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THERMODYNAMIC AND KINETIC CHARACTERIZATION OF CHIRAL
SEPARATIONS WITH B-CYCLODEXTRIN STATIONARY PHASE

By

Xiaoping Li

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Chemistry

2006

ABSTRACT

THERMODYNAMIC AND KINETIC CHARACTERIZATION OF CHIRAL
SEPARATION WITH B-CYCLODEXTRIN STATIONARY PHASE

By

Xiaoping Li

Chiral separation by liquid chromatography using chiral stationary phases
is the most popular approach in industry. In this dissertation. a series of
coumarin related compounds is analyzed using a packed capillary B-cyclodextrin
column with on-column laser-induced fluorescence detection.

In our approach for data analysis, the exponential modified Gaussian
(EMG) model is employed. In order to validate this model, a three-dimensional
stochastic simulation is first performed. Five methods are applied to extract the
thermodynamic and kinetic information: “true” method, Statistical moment
method. EMG method. Thomas method and Giddings method. Comparison of
the accuracy relative to the “true” retention factors and “true” rate constants
demonstrates that the EMG model provides similar results to the other models.

The experimental data are examined with the EMG model to observe the
effect of mobile phase composition, temperature and pressure on the
thermodynamics and kinetics of chiral separation. A polar-organic mobile phase
composed of acetonitrile, methanol, acetic acid, and triethylamine is utilized.

Mobile phase composition affects the equilibration time, isotherm,
retention, chiral selectivity, as well as the kinetic rate constants of the chiral

separation. Both acid and amine modifiers can help to shorten the equilibration

time greatly. Acid modifier increases the linear isotherm range but decreases
chiral selectivity. Amine modifier decreases retention and benefits chiral
selectivity. Methanol decreases retention by hydrogen bonding. The mass
transfer rate constant usually increases as the retention decreases. However.
the second enantiomer often has a surprisingly faster mass transfer rate than the
first enantiomer although it is more retained.

Temperature and pressure also affect retention, chiral selectivity, and
kinetic rate constants. Temperature decreases retention and chiral selectivity for
all compounds. Pressure decreases retention but does not significantly affect
chiral selectivity. The changes in molar enthalpy are negative for all compounds,
indicating an energetically favorable transfer from mobile to stationary phase.
The changes in molar volume are positive for all compounds. indicating the
compounds occupy more space in the stationary phase than in the mobile phase.
No enthalpy-entropy compensation is achieved, hence different retention
mechanisms are responsible for each compound.

In addition to chiral separation. a series of nitrogen-containing polycyclic
aromatic hydrocarbons (N-PAHs) are investigated in a similar manner to observe
the effects of mobile phase composition, temperature and pressure on an
octadecylsilica column. The results demonstrate that the partition mechanism is
dominant in methanol mobile phase but the adsorption mechanism is dominant in
acetonitrile mobile phase. Another technique. fluorescence quenching. is also
utilized to differentiate different types of N-PAHs with aliphatic amine quenchers.

Aliphatic amines can selectively quench aza-PAHs over amino-PAHs.

To My Family...

ACKNOWLEDGEMENTS

First of all, I like to express my sincerest thanks to my advisor, Dr. Victoria
L. McGuffin. Her profound knowledge and passion in science not only helped me
though five years of graduate works, but also will encourage and lead me in my
future careers. I would also like to thank all of my committee members. Dr. Jack
Throck Watson, Dr. Merlin L. Bruening, Dr. Gregory L. Baker and Dr. Katharine
C. Hunt, for their critical evaluations and suggestions.

To all of my group members: Dr. Samuel Howerton and Dr. Carl Newman
are two excellent senior labmates. Their patience in teaching, dedication in
research and humor in life help me through the toughest first few years. Rashad
is my “same-year-buddy”, who experienced every bit of graduate school life with
me. It’s so great to have such a company. Melissa and Amber are two sweetest
“sisters” in the lab. Melissa always surprises me with her creativity. and Amber
always impresses me with her smile. Thank you two for being my friend. I have
no doubt that both of you will succeed in your future. Good luck to the youngest
Iabmate, Kahsay, for his future graduate works as well. I am so blessed to have
such a small but sweet group.

I would also like to thank my husband, Feng, for his love and
encouragement. Without his love and company, the graduate school will be so
much harder for me. To my parents, their love and support are the main sources
of energy helped me through any difficult time. Thank you for always believing in
me. Of course. thanks to all of my friends I got to know in these five years. you

make my life in East Lansing so much colorful.

TABLE OF CONTENTS

LIST OF TABLES
LIST OF FIGURES

Chapter 1: Introduction and Background

1.1 Importance of Chiral Separation

1.2 Chiral Separation with Liquid Chromagraphic Methods
1.2.1 Indirect Methods
1.2.2 Direct Methods

1.3 Thermodynamic and Kinetic Theory
1.3.1 Thermodynamics
1.3.2 Kinetics

1.4 Methods for Thermodynamic and Kinetic Studies
1.4.1 Perturbation Methods
1.4.2 Shallow-Bed Methods
1.4.2 Chromatographic Methods

1.5 Previous Investigations of Chiral Separations
1.5.1 Inclusion-Type CSP
1.5.2 Brush-Type CSP
1.5.3 Amylase- and Cellulose-Type CSP
1.5.4 Protein-Type CSP

1.6 Conclusions

1.7 References

Chapter 2: Theoretical Evaluation of Methods for Extracting
Retention Factors and Kinetic Rate Constants in
Liquid Chromatography

2.1 Introduction
2.2 Computer Simulation Methods
2.3 Data Analysis Methods
2.3.1 True Extraction Method
2.3.2 Statistical Moment Extraction Method
2.3.3 EMG Model Extraction Method
2.3.4 Giddings Model Extraction Method
2.3.5 Thomas Model Extraction Method
2.4 Results and Discussion
3.4.1 Homogeneous Systems
3.4.2 Heterogeneous Systems
2.5 Conclusions
2.6 References

vi

ix

xii

sub

57

58
60
62
62
63

107
120
125

Chapter 3: Experimental Methods 127

3.1 Experimental Systems 127
3.1.1 Column Packing 127

3.1.2 Chromatographic System 128

3.2 Data Analysis 134
3.3 Conclusions 136
3.4 References 137

Chapter 4: Effect of Mobile Phase Composition to Chiral Separations

With B-Cyclodextrin Stationary Phase 138

4.1 Introduction . 138
4.2 Experimental Methods 139
4.2.1 Chemicals 139

4.2.2 Experimental System 140

4.3 Results and Discussion 140
4.3.1 Memory Effect 140

4.3.2 Two-Component Mobile Phase 145

4.3.3 Three-Component Mobile Phase 153

4.3.4 Four-Component Mobile Phase 161

4.4 Conclusions 175
4.5 References 177

Chapter 5: Effect of Temperature and Pressure to Chiral Separations

With B-Cyclodextrin Stationary Phase 179

5.1 Introduction 179
5.2 Experimental Methods 180
5.2.1 Chemicals 180

5.2.2 Experimental System 180

5.3 Results and Discussion 180
5.3.1 Thermodynamic Behavior 181

5.3.2 Kinetic Behavior 197

5.4 Conclusions 204
5.5 References 206

Chapter 6: Thermodynamic and Kinetic Characterization of
Nitrogen-Containing Polycyclic Aromatic Hydrocarbons

in Reversed-Phase Liquid Chromatography 207
6.1 Introduction 207
6.2 Experimental Methods 209
6.2.1 Chemicals 209
6.2.2 Experimental System 209
6.3 Results and Discussion 212

6.3.1 Methanol Mobile Phase 215

vii

6.3.2 Acetonitrile Mobile Phase 236

6.4 Conclusions 243
6.5 References 246
Chapter 7: Spectroscopic Study of Nitrogen-Containing Polycyclic

Aromatic Hydrocarbons by Fluorescence Quenching 249

7.1 Introduction 249
7.1.1 Nitrogen-Containing Polycyclic Aromatic Hydrocarbons

(N-PAHs) 249

7.1.2 Fluorescence Quenching 249

7.2 Experimental Methods 253

7.2.1 Chemicals 253

7.2.2 Fluorescence Quenching Measurements 253

7.2.3 Fluorescence Lifetime Measurements 258

7.3 Results and Discussion 259

7.3.1 Effect of Water 259

7.3.2 Effect of Amine Structure 260

7.3.3 Effect of Fluorophore Structure 268

7.4 Conclusions 274

7.5 References 276

Chapter 8: Conclusions and Future Directions 278

8.1 Theoretical Simulations 278

8.2 Chiral Separations 280

8.3 Characterization of Nitrogen-Containing Polycyclic Aromatic
Hydrocarbons (N-PAHs) 284
9.5 References 286

viii

LIST OF TABLES

Table 2.1: Retention factors (k) with varying column length (L) 66
Table 2.2: Kinetic rate constants from stationary to mobile phase

(kms. 8") with varying column length (L) 67
Table 2.3: Retention factors (k) with varying linear velocity (uo) 77

Table 2.4: Kinetic rate constants from stationary to mobile phase
(k...., s") with varying linear velocity (uo) 78

Table 2.5: Retention factors (k) with varying stationary-phase diffusion
coefficient (0.) 86

Table 2.6: Kinetic rate constants from stationary to mobile phase
(kms. 8") with varying stationary-phase diffusion coefficient
(De) as

Table 2.7: Retention factors (k) with varying interfacial mass transfer

coefficient (a) 94

Table 2.8: Kinetic rate constants from stationary to mobile phase
(km. s") with varying interfacial mass transfer coefficient (a) 96

Table 2.9: Retention factors (k) with varying equilibrium constants (K) 105

Table 2.10: Kinetic rate constants from stationary to mobile phase
(kn... s") with varying equilibrium constants (K) 106

Table 2.1 1: Different parameters for multiple interaction sites at the
heterogeneous surface 109

Table 2.12: Retention factors (k) along the column for equally distributed
heterogeneous surface 112

Table 2.13: Kinetic rate constants from stationary to mobile phase
(kms. 8") along the column for equally distributed
heterogeneous surface 114

Table 2.14: Retention factors (k) along the column for unequally
distributed heterogeneous surface 121

Table 2.15: Kinetic rate constants from stationary to mobile phase

Table 4.1:

Table 4.2:

Table 4.3:

Table 4.4:
Table 4.5:
Table 4.6:

Table 4.7:
Table 4.8:

Table 4.9:

(km, 5") along the column for unequally distributed
heterogeneous surface

Retention time of 1“t warfarin enantiomer over successive
days in a two-component mobile phase

Retention time of 1“ warfarin enantiomer over successive
days in two-component and three-component mobile phases

Comparison of thermodynamic and kinetic behaviors of
solutes at reference mobile phase composition

Effect of methanol concentration on thermodynamics
Effect of methanol concentration on kinetics

Effect of triethylamine (TEA) concentration on
thermodynamics

Effect of triethylamine (TEA) concentration on kinetics

Effect of acetic acid concentration on thermodynamics when
amine is present

Effect of acetic acid concentration on kinetics when amine is
present

Table 4.10: Effect of acetic acid concentration on thermodynamics and

Table 5.1:
Table 5.2:

Table 5.3 :

Table 5.4 :

Table 5.5 :
Table 5.6 :

kinetics of warfarin without amine present
Retention factors for the coumarin-based solutes

Changes in molar enthalpy and molar volume for coumarin-
based solutes

Differential changes in molar enthalpy and molar entropy for
the chiral coumarin-based solutes

Co—elution temperature (T be) for the chiral coumarin-based
solutes

Kinetic rate constants for the coumarin-based solutes

Activation energy for the coumarin-based solutes

122

149

155

162
166
168

169
170

172

173

174
182

187

194

198

203

Table 6.1: Retention factors for N-PAHs in methanol mobile phase 216

Table 6.2: Changes in molar enthalpy and molar volume for N-PAHs in
methanol mobile phase 221

Table 6.3: Rate constants for N-PAHs in methanol mobile phase 228

Table 6.4: Activation energies and activation volumes for N-PAHs in
methanol mobile phase 230

Table 6.5: Thermodynamic data for N-PAHs in acetonitrile mobile phase 239
Table 6.6: Kinetic data for N-PAHs in acetonitrile mobile phase 242
Table 7.1: Stem-Volmer constants for pyrene with triethylamine in

acetonitrile at room temperature with different water

concentration (vlv) in the amine solution. 261
Table 7.2 : Stem-Volmer constants for pyrene with triethylamine in

acetonitrile at room temperature with different water

concentration (vlv) in the solvent 262

Table 7.3: Stem-Volmer constants for PAHs and N-PAHs with three
aliphatic amines in acetonitrile at room temperature 264

Table 7.4: Stem-Volmer constants for altemant PAHs and aza-PAHs
with diisopropylamine in acetonitrile at room temperature 270

Table 7.5 : Ionization potentials for the fluorophores (PAHs and N-PAHs) 273

xi

Figure 1.1:

Figure 1.2:

Figure 1.3:
Figure 1.4:

Figure 2.1:

Figure 2.2:

Figure 2.3:

Figure 2.4:

LIST OF FIGURES

(A) Structure of B-cyclodextrin. (B) Schematic diagram of
the separation process with B-cyclodextrin stationary
phase in 1) reversed-phase mode and 2) polar-organic

phase mode. 5
Schematic diagram of three-point model responsible for

chiral separation. 8
Energy coordinate diagram. 11

Three typical adsorption isotherms. q: loading,
c: concentration, t: time. 23

Comparison of zone profiles with varying column length.

From left to right, column length L = 1, 2, 4, 7, and 9 cm.

Other simulation conditions: N = 5000, t = 5.0x10" 3,

o... = 1.0x10’5 cmzls. o. = 5.0x10‘8 cmzls, K = 1.0,

un = 0.1 cmls, R... = 2.0x10‘3 cm, d. = 8.28x10“ cm,

a = 1.0. 69

Comparison of zone profiles with varying linear velocity.

From left to right, linear velocity uo = 0.5, 0.3, 0.2, 0.1, and

0.05 cm/s. Other simulation conditions: N = 5000,

t = 5.0x10“1 5, o... = 1.0x10’5 cmzls, o. = 5.0x10'8 cmzls,

K = 1.0, L = 8 cm, R... = 2.0x10'3 cm, d. = 8.28x10“ cm,

a = 1.0. 74

Comparison of zone profiles at similar time with varying

linear velocity. Peak (—) at L = 3 cm with uo = 0.05 cm/s,
(----)atL=60mwith uo=0.1 cm/s, (---)atL= 18cm

with uo = 0.3 cm/s. Other simulation conditions: N = 5000,

t = 5.0x10" s, o... = 1.0x10‘5 cm2/s, o. = 5.0x10'3 cmzls,

K = 1.0, R... = 2.0x10’3 cm, d. = memo:4 cm, a = 1.0. 79

Comparison of zone profiles (A) and statistical moments

(B) with varying stationary-phase diffusion coefficient.

(A) From left to right, stationary-phase diffusion

coefficient 0. = 1.0xioi, 5.0x10'8, 1.0x10'7, 5.0x10‘7,

and 1.0)(10'6 cmzls. (B) First moment M1 (0),

second moment M2 (I), third moment M3 (A),

and skew M3/M23’2 (t . Other simulation conditions:

N = 5000, t = 5.0x10 5, o... = 1.0x10'5 cm2/s,

uo = 0.1 cm/s, K = 1.0, L = 5 cm, R... = 2.0x10’3 cm,

d. = 8.28x10“ cm, a = 1.0. 32

xii

Figure 2.5: Comparison of zone profiles (A) and statistical moments
(B) with varying interfacial mass transfer coefficient.
(A) lnterfacial mass transfer coefficient 01= 1 ( ),
0.5( ------ ),0.1( ----- )and0.05(- ----- ).
(B) First moment M1 (0), second moment M2 (I),
third moment M3 (A), and skew M3/M23’2 (in). Other
simulation conditions: N= 5000, t= 5. 0x10"s,
0...: 1 0x1050m Is, 0.: 5.0x10:i cm ls, uo= 01 cm/s,
K = 1.0, L = 6 cm, R... = 2.0x10'3 cm, d, = 8.28x10‘ cm. 91

 

Figure 2.6: Comparison of zone profiles (A) and statistical moments
(B) with varying equilibrium constant. (A) From left to right,
equilibrium constant K = 1.0, 2.0, 5.0, and 10.0.
(B) First moment M. (9), second moment M2 (I),
third moment M3 (A), and skew M3/M33’2 (it). Other
simulation conditions: N= 5000, t= 5. 0x10 3,
o... = 1.0x10'5 cmzls, 0.: 5. 0x104 cm 2,/s
uo=0.1cmls,L=20m.R...=2.0x10“3cm
d.= 8. 20x104 cm,a=1..0 98

Figure 2.7: Comparison of zone profiles (A) and statistical moments
(B) at similar time with varying equilibrium constant (K).
(A) From left to right, K = 5.0 at L = 2 cm, K = 2.0 at
L=4cm,K=1.0atL=6cmandK=0.5atL=8cm.
(B) First moment M1 (0), seconds,2 moment M2 (I), third
moment M3 (A), and skew Mszm (t). Other simulation
conditions: N= 5000, t - 5. 0x10 s,Dm=1.Ox10’5cmzls,
0.: 5.0x10’° cmzls uo= 0. 1 cmls, R...= 2. 0x103 cm,
d. = 8.28x10“ cm, a = 1.0. 101

Figure 2.8: Comparison of zone profiles with equally distributed
heterogeneous surface. From left to right, detector
distance L = 0.5, 2, 5, and 7 cm. Other simulation
conditions: N = 5000, t = 5.0x10" s, o... = 1.0x10'5 cmzls,
uo = 0.1 cm/s, R... = 2.0x10’3 cm, d, = 8.28x10" cm
a = 1.0, P(1) conditions are given in Table 2.11. 110

Figure 2.9: Comparison of zone profiles with unequally distributed
heterogeneous surface. From left to right, detector
distance L = 1, 5, 8, 15, and 20 cm. Other simulation
conditions: N = 5000, t = 5.0x10“ 3, o... = 1.0x10’5 cmzls,
uo = 0.1 cmls, R... = 2.0x10‘3 cm, d. = 0.20::104 cm
a = 1.0, P(2) conditions are given in Table 2.11. 116

Figure 2.10: Comparison of skews among equally distributed (9),
unequally distributed (I) heterogeneous systems,

xiii

Figure 3.1:

Figure 3.2:

Figure 4.1:
Figure 4.2:

Figure 4.3:

Figure 4.4:

Figure 4.5:

homogeneous system with D. equal to 1.0x10'7 cmzls (A)

and homogeneous system with D. equal to 1.0x10'° cmzls

(t). For heterogeneous systems, simulation details as

given in Figures 2.8 and 2.9. For homogeneous systems,
simulation details are given in Figure 2.4. 118

Schematic diagram of the experimental system for capillary
liquid chromatography with one on-column laser-induced
fluorescence detector for mobile phase study. I: injection

valve. S: splitting tee, F: filter, PMT: photomultiplier tube,

AMP: current to voltage amplifier. 129

Schematic diagram of the experimental system for capillary
liquid chromatography with four on-column laser-induced
fluorescence detectors for temperature and pressure study.

