chapter 4. The program
TETRA.OPT, whose copy is attached, was written in the Forth-based
programming language Asyst (version 2.1, Keithley Asyst, Rochester, NY) to be
executed on a 80-286 microprocessor-based computer. A schematic
representation of the main program and most relevant subroutines are given in
Figure A2.1. The program is based on four nested loops, in which all possible
combinations of the variables pH, applied current, ionic strength and buffer
concentration are evaluated. The quality of the separation obtained with each
set of conditions is analysed according to the response function CRS (Equation
4.1, Chapter 4). The resulting CRS is then compared with the value obtained
from the previous set of conditions. The set of conditions that leads to the
separation with the minimum value of CR8 is saved along with other important
parameters of the system, such as illustrated by a typical output of the program
(Figure A2.2). The non-optimal sets of conditions, or user-selected sets of
conditions, can either be stored in a file (version 2.0, Lotus Development
Corporation, Cambridge, Massachussets) for further graphic manipulation or

disregarded.

289

 

 

290

Figure A2.1 Schematic representation of the computer optimization main

program.

 

 

 

mm
Figure A2.1

 

OPTIMIZE.SEP

 

 

 

 

DATA.INPUT I

 

 

 

 

PI
aortic]
I e

I EQUILIBRIUMCALC I

 

 

 

 

 

IMOBILITYCORRECT I

 

 

 

I VOLTAGE.CALC I
J

 

 

 

I F LOW.CALC I

 

 

IEFFECTIVEMOBILITY I

 

 

 

I ELUTION.TIME I
* J

 

I ,
FESOLUTIONCALC I

 

 

ICRSCALC I

 

 

l >LZI
LDISPLACECRSI
. _ j ,
I PRINT.OPT I

 

 

 

 

292

Figure A2.2 Typical output of the computer optimization program representing a
separation of (a) nucleotides, and (b) tetracyclines.

 

 

-g...

 

293
Figure A2.2a

 

 

PREDICTED OPTIHUH CONDITIONS FOR THE SEPARATION:
CURRENT, in nicroanperol - 12.500
pH I 10.000

IONIC STRENGTH, in moles/liter - 1.24758 -2
BUFFER CONCENTRATION, in moles/liter - 2.43558 -3

CAPILLARY DIMENSIONS:

TOTAL LENGTH, in on - 112.15

Correction Factor, in pH units -

TYPE OF INJECTION: HYDRODYNAMIC
HEIGHT DIFFERENCE, in cm I 2.00

.0850

DETECTOR LENGTH, in cm - 43.40 INJECTION TIHE, in sec - 60.00
I. D., in micrometers - 75.50 HYDRODYNAMIC VELOCITY, in cm/s - 3.558 -3
ELUTION TIME WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
in min in min MOBILITY VARIANCE
1n cn2/VI in cnz
AMP - 7.58 .129 -.31B6E -3 9.108 -3 5.568 4 1.61
CH? I 7.79 .133 -.33008 -3 9.358 -3 5.528 4 8.85
GNP - 9.08 u158 -.38858 -3 1.098 -2 5.288 4 3.94
UHP I 9.73 .171 -.41218 -3 1.178 -2 5.178 4 1.09
ADP - 9.92 .175 -.41848 -3 1.198 -2 5.138 4 2.82
CDP - 10.43 .186 -.43438 -3 1.258 -2 5.058 4 5.65
GDP I 11.54 .209 -.46408 -3 1.388 -2 4.878 4 6.21
UDP I 12.93 .239 -.49408 -3 1.558 -2 4.678 4 CR5 - 5.31
INJECTION ZONE, in on I .21 INJ VARIANCE, in cm2 I 3.788 -3

DETECTOR WINDOW, in cm I .50

FLOR CHARACTERISTICS:
ZETA POTENTIAL, in nv -
ZETAZERO, in IV - 26.44
kPOTNa - 2.23478 -1
ELECTROOSHOTIC HOBILITY, in an2/VC I 7.42628 -4
ELECTROOSMOTIC VELOCITY, in ca]. - .1667
VOLTAGE, in RV - 25.170

RESISTANCE, in ohm - 2.01368 9

'93.49

BUFFER CHARACTERISTICS (cone in moles/liter):
pH - 10.000

IONIC STRENGTH - 1.24758 -2
BUFFER CONCENTRATION - 2.43558 -3
BUFFER CAPACITY - 3.11398 -4
CHARGE CONC - 2.00038 -2
[N]bu££er - 5.00088 -3

[Njolectr - 5.00078 -3

BUFFER FORMULATION:

CONC H-H3A - 0.00008 -1

CONC H-HZA - 0.00008 '1

CONC H-HA - 2.30578 -3

CONC H-A - 1.29848 -4

CONC H-X - 5.00078 -3

OK

DET VARIANCE, in cm2 3 2.088 '2

 

 

 

 

 

 

2Eh4
Figure A2.2b

 

 