I: injection valve, S: splitting tee, R: restrictor, FOP: fiber-optic
positioner, F: filter, PMT: photomultiplier tube, AMP: current

to voltage amplifier 132

Structure of coumarin-based solutes 140

Representative chromatograms of memory effect from

acetic acid and triethylamine. Column: B—cyclodextrin.

Solute: racemic warfarin. Mobile phase composition:
acetonitrilezmethanol (90%:10%) (A) original data before

acid and amine modifier added; (8) acetic acidztriethylamine
(0.30%:0.20%) added; (C) removal of acid and amine

modifier at hour 4; (D) day 1; (E) day 3; (F) day 10. 143

Representative chromatograms of memory effect from

methanol. Column: B—cyclodextrin. Solute: racemic

warfarin. Mobile phase composition: acetonitrilezmethanol
(90%:10%) after removal of pure methanol mobile phase

at (A) day 1; (B) day 2; (C) day 3; (D) day 10 146

Comparison of chromatograms in two-component mobile

phase. Column: B—cyclodextlin. Solute: racemic warfarin.
Mobile phase composition: acetonitrilezmethanol (80%:20%)

(A) day 2; (B) day 3; (C) day 6. 151

Warfarin peak shape in the presence of acetic acid.

Column: B-cyclodextrin. Mobile phase composition:
acetonitrilezmethanolzacid (90%:10%z0.30%). Warfarin
concentration from highest to lowest: 8x10" M; 4x104 M;

2x104 M. 157

xiv

Figure 4.6:

Figure 5.1:

Figure 5.2:

Figure 5.3:

Figure 5.4:

Figure 5.5:

Figure 6.1:

Figure 6.2:

Warfarin peak shape in the presence of triethylamine.

Column: B-cyclodextrin. Mobile phase composition:
acetonitrile:methanol:amine (90%:10%z0.05%). Warfarin
concentration from highest to lowest: 8x104 M; 4x104 M;

2x104 M; 1x104 M ; 5x10‘5 M. 159

Representative graph of the retention factor versus inverse
temperature used to calculate the change in molar enthalpy.
Mobile phase: acetonititlilezmethanol:acetic acidztriethylamine
99%:1%:0.15%:0.1% (v/v/v/v), 1300 psi, Solutes: coumafuryl

( <> ), warfarin (O ), coumachlor( O ), coumatetralyl ( I ),
4-hydroxycoumarin ( A ). Other experimental details are

given in the text. 184

Representative graph of the retention factor versus pressure
used to calculate the change in molar volume. Mobile phase:
acetonititrilezmethanolzacetic acidztriethylamine
99%:1%:0.15%:0.1% (vlv/v/v), 293 K, Solutes: coumafuryl

( <> ), warfarin (O ), coumachlor( O ), coumatetralyl ( I ),
4-hydroxycoumarin ( A ). Other experimental details are

given in the text. 189

Representative graph of the chiral selectivity versus inverse
temperature used to calculate the chiral difference in molar
enthalpy and molar entropy. Mobile phase:
acetonititrilezmethanol:acetic acidztliethylamine 99:1 :0.15:0.1
(vlv/v/v), 1300 psi, Solutes: coumafuryl ( <> ), warfarin (O ),
coumachlor( O ), coumatetralyl ( I ). Other experimental
details are given in the text. 191

Representative graph of the retention factor versus change in
molar enthalpy used to observe enthalpy-entropy compensation.
Mobile phase: acetonititlilezmethanolzacetic acidztriethylamine
99%:1%:0.15%:0.1% (v/vIv/v), 1300 psi. 195

Representative graph of the kinetic rate constant versus inverse
temperature used to calculate the change in activation energy.
Mobile phase: acetonititlile:methanol:acetic acidztriethylamine
99%:1%:0.15%:0.1% (v/v/v/v), 1300 psi, Solutes: coumafuryl

( <> ), warfarin (O ), coumachlor( O ), coumatetralyl ( I ).
Other experimental details are given in the text. 201

Structures of PAHs and N-PAHs for liquid chromatographic
study. 210

Representative chromatograms of 4-azapyrene in reversed-
phase liquid chromatography. Column: polymeric

XV

Figure 6.3:

Figure 6.4:

Figure 6.5:

Figure 6.6:

Figure 7.1:

Figure 7.1:

octadecylsilica. Mobile phase: (A) methanol, 303 K,

2085 psi, 0.08 cmls; (B) acetonitrile, 303 K, 2185 psi,

0.08 cmls. Column: polymeric octadecylsilica. Other
experimental details are given in the text. 213

Representative graph of the retention factor versus inverse
temperature used to calculate the change in molar enthalpy.
Mobile-phase: methanol, 2085 psi, 0.08 cmls (—);

acetonitrile, 2185 psi, 0.08 cmls (— — —). Solutes:

1-aminopyrene ( <> ), 1-azapyrene (O ), 4-azapyrene

( O ), benz[a]acridine ( I ), dibenz[a,j]acridine ( A ).

Other experimental details are given in the text. 218

Representative graph of the retention factor versus

pressure used to calculate the change in molar volume.

Mobile phase: methanol, 283 K, 0.08 cmls. Symbols

defined in Figure 6.3. Other experimental details are given

in the text. 225

Representative graph of the rate constant (k...) versus

inverse temperature used to calculate the activation energy.
Mobile phase: methanol, 2085 psi, 0.08 cmls (——);

acetonitrile, 2185 psi, 0.08 cmls (- — —). Symbols defined

in Figure 6.3. Other experimental details are given in the

text. 232

Representative graph of the rate constant (k...) versus

pressure used to calculate the activation volume. Mobile

phase: methanol, 283 K, 0.08 cmls. Symbols defined in

Figure 6.3. Other experimental details are given in the text. 234

Representative examples of altemant N-PAH and nonaltemant
N-PAH. 250

Structures of PAHs and N-PAHs for fluorescence quenching
study. 254

CHAPTER 1
INTRODUCTION AND BACKGROUND
1.1 IMPORTANCE OF CHIRAL SEPARATIONS

Enantiomers are those pairs of molecular entities that are mirror images of
each other and non-superimposable. The enantiomers have the same physical
and chemical properties in an achiral environment and, thus, are difficult to
separate. Separation of chiral compounds has been of great interest in
academia and industry because of their prevalence and biological importance.
The “building blocks” for the body, including proteins, nucleic acids and
polysaccharides are composed of chiral biomolecules. Naturally, these
biomolecules exist in only one of the two possible enantiomeric forms,
demonstrating different responses to each enantiomer in drugs, foods, pesticides,
wastes, and so on [1]. In previous years, the pharmaceutical industry suffered
from failure to discriminate of the two enantiomers. Whereas one isomer may
produce the expected therapeutic effect, the other may be inactive or, even
worse, may produce unwanted side effects [2]. In 1992, the 0.8. Food and Drug
Administration (FDA) issued guidelines for development of stereoisomeric drugs.
Not only the drugs, but also their metabolites, must be separated and analyzed
individually. Only the therapeutically active isomer can be put on the market if
the other isomer is detrimental. Thus, the separation of enantiomers is

necessary and important.

1.2 CHIRAL SEPARATION WITH LIQUID CHROMATOGRAPHIC
METHODS

Although chiral separations represent one group of the most complicated
separations, great progress has been made ever since the extension of chiral
separation to chromatography. Chromatographic methods can be divided into
indirect methods, which utilize derivatizing agents, or direct methods, which
utilize chiral mobile phases or chiral stationary phases.

1.2.1 Indirect Methods

In the indirect method, the racemic mixtures react with chiral reagents to
form a pair of diastereomers. Because diastereomers possess different
physiochemical properties, they can be separated in an achiral environment.
The advantages of the indirect approach are the following: (1) less expensive,
because conventional chromatographic columns can be used; (2) flexible,
because various achiral columns and mobile phase conditions can be used; and
(3) different selectivities can be achieved. On the other hand, the disadvantages
of this method are: (1) long analysis time that includes sample preparation and
verification of the derivatization chemistry; (2) inconvenience, specifically in
preparative chromatography, when reversal of derivatization is needed to recover
the pure enantiomers.

1.2.2 Direct Methods

Chiral high-performance liquid chromatography has proven to be one of

the best methods for the direct separation of enantiomers [3]. Some optically

pure chiral molecules are either added into the mobile phase (chiral additive) or

attached to the stationary phase (chiral stationary phase, CSP). Both of these
two methods are based on the formation of temporary diastereoisomers.
1.2. 2. 1 Chiral mobile phase additive

In this method, chiral separation is accomplished by the formation of a pair
of transient diastereomeric complexes between racemic analytes and the chiral
mobile phase additive. Chiral discrimination is due to differences in the stabilities
of the diastereomeric complexes, salvation in the mobile phase, and/or binding of
the complexes to the solid support. The more stable complex will be
preferentially eluted and the less stable one will be eluted later. The three major
approaches in the formation of diastereomeric complexes are transition metal ion
complexes (ligand exchange), ion pairs, and inclusion complexes. Advantages
of this technique are as follows [4]: (1) less expensive, conventional liquid
chromatographic columns can be used; (2) a wide variety of possible additives
are available; and (3) different selectivities from the chiral phases can be
obtained by adding different additives. However, the disadvantage with this
technique include: (1) need to synthesize optically pure additives, (2)
inconvenience of the need to remove the chiral additive from the enantiomeric
solutes for preparative applications; and (3) additives limit choice of detection
system.
1.2.2.2 Chiral stationary phase (CSP)

Chiral separation by using chiral stationary phases (CSPs) is based on the
formation of transient diastereomeric complexes between the enantiomers and

the chiral molecule that is an integral part of the stationary phase. The more

stable one will be preferentially retained and the less stable one will be eluted
first. So far, the CSPs have been categorized under several different types
including inclusion-type, brush-type, affinity-type, and also amylose- and
cellulose-type CSPs.
1. 2. 2.2.1 Inclusion-type CSP

One of the most common examples of inclusion CSPs are the native and
derivatized cyclodextrins. Cyclodextrins are cyclic oligosaccharides containing
six or more D-glucose units connected through 01-1,4—glycosidic bonds. The
structure of B-cyclodextiin contains seven glucose units with 35 chiral centers,
while 01- and y- cyclodextrins contain six and eight glucose units, respectively.
The structure of B-cyclodextn’n is shown in Figure 1.1A. In reversed-phase mode,
the mobile phase is relatively more polar than the stationary phase, and mainly
composed of water and acetonitrile or methanol. The hydroxyl groups of the
cyclodextrin are oriented toward the exterior surface, which makes the interior of
the cavity relatively nonpolar and hydrophobic. Consequently, solutes may enter
the cavity and be retained by dispersion and hydrogen-bonding interactions. In
the polar organic-phase mode, the mobile phase is mainly composed of
acetronitrile and methanol. It is generally believed that the acetonitrile will enter
the cavity, so the solute will be on top of the cyclodextrin cavity and be retained
mainly by hydrogen bonding. The separation process is illustrated in Figure 1.18.
A naphthalene-related compound is illustrated as the model solute, because 8-
cyclodextrin is known for separating two-ring compounds. In reversed-phase

mode, the model solute is included into the cyclodextrin cavity; in polar-organic

Figure 1.1 (A) Structure of B-cyclodextrin. (B) Schematic diagram of the
separation process with B-cyclodextn’n stationary phase in 1) reversed-phase

mode and 2) polar-organic phase mode.

(A)

 

HOHZC o
0
Hon2 OH H
o H
OH
0
HOH2 OH
° ,H
H O
O 01:) OH on()
HOHZC o CHZOH

(B)

1) In reversed-phase mode

maes—

2) In polar organic-phase mode

%:0.va

 

 

phase mode, the acetonitrile is included into the cyclodextrin cavity, while the
solute is only stay on top of the cyclodextrin cavity. These two processes are
demonstrated in Figures 1.181 and 1.1B2, respectively.
1.2. 2. 2.2 Brush-type CSP

Brush CSPs distinguish themselves from other CSPs by having a small
chiral molecule covalently bonded to the solid phase, usually silica. The organic
groups of the chiral molecule remain directed away from the silica surface,
appearing as bristles of a brush. Among the brush CSPs, the most widely known
and commercially successful are those developed by Pirkle and coworkers. Most
of the Pirkle-type CSPs emphasize electron donor-acceptor interactions of the
nonbonding (n) and aromatic (1:) type. Chiral separations are achieved by
establishing three points of interaction between an enantiomer and the CSP
(Figure 1.2), where at least one of these interactions is stereospecific [5].
Consequently, the other enantiomer is only able to sustain two points of
interaction with the CSP and is less retained. Most separations with Pirkle-type
CSPs are performed in the nonnaI-phase mode, where a nonpolar mobile phase
is utilized.
1. 2. 2. 2.3 Amy/ose- and Cellulose-type CSP

Polysaccharides such as amylose and cellulose are naturally occurring,
optically active polymers. Amylose is composed of glucose units connected with
a-1,4-glycosidic bonds, and it adopts a helical structure in its native form.
Cellulose is based on B-1,4-glycosidic bonds, and adopts a more linear structure.

Native polysaccharides have long been known to exhibit chiral selectivity [6],

CSP Enantiomers

Three-point interaction A """ A
More retained "mm" B """ B “"‘"'D
c ------ c
A ------ A
Two-point interaction .milllll B D lllllm-B
Less retained C ______ C

 

Figure 1.2 Schematic diagram of three-point model responsible for chiral

separation.

however. their chiral resolving abilities are not sufficient for practical usage. Poor
resolution and broad peaks are obtained due to nonstereoselective binding and
slow mass transfer processes, and also because of slow diffusion through the
polymer network. Comparatively, derivatized polysaccharide CSPs have much
better chromatographic and enantiomeric properties than native polysaccharide
CSPs, which has led to their successful commercialization. The chiral
recognition mechanism for polysaccharide CSPs is generally thought to consist
of cohesive attraction followed by steric fit of the chiral solute onto the chiral
surface. The structural differences between amylose and cellulose are
responsible for the difference in their retention mechanisms.

1.2. 2. 2.4 Afiinity- type CSP (protein)

Proteins are naturally occurring, optically active polymers composed of L-
amino acids. As a result, immobilized proteins on solid supports are capable of
discriminating enantiomers. Protein-based CSPs are of special interest because
of their unique enantioselective properties and wide applications.
Chromatographic methods are distinguished on the basis of whether the proteins
are soluble or immobilized, where the latter is known as affinity chromatography.

The most commonly used proteins are as follows: (1) albumins, such as
human serum albumin and bovine serum albumin; (2) glycoproteins, such as (11-
acid glycoprotein, ovomucoid, and avidin; (3) enzymes, such as
cellobiohydrolase I, lysozyme, and pepsin; and (4) other miscellaneous proteins,
such as B-lactoglobulin. Although protein CSPs are widely used, the elucidation

of their retention mechanism is relatively difficult due to their complex structures.

These complex structures are the result of different amino acid sequences
(primary structure) as well as different disulfide bridges, hydrogen bonding, and
other types of intramolecular bonding (secondary and tertiary structure).
Because of their structure, protein CSPs usually rely on different numbers or
types of binding sites for discrimination of enantiomers. To retain the protein
structure and avoid denaturation, most separations are performed in the

reversed-phase mode.
1.3 THERMODYNAMIC AND KINETIC THEORY

When the retention process is considered as a chemical reaction, an
energy-coordinate diagram (Figure 1.3) can be constructed to explain the
thermodynamic and kinetic contributions. In this diagram, the solute transfers
from the mobile phase (X...) to the stationary phase (X.) through a high-energy
transition state (X3). The thermodynamic parameters, e.g., the change in molar
enthalpy (AH) and molar volume (AV), are characterized by the difference
between the final and initial states. These thermodynamic quantities represent
the weighted average of all of the available states in the heterogeneous
stationary and mobile phases, respectively. The kinetic aspects of the retention
event can be described by using transition-state theory. The transfer from mobile
to stationary phase is characterized by a fast equilibrium between the mobile
phase and transition state with pro-equilibrium constant Km, followed by a rate-
Iimiting step between the transition state and the stationary phase with rate

constant k..... The kinetic parameters, eg. the activation enthalpy (AHm) and

activation volume (AVne). can be used to elucidate the kinetic description of the

10

ENERGY

 

 

Initial State

   

 

Final State

 

REACTION COORDINATE

Figure 1.3 Energy coordinate diagram

11

 

 

retention event. For the transfer from stationary to mobile phase, the pre-
equilibrium constant K33 and rate constant km. are used to determine the
corresponding activation enthalpy (AH33) and activation volume (Ava). These
kinetic quantities represent the weighted average of all available paths between
the final and initial states. The derivation of these thermodynamic and kinetic
quantities is described in the following sections.
1.3.1 Thermodynamics

Thermodynamics is the study of the system at steady state. At the
microscopic level, steady-state conditions may be achieved in which the activity
(or concentration) of the solute in the mobile and stationary phases (am and a.,

respectively) achieves a constant value

title)
I

where K is the equilibrium constant, k is the retention factor, and [3 is the phase
ratio. The phase ratio is defined as the volume of the mobile phase divided by
the volume of the stationary phase. The ratio of the equilibrium constants or

retention factors for two solutes defines the selectivity (a)

X
7?

._2_=._2 1.2
K. k, ( )

a =
where the subscripts 1 and 2 denote the less and more retained solutes,
respectively. This ratio may reflect the differences between chiral solutes (chiral
selectivity in Chapter 4 and 5).

The equilibrium constant is related to the change in molar Gibbs free

energy (AG) by

12

where R is the gas constant and T is the absolute temperature. The selectivity

for two solutes is correspondingly related as

Ina=ln§f=¥ (1.4)
where AAG represents the difference in molar Gibbs free energy for chiral
selectivity. The Gibbs free energy is related to the changes in molar enthalpy
(AH) and molar entropy (AS) by the Gibbs-Helmholtz equation [7]

AG=AH—T AS (1.5)
By substitution, the retention factor can be related to the molar enthalpy and

molar entropy as follows

lnk=InK-lnfl=%fl+%S-—lnfi (1.6)

The change in molar enthalpy can be determined by graphing the natural
logarithm of the retention factor versus inverse temperature at constant pressure.
This will yield a slope that is related to the change in molar enthalpy, and an
intercept that contains information about the change in molar entropy and the
phase ratio. When the phase ratio is known, the molar entropy can be
determined from the intercept. However, the phase ratio is often not known and
accurate determination of the molar entropy is not possible. The phase ratio and
the molar entropy must be independent of temperature for accurate
determination of the molar enthalpy. The change in molar enthalpy will be

positive for an endothermic transfer and negative for an exothermic transfer of

13

the solute from mobile to stationary phase. The change in molar entropy will be
positive when there is a favorable dissipation of energy through an increase in
die number or distribution of microstates. This most commonly occurs through a
change in volume or concentration, leading to a change in configurational
entropy, as the solute is transferred from the mobile to stationary phase. The
selectivity for two solutes is correspondingly related as

-AAH AAS
= +

In
a RT 12

 

(in

Thus, a graph of the natural logarithm of the selectivity versus inverse
temperature will yield from the slope and intercept the differential change in
molar enthalpy (AAH) and molar entropy (AAS), respectively, associated with the
chiral selectivity (Chapter 5).
From the definition of the molar enthalpy

AH = AE + PAV (1.8)
where AE is the change in molar internal energy, AV is the change in molar
volume, and P is the pressure. Substitution of Equation 1.8 into Equation 1.6
yields

—AE_PAV+AS

lk= ———l 10
" RT RT R "B ( )

 

The change in molar volume can be determined by graphing the natural
logarithm of the retention factor versus pressure at constant temperature. This
will yield a slope that is related to the change in molar volume, and an intercept
that contains information about the molar internal energy, molar entropy, and

phase ratio. These parameters must be independent of pressure for accurate

14

determination of the molar volume. The change in molar volume will be positive
when the solute occupies a larger volume and negative when the solute occupies
a smaller volume in the stationary phase man in the mobile phase.

To gain a greater understanding of the balance of thermodynamic
contributions to solute retention, enthalpy-entropy compensation is very useful.
For a pair or series of solutes that obey a linear free energy relationship [8], there
exists a hypothetical temperature at which the relative changes in enthalpy and
entropy are balanced and the not change in free energy is zero. By

rearrangement of Equation 1.5, this compensation temperature (To) can be

expressed as
AAH
T =— 1.10
° AAS ( )

At this temperature, the pair or series of solutes would co-elute and no
separation would be achieved (a = 1.0). Hence, it is also called the isoselective
temperature or iso-enantioselective temperature (T r...) in chiral separations. A
compensation temperature that is substantially greater than ambient temperature
suggests that the retention mechanism is enthalpy-dominated, whereas a
compensation temperature that is less than ambient temperature is entropy-
dominated.

The compensation temperature can be determined from the slope of a
graph of the change in molar enthalpy versus the change in molar entropy, both
derived from Equation 1.6. However, for statistical reasons, a linear relationship
may be observed between AH and AS even in the absence of enthalpy-entropy

compensation [9]. Krug et al. [10] investigated different methods to identify true

15

enthalpy-entropy compensation that is not influenced by statistical artifacts. By
means of Equation 1.6, the free energy at a specific temperature (T) can be

related to the free energy at the compensation temperature (T c) by

1' TAGT
AG=AH 1-— +———°- (1.11)
TC TC

The retention factor can then be related to the free energy at the compensation

temperature by

AH 1 1 AG
n [ J + RTc n B ( )

Thus, a graph of the natural logarithm of the retention factor versus the change in
molar enthalpy may be used to evaluate enthalpy-entropy compensation. If
compensation occurs, this graph will be linear and the slope can be used to
calculate the compensation temperature. The compensation temperature may
be used to compare the retention mechanisms for different solutes, different
mobile phases, or different stationary phases. As discussed by Ranatunga et al.
[11], if the compensation temperatures are identical, then the relative
contributions of enthalpy and entropy to the overall free energy are the same for
the two systems. However, if compensation temperatures are different, then the
underlying retention mechanisms must be distinctly different.
1.3.2 Kinetics

Whereas thermodynamic information is vital, kinetic information provides a
deeper understanding of the retention mechanism. If the retention process is
treated as a first-order or pseudo-first-order reaction, k.... and k... are the

corresponding rate constants for solute transfer from mobile to stationary phase

16

and from stationary to mobile phase, respectively. These are “lumped“ rate
constants, i.e., they comprise all contributions to the kinetic behavior including
the sorption/desorption event, diffusion in the mobile and stationary phases.
diffusion in pores and stagnant layers, interfacial resistance to mass transfer, etc.
The rate constants, which reflect the kinetic behavior, are related to the retention
factor, which reflects the thermodynamic behavior, by

"W (1.13)

k = —
k...

The detailed kinetic parameters can be elucidated by applying a
combination of thermodynamic and transition-state theories. The rate constant

k... is expressed by the Arrhenius equation as

—AE
km = Am, exp[ RT”) (1.14)

 

where Am; is the pre-exponential factor and AEm3 is the activation energy for the
transfer from mobile to stationary phase. By rearrangement,

AEm

RT (1.15)

lnkm=lnAm-

The activation energy can be determined by graphing the natural logarithm of the
rate constant versus inverse temperature at constant pressure. This will yield a
slope that is related to the activation energy, and an intercept that contains
information about the pro-exponential factor. The activation energy represents
the energetic barrier that must be overcome for the solute transfer from mobile to

stationary phase.

17

By using classical thermodynamic relationships, the activation energy is
given by

A5,“, =Al-lm, +RT—P Avm, (1.16)

By substitution into Equation 1.15

AH,“1 + RT — P Avm,
RT

 

in it", =ln Am- (1.17)

The activation volume can be determined by graphing the natural logarithm of the
rate constant versus pressure at constant temperature. This will yield a slope
that is related to the activation volume, and an intercept that contains information
about the activation enthalpy and pre-exponential factor. The activation enthalpy
and pre-exponential factor must be independent of pressure for accurate
determination of activation volume. The activation volume represents the
volumetric barrier that must be overcome for the solute transfer from mobile to
stationary phase. In a similar manner, the rate constant k... can be used to
determine the activation energy (AEq) and activation volume (Ava) for the solute
transfer from stationary to mobile phase. These kinetic quantities provide a
detailed description of the energetic and volumetric requirements of the retention

process that complement the thermodynamic description.
1.4 METHODS FOR THERMODYNAMIC AND KINETIC STUDIES

1.4.1 Perturbation Methods
Among the available methods for evaluation of thermodynamic and kinetic
parameters, perturbation methods play an important role [12]. Perturbation

methods represent the simplest approach, wherein the solute, mobile phase, and

18

stationary phase of interest are contained in a small, static cell. A fast
perturbation is applied to the equilibrium in order to alter the activity or
concentration of the solute in the mobile and stationary phases. The perturbation
may be achieved by rapidly changing conditions such as temperature, pressure,
or dipole moment. After perturbation, the rate of relaxation of the system to the
new conditions is monitored, followed by mathematical extraction of the
equilibrium and rate constants. The advantage of the perturbation methods is
their simplicity, where thermodynamic and kinetic behavior can be measured
without interference from flow contributions. The measured rate constants
consist of the sorptionldesorption process and diffusional contributions to mass
transfer. One of the limitations of these methods is that they require perturbation,
during which the actual thermodynamic and kinetic behavior of the system is
altered. Hence, the determined values of equilibrium and rate constants are
neither those of the initial state nor of the final state after perturbation. In order to
minimize the required perturbation, the equilibrium constant should be as close to
unity as possible. This ensures the greatest change in activity or concentration
for a given perturbation of the system. In addition, the perturbation must be
applied uniformly to the entire system and with sufficient speed that it does not
contribute to the observed kinetic behavior. Although these methods are very
promising, their application to chromatographic systems has been relatively

limited.

19

1.4.2 Shallow-Bed Method

The shallow-bed method can be considered as an intermediate between
perturbation methods and chromatographic methods. In this method, the
stationary phase particles are packed in an extremely short (“zero length”)
column. The experiments may be performed in two ways: sorption (uptake) or
desorption (release) methods. In the sorption method, a mobile phase solution
containing the solute flows through the shallow bed at a high linear velocity. The
concentration of the solute in the effluent solution is nearly identical to that in the
influent solution. If the linear velocity is sufficiently high, the stagnant diffusion
layer surrounding the particle will be thin. Hence, the time required for diffusion
through this layer will be small compared to the time required for the slow
intraparticle processes. As a result, the intraparticle processes will determine the
observed sorption rate. After a certain time, the flow is stopped and the amount
of solute that has been sorbed is measured by eluting it out of the shallow bed.
This measurement provides a single point on the sorption curve. This
experiment is then repeated for varied sorption times to construct the complete
sorption rate curve.

An alternative approach that is less time-consuming and labor-intensive is
the desorption method. In this method, the shallow bed is pre—equilibrated by
flow of a mobile phase solution containing the solute. To initiate the experiment,
the flow is abruptly shifted to a solute-free mobile phase, which causes the solute
to be desorbed from the bed. By detecting the eluted solute concentration as a

function of time, the desorption curve can be constructed from a single

20

experiment. Specifically speaking, the concentration C(t) is a function of the
instantaneous molecular desorption rate of the solute (dni(t) l dt) and of the flow

rate (F) as follows

00km (1.18)

F

After integration, the desorption rate curve is constructed as

n.(t)

II
11
‘—.
,Q
n
V
O.
F.

(1.19)

The desorption rate curve is then fit by nonlinear regression to different
theoretical models, such as the linear driving force model and spherical diffusion
model, to extract the rate constants [13-16].
1.4.3 Chromatographic Methods

Chromatographic methods are the most widely used methods for
determining thermodynamic and kinetic behavior of the system.
Chromatographic methods are dynamic with mobile phase flowing though the
column at all times. In this way, the contribution of flow phenomena to the zone
profile cannot be neglected. The two most common chromatographic methods
are frontal and impulse methods.
1.4.3. 1 Frontal method

In frontal analysis, the column is pre-equilibrated with the mobile phase.
Then, a solution containing a known concenfiation of solute in the mobile phase
is introduced continuously. As the solute sorbs onto the stationary phase, the
column becomes saturated and the concentration of solute eluting from the

column gradually increases, forming a characteristic breakthrough curve. The

21

mean position of the breakthrough curve can be related to the concentration and
equilibrium constant of the solute as well as the sorption capacity of the column.
The amount of solute sorbed is calculated from the breakthrough curve in order
to derive a single point on the equilibrium isotherm. This process is repeated for
progressively increasing concentrations of the solute to construct the complete
isotherm. Three represented isotherm types are illustrated in Figure 1.4. Linear
isotherm would produce a Guassian peak shape, Langmuir isotherm would
produce a tailing peak shape, and Anti-Langmuir isotherm would produce a
fronting peak shape.

To obtain kinetic information, theoretical breakthrough curves are
numerically calculated for each concentration step. These theoretical curves use
different values of the rate constant in the transport model, together with the
equilibrium isotherm determined from the breakthrough data. The theoretical
breakthrough curves are then compared to the experimental ones. The rate
coefficient is determined in such a way that the best agreement is observed
between the theoretical and experimental breakthrough curves. In this approach,
it is assumed that the rate constant remains constant during each concentration
step in the frontal analysis measurement and that this rate constant corresponds
to the average concentration of each step [17].
1.4.3.2 Impulse method

The impulse method is generally performed by injecting a small volume of
the solute onto the column. The elution of the solute zone is monitored by on-

column or post-column detection. The retention factor and rate constants can be

22

Linear Langmuir Anti-Langmuir

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

U' 0' U
C C C
o 0 K o \
2 2 2
0' O' 0'
'O 'O “D
c c c
0 O 0
t t t
Gaussian Talling F rontlng

Figure 1.4 Three typical adsorption isotherms. q: loading, 0: concentration, t:

time.

23

extracted by any of the following models.
1 . 5.3.2.1 Plate-height model

In this model, the thermodynamic and kinetic parameters are determined
from the mean and the broadening of the zone profile, respectively. The
broadening or plate height may be determined in a variety of ways, but the most
accurate is the statistical moments as they make no assumptions about the
shape of the zone profile. The first and second statistical moments are

calculated from the zone profile as

C(t) t dt

M1 = 1r— (1.20)
C(t) dt

M = joltllt-Ivtldt

2 [0(1) dt “'21)

 

The first moment (M1) represents the mean retention time. It can be directed
related to the retention factor by

_M1‘t0

k _ (1.22)
t0

where to is the elution time for a non-retained compound.
The method of calculating kinetic rate constants is derived by
extrapolation of Giddings’ work [18]. The plate height in the length domain (H)

can be related to the second moment (M2) in the time domain by

0’2 M u 2
L (1+k) ( )

24

where uo is the mobile-phase linear velocity. The mass transfer term (0.) for

slow kinetics in a system that exhibits a partition or adsorption mechanism is

given by
2k

=——————- 124
' 0+kfkm ( )
Thus,

2
ms =__?_|.‘_l_’°_ and km =_i29_ (125)
(1+1:deL (1+1:deL

where dHL is the contribution to plate height arising from slow mass transfer.
Miyabe and Guiochon have evaluated the plate height contributions to
various mass transfer processes [18]. In their approach, the statistical moments

can be further elucidated as

M=fh mm)

0

M2 = %(aug. 5, + a.) (1.27)
0

where 80 is a dimensionless retention parameter, equal to 1 + k. and is given by
50 = a + (1 — a)(ep + ppK) (1.28)
The contributions to M2 from axial dispersion (632), external mass transfer (8i),

and intra-particle diffusion (63), respectively, are given by

5,, = [929] 53 (1.29)
u0
RD
5, = (1 nob?) (ep + p,,K)2 (1.30)

25

 

R2
is, =(1-e)[15l"D ](::p +9.,K)2 (1.31)

where a is the inter-particle void fraction, 9., and pp are the porosity and density of
the packing material, Rp is the particle radius, DL is the axial dispersion
coefficient, kr is the external mass transfer coefficient, D. is the intra-particle
diffusivity, and K is the equilibrium constant. Under conditions where the rate of

sorptionldesorption is negligibly small, the plate height can be written as
M L D 6 6

H = __2 = __L- + ._I + _d 1.32
[vii ] i a: a: ‘ ’

The different parameters that are related to mass transfer processes can be

 

estimated or calculated based on the above equations. For example, the
external mass transfer coefficient, diffusion coefficient in the mobile phase, and
pore diffusion coefficient can all be estimated, and the diffusion coefficient in the
stationary phase can thus be calculated. More specific information on the
foundations and application of this model can be found in the excellent review by
Miyabe and Guiochon [18].

The plate-height model assumes that all contributions to variance, both
symmetric and asymmetric, that are not directly attributable to fast processes
such as axial dispersion arise from slow kinetics. There are several potential
sources of error in this method. First, this method requires that the solute
concentration be within the linear region of the isotherm, such that it does not
contribute to the variance. Second, this method relies on the accurate
calculation and subtraction of all fast mass transfer terms, which is difficult for

packed columns in liquid chromatography. Empirical estimations of these

26

parameters will introduce errors. Moreover, any extra-column contributions to
variance, including those from the injector, detector, connectors, etc., must be
accurately calculated and subtracted. Again, there are no theoretical methods
for the calculation of these parameters, so empirical estimations are necessary.
1.4. 3. 2.2 Exponentially modified Gaussian (EMG) model

Consider an incremental length of the chromatographic column. Zone
broadening can arise from multiple paths, diffusion, and mass transfer processes
that are fast relative to the time spent in the incremental length. These
processes contribute to the symmetric broadening, which is described by a

Gaussian function

C(t) = 42—20 exp[- 0.5 [:t' T] (1.33)

where A is the area, tg is the retention time of the Gaussian component, and 09 is

 

 

the standard deviation of the Gaussian component.

In addition, zone broadening can arise from mass transfer processes that
are slow relative to the time spent in the incremental length. These processes
contribute to the asymmetric broadening. For a partition or adsorption
mechanism that can be considered as a first-order or pseudo-first-order reaction,

this contribution is given by an exponential function
c(:) = A 323(fl] (1.34)
T

where 1: is the standard deviation of the exponential component.

27

The zone profile observed at the end of the total column length is the
convolution of the Gaussian and exponential contributions, i.e., the multiplication
of the functions and integration within each incremental length. This convolution

is given by the exponentially modified Gaussian (EMG) equation

 

 

-3 ’2: 3;: Fig.5
C(t)—ZrexD(212+ I Mel-{.509 J21]+1] (1.35)

where art is an statistical error function. The zone profile is fit to the EMG
equation by nonlinear regression to extract the regression parameters (A, t9, 0...
1:). From these parameters, the retention time t, is calculated as

tr = t" + T (1.36)

and the corresponding retention factor is calculated as

 

(1.37)

The method of calculating kinetic rate constants from the EMG model is
derived by extrapolation of Giddings’ work [19]. The mass transfer term for slow
kinetics in the partition or adsorption mechanism is given by Equation 1.24. By

rearrangement, the rate constants are given by

 

 

2
=2kt0 and k =2kto

"1‘ 8m
12 12

k (1.38)

The EMG model assumes that all contributions to asymmetric broadening
(t) arise from slow kinetics. There are several potential sources of error in this
method. First, this method requires that the solute concentration be within the

linear region of the isotherm, such that it does not contribute to the asymmetry.

28

Second, any extra-column contributions to asymmetry must be minimized or
eliminated. In practice, this is achieved by detection at several points along the
chromatographic column and subtraction of the parameters determined at each
detector [19]. It is noteworthy that the EMG method does not require a prion“
estimation, whether by theoretical or empirical means, of symmetric column or
extra-column contributions to broadening.
1.4. 3.2.3 Giddings model

By means of stochastic theory [14], Giddings derived a model suitable for
theoretical treatment of the adsorption mechanism under first-order or pseudo-

first-order conditions
C(x) = A7 J52 i,(2y./k—x)exp(— yx-yk) (1.39)

where y is a dimensionless constant, equal to the product of the desorption rate
constant (k...) and the elution time of a nonretained compound (to). After
conversion from the time domain (t) to the retention factor domain (x), the zone
profile is fit by nonlinear regression to Equation 1.39. From the regression
parameters (A, k, y), the corresponding retention factor and rate constants are
calculated.

The Giddings model assumes that all contributions to symmetric and
asymmetric broadening arise from slow kinetics. There are several potential
sources of error in this method. First, this method requires that the solute
concentration be within the linear region of the isotherm, such that it does not
contribute to the broadening. Second, this method requires that column

contributions from multiple paths and diffusion in the mobile and stationary

29

phases be negligible. Moreover, any extra-column contributions, including those
from the injector, detector, connectors, etc., must also be negligible. Unlike the
plate height and EMG methods, there is no a posteriori method to correct for
these contributions.

1.4. 3. 2.4 Nonlinear chromatography models

All of the impulse methods described above are suitable for
thermodynamic and kinetic measurements within the linear region of the isotherm.
However, some mechanisms such as adsorption, ion exchange, and
complexation have stationary phases with a limited number of sites that may be
easily overloaded. Hence, it is desirable to be able to evaluate their behavior
under nonlinear conditions.