PREDICTED OPTIMUM CONDITIONS FOR THE SEPARATION:
CURRENT, in nicroanporoc I 20.000

pH I 7.500 Correction Factor,

IONIC STRENGTH, 1n solos/litor I 1.82078 -2
BUFFER CONCENTRATION, in nolos/litor I 4.29278 -3

in pH units I .2000

CAPILLARY DIMENSIONS: TYPE OF INJECTION: HYDRODYNAMIC
TOTAL LENGTH, in CI I 111.90 HEIGHT DIFFERENCE, in an I 2.00
DETECTOR LENGTH, in C! I 43.40 INJECTION TIME, in Dec I 30.00
I. D., in micronctorc I 75.50 HYDRODYNAMIC VELOCITY, in ca]: I 3.568 -3
SOLUTE ELUTION WIDTH EFFECTIVE DIFFUSION EFFICIENCY RESOLUTION
TIME in min MOBILITY VARIANCE
in min in cuZ/Vs in CIZ
MNC 4.45 .086 I.22318 I4 5.348 I3 4.288 4 1.02
DOC 4.54 .088 I.34928 I4 5.448 I3 4.268 4 .99
TC 4.62 .090 I.46908 I4 5.558 I3 4.258 4 .57
OTC 4.67 .091 ‘.53708 I4 5.618 I3 4.258 4 .17
MTC 4.69 .091 I.5573E I4 5.638 I3 4.258 4 1.34
CTC 4.81 .094 I.7143E I4 5.788 I3 4.238 4 .23
RMIN - .so_
INJECTION ZONE, in cm I .11 INJ VARIANCE, 1n Cn2 I 1.788 I2
in cnz I 2.088 -2

DETECTOR WINDOW, in CD I .50 DET VARIANCE,

FLOW CHARACTERISTICS:

ZETA POTENTIAL, 1n nV - -94.14

ZETAZERO, in av - 28.37

kPOTNa - 2.23478 -1

ELECTROOSMOTIC MOBILITY, in cnz/Vs . 6.68368 -4
ELECTROOSMOTIC VELOCITY, in cm]. - .1681
VOLTAGE, in xv - 20.139

RESISTANCE, in on- - 1.4070: 9

BUFFER CHARACTERISTICS (cone in noloo/liter):
pa - 7.500

IONIC STRENGTH - 1.82078 -2
BUFFER CONCENTRATION . 4.29272 -3
BUFFER CAPACITY - 1.86938 -3
CHARGE CONC - 3.00002 -2
[M]buttor - 7.50018 -3

[M]olectr - 7.49978 -3

BUFFER FORMULATION:

CONC MIH3A - 0.0000: -1

CONC NIHZA - 1.08538 -3

CONC MIHA - 3.20748 -3

CONC MIA - 0.0000E -1

CONC N-x - 7.49978 -3

OK

 

 

 

 

 

 

 

295

The first block of the program is reserved for data input. In this block, the
capillary dimensions, type and conditions of sample injection, detector position
and window length are supplied. Additionally, the initial and final values as well
as increments of the parameters to be optimized are entered, which are the pH,
ionic strength, and concentration of the buffer and the applied current. The
thermodynamic dissociation constants, as pKa values, in addition to the
electrophoretic mobilities of the buffer species and the solutes under
investigation are permanently stored during the program loading.

The next block of the program performs the calculations to correct the
dissociation constants and mobilities for ionic strength effects and to find the
equilibrium concentrations and distribution functions of all species. If a
combination of variables indicates a buffer formulation with negative values for
any species concentration, that set of conditions is disregarded and an arbitrary
value of 510 is assigned to CRS. Moreover, the program imposes that the
concentration of sodium chloride always surpasses the concentration of sodium
originated from the buffer salts. In case this restriction is not obeyed, a value of
520 is assigned to CRS. A value of 515 is assigned to CRS when both
restrictions, feasible buffer formulation and sodium chloride concentration larger
than sodium concentration from buffer salts, are not met.

In the next block of the program, the overall electrical resistance of the
system is calculated and the voltage is predicted. If the voltage value falls
ouside the range between 5 kV and 35 kV, that particular set of conditions is
disregarded and a value of 530 is assigned to CRS.

The program follows with the prediction of the electroosmotic flow,
effective mobility of the solutes and migration time. A negative value of
migration~time results if the electroosmotic velocity is smaller in magnitude and

opposite in sign than the electrophoretic velocity. In this particular case, the

 

 

 

296
solute do not migrate towards the cathode under the influence of the applied
electric field. Therefore, the correspondent set Of conditions is disregarded and
a value of 540 is assigned to CRS.

Once the migration time of the solutes is available, the resolution between
all adjacent pairs is calculated and the CRS is detemined. If the CRS value
exceeds 500, a value of 500 is assigned to CRS, which indicates that that
particular set of conditions is further from the system optimum. The minimum
value that the CRS function can achieve is 1.0, however the obtainable CRS
value depends on the system of solutes under examination. Generally, CRS

values of less than 3.0 are indicative of good separation characteristics.

A2.2 NUCLE0.0PT and TETRA.OPT Programs

A copy of the programs for the Optimization of the separation of
nucleotides (NUCLE0.0PT) and tetracyclines (TETRA.OPT) is available upon

request.

 

 

 

 

 

 

 

 

 

 

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