A convenient method to extract thermodynamic and kinetic information
from frontal profiles was reported by Thomas [20] and later modified for elution
zone profiles by Wade et al. [21]. This model was derived for mechanisms that
can be considered as second-order sorption and first-order desorption reactions

under linear and nonlinear conditions. This theoretical model is given by

000 = [3%] (1 - exp(— 1K0. )) [(1 'fi/ $231)? (figs?) (1.40)

 

where
T(u,v) = e" u[e410 (va7 )dt (1.41)

In this equation, 1 is a dimensionless constant equal to the product of the
desorption rate constant (k...) and the elution time of a nonretained compound

(to), k is the retention factor, K is the equilibrium constant, and Co is the initial

30

concentration. After conversion from the time domain (t) to the retention factor
domain (x), the zone profile is fit by nonlinear regression to Equation 1.41. From
the regression parameters (A, k, y, KCo), the corresponding retention factor and
rate constants are obtained.

The Thomas model assumes that all contributions to symmetric and
asymmetric broadening arise from nonlinear isotherms and slow kinetics, which
is a combination of mass transfer and sorptionldesorption processes. There are
several potential sources of error in this method. First, this method assumes the
kinetics and the isotherm to be Langmuirian. Second, this method requires that
column contributions from multiple paths and diffusion in the mobile and
stationary phases be negligible. Moreover, any extra-column contributions,
including those from the injector, detector, connectors, etc., must also be
negligible. Unlike the statistical moment and EMG methods, there is no a
posten'on' method to correct for these contributions.

Other nonlinear chromatography models have been reviewed by Golshan-
Shirazi and Guiochon [22,23]. Among those that provide both thermodynamic
and kinetic information are the reaction-dispersive and transport-dispersive
models. The reaction-dispersive model presumes that sorptionldesorption
kinetics are slow relative to the fast kinetics of mass transfer. The transport-
dispersive model presumes that mass transfer kinetics are slow relative to the
fast kinetics of sorption/desorption. These simplifications allow numerical

solution of the general rate model for comparison of theoretical and experimental

31

zone profiles. Further information, including direct comparison of these models

with the Thomas model, can be found in the previously published review [23].
1.5 PREVIOUS INVESTIGATIONS OF CHIRAL SEPARATIONS

1.5.1 Inclusion-Type CSP

Cyclodextrins were first immobilized to solid supports in 1978 [24]. Since
then, extensive work has been done to improve the stability and versatility of
cyclodextrinsilica CSPs, which made possible their commercialization in the
1980s. However, despite the large number of publications, only limited
information is available on the thermodynamic characterization of these CSPs,
and even less information is available on the kinetic characterization. Both
thermodynamic and kinetic information are important for elucidation of the
retention mechanism.

The earliest studies of temperature effects were focused on optimization
of the separation process [25,26]. In these studies, lower temperature was
shown to increase retention, due to stronger interactions between the solutes
and the CSP, and also to increase enantioselectivity. A more detailed study of
temperature was carried out by Cabrera and Lubda [27]. They separated two
chiral pharmaceuticals, oxazepam and mephobarbital (Prominal), on native [3-
cyclodextrinsilica operated in the reversed-phase mode. A decrease in
temperature caused an increase in retention factor for both solutes, however, it
caused different effects on their enantioselectivity. The enantioselectivity was
increased by reducing temperature for oxazepam, but increased by increasing

temperature for mephobarbital. The van’t Hoff plots were linear for both solutes

32

over the temperature range of 5 to 40 °C. From the thermodynamic data, the
authors concluded that the differences in enantioselectivity were related to the
enthalpy-controlled separation of oxazepam enantiomers (AAH = -332 cal/moi,
AAS = 55 cal/moi) and the entropy-controlled separation of mephobarbital
enantiomers (AAH = 374 cal/moi, AAS = 419 cal/moi). Morin et al. [28] also
studied the effect of temperature on B—cyclodextrinsilica with a series of six
imidazole derivatives. Over the temperature range of 20 to 55 °C. the van’t Hoff
plots for all solutes were linear at pH 7.0 and 7.5, but curved at pH 6.5, 8.0, and
8.5. The curved plots showed a minimum in the logarithm of the retention factor
between 35 and 40 °C. The changes in molar enthalpy and entropy were
determined from the van’t Hoff plots. An enthalpy-entropy compensation
analysis revealed that the retention mechanism was the same for all solutes at
pH 7.0 and 7.5, and also the same for all solutes at pH 6.5, 8.0, and 8.5. From
thermogravimetric analysis and differential scanning calorimetry, the authors
speculated that a phase transition occurred at 43 °C between the ordered and
disordered state of the cyclodextrin cavity at pH 6.5, 8.0, and 8.5, but not at pH
7.0 and 7.5. In the disordered state, a gain in freedom of the hydroxyl groups on
each edge of the cyclodextrin cavity was obtained, with the minimum extent of
hydrogen bond formation between them. In contrast, in the ordered state, a loss
in freedom of the hydroxyl groups was obtained, with the maximum extent of
hydrogen bond formation. As a result, the hydrophobic character, surface
tension, and structure of the cyclodextrin cavity were all affected, thereby altering

the retention mechanism.

33

Peyrin et al. [29] investigated the inclusion phenomena between [3-
cyclodextrinsilica CSP and a series of dansyl amino acids with the salting-out
agent sucrose. When the solute transfers from mobile to stationary phase.
sucrose is displaced from the cyclodextrin cavity. With a simple physicochemical
model, the number of displaced sucrose molecules can be determined, and the
relative extent of solute inclusion can thus be calculated. The authors concluded
that the L-enantiomers of the dansyl amino acids displaced a constant number of
1.9 sucrose molecules regardless of the R group. In contrast, the D-enantiomers
displaced a larger number of sucrose molecules that decreased from 2.7 to 2.2
as the accessible surface area of the R group increased. Hence, the chiral
recognition and enantioselectivity decreased with increasing size of the R group.
The theoretical value of the accessible surface area that corresponded to no
chiral resolution was 191 A2. It is noteworthy that the equivalent length of the R
group (7.8 A) is equal to the internal diameter of the native B—cyclodextrin cavity.
The authors concluded that the inclusion process was largely dependent on
steric hindrance. Temperature was also varied from 20 to 45 °C to observe the
thermodynamic effects on enantioselectivity. The negative AAH and AAS values
were determined from the linear van’t Hoff plots, which indicated an enthalpy-
controlled separation for all dansyl amino acids. The AAH and AAS values
became less negative with increasing accessible surface area of the R group and
more negative with increasing sucrose concentration. A similar approach was
utilized by Guillaume et al. [30] using water as a surface tension modifier in the

mobile phase. In this case, water was displaced when the dansyl amino acids

were transferred to the B-cyclodextrin cavity. Similar results were concluded on
the relative degrees of inclusion of the D- and L- enantiomers and the importance
of steric effects in the chiral recognition mechanism.

The effect of pressure on the separation process with a [3-
cyclodextrinsilica CSP was investigated by Ringo and Evans. With the positional
isomers of nitrophenol as model solutes, a shift in retention with modest pressure
change (300 bar) was observed and correlated to the change of partial molar
volume for the complexation process [31]. The same method was applied to
chiral separations with barbiturates, B-blockers, and anticoagulants as model
solutes [32-34]. Most chiral compounds showed a dependence of the retention
factor, enantioselectivity, and separation efficiency on pressure. The retention
factor dependence reflected the statistical non-zero changes of molar volume for
the complexation processes. The retention factors exhibited an increase or no
change with pressure, and the change in molar volume was negative or
negligible in the reversed-phase mode. However, in the polar-organic mode, the
retention factors showed a decrease with pressure, and the change in molar
volume was positive or negligible. The change in molar volume ranged from -12
to 17 cmalmol. The enantioselectivity dependence reflected the unequal
changes of molar volume between the enantiomers. Mephobarbital, metoprolol,
and warfarin demonstrated a dependence of selectivity on pressure, with both
positive and negative dependence observed. These pressure experiments
provided insight into the differential volume of enantiomeric complexes formed

with B—cyclodextrin.

35

Recently, Ching et al. [35,36] investigated both thermodynamic and kinetic
behavior of derivatized B—cyclodextrinsilica CSPs. The equilibrium and kinetic
constants for the chiral separation were obtained by moment analysis on the
basis of the equilibrium-dispersive and transport-dispersive (solid-film linear
driving force) models. The overall mass transfer coefficients, axial dispersion
coefficients, and equilibrium constants were used to simulate the enantiomeric
band profiles. Excellent correlation between simulated and experimental results
confirmed the accuracy of the method as well as the results. The overall mass
transfer coefficients were determined to be 58 and 73 min"1 for S- and R-
fluoxetine, respectively, and 669, 846, and 106 min'1 for the co-eluted SRS- and
SSR—nadolol, RRS-nadolol. and RSR-nadolol, respectively. These kinetic data
indicate that mass transfer processes in the derivatized B-cyclodextrinsilica CSPs
are relatively rapid.

1.5.2 Brush-Type CSP

Although there have been few systematic thermodynamic studies of
Pirkle-type CSPs, temperature has been successfully utilized as an optimization
tool. Mazzo et al. [37] optimized the chiral separation of an antihypertensive drug,
MK-286, with an N-(3,5—dinitrobenzoyl)phenylglycine CSP. The retention factors
and enantioselectivity increased with decreasing temperature, however, the peak
broadening (plate height) also Increased. Because of these concomitant
changes, the resolution increased from 0.75 at room temperature to 1.25 at 0 °C.
Although no thermodynamic parameters were reported here, it was probably an

enthalpy-controlled process that facilitated separation at lower temperature.

36

Pescher et al. [38] optimized the separation of tertiary phosphine oxides with N-
(3,5—dinitrobenzoyl) derivatives of phenylglycine, serine, and alanine as CSPs.
They observed a similar effect of temperature, where the enantioselectivity with
the phenylglycine CSP increased from 1.52 to 2.33 with a decrease in
temperature from 50 to -15 °C. A nonlinear dependence of enantioselectivity on
temperature was observed by Weaner and Hoerr [39]. They investigated a
series of fatty acid esters and amide epoxides on an N-(3,5-
dinitrobenzoyl)phenylglycine CSP. While the enantioselectivity of the ester
decreased rapidly above 0 °C. those of the amide reached a maximum at 10 °C
and remained constant up to 40 °C. This behavior was attributed to the weak
interaction forces between the ester and CSP, and to the relatively strong forces
between the amide and CSP. Pirkle also observed some unusual temperature-
dependent behavior [40]. In the separation of spirolactam enantiomers on an N-
(3,5-dinitrobenzoyl)phenylglycine CSP, a nonlinear van’t Hoff plot was obtained.
The curvature of these plots was dependent on the concentration of 2-propanol
in the mobile phase, which indicated a temperature-dependent interaction of 2-
propanol with the stationary phase or with the solute. However, the natural
logarithm of enantioselectivity versus the inverse temperature gave a linear
relationship, which indicated that this behavior affected both enantiomers equally
and had little influence on the chiral recognition mechanism. Another example
with the separation of N-(3,5-dinitrobenzoyl)-1-phenylethylamine enantiomers
showed an initial decrease in enantioselectivity with a reduction of temperature,

followed by an inversion of elution order and, subsequently, an increase in

37

enantioselectivity [41]. The observed temperature effects showed a dependence
on the type and concentration of organic modifier in the mobile phase.

Pirkle and Welch [42] systematically investigated the role of solvation on
the separation of N-(2-naphthyl)alanine derivatives on an N-(3,5-
dinitrobenzoyl)leucine CSP. In general, both retention and enantioselectivity
decreased with increasing mobile phase polarity in both normal- and reversed-
phase modes. The van’t Hoff plots, obtained over a temperature range of 0 to 90
°C. were used to evaluate the thermodynamic changes in molar enthalpy and
entropy as a function of mobile phase composition. Under all conditions, the
changes in molar enthalpy and entropy were negative as were the differential
changes (AAH and AAS) for each pair of enantiomers. The enthalpy and entropy
changed in a similar manner with the polarity of the mobile phase, which
indicated that the highly exothermic sorption was accompanied by a
correspondingly large loss in entropy. The authors noted that this behavior is
analogous to enthalpy-entropy compensation, as discussed previously. The
steric effects of the organic modifier were further investigated by Blackwell et al.
[43]. Their detailed study used linear, branched, and cyclic alcohols (ranging in
size from ethanol to octanol) in the normal-phase mode with amide derivatives of
1-phenylethylamine as model solutes. The enantioselectivity varied slightly (1.15
— 1.35) as a function of the modifier structure for an N-(3,5-
dinitrobenzoyl)phenylglycine CSP. The enantioselectivity was higher and varied
more greatly (1.53 - 2.44) with modifier structure for an N-(3,5-dinitrobenzoyl)-4-
amino-1,2,3,4-tetrahydrophenanthrene (Whelk-O) CSP. For both CSPs, the

38

smallest selectivities were observed for 1-hexanol and cyclohexanol. The
greatest selectivities were observed for bulky modifiers, such as 2-propanol, 2-
butanol, and 2-methyl-2-propanol. The greater selectivities were the result of a
dramatic increase in retention of the second enantiomer. Based on detailed
thermodynamic measurements, the authors suggested that the bulky modifiers
cannot penetrate into the tight complex formed between the second enantiomer
and the CSP. They also suggested that chiral separations giving large
enantioselectivity (a > 2). such as those with the Whelk-O CSP, were not
consistent with the classical three-point interaction model of Dalgliesh [44]
(Figure 1.3). These separations exhibited a wide range of selectivities, were not
well described by linear salvation energy relationships, and did not exhibit
consistent enthalpy-entropy compensation behavior with varying modifier
structure.

Thermodynamic studies can also be used to examine the nature of the
surface for covalently bonded CSPs. Pirkle and Readnour [45] designed a
chromatographic system utilizing rt-basic CSPs with a series of n-acidic solutes,
bis-(2.4-dinitrophenyl)—a,to-diaminoalkanes (bis-DNPs). The number of
methylene groups in the bls-DNPs was varied in order to influence their ability to
interact with the CSP. The enthalpy of sorption. determined from van’t Hoff plots,
was expected to be maximized (most negative) when the length of the bis-DNPs
matched the distance between strands of the stationary phase. By using this
approach, the authors found maximum enthalpy when the number of methylene

groups was equal to five. For CSPs having different surface coverage (0.36 to

39

1.36 pmol/mz), maximum enthalpy occurred with the same number of methylene
groups, but with different maximum enthalpy values. These interesting results
suggested that the strands were not randomly distributed on the silica surface,
but clustered with similar distributions of interstrand distances. The surface
coverage thus affected the size of the cluster rather than the average distance
between clusters.
1.5.3 Amylose- and Cellulose-Type CSP

The temperature dependence of chiral discrimination was investigated by
Smith et al. [46]. Two analogues of Cromakalim, a potassium channel activator,
were separated on cellulose derivatized with tris(3,5-dimethylphenylcarbamate)
(ChiralceI-OD) over the temperature range from 0 to 42 °C. Although the two
analogs differ only by replacement of a benzoyl group with an n-pentanoyl group,
they showed different temperature dependence. The benzoyl enantiomers
exhibited an increasing trend in resolution with increasing temperature, whereas
the n-pentanoyl enantiomers had a decreasing trend. The van't Hoff plots were
linear for all enantiomers, from which the changes in molar enthalpy and entropy
were determined. A large difference was observed for AAH (1.929 and 4.265
kJ/mol for the benzoyl and n-pentanoyl enantiomers, respectively), but relatively
small difference for AAS (10.3 and 13.6 J/mol K, respectively). The
isoenantioselective temperature, which is analogous to the enthalpy-entropy
compensation temperature. also differed greatly (-86 and 41 °C. respectively).
Hence, the benzoyl enantiomers exhibited an entropy-dominated separation,

whereas the n-pentanoyl enantiomers had an enthalpy-dominated separation.

40

The authors concluded that increased temperature should be beneficial for any
chiral separation that predominantly involves n-type electron donor-acceptor
interactions and, conversely, that decreased temperature should be beneficial for
separations that predominantly involve hydrogen bonding interactions. This
general conclusion was confirmed by Kuesters and Spoendlin [47] for the
separation of rolipram and a series of structurally related compounds on the
same ChiralceI-OD CSP over the temperature range from 10 to 60 °C. These
aromatic compounds showed an unusual entropy-dominated separation with
AAH of 1.62 kJ/mol and AAS of 5.72 Jlmol K for rolipram, similar to the entropy-
dominated separation of the benzoyl analog discussed above. More enthalpy-
dominated separations were observed by Mesplet et al. [48] for some
phosphoramidate derivatives of anti-H IV nucleosides.

A detailed mechanistic investigation was undertaken by O'Brien et al. [49]
with a diol intermediate for a Ieukotriene D4 antagonist separated on cellulose
derivatized with tris(4-methylbenzoate) (ChiralceI-OJ). A nonlinear van’t Hoff plot
was observed over the temperature range of 5 to 50 °C for both retention factor
and selectivity. At low temperature, the enantioselectivity was entropy-controlled
with positive values for AAH and AAS, but at high temperature, it was enthalpy-
controlled with negative values for AAH and AAS. This temperature dependence
was very unusual. In general, the entropy contribution (T AAS) should tend to
increase with increasing temperature and overcome the enthalpy contribution
(AAH), thereby changing the separation mechanism from enthalpy-dominated to

entropy-dominated with increasing temperature. The unusual temperature

41

dependence observed by O’Brien et al. suggested a phase transition in the CSP.
The transition observed in the van’t Hoff plots occurred at a temperature of
approximately 18 °C. where a conformational change in the stationary phase was
confirmed by infrared spectroscopy and differential scanning calorimetry. The
thermodynamic behavior was also examined for different mobile phase
compositions in the normal-phase mode. With an increase in concentration of
the organic modifier, 2-propanol, an increase in AAH was observed,
accompanied by an increase in AAS. These two effects cancelled each other by
means of enthalpy-entropy compensation and resulted in a negligible change in
molar free energy. This explained why an increase in the concentration of 2-
propanol had virtually no effect on enantioselectivity. The authors suggested that
the loss of interaction energy for the more retained R-enantiomer relative to the
S-enantiomer with increasing 2-propanol concentration was balanced by a
relative increase in the space available for the R-enantiomer when it entered the
stationary phase. This was indicative of a swelling of the cellulose CSP with
increasing 2-propanol concentration. The kinetic behavior was also evaluated by
means of the plate-height method. Reduced plate height is calculated the plate
height divided by the particle size. For the more retained R-enantiomer, the
reduced plate height was large at temperatures up to 10 °C. but showed a sharp
decrease above 15 °C. However, for the S-enantiomer, the reduced plate height
showed a gradual decrease over the entire temperature range of 5 to 50 °C.
These data suggested that slow mass transfer processes occurred for the R-

enantiomer at lower temperatures. This behavior was attributed to the relatively

42

slow inclusion of the R-enantiomer at low temperature, where the cellulose
chains are rigid.

In closely related studies, Wang et al. [50-52] have also reported some
unusual temperature effects with polysaccharide CSPs. They separated the
enantiomers of dihydropyrimidinone (DHP) acid and its methyl ester on both
amylose and cellulose derivatized with tris(3,5-dimethylphenylcarbamate)
(Chiralpak—AD and Chiralcel-OD). A nonlinear van't Hoff plot was observed for
R- and S-DHP acid on Chiralpak-AD, but a linear relationship was observed on
ChiralceI-OD. Moreover, the van’t Hoff plots obtained with Chiralpak-AD upon
cyclic heating and cooling between 5 and 50 °C were not superimposable. This
suggested an irreversible, thermally induced conformational change of Chiralpak-
AD at approximately 30 °C. Solid-state NMR was utilized to verify and to
characterize this conformation change. Booth and Wainer [53] investigated the
separation of mexiletine and a series of structurally related solutes on Chiralpak-
AD CSP. Although a nonlinear van't Hoff plot was observed for one solute
(which was subsequently eliminated), linear van’t Hoff plots were observed for all
others over the temperature range from 0 to 30 °C. The change in molar
enthalpy was, thus, constant and negative for these solutes. An enthalpy-
entropy compensation plot of In k versus -AH was then constructed. The data for
these solutes fell into two distinct groups, with linearity observed within each
group. This linearity was indicative of an enthalpy-entropy compensation
phenomenon within that group of solutes. The two groups had different

compensation temperatures and, hence, different retention mechanisms. It was

43

interesting to note that one group contained the solutes with hydroxyl
substituents, while the other group contained all other solutes.

The frontal analysis method has been utilized by Guiochon et al. [54,55] to
elucidate thermodynamics and mass transfer kinetics. The sorption isotherms of
Troeger's base were determined on a microcrystalline cellulose triacetate CSP
over a temperature range of 30 to 60 °C. Whereas the S-enantiomer exhibited a
Langmuir isotherm, the R-enantiomer could best be described by a quadratic
equation for an S-shaped isotherm. The sorption enthalpies of both enantiomers
increased with increasing temperature. The mass transfer kinetics for the S-
enantiomer was studied by two different models, the equilibrium-dispersive and
transport-dispersive (solid-film linear driving force) models. The two approaches
gave almost identical results. The mass transfer rate constant was determined to
be around 7-11 min'1 for concentration steps from 0 to 3.2 glL of Troeger’s base.
1.5.4 Protein-Type CSP

Loun and Hage [56,57] have systematically investigated the chiral
separation mechanism of a human serum albumin (HSA) CSP by using warfarin
as a model solute. From frontal analysis, it was found that both enantiomers
have a single type of binding site in the same area of HSA. Temperature-
dependent measurements of the equilibrium constant. obtained over the range
from 4 to 45 °C. enabled the calculation of specific thermodynamic parameters.
Although the changes in molar free energy were similar for R- and S-warfarin
(-7.5 and -7.7 kcal/mol, respectively, at 37 °C), the contributions from molar

enthalpy and entropy were different. The R-enantiomer had a smaller

contribution than the S-enantiomer from the enthalpy change (-3.5 and -5.6
kcallmol, respectively), but a larger contribution from the entropy change (13 and
7 cal/moi K, respectively). The larger entropy change for R-warfarin indicated
that more solvent molecules were released during the binding, while the larger
enthalpy change for S-warfarin indicated stronger interaction during the binding.
This is consistent with a model in which R-warfarin interacts with amino acid
residues deep within the binding pocket of HSA mainly by hydrophobic
interactions, whereas S-warfarin interacts with residues at or near the outer rim
of the binding site mainly by polar interactions. The effect of mobile phase was
investigated by increasing the concentration of the polar organic modifier, 2-
propanol, in aqueous phosphate buffer. Concomitantly, the retention factor for R-
warfarin decreased, but that for S-warfarin increased. This result provided
further support for the authors’ suggestion that R-warfarin interacted by nonpolar
interaction, while S-warfarin interacted by polar interaction. From elution analysis,
the plate height model was utilized to study the band broadening processes and
to measure sorption/desorption kinetics. With an increase in temperature, both
the sorption and desorption rate constants increased, while the equilibrium
constant decreased. The faster kinetics resulted in a decrease in plate height
and an increase in column efficiency. The measurement of mass transfer
kinetics at different temperatures allowed the calculation of activation energy,
activation enthalpy, and activation entropy. Although the activation energy was
similar for R- and S-warfarin (10.8 and 11.5 kcallmol, respectively, at 37 °C), the

contributions from activation enthalpy and entropy were different. The R-

45

enantiomer had a larger activation enthalpy (10.5 and 1.9 kcallmol), but a smaller
activation entropy (-0.9 and 31 cal/moi K) than the S-enantiomer. The large
positive activation enthalpy for R-warfarin indicated more bonds breaking than
forming during the complex-formation process, whereas the more negative
activation entropy for S-warfarin indicated a higher degree of order. These
results also corresponded well with the retention model presented previously. In
this way, thermodynamic and kinetic information help to elucidate specific
retention and separation mechanisms. Similar experiments were performed for
another chiral solute, tryptophan, by Yang and Hage [58-60]. Both D- and L-
tryptophan had a single type of binding site but, unlike the warfarin enantiomers,
they were in different areas of HSA. The strength of L-tryptophan binding was
enthalpy-dominated, while D-tryptophan was entropy-dominated. Consequently,
L-tryptophan showed greater changes when varying the temperature, pH, ionic
strength, and modifier concentration of the mobile phase. These changes were
predominantly due to changes in the equilibrium constant, but also to changes in
the moles of binding sites (phase ratio). From kinetic studies, L-tryptophan
showed much greater broadening and, hence, slower kinetics than D-tryptophan.
The primary contribution was the much lower desorption rate of L-tryptophan
from the HSA phase.

Fomstedt et al. systematically investigated another type of protein CSP,
immobilized cellobiohydrolase l (CBH l), with some B—andrenergic blocking
agents as chiral solutes [61-64]. The sorption isotherms for both R- and S-

propranolol fit well to the bi-Langmuir model. One of the contributions was the

46

same for both enantiomers, whereas the other was different. The common
contribution was considered to be the nonchiral (Type I) interaction, while the
other was the chirally selective (Type II) interaction. It was suspected that the
chirally selective interaction involved the formation of ion pairs on this CSP.
Thus, the saturation capacity of the Type II sites was lower because of the limited
number of ionic sites. As a result, the enantioselectivity decreased with an
increase in solute concentration and eventually vanished when the nonchiral
interactions became predominant. Also, due to the ionic nature of the chirally
selective sites, retention behavior was pH dependent. At pH 4.7, the retention
times of both enantiomers decreased with increasing temperature from 5 to 55
°C. However, at pH 5.5, the retention time of the more retained S-propranolol
increased, while that of R-propranolol decreased with increasing temperature.
Thus. at this pH, an unusual increase in chiral selectivity was observed with an
increase in temperature. Detailed thermodynamic parameters were determined
at this pH to try to explain this phenomenon. The changes in molar enthalpy and
entropy on Type I sites were calculated as -1.1 kcallmol and 0.1 cal/moi K,
respectively. On Type II sites, R-propranolol had negative changes in molar
enthalpy and entropy at -1.9 kcallmol and -2.6 cal/moi K, respectively, whereas
S-propranolol had positive changes at 1.6 kcallmol and 11.6 cal/moi K,
respectively. The authors attributed the large positive entropy change to a
considerable decrease in the organization of water molecules around the chiral
(Type II) sites in the protein CSP. The positive enthalpy change suggested that

this disorganization was associated with weakening of the hydrogen bonding of

47

water molecules. The endothermic interaction for the S-enantiomer and
exothermic interaction for the R-enantiomer accounted for the unusual
temperature-dependent behavior. Peak tailing was observed at both low and
high concentration of solutes. At low concentration, the Type II sites were within
the linear range of the isotherm. The tailing observed was a result of slow
heterogeneous mass transfer kinetics. At high concentration, the Type II sites
were saturated and no longer within the linear range. As a result, the more
pronounced tailing observed was a combination of heterogeneous
thermodynamics and heterogeneous kinetics. The transport-dispersive model
using the solid-film linear driving force model with homogenous kinetics failed to
account for the pronounced peak tailing, while the same model with
heterogeneous kinetics accounted well. For example, a sorption rate constant of
10,000 min'1 and desorption rate constant of 18 min‘1 were determined for best fit
to the experimental zone profile produced with 100 uL of 0.36 mM propranolol.
The rate constants were found to be concentration dependent. With higher
concentrations of 1.02 and 1.55 mM propranolol. the sorption rate constant was
decreased to 90 and 60 min", respectively, when the desorption rate constant
was held constant at 18 min“.

Some other interesting thermodynamic studies have been performed on
other types of protein CSPs. Gilpin et al. [65] separated tryptophan enantiomers
on a bovine serum albumin CSP at varying temperatures and pH. For D-
tryptophan, the van’t Hoff plot was reasonably linear over the temperature range

from 0.5 to 45 °C. However, for L-tryptophan, a nonlinear plot was observed with

48

a maximum value at approximately 20 - 24 °C. The authors noted that the initial
increase in the retention factor of L-tryptophan with temperature is
thermodynamically inconsistent with a simple retention mechanism, where
binding occurs at a fixed number of specific sites with a constant, negative
change in molar enthalpy. They speculated that the observed nonlinearity may
be due to an increase in the number of binding sites due to gross changes In
protein surface orientation or an increase in the binding energy due to induced
conformational changes of the protein. These changes are apparently not
consequential for D-tryptophan, which does not have a specific binding site with
BSA.

Amyloglucosidase was immobilized onto the silica support by Strandberg
et al. [66]. Both retention and enantioselectivity increased with column
temperature. The ionic strength of the mobile phase and the concentration of the
organic modifier, 2-propanol, both affected the chiral selectivity. The pH value of
the mobile phase affected the charges on the CSP and the solute, thereby
influencing their interactions. A pH above the isoelectric point of the protein CSP
introduced more electrostatic interaction between the positively charged solute
and the negatively charged protein. The thermodynamic results indicated that
the interaction could be enthalpy- or entropy-dominated, depending on the
mobile phase composition. An inversion of elution order was observed for
enantiomers of mosapride on an 0.1-301d glycoprotein CSP with the change of
temperature and pH [67]. A linear van’t Hoff plot was obtained at lower pH (4.2),

but a nonlinear plot was obtained at higher pH (7.4). Thermodynamic results

49

showed the separation was enthalpy-dominated at lower pH, but entropy-
dominated at higher pH.

A vancomycin-based CSP was used to separate a series of dansyl amino
acids in the temperature range of 0 to 28 °C [68]. Linear van’t Hoff plots were
obtained for all enantiomers. However, their thermodynamic parameters were
distinguished in two groups, where the first group had a more negative AH with
smaller molecular size (e.g., dansyl valine and leucine) and the second group
had a much less negative AH with a larger molecular size (e.g., dansyl
tryptophan). Enthalpy-entropy compensation was observed for the chiral
compounds within the same group. indicating a similar retention mechanism.
The size of the solute affected their retention and chiral recognition by affecting
the hydrophobic interaction and steric hindrance with the CSP. Berthod et al. [69]
observed linear van’t Hoff plots on four macrocyclic glycopeptide CSPs with 71
chiral compounds, which indicated that no conformational transitions were
observed for these CSPs. Most chiral separations were enthalpy-controlled with
a few exceptions, depending on the mobile phase composition and the solute
structure as well. Enthalpy-entropy compensation was observed in most cases.

In summary, protein CSPs have a much complex structure than those
CSPs containing only small chiral molecules. Temperature and pH are the most
important parameters that control retention and separation behavior in this type
of CSP. Broader peaks are usually observed due to the slow mass transfer
kinetics. More investigations need to be performed to find ways to increase

mass transfer kinetics and enable higher column efficiency for protein CSPs.

50

1.6 CONCLUSIONS

Chiral separation is an important issue in both academia and industry.
Although great efforts have been made to separate enantiomers with various
methods or CSPs, the mechanisms for the chiral separation process still remain
unclear. Thus, the goal of this thesis is to investigate the detailed
thermodynamic and kinetic information concerned with B-cyclodextrin chiral
stationary phase. At first, the method to extract thermodynamic and kinetic
information will be evaluated in Chapter 2. Then the detailed mobile phase effect
(Chapter 4) and temperature and pressure effects (Chapter 5) will be discussed.
Such investigations will lead to a better understanding of the retention and

separation process in chiral separation.

51

1.7

[1]

[2]

[3]

[4]

[5]
[6]

I7]

[3]

[9]

[10]

[11]
[12]

[13]

I14]
[15]
I16]
[17]

REFERENCES

S. Ahuja, Chiral separations: Application and technology, American
Chemical Society, Washington, DC, 1997

G. Blaschke, H.P. Kraft, K. Fickentscher and F. Kohler. Ameiz.-Forsch.,
29 (1979) 1640.

G. Subramanian, Chiral separation techniques: A practical approach,
Wiley-VCH, 2001

G. Subramanian, A practical approach to chiral separations by liquid
chromatography, Wiley-VCH, 1994

CE. Dalgliesh, J. Chem. Soc. 137 (1952) 3940-3942.

M. Kotake, T. Sakan, N. Nakamura, S. Senoh, J. Am. Chem. Soc. 73
(1951) 2973-2974.

P.W. Atkins, Physical Chemistry, 6th Ed; W. H. Freeman: New York, NY,
1997.

J. Leffler, E. Grunwald, Rates and Equilibria of Organic Reactions; Wiley:
New York, NY, 1963.

RR. Krug, W.G. Hunter, R.A. Grieger, J. Phys. Chem. 80 (1976) 2335-
2341 .

R.R. Krug, W.G. Hunter, R.A. Grieger, J. Phys. Chem. 80 (1976) 2341-
2351 .

R. Ranatunga. M.F. Vitha, P.W. Carr, J. Chromatogr. A 946 (2002) 47-49.

C.F. Bemasconi, Relaxation Kinetics; Academic Press: New York, NY,
1976.

D. Gowanlock, R. Bailey, F.F. Cantwell, J. Chromatogr. A 726 (1996) 1-
23.

J. Li, L.M. Litwinson, F.F. Cantwell, J. Chromatogr. A 726 (1996) 25-36.
J. Li, F .F . Cantwell, J. Chromatogr. A 726 (1996) 37-44.

R. Bujalski, F .F . Cantwell, J. Chromatogr. A 1048 (2004) 173-181.

K. Miyabe, G. Guiochon, J. Separ. Sci. 26 (2003) 155-173.

52

I18]

[1 9]
[20]
[21]
I22]
[23]
I24]

[25]

[26]

[27]
I28]

[29]
[30]
[31]
I32]
[33]
I34]
[35]
[36]
I37]

I33]

[39]

J.C. Giddings, Dynamics of Chromatography; Marcel Dekker: New York,
NY, 1965.

SB. Howerton, V.L. McGuffin, Anal. Chem. 75 (2003) 3539-3548.

H.C. Thomas, J. Am. Chem. Soc. 66 (1944) 1664-1666.

J.L. Wade, A.F. Bergold, P.W. Carr, Anal. Chem. 59 (1987) 1286-1295.
S. Golshan-Shirazi, G. Guiochon. J. Chromatogr. 603 (1992) 1-1 1.

G. Guiochon, J. Chromatogr. A 965 (2002) 129-161.

A. Harada, M. Furue, S. Nozakura, J. Polym. Sci., Part A: Polym. Chem.
16 (1978) 189-196.

W.L. Hinze, T.E. Riehl, o.w. Armstrong. w. DeMond, A. Alak, T. Ward,
Anal. Chem. 57 (1935) 237-242.

H.Y. AbouI-Enein, M.R. Islam, S.A. Bakr, 1 1 (1988) 1485-1493.
K. Cabrera, D. Lubda, J. Chromatogr. A 666 (1994) 433-438.

N. Morin, Y.C. Guillaume, E. Peyrin, J.C. Rouland, Anal. Chem. 70 (1998)
2819-2826.

E. Peyrin, Y.C. Guillaume, A. Ravel, Anal. Chem. 72 (2000) 1263-1267.
Y.C. Guillaume, J. F. Robert, C. Guinchard, Talanta 55 (2001) 263-269.
M.C. Ringo, C.E. Evans, Anal. Chem. 69 (1997) 643-649.

M.C. Ringo, C.E. Evans, J. Phys. Chem. B 101 (1997) 5525-5530.
M.C. Ringo, C.E. Evans, Anal. Chem. 69 (1997) 4964-4971.

M.C. Ringo, C.E. Evans, J. Microcolumn Sep. 10 (1998) 647-652.

X. Wang, C.B. Ching, Sep. Sci. Technol. 37 (2002) 2567-2586.

H.W. Yu, C.B. Ching, Chromatographia 54 (2001) 697-702.

D.J. Mazzo, C.J. Lindemann, G.S. Brenner, Anal. Chem. 58 (1986) 636-
638.

P. Pescher, M. Caude, R. Rosset, A. Tambute, J. Chromatogr. 371 (1986)
159-175.

L.E. Weaner, D.C. Hoerr, J. Chromatogr. 437 (1988) 109-119.

53

[40]
[41]

[42]
I43]

[44]
I45]
I46]

I47]
[48]

[49]

[50]

[51]

[52]

I53]
[54]
[55]

[56]
[57]
[58]
I59]

W.H. Pirkle, J. Chromatogr. 558 (1991) 1-6.

W.H. Pirkle, P.G. Murray, J. High. Resolut. Chromatogr. 16 (1993) 285-
288.

W.H. Pirkle, C.J. Welch, J. Liq. Chromatogr. 14 (1991) 2027-2042.

J.A. Blackwell, R.E. Walterrnire, R.W. Stringham, Enantiomer 6 (2001)
353-367.

C.E. Dalgliesh, J. Chem. Soc. 137 (1952) 3940-3942.
W.H. Pirkle, R.S. Readnour, Anal. Chem. 63 (1991) 16—20.

R.J. Smith, D.R. Taylor, s.M. Wilkins, J. Chromatogr. A 697 (1995) 591-
596.

E. Kuesters. C. Spoendlin, J. Chromatogr. A 737 (1996) 333-337.

N. Mesplet, Y. Saito, P. Morin, L.A. Agrofoglio, J. Chromatogr. A 983
(2003) 115-124.

T. O'Brien, L. Crocker, R. Thompson, K. Thompson, P.H. Toma, D.A.
Conlon, B. Feibush, C. Moeder, G. Bicker, N. Grinberg, Anal. Chem. 69
(1997) 1999-2007.

F. Wang, T. O'Brien, T. Dowling, G. Bicker, J. Wyvratt, J. Chromatogr. A
958 (2002) 69-77.

F. Wang, T. Dowling, D. Ellison, J. Wyvratt, J. Chromatogr. A 1034 (2004)
1 17-123.

F. Wang, R.M. Jr. Wenslow, T.M. Dowling, K.T. Mueller, l. Santos, J. M.
Wyvratt, Anal. Chem. 75 (2003) 5877-5885.

T.D. Booth, I.W. Wainer, J. Chromatogr. A 741 (1996) 205-211.
P. Rearden, P. Sajonz, G. Guiochon, J. Chromatogr. A 813 (1998) 1-9.

A. Seidel-Morgenstem, G. Guiochon, Chem. Eng. Sci. 48 (1993) 2787-
2797.

B. Loun, D.S. Hage, Anal. Chem. 66 (1994) 3814-3822.
B. Loun, D.S. Hage, Anal. Chem. 68 (1996) 1218-1225.
J. Yang, D.S. Hage, J. Chromatogr. A 645 (1993) 241-250.
J. Yang, D.S. Hage, J. Chromatogr. A 725 (1996) 273-285.

54

I50]
I61]

I62]

[63]

I54]

[65]

[66]

[67]

[68]

[69]

J. Yang, D.S. Hage, J. Chromatogr. A 766 (1997) 15-25

T. Fomstedt, G. Zhong, Z. Bensetiti, G. Guiochon, Anal. Chem. 68 (1996)
2370-2378.

T. Fomstedt, P. Sajonz, G. Guiochon, J. Am. Chem. Soc. 1 19 (1997)
1254-1264.

T. Fomstedt, G. Goetrnar, M. Andersson, G. Guiochon, J. Am. Chem. Soc.
121 (1999) 1164-1174.

G. Goetrnar, T. Fomstedt, G. Guiochon, Anal. Chem. 72 (2000) 3908-
3915.

R.K. Gilpin, S. E. Ehtesham, R.B. Gregory, Anal. Chem. 63 (1991) 2825-
2828.

A. Strandberg, A. Nystrom, S. Behr, A. Karlsson, Chromatographia 50
(1999) 215-222.

A. Karlsson, A. Skoog, K. Ohlen, J. Biochem. Biophys. Methods 54 (2002)
347-356.

I. Slama, E. Jourdan, A. Villet, C. Grosset, A. Ravel, E. Peyrin,
Chromatographia 58 (2003) 399-404.

A. Berthod, B.L. He, T.E. Beesley, J. Chromatogr. A 1060 (2004) 205-214.

55

CHAPTER 2

THEORETICAL EVALUATION OF METHODS FOR EXT RACTING
RETENTION FACTORS AND KINETIC RATE CONSTANTS IN
LIQUID CHROMATOGRAPHY

2.1 INTRODUCTION

The importance of kinetics in separation science has been recognized
since the pioneering work of Giddings [1 -5]. While thermodynamics governs the
separation strength and selectivity, kinetics governs the extent of zone
broadening and asymmetry, all of which affect the resolution. Thermodynamic
processes have been studied for many years, but comparatively, kinetic
processes have not been fully elucidated. A detailed understanding of kinetic
behavior is essential to identify the rate-limiting processes so that separation
speed may be increased without sacrificing resolution. For a better
understanding of kinetic behavior, accurate measurement of the kinetic rate
constants is required.

The different methods for extracting thermodynamic and kinetic
information have been discussed in Chapter 1.5. To the best of our knowledge,
there have been no studies dedicated to the validation and comparison of
experimental methods for extracting kinetic rate constants. For this purpose,
stochastic simulation can be of great benefit [6-11]. Stochastic simulations are
based on the migration of individual molecules by the sequential application of
independently defined transport processes (Markov chain). The fundamental
equations of motion used to describe these transport processes require few. if

any, assumptions that limit their general applicability. Stochastic simulation

56

models have shown excellent correspondence with macroscopic kinetic models
[12.13]. All of the simulation parameters are specified, so the associated
retention factors and kinetic rate constants can be easily calculated or extracted
to serve as the "true” values. These true values can be used to compare the
values from all other methods to validate the accuracy of the experimental
methods.

The goals of this research are as follows: (1) to perform stochastic
simulations under different conditions in liquid chromatography systems with
homogeneous or heterogeneous stationary phases, (2) to compare the
generated zone profiles under different conditions, (3) to extract retention factors
and kinetic rate constants by using different theoretical models, and (4) to
compare the different methods with respect to their accuracy, advantages. and
limitations.

2.2 COMPUTER SIMULATION METHOD

A three-dimensional stochastic simulation was written in the FORTRAN 90
programming language. This simulation has been described in detail elsewhere
[14-17]. This program incorporates algorithms for the processes of diffusion,
laminar convection, and retention. The molecules can interact with a
homogeneous or heterogeneous stationary phase by a partition (absorption)
mechanism. These processes are repeated for each molecule at each time
increment until the total simulation time is reached.

The input parameters required for the simulation are divided into three

categories. The system parameters describe properties of the mobile and

57

stationary phases, as well as the spatial dimensions of the system to be
simulated. These include the radius of the mobile phase (Rm), depth of the
stationary phase (d3), column length (L), linear velocity (uo), etc. The molecular
parameters describe attributes of the molecules, such as the diffusion
coefficients in the mobile (D...) and stationary (D3) phases, and the distribution
coefficient between the two phases (K). The computational parameters describe
certain constraints that are required for the simulation, such as the number of
molecules (N), time increment (t), and total simulation time (T). To initialize the
simulation, the molecules are distributed in a statistically random manner entirely
in either the mobile or stationary phase.

The results of the simulation are output as the time distribution of
molecules at specific distances or, correspondingly, as the distance distribution
of molecules at specific times. The statistical moments of the molecular
distribution are calculated in time units for simulations at specified distances (or
in length units at specified times). In addition to these numerical output
parameters, the molecular population is summed in discrete segments of time
and then connected in a continuous zone profile for graphical display or for zone
profile fitting by the different models.

2.3 DATA ANALYSIS METHODS
2.3.1 “True” Extraction Method

In the partition process, the solute molecules are distributed between the

mobile and stationary phases. The rate of distribution between these two phases

can be treated as a pseudo-first-order reaction. Under these conditions, the

distribution can be described by a simple kinetic model of reversible reactions.
To determine the rate constants, the number of molecules in each phase is
recorded as a function of simulation time. The mass transfer rate constants from
the mobile to stationary phase (k...) and from the stationary to mobile phase (k...)
are determined by fitting the data to the kinetic equation for a first-order

reversible reaction

Nm = [kms +ksm exp(— (ksm +kms )T)] (2 1)

where N... is the number of molecules in the mobile phase, N is the total number
of molecules, and T is the time elapsed in the simulation. The rate constants
determined in this manner will be called the “true” kinetic rate constants.

Furthermore, the ratio of the kinetic rate constants defines the retention factor (k),

ksm

k=—=

2.2
kms ( )

azllezl

which is equal to the ratio of the number of molecules in the stationary phase to
those in the mobile phase at equilibrium (N: and NI, respectively). The

retention factor determined in this manner will be called the “true” retention factor.
Three repetitive simulations with 10,000 molecules are performed for each set of
simulation conditions. Rate constants are then determined by nonlinear
regression of the data to Equation 2.1. The three values are then averaged to
obtain the rate constants and their standard deviations. Similarly, the retention

factor and its standard deviation are determined by Equation 2.2.

59

2.3.2. Statistical Moment Extraction Method
Statistical moment method is parallel to the plate height method. In this
method, all of the moments are directly obtained from the molecular zone profiles.

These statistical moments are calculated in the time domain as

N
M1 = N‘12Ti (2-3)
i=1
N
M2 = N4 XITi - M1 )2 (2-4)
i=1
N
M3 = N‘1Z(Ti - M1 )3 (2.5)

where T. is the arrival time of an individual molecule (i) at the specified distance
and N is the total number of molecules. The first moment (M1) is the mean

retention time. It can be related to the retention factor by

k = M (2.6)
t0

where to is the elution time for a non-retained compound, which is calculated
from the column length (L) and the mobile-phase linear velocity (uo).

As discussed in Chapter 1.5, the method of calculating kinetic rate
constants from moment analysis is derived by extrapolation of Giddings’ work [1].
The plate height in the length domain (Ht) can be related to the second moment

(M2) in the time domain by

2
HL =—=— —"°— 2 (2.7)
L L 1+1:

60

The mass-transfer term (0.) for slow kinetics in a system that exhibits a partition
mechanism is given by

2k

6s = —— (2.8)
(1+ k)2kms
Thus,
2
kms = £92.— and ksm = im— (29)
(1+ k)2dHL (1+ k)2dHL

where dHL is the contribution to plate height arising from slow mass transfer, and
is calculated by

dHL =HL -A—Bmluo -leuo -Cmuo (2.10)
The terms for multiple paths (A), diffusion in the mobile phase (8...), diffusion in
the stationary phase (83), and resistance to mass transfer in the mobile phase

(C...) are calculated from the Golay equation for an open tubular column as

 

A =0 (2.11)
B =2. 0 k (2.13)
S S S
h+ 6k+11k2)R.-'$.
c... = (2.14)
24(1+k)2Dm

where y... is the obstruction factor in the mobile phase, which is unity for an open
tubular column, and 13 is the obstruction factor in the stationary phase, which is
unity for a uniform surface.

This method relies on the accurate calculation and subtraction of all fast

mass transfer terms, which include A, 8..., B3, and C.... These corrections are

61

relatively simple for these simulations in open tubular columns, but more difficult
in experimental systems, especially those in packed columns. The equations for
A and C... terms in packed beds are largely empirical and cannot provide
accurate values [1 ,18-21].
2.3.3. EMG Model Extraction Method

EMG model is the convolution of the Gaussian and exponential

contributions as described by the following equation

2
A _ _
C(t)=—‘°—‘9—ex 2 U“ t errt A1- A2 +1 (2.15)
2A3 2A32 A3 JEAZ JEA3

where erf is an statistical error function. The zone profile is fit to the EMG

 

 

equation by nonlinear regression (PeakFit, Jandel Scientific) to extract the
relevant parameters, A... A., A2, and A3. From these parameters, the retention
time t. is calculated as

tr = A1+A3 (2.16)

The corresponding retention factor is calculated as

k Jag—t9. (2.17)

where to is the elution time for a non-retained compound, which is calculated
from the column length (L) and the mobile-phase linear velocity (uo). The rate

constants are calcuated by

2
kms =1“-% and ksm £1129 (2.18)
As As

62

2.3.4. Giddings Model Extraction Method

Concentration, C(x), in the Giddings model is expressed as
C(x) = AyJ-I‘Z|1(27JK_X)exp(— yx - yk) (2.19)

where y is a dimensionless constant, equal to the product of the desorption rate
constant (k...) and the elution time of a nonretained compound (to). After
conversion from the time domain (t) to the retention factor domain (x), the zone
profile is fit by nonlinear regression (PeakFit, Jandel Scientific). From the
regression parameters (A, k, y), the corresponding retention factor and rate
constants are calculated.

2.3.5. Thomas Model Extraction Method

Concentration, C(x), in the Thomas equation is given by

f \
Jil{z‘/a1x]exp - x — a1]
X 82 \ 82

\

 

 

 

 

 

 

 

\
C(x) = 3—[1 — expf— a_3J (2.20)
3283 i 32 ’ 1-T[fl,—"— 1—ex0(-fl])
( a2 a2 ( a2 1
where
U
T(u,v) = e"" [e'tlo(./27)dt (2.21)

0
and lo and I. are modified Bessel functions of the first kind. After conversion from
the time domain to the retention factor domain (denoted as x), the zone profile is
fit by nonlinear regression (PeakFit, Jandel Scientific). The fitting parameters

that are incorporated in the Thomas model are the area (an), position (a.), width

63

(a2), and distortion (a3). From the definition of the parameters in the Thomas
model, the retention factor is simply the position parameter a.

k = 81 (2.22)
The kinetic rate constants are related to the width parameter a2

km: 1 and k3,“: " - a‘ (2.23)

azto azto - azto

 

 

2.4. RESULTS AND DISCUSSION

2.4.1. Homogenous Systems

In a homogeneous system, there is only one type of interaction site in
each simulation system. The simulation conditions are varied with respect to the
column length (L), linear velocity (uo), stationary-phase diffusion coefficient (0.),
interfacial mass transfer coefficient (01) [39], and equilibrium constant (K). For
each set of conditions, the four different theoretical methods are applied to
extract the retention factors and kinetic rate constants. The retention factors
reflect the thermodynamic or equilibrium behavior, whereas the rate constants
reflect the kinetic behavior of the system.
2.4. 1. 1. Effect of column length an equilibrium and kinetic processes

To elucidate the effect of column length, the molecular distribution is
examined at values of 1, 2, 4, 5, 7, and 9 cm. The simulation conditions are
chosen with linear velocity of 0.1 cmls, equilibrium constant of 1.0, mobile-phase
diffusion coefficient of 1.0x10'5 cmzls, and stationary-phase diffusion coefficient
of 5.0x10‘8 cmzls. Other simulation parameters are specified in the figure

legends.

The retention factors and kinetic rate constants are extracted by using the
true kinetic method with Equations 2.1 and 2.2. An average value for the square
of the correlation coefficient (R2) of 0.96 indicates the good quality of the
nonlinear regression. Extracted values for retention factors and rate constants
along the column length are summarized in Tables 2.1 and 2.2, respectively.
Since the true kinetic method only deals with the number of molecules in each
phase, it is independent of the column length. The retention factors are constant
at 1.004, and the kinetic rate constants from stationary to mobile phase are
constant at 0.203 s'1 along the column.

When retention factors and kinetic rate constants are compared between
the different methods, the concept of steady state (equilibrium) needs to be
considered. The true kinetic method helps to describe the overall kinetic
behavior in terms of the characteristic time 1:

1

_ ksm +kms

 

(2.24)

T

which represents the time required for the number of molecules in the mobile
phase (N...) to reach 1 — We) of the number at equilibrium (N; = N/(1+k)). It will

usually require at least 20 to 50 ‘I.’ for the chromatographic system to reach
steady state. In this case where k... = k... = 0.203 s", approximately 50 to 120 s
are needed for steady state achievement, which corresponds to a mean zone
distance of 2.5 to 6 cm. Among the six column lengths, the zone profiles

achieved after 4 cm should have reached steady state.

65

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2.1 Retention factors (k) with varying column length (L)."
L
1 cm 2 cm 4 cm‘ 5 cm" 7 cm" 9 cm"
Model
1.0041: 1.0041 1.0043: 1.0043: 1.004: 1.0043:
True
0.007 0.007 0.007 0.007 0.007 0.007
Moment 0.994 0.991 1.008 1.004 1 .004 1.004
EMG N/A 1.184 1.066 1.040 1.022 1.011
Giddings N/A 0.918 0.989 0.991 0.996 0.996
Thomas N/A 2.364 1.258 1.160 1.076 1.052
' Simulation conditions given in Figure 2.1.

N/A Not available

* Steady state achieved

66

 

Table 2.2

Kinetic rate constants from stationary to mobile phase (km. s") with

varying column length (L).°

 

 

 

 

 

 

 

L
1 cm 2 cm 4 cm* 5 cm‘ 7 cm* 9 cm‘
Model
0.203 :I: 0.203 :t 0.203 :t 0.203 :t 0.203 :I: 0.203 1

True
0.003 0.003 0.003 0.003 0.003 0.003
Moment 0.182 0.187 0.177 0.184 0.186 0.181
EMG N/A 0.0846 0.127 0.157 0.199 0.232
Giddings N/A 0.216 0.175 0.177 0.177 0.172
Thomas N/A 0.162 0.170 0.174 0.175 0.170

 

 

 

 

 

 

 

N/A Not available

* Steady state achieved

Simulation conditions given in Figure 2.1.

67

 

 

The zone profiles at each column length are illustrated and compared in
Figure 2.1. The zone profile at 1 cm is highly asymmetric. It has a narrow
central region with a long exponential tail, which makes it appear bimodal. The
reason for this appearance is the non-equilibrium nature at 1-cm column length.
There are two populations of molecules present: One population has no
opportunity to interact with the stationary phase, but travels only in the mobile
phase; these molecules compose the narrow central zone profile. The other
population has already interacted with the stationary phase; these molecules
compose the long exponential tail. The zone profile at 2 cm is still highly
asymmetric, but seems to lose the bimodal character as more molecules interact
with the stationary phase. The zone profiles at 4, 7, and 9 cm are all slightly
asymmetric, similar to the profiles usually seen in chromatography. The
asymmetry decreases, but the broadening of the zone profile increases
continuously along the column. These phenomena have direct effects on the
retention factor and kinetic rate constants, as discussed below.

The retention factors and kinetic rate constants from stationary to mobile
phase with the different methods are summarized in Tables 2.1 and 2.2.
Theoretically, the retention factor is given by

"KY;

k
Vm

(2.25)

where v... = n R...2 L and v. = n (d.2 + 2 R... d.) L. For these simulations, the
phase ratio (V...N.) has been carefully calculated and set as 1.0. Hence, a
retention factor of 1.0 is expected and is verified by the results of the true kinetic

method. In Table 2.1, the statistical moment method gives constant and

68

Figure 2.1: Comparison of zone profiles with varying column length. From left to
right, column length L = 1, 2, 4, 7, and 9 cm. Other simulation conditions: N =
5000, t = 5.0x10“ 5, o... = 1.0x10‘5 cmils, o. = 5.0x10i cmzls, K = 1.0, u. = 0.1

cmls, R... = 2.0x10‘3 cm, d. = 8.28x10" cm, a = 1.0.

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accurate values along the column. Even the zone profile at the first column
length can be used to calculate a retention factor that is similar to the expected
value. However, non-constant values are observed for the EMG, Giddings and
Thomas models. None of the three models is able to fit the zone profile at the
first column length accurately because of its bimodal shape. However, for all
subsequent lengths, all models can fit the zone profiles well. Their statistical
parameters indicating the quality of the fitting, R2 and F, are similar to each other.
Table 2.1 clearly demonstrates a decreasing trend for retention factors along the
column length from both EMG and Thomas models, and an increasing trend from
Giddings model. However, the retention factors from the EMG and Giddings
models are closer to the expected value of 1.0 than those from the Thomas
model. When comparing the different methods to extract retention factors, it may
be concluded that the statistical moment method is independent of the zone
profile. The statistical moment method is not a regression approach and makes
no assumptions about the zone profile. It is also independent of the column
length and the associated achievement of steady-state conditions. However, the
EMG. Giddings, and Thomas models are dependent on the zone profile and
column length. It is noteworthy that all of these methods yield retention factors
that are similar to the true kinetic value.

With respect to the kinetic behavior in Table 2.2, the rate constants from
stationary to mobile phase are relatively constant along the column length for the
statistical moment model. For the EMG model, an increasing trend in rate

constant is observed along the column. Before steady state is reached, the

71

kinetic rate constant is more than 50% smaller than the true value. After the
steady state condition has been reached, the kinetic rate constant begins to
approach and even surpass the true value. The reason for the increasing trend
along the column length derives from the EMG method itself. This method only
deals with the exponential tail of the zone profile. As the zone profile progresses
along the column, it evolves from a highly asymmetric zone profile to a more
symmetric Gaussian zone profile. In other words, the ratio of exponential
variance and column length (1:2/L) decreases along the column length. As the
rate constants are inversely related to 172/L (Equation 2.18), they increase along
the column length. The reason that the final value is larger than the true kinetic
value also derives from the limitations of the EMG method. As the zone profile
approaches a Gaussian shape, where the ratio of do is less than 0.4, the EMG
model cannot be used to extract reliably the exponential variance [22]. The rate
constants calculated under these conditions are statistically inaccurate. The
closest value to the true kinetic rate constant is observed at 7 cm, which
corresponds to 50 to 60 t. The kinetic rate constants from the Giddings and
Thomas models are similar and relatively constant along the column, especially
after steady state achievement. The constant values derive from the nature of
the statistical moment, Giddings, and Thomas methods. All of these methods
deal with the total variance of the zone profile, which increases linearly along the
column. As the kinetic rate constants are directly related to the ratio of total
variance and column length (Equations 2.9 and 2.23), they remain constant

along the column length. Although the statistical moment, Giddings, and Thomas

72

models give constant rate constants, their values are slightly different. Those
from the statistical moment model are about 10% smaller than the true values,
whereas those from Giddings and Thomas models are 15% smaller. When
comparing the different methods to extract kinetic rate constants, the EMG model
strongly depends on the zone profile, column length, and the associated
achievement of steady-state conditions. However, the statistical moment,
Giddings, and Thomas models are much more independent. It is noteworthy that
all of these methods yield rate constants that are similar to the true kinetic value.
2.4. 1.2. Effect of linear velocity an equilibrium and kinetic processes

To elucidate the effect of linear velocity, the molecular distribution is
examined at values of 0.05, 0.1, 0.2, 0.3, and 0.5 cmls. These velocities include
the common range in practical application of liquid chromatography. The
simulation conditions are chosen with equilibrium constant of 1.0, mobile-phase
diffusion coefficient of 1.0x10‘5 cmzls, and stationary-phase diffusion coefficient
of 5.0x10'8 cmzls. Other simulation parameters are specified in the figure
legends.

Figure 2.2 shows the simulated zone profiles at varying velocities with a
single column length of 8 cm. The zone profile at the highest velocity is detected
in the shortest time with a highly asymmetric zone profile, whereas the zone
profile at the lowest velocity is detected in the longest time with a fairly Gaussian
zone profile. With decreasing velocity, the zone profile gradually changes from
asymmetric to Gaussian. At the same time, retention time increases. These

trends are identical with those discussed above for increasing column length. In

73

Figure 2.2: Comparison of zone profiles with varying linear velocity. From left to
right, linear velocity uo = 0.5, 0.3, 0.2, 0.1, and 0.05 cmls. Other simulation
conditions: N = 5000, t = 5.0::10‘4 s, 0...: 1.0x10‘ cmzls, o.= 5.0x10“ cmzls, K

= 1.0, L = 8 cm, R... = 2.0x10'3 cm, (is = 8.28x10'4 cm, or = 1.0.

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other words, decreasing the linear velocity should have the same effect as
increasing the column length.

The retention factors calculated by using the different methods are
summarized in Table 2.3. The retention factors from the true kinetic method are
constant and statistically equivalent (0.999 - 1.004) at different velocities. The
retention factors from the statistical moment model give very accurate and
constant values at every velocity. In contrast, the retention factors from the EMG
and Thomas models clearly show an increasing trend with increasing linear
velocity, while those from the Giddings model show a decreasing trend. Those
determined at the lowest velocity are most accurate and closest to the expected
value of 1.0, according to Equation 2.25. Again, the EMG model yields a more
accurate value than the Giddings and Thomas models.

The true kinetic rate constants extracted at different velocities are constant
and statistically equivalent (0.194 — 0.203 s"), as shown in Table 2.4. In other
words, the change in velocity should have no effect, theoretically, on the kinetic
processes. A similar amount of time should be required for each system to reach
steady state. However, the column length where steady-state conditions are
achieved will be different at each velocity. For example, the simulation with 0.1
cmls linear velocity will achieve steady state at a column length of 4 cm, but the
simulation with 0.5-cmls velocity will achieve steady state at a column length of
20 cm, approximately 5 times longer. If molecules spend the same amount of
time on the column, the zone profile they achieve should be identical as long as

the kinetic processes remain constant. Figure 2.3 shows the simulated zone

76

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2.3 Retention factors (k) with varying linear velocity (uo).'
U0
0.05 cmls" 0.1 cmls" 0.2 cmls" 0.3 cmls 0.5 cmls
Model
1.001 1 1.004 :I: 0.999 t 1.002 :I: 1.002 :I:
True
0.012 0.007 0.011 0.005 0.012
Moment 1 .003 1 .005 1.004 1 .003 1.004
EMG 1.007 1.016 1.025 1.028 1.138
Giddings 0.994 0.999 0.984 0.955 N/A
Thomas 1 .022 1 .047 1.098 1 .280 N/A
a Simulation conditions given in Figure 2.2.

N/A Not available

* Steady state achieved

77

 

Table 2.4

varying linear velocity (uo).“‘

Kinetic rate constants from stationary to mobile phase (km. s") with

 

 

 

 

 

 

 

 

 

 

 

 

 

00
0.05 cmls" 0.1 cmls" 0.2 cmls" 0.3 cmls 0.5 cmls
Model
0.200 :I: 0.203 :I: 0.197 :I: 0.195 :I: 0.194 :I:
True
0.003 0.003 0.001 0.001 0.003
Moment 0.175 0.183 0.184 0.179 0.175
EMG 0.289 0.224 0.171 0.137 NIA
Giddings 0.181 0.175 0.187 0.193 NIA
Thomas 0.180 0.174 0.183 0.184 NIA
a Simulation conditions given in Figure 2.2.

N/A Not available

* Steady state achieved

78

 

Figure 2.3: Comparison of zone profiles at similar time with varying linear
velocity. Peak (—) at L = 3 cm with uo = 0.05 cmls, (— - - -) at L = 6 cm with no
= 0.1 cmls, (- — -) at L = 18 cm with uo = 0.3 cmls. Other simulation conditions:
N = 5000, t = 5.0x10“ s, 0...: 1.0x10'5 cm2/s, o,= 5.0x108 cmzls, K = 1.0, R... =

2.0x10’3 cm, d. = 8.28x10" cm, a = 1.0.

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100

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profiles at three different velocities (uo), detected at different column lengths (L),
but the ratios of L/uo are constant. Their zone profiles are identical to each other,
as discussed above. This further demonstrates that decreasing the linear
velocity has the same effect as increasing the column length.

The kinetic rate constants from the other methods are also summarized in
Table 2.4. The rate constants from the statistical moment, Giddings, and
Thomas methods have a relatively constant value at all velocities, approximately
10% smaller than the true value. However, those from the EMG model
continually decrease with increasing linear velocity. The range of values includes
the true kinetic rate constant. Again, the trends from the EMG model are related
to the asymmetric zone profile at the highest linear velocity and the Gaussian
zone profile at the lowest velocity. Overall, these trends in kinetic rate constants
are the same as discussed above when varying the column length.
2.4. 1.3. Effect of stationary-phase diffusion coefficient an equilibrium
and kinetic processes

Molecules will have very similar diffusion coefficients in the mobile phase,
typically 1.0x10’5 cmzls in liquid chromatography. However, the diffusion
coefficient in the stationary phase can vary greatly, given the wide variety of
phases that are available. To elucidate the effect of stationary-phase diffusion
coefficient, the molecular distribution is examined at values of 1.0x10'°, 5.0x10”,
1.0x10’7, 5.0x10'8, and 1.0x10‘8 cmzls. For each diffusion coefficient, the column
length is individually selected to ensure achievement of steady-state conditions

(30 — 75 t). The simulation conditions are chosen with linear velocity of 0.1 cmls,

81

equilibrium constant of 1.0, and mobile-phase diffusion coefficient of 1.0x10'5
cmzls. Other simulation parameters are specified in the figure legends.

For a clear comparison, the zone profiles for different diffusion coefficients
are compared at a single column length (5 cm) in Figure 2.4A. The zone profile
with the largest stationary-phase diffusion coefficient (1 .0x10'° cmzls) is a narrow
and symmetric Gaussian zone profile. With decreasing diffusion coefficient, the
zone profiles evolve gradually to broader and more asymmetric shapes. The
zone profile with the smallest stationary-phase diffusion coefficient (1.0x10‘°
cmzls) has not reached steady state yet at column length of 5 cm. But the
asymmetric character of the zone profile can be clearly seen by its extremely
long tail. The statistical moments associated with each zone profile are
compared in Figure 2.4B as well. The first moment for all of the zone profiles is
virtually the same, and is independent of stationary-phase diffusion coefficient.
However, the second moment increases in a linear manner and the third moment
increases in a quadratic manner as the stationary-phase diffusion coefficient
decreases. Hence the skew, which is the ratio M3/M23’2, increases in a square-
root manner with decreasing diffusion coefficient, indicating a more asymmetric
zone profile.

The retention factors are summarized in Table 2.5. The true kinetic
method gives accurate and statistically equivalent retention factors (0.994 —
1.004) for different diffusion coefficients. The retention factors from the statistical
moment method are all within 1.5% error, those from the EMG model within 3.0%

error, and those from the Giddings model within 3.5% error. However, those

82

Figure 2.4: Comparison of zone profiles (A) and statistical moments (B) with
varying stationary-phase diffusion coefficient. (A) From left to right, stationary-
phase diffusion coefficient 0. = 1.0x10‘8, 5.0x10‘8, 1.0x10'7, 5.0x10”, and 1.0x10

4’ cm2/s. (B) First moment M. (9), second moment M2 (I), third moment M3 (A),
and skew M3/M23’2 (1:). Other simulation conditions: N = 5000, t = 5.0x10“ s, D...
= 1.0x10'5 cm2/s, u. = 0.1 cmls, K = 1.0, L = 5 cm, R... = 2.0x10‘3 cm, d. =

8.28x10“ cm, a = 1.0.

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Table 2.5

Retention factors (k) with varying stationary-phase diffusion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

coefficient (D..).’
”8 1.0x10'6 5.0x107 1.0x107 5.0x10'8 1.0x10'8
Model cmzls cmzls cmzls cmzls cmzls
0.999 :I: 0.994 t 0.997 t 1.004 :I: 0.996 2
True
0.003 0.007 0.005 0.007 0.019
Moment 1 .004 1 .007 1.002 1.005 0.986
EMG 1.006 1.015 1.020 1.028 1.000
Giddings 1.015 1.002 0.997 0.990 0.966
Thomas 1.016 1.018 1.051 1.103 1.093
0.5 cm 1 cm 3 cm 6 cm 18 cm
L
(65 t) (75 1:) (50 t) (50 1') (30 r)
a Steady state achieved for all systems at the specified column length (L).

Other simulation conditions given in Figure 2.4.

 

from the Thomas model can have errors as high as 10%, especially for the
smallest diffusion coefficients. It may be concluded that the moment, EMG, and
Giddings models are relatively more accurate than the Thomas model in
extracting retention factors.

The kinetic rate constants from stationary to mobile phase are
summarized in Table 2.6. As shown for the true kinetic method, the rate
constants decrease proportionally with the stationary-phase diffusion coefficient.
This behavior is expected when the stationary-phase diffusion coefficient is
substantially smaller than the mobile-phase diffusion coefficient and, therefore.
dominates mass transfer processes [38]. Accordingly, when comparing the
extracted kinetic rate constants from the three models with the true kinetic
method, the largest error is found for the largest diffusion coefficient of 1.0x10“
cmzls. For the statistical moment method, this error arises from the assumptions
of the model in Equation 2.10. When the diffusion coefficients in the mobile and
stationary phases are comparable, both processes contribute to the observed
rate constant. Under these conditions, the mass transfer term in the stationary
phase is not the only source of “slow” kinetics, and the kinetic rate constant
calculated from the C. term alone will not be correct. When the C... term is
considered in Equation 2.10, the kinetic rate constant determined with the
statistical moment method is 2.349 5“, rather than 3.626 s", for the simulation
with stationary-phase diffusion coefficient 1.0x1043 cmzls. This value is notably
smaller than the true kinetic method (3.241 s"), suggesting that mobile-phase

diffusion does not contribute wholly to slow mass transfer processes. For

87

Table 2.6

Kinetic rate constants from stationary to mobile phase (km... s") with

varying stationary-phase diffusion coefficient (D.).‘

 

 

 

 

 

 

 

 

9* 1.0x10'6 5.0x107 1.0x107 5.0x108 1.0x10'8
Model cmzls cmzls cmzls cmzls cmzls
3.241 :I: 1.906 :I: 0.411 :I: 0.203 :I: 0.041 :1:
True
0.060 0.043 0.008 0.003 0.002
Moment 3.626 1 .702 0.370 0.183 0.037
EMG 3.875 1.898 0.392 0.179 0.034
Giddings 2.289 1 .374 0.348 0.180 0.037
Thomas 2.284 1 .365 0.345 0.176 0.036
0.5 cm 1 cm 3 cm 6 cm 18 cm
L
(65 t) (75 'c) (50 t) (50 T) (30 t)

 

 

 

 

 

 

a Steady state achieved for all systems at the specified column length (L).

Oflier simulation conditions given in Figure 2.4.

 

stationary-phase diffusion coefficients smaller than 1.0x1043 cmzls, the kinetic
rate constants from the statistical moment method have constant error of
approximately -10°/o. For the EMG, Giddings, and Thomas models. a different
source of error arises because these models do not work well for Gaussian zone
profiles, i.e., for the largest diffusion coefficient of 1.0x10'° cmzls. VWth
decreasing diffusion coefficient, the rate constants from the EMG model have
more negative enor, whereas those from the Giddings and Thomas models have
less negative error. When comparing the different methods to extract rate
constants, it is noteworthy that all four models provide values that are reasonably
close to the true kinetic values, which vary over a range of two orders of
magnitude. This indicates the inherent reliability of all models.
2.4. 1.4. Effect of interfacial mass transfer on equilibrium and kinetic
processes

In these studies, the simulation approach is extended to consider
resistance to mass transfer at the interface between the mobile and stationary
phases. This resistance is associated with an energetic barrier for the kinetic
transfer between mobile and stationary phases. Not every collision is sufficiently
energetic to overcome this barrier. To represent the efficiency of collisional mass
transfer, the interfacial mass transfer coefficient a is introduced. This coefficient
is varied as 1.0, 0.5, 0.1, and 0.05 to represent 100%. 50%, 10%. and 5%
efficient mass transfer, respectively. The simulation conditions are chosen with
linear velocity of 0.1 cmls, equilibrium constant of 1.0, mobile-phase diffusion

coefficient of 1.0x10“'5 cmzls, stationary-phase diffusion coefficient of 5.0x10“

89

cmzls, and column length of 6 cm, where steady-state conditions should have
been achieved. Other simulation parameters are specified in the figure legends.

The simulated zone profiles for different interfacial mass transfer
coefficients are compared in Figure 2.5A. When the interfacial mass transfer
coefficient is decreased from 1.0 to 0.5, the zone profile does not appear to
change significantly. However, when the coefficient is further decreased to 0.1
and 0.05, the zone profile begins to show slightly more broadness and tailing.
These changes can be seen from the comparison of statistical moments in
Figure 2.58. The first statistical moment is independent of the interfacial mass
transfer coefficient a, whereas the second and third moment are dependent upon
a. Decreasing a will increase both the second and third moments. but the third
moment will be affected more greatly. As a result, the skew will increase slightly
as well, which indicates a more asymmetric zone profile.

The retention factors with varying interfacial mass transfer coefficient a
are summarized in Table 2.7. The true kinetic method gives accurate and
statistically equivalent values for the retention factor (0.997 - 1.008) with varying
interfacial mass transfer coefficient. For the other four methods. a slightly
decreasing and increasing trend in retention factor is observed with decreasing
interfacial mass transfer coefficient. The errors introduced in extracting the
retention factor are within 1% for the statistical moment model, 3% for the EMG
model, 2% for the Giddings model, and 10% for the Thomas model. Comparing
the three models, the statistical moment, EMG. and Giddings models give more

accurate results than the Thomas model.

90

Figure 2.5: Comparison of zone profiles (A) and statistical moments (B) with
varying interfacial mass transfer coefficient. (A) lnterfacial mass transfer

coefficient a = 1 (

 

), 0.5( ------ ), 0.1 ( ————— ) and 0.05 (- ----- ). (B)
First moment M1 (0), second moment M2 (I), third moment M3 (A). and skew
M3/M23’2 (in). Other simulation conditions: N = 5000, t = 5.0x10“ s. 0...: 1.0x10'5
cmzls, D. = 5.0x10‘9 cm2/s, uo = 0.1 cmls, K = 1.0, L = 6 cm. R... = 2.0x10‘3 cm, (1.
= 8.28x10“ cm.

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Table 2.7

coefficient (at).a

Retention factors (k) with varying

interfacial mass transfer

 

 

 

 

 

 

 

1.0 0.5 0.1 0.05
Model
True 1.004 t 0.007 0.997 t 0.001 1.003 t 0.006 1.008 t 0.019
Moment 1 .005 0.999 0.991 0.998
EMG 1.028 1.018 0.995 1.005
Giddings 0.990 0.983 0.990 0.985
Thomas 1.103 1.092 0.990 1.016

 

 

 

 

 

Simulation conditions given in Figure 2.5.

 

The kinetic rate constants with varying a are summarized in Table 2.8.
From the true kinetic method. it is apparent that a decrease in a will decrease the
kinetic rate constants. This is consistent with observing the most tailing zone
profile for the smallest value of a in Figure 2.5A. This decreasing trend can be
easily observed from the moment, Giddings and Thomas models, but more
difficult to observe from the EMG model. Again, this behavior is strongly affected
by the achievement of steady-state conditions, which corresponds to different *
column lengths for different simulation conditions. When the interfacial mass
transfer coefficient or is equal to 1.0, the four models give comparable results in
extracting rate constants. However, when 0. decreases to 0.1 and 0.05, the
moment, Giddings, and Thomas models give more accurate results than the
EMG model.
2.4. 1.5. Effect of equilibrium constant on equilibrium and kinetic
processes

The equilibrium constant governs the molecular distribution between the
mobile and stationary phases in liquid chromatography. Different mobile phase
composition, stationary phase structure, temperature, and pressure will all affect
the equilibrium constant of a specific solute. Within the same system. different
solutes will have different equilibrium constants as well. To elucidate the effect of
the equilibrium constant, the molecular distribution is examined at values of 0.5.
1.0, 2.0, 5.0, and 10.0. For each value of the equilibrium constant, the column
length is individually selected to insure achievement of steady-state conditions

(40 - 130 r). The simulation conditions are chosen with linear velocity of 0.1

95

Table 2.8

varying interfacial mass transfer coefficient (a).“

Kinetic rate constants from stationary to mobile phase (km. s") with

 

 

 

 

 

 

 

1.0 0.5 0.1 0.05
Model
True 0.203 t 0.003 0.183 :t 0.002 0.143 1: 0.004 0.113 1 0.002
Moment 0.183 0.176 0.143 0.114
EMG 0.179 0.183 0.173 0.119
Giddings 0.180 0.178 0.139 0.116
Thomas 0.176 0.175 0.139 0.115

 

 

 

 

 

Simulation conditions given in Figure 2.5.

96

 

cmls, mobile-phase diffusion coefficient of 1.0x10'5 cmzls, and stationary-phase
diffusion coefficient of 5.0x10‘8 cmzls. Other simulation parameters are specified
in the figure legends.

For a clear comparison. the peak shapes for different equilibrium
constants are compared at a single column length (2 cm) in Figure 2.6A. With
increasing equilibrium constant, the zone profiles take longer time to elute and
become broader. The statistical moments associated with each simulated zone
profile are also graphed in Figure 2.68. With the increase of equilibrium constant,
all three statistical moments will increase accordingly. However, the skew
decreases greatly, which indicates less tailing for zone profiles associated with a
larger equilibrium constant. In part, this decrease in tailing results from the
longer time spent on the column with an increase in equilibrium constant. From
the previous discussion of both column length and linear velocity. tailing
decreases when more time is spent on the column. To eliminate this effect and
consider only the innate effect of the equilibrium constant, another graph with the
simulated zone profiles at similar time is shown in Figure 2.7A. where the ratio of
column length and the individual flow rate (L(1+k)luo) remains constant. The
associated statistical moments are shown in Figure 2.78. After spending a
similar time on the column, all the zone profiles reach the same distance along
the column, which is illustrated by their similar first statistical moments. However.
the second and third moments increase with an increase in equilibrium constant.

The second moment increases at a greater rate than the third moment, which

97

Figure 2.6: Comparison of zone profiles (A) and statistical moments (8) with
varying equilibrium constant. (A) From left to right. equilibrium constant K = 1.0,
2.0, 5.0, and 10.0. (8) First moment M. (0), second moment M2 (I), third
moment M3 (A), and skew M3/M23’2 (it). Other simulation conditions: N = 5000, t
= 5.0x10“ 3, o... = 1.0x10'5 cmzls, o. = 5.0x1043 cmzls. uo= 0.1 cmls. L = 2 cm,

R... = 2.0x10'3 cm, d. = 8.28x10“ cm. a = 1.0.

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Figure 2.7: Comparison of zone profiles (A) and statistical moments (8) at
similar time with varying equilibrium constant (K). (A) From left to right. K = 5.0 at
L=20m.K=2.0atL=4cm,K=1.0atL=6cmandK=0.5atL=8cm. (8)
First moment M1 (0), second moment M2 (I), third moment M3 (A). and skew
M31M23'2 (.9, Other simulation conditions: N = 5000, t = 5.0x10" 5. 0...: 1.0x10'5
cmzls. o.= 5.0x10i cmzls, uo= 0.1 cmls, R... = 2.0x10’3 cm, d. = 8.28x10" cm, a

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results in a slight decrease of the skew. In other words, the simulated zone
profiles become broader, but more symmetric with higher equilibrium constant.

The retention factors associated with various equilibrium constants are
summarized in Table 2.9. The true kinetic method yields accurate values.
according to Equation 2.25. While the statistical moment, EMG, and Giddings
models give results that are consistent with the true value within 3% error, the
Thomas model can introduce errors as high as 20%. Thus. the statistical
moment, EMG, and Giddings models are more accurate than the Thomas model
in extracting retention factors.

The kinetic rate constants associated with various equilibrium constants
are summarized in Table 2.10. Considerable discrepancy is observed among the
results from the five methods. In the true kinetic method, the rate constant from
stationary to mobile phase increases with increasing values of the equilibrium
constant. In the statistical moment method. the rate constant remains relatively
constant, whereas in the EMG, Giddings and Thomas models, the rate constant
decreases with increasing equilibrium constant. It is difficult to draw conclusions
about which model provides the most accurate results. Even the true kinetic
model gives poor fit of the simulation data to the single exponential decay with
increasing equilibrium constant. For example, the correlation coefficient R2
decreases from 0.97 to 0.89 as K increases from 0.5 to 10. This makes the true

kinetic results unreliable for comparison to the other methods.

104

Table 2.9

Retention factors (k) with varying equilibrium constants (K).'

 

 

 

 

 

 

 

 

0.5 1.0 2.0 5.0 10.0
Model
0.500 :I: 1.004 :t 2.026 1: 4.995 t 9.952 :t
True
0.003 0.007 0.011 0.058 0.154
Moment 0.500 1 .005 1 .995 4.937 10.287
EMG 0.498 1.028 2.016 4.990 10.187
Giddings 0.491 0.990 1 .955 4.696 10.031
Thomas 0.493 1 .103 2.104 6.599 12.009
9 cm 6 cm 3 cm 0.5 cm 0.3 cm
L
(40 t) (50 1:) (53 t) (48 t) (130 1:)

 

 

 

 

 

 

‘3 Steady state achieved for all systems at the specified column length (L).

Other simulation conditions are given in Figure 2.6.

 

Table 2.10 Kinetic rate constants from stationary to mobile phase (k.... s") with

varying equilibrium constants (K)?

 

 

 

 

 

 

 

 

K
0.5 1.0 2.0 5.0 10.0
Model
0.194 :I: 0.203 t 0.196 :t 0.264 :I: 0.375 1:
True
0.010 0.003 0.005 0.017 0.016
Moment 0.176 0.183 0.182 0.182 0.181
EMG 0.212 0.179 0.200 0.125 0.128
Giddings 0.184 0.180 0.183 0.177 0.156
Thomas 0.184 0.183 0.181 0.167 0.151
9 cm 6 cm 3 cm 0.5 cm 0.3 cm
L
(40 1:) (50 r) (53 1:) (48 t) (130 t)

 

 

 

 

 

 

8' Steady state achieved for all systems at the specified column length (L).

Other simulation conditions are given in Figure 2.6.

 

2.4.2. Heterogeneous Systems

In the simulation of homogeneous systems, the asymmetry tends to
decrease and eventually disappear as molecules travel along the column. In
other words, all zone profiles will eventually approach a Gaussian shape if given
enough time and distance. However. in many of our experimental studies,
persistent peak tailing has been observed that increases with column length [23-
26]. Giddings attributed the kinetic origin of tailing to a heterogeneous surface
with different types of sites, where one site is relatively scarce and with a high
energy [27]. Weiss used a theoretical approach to conclude that persistent
tailing can only occur if there exists a random distribution of first-order rate
constants or an infinite number of interaction sites [28,29]. In each case. a
heterogeneous surface is implicated as a contributing cause of persistent tailing.
Hence. it is instructive to study the effect of multiple interaction sites on the zone
profiles as well as the thermodynamic and kinetic behavior.

For these simulations of heterogeneous systems. five interaction sites are
chosen to have different equilibrium constants and stationary-phase diffusion
coefficients. The parameters are chosen based on previous experimental
measurements for fatty acids in reversed-phase liquid chromatography. For
example, we may consider a C13 fatty acid to have contributions to the retention
mechanisms in which 10, 12, 14, 16. and 18 carbon atoms are inserted into the
stationary phase. The corresponding equilibrium constants and stationary-phase
diffusion coefficients are chosen based on the experimentally measured retention

factors and rate constants for the fatty acids. The natural logarithm of the

107

equilibrium constants and stationary-phase diffusion coefficients increases
linearly with carbon number. The probability for each site is either kept constant
or varied individually as well. The specific information for different simulation
parameters is listed in Table 2.11.
2.4.2. 1. Equally distributed multiple sites for heterogeneous surface

In the system with equally distributed sites. the probability for each of the
five sites is maintained constant at 0.2. This is a simple system with
straightforward physical meaning; the fraction of different surface sites is equally
weighted. Representative zone profiles are shown at varying column lengths in
Figure 2.8. The first zone profile at 0.5 cm has not yet reached steady state. but
steady state should have been achieved for all subsequent zone profiles. As the
simulated zone profiles travel along the column. their broadness increases. but
their asymmetry decreases in the same manner as for a homogeneous surface.

The retention factor for a heterogeneous surface may be calculated as the
sum of the retention factor at each interaction site multiplied by its probability. A
calculated retention factor of 6.33 is expected for equally distributed multiple sites
under these conditions (Table 2.11). The true kinetic method gives an accurate
result of 6.263. as shown in Table 2.12. Among the other four methods, the
statistical moment method provides an accurate result before and after steady
state has been achieved. The EMG model gives a slightly smaller retention
factor before steady state. It reaches a maximum value immediately after steady
state. followed by a decreasing trend along the column length tending toward the

true value. The Giddings model shows an increasing trend. and the

108

Table 2.11

heterogeneous surface.a

Different parameters for

multiple

interaction sites at the

 

 

 

 

 

 

Site
#1 #2 #3 #4 #5
Parameters
13. 1.0x1043 3.0x10'7 1.0x107 3.0x10'° 1.0x10“
K 0.55 1.29 3.12 7.88 18.8
P (1) 0.200 0.200 0.200 0.200 0.200
P (2) 0.583 0.253 0.105 0.042 0.017

 

 

 

 

 

 

° P(1) is the probability selected for equally distributed sites, while P(2) is

the probability selected for unequally distributed sites.

109

 

Figure 2.8: Comparison of zone profiles with equally distributed heterogeneous
surface. From left to right, detector distance L = 0.5, 2. 5. and 7 cm. Other
simulation conditions: N = 5000, t = 5.0x10“ s. o... = 1.0x105 cmzls. uo = 0.1 cmls.
R... = 2.0x10'3 cm, d. = 8.28x10" cm. a = 1.0, P(1) conditions are given in Table

2.11.

110

 

 

 

 

 

EON":—

 

 

 

EOm.Ofll_ IV

 

 

111

Table 2.12 Retention factors (k) along the column for equally distributed

heterogeneous surface.“

 

 

 

 

 

 

 

 

 

 

 

 

 

0.5 cm 2 cm* 5 cm* 7 cm*
Model
Calculated 6.33 6.33 6.33 6.33
True 6.263 1 0.062 6.263 1 0.062 6.263 1 0.062 6.263 1 0.062
Moment 6.35 6.35 6.32 6.36
EMG 5.06 6.55 6.42 6.44
Giddings 3.55 5.82 6.13 6.24
Thomas 17.10 8.68 7.25 7.02
a Simulation conditions given in Figure 2.8.

* Steady state achieved

112

 

Thomas model shows a decreasing trend toward the true value. The Thomas
model has much larger error (35%) than the statistical moment (0.5%), EMG
(3%). and Giddings (8%) models.

The kinetic rate constants are summarized in Table 2.13. The statistical
moment. EMG. Giddings. and Thomas models all give similar results at steady
state. but deviate significantly from the true kinetic method. The reliability of the
true kinetic method is in doubt. This method assumes first-order or pseudo-first-
order kinetics of transfer between the mobile and stationary phases. which is
clearly not the case for heterogeneous surfaces. Accordingly, the square of the
correlation coefficient (R2) for regression to the single exponential decay is
relatively low at 0.89. In this case. the statistical moment, EMG. Giddings and
Thomas models are more reliable in extracting kinetic rate constants than the
true kinetic method. The rate constant from stationary to mobile phase for this
system is around 0.05 s". which is only slightly larger than the value 0.04 s'1
observed in Table 2.6 for the homogeneous system with the smallest stationary-
phase diffusion coefficient (1 .0x10‘8 cmzls).

2.4. 2. 2. Unequaily distributed multiple sites for heterogeneous surface

In the system with unequally distributed sites. the probability of each site is
chosen to be exponentially distributed. It is well known that the retention factor is
exponentially related to the free energy (AG) of transfer between the mobile and
stationary phases [1]. Thus. the physical meaning for this particular system is
that the probability of each site is inversely proportional to the interaction energy.

This yields increasingly smaller populations of higher energy sites.

113

Table 2.13 Kinetic rate constants from stationary to mobile phase (k..... 5")

along the column for equally distributed heterogeneous surface.‘I

 

 

 

 

 

 

 

0.5 cm 2 cm* 5 cm* 7 cm*
Model
True 0.254 1 0.004 0.254 1 0.004 0.254 1 0.004 0.254 1 0.004
Moment 0.055 0.052 0.053 0.051
EMG 0.094 0.043 0.054 0.059
Giddings 0.197 0.065 0.056 0.052
Thomas 2.176 0.062 0.055 0.051

 

 

 

 

 

* Steady state achieved

Simulation conditions given in Figure 2.8.

114

 

Representative zone profiles at varying column length are compared in Figure
2.9. The first zone profile at 1.0 cm has not yet reached steady state. but steady
state should have been achieved for all subsequent zone profiles. These zone
profiles show more asymmetry than those from the equally distributed
heterogeneous system in Figure 2.8. However, the extent of asymmetric tailing
still decreases along the column. In other words. the heterogeneous system with
unequally distributed sites does not successfully produce permanent tailing. But
it does increase the tailing and maintain the tailing longer than the
heterogeneous system with equally distributed sites. This can be clearly seen in
Figure 2.10, in which the unequally distributed heterogeneous system has more
skew than the equally distributed heterogeneous system. For comparison. the
skew of two homogeneous systems with stationary-phase diffusion coefficients of
1.0x10'7 cmzls and 1.0x10"3 cmzls are also shown in Figure 2.10. Both
heterogeneous systems show more skew than the homogeneous system with D.
equal to the median value of 1.0x10‘7 cmzls. But the unequally distributed
heterogeneous system has comparable skew to the homogeneous system with
D. equal to the smallest value of 1.0x1043 cmzls before 8 cm. and only slightly
larger skew thereafter. This behavior is interesting, given that the probability for
the smallest value of D, in the unequally distributed system is as small as 0.017.
However. this 1.7% distribution site clearly dominates the resultant zone profiles.
Based on the retention factors and probabilities given in Table 2.11. a
calculated retention factor of 1.63 is expected for unequally distributed multiple

sites under these conditions. The retention factors derived from the different

115

Figure 2.9: Comparison of zone profiles with unequally distributed
heterogeneous surface. From left to right, detector distance L = 1, 5. 8. 15, and
20 cm. Other simulation conditions: N = 5000, t = 5.0x10“ s. o... = 1.0x10’5 cmzls.
uo = 0.1 cmls, R... = 2.0x10‘3 cm, d. = 8.28x10“ cm, a = 1.0, P(2) conditions are

given in Table 2.11.

116

 

E 2::

 

 

 

o8 8e 8N
.. H 1 C

om ._ somsuu fl
EOQHJ a

EomflJ

EDP":—

 

117

 

 

 

Figure 2.10: Comparison of skews among equally distributed (0), unequally
distributed (I) heterogeneous systems, homogeneous system with D. equal to
1.0x10'7 cm2/s (A) and homogeneous system with D. equal to 1.0x10'° cmzls (t).
For heterogeneous systems, simulation details as given in Figures 2.8 and 2.9.

For homogeneous systems. simulation details are given in Figure 2.4.

118

oo_.

0..

Es Sasha

_..o

 

 

 

 

 

_..o

or

119

methods are compared in Table 2.14. The true kinetic method gives an accurate
value at 1.613. The statistical moment method gives accurate and reliable
results before and after steady state has been achieved. The EMG method is
relatively accurate (1% error) after steady state, followed by the Giddings model
(13% error). and the Thomas method produces the largest errors (30% error).
The kinetic rate constants are summarized in Table 2.15. The accuracy of
the true kinetic method is still unreliable because of the first-order kinetic model.
All the other methods have comparable results, but still deviate from the true
kinetic method. Again, the statistical moment, EMG, Giddings and Thomas
models are more reliable in extracting the kinetic rate constant than the true
method. The rate constant for this system is around 0.12 s", which is higher
than that of the equally distributed sites, which is around 0.05 s". But this rate
constant is intermediate between that for the two homogeneous systems with the
smallest stationary-phase diffusion coefficients of 1.0x10"3 and 3.0x10'a cmzls.
Based on the simulated results above for the two heterogeneous systems,
peak tailing is still considered to be a complicated phenomenon that requires
further investigation. In contrast to Giddings” original proposition. it appears that
one scarce, high-energy site is not sufficient to cause persistent tailing. Indeed.
the five sites demonstrated herein are also not sufficient. According to Weiss’

work, more sites are needed to cause persistent tailing.
2.5. CONCLUSIONS

This study is the first to validate and compare the accuracy of different

experimental methods for extracting retention factors and kinetic rate constants

120

Table 2.14 Retention factors (k) along the column for unequally distributed

heterogeneous surface.a

 

 

 

 

 

 

 

 

L
1 cm 5 cm* 8 cm* 15 cm” 20 cm*
Model
Calculated 1 .63 1 .63 1 .63 1 .63 1 .63
1.6131 1.6131 1.6131 1.6131 1.6131
True
0.001 0.001 0.001 0.001 0.001
Moment 1 .63 1 .62 1 .63 1 .63 1 .63
EMG 1.36 1.60 1.65 1.65 1.64
Giddings 1.10 1.43 1.48 1.55 1.57
Thomas 2.23 2.14 2.17 1.97 1.89

 

 

 

 

 

 

* Steady state achieved

Simulation conditions given in Figure 2.9.

 

Table 2.15 Kinetic rate constants from stationary to mobile phase (km. s")

along the column for unequally distributed heterogeneous surface.”

 

 

 

 

 

 

 

1 cm 5 cm* 8 cm* 15 cm* 20 cm*
Model
0.800 1 0.800 1 0.800 1 0.800 1 0.800 1
True
0.006 0.006 0.006 0.006 0.006
Moment 0.124 0.134 0.126 0.125 0.124
EMG 0.351 0.151 0.116 0.117 0.131
Giddings 0.706 0.260 0.201 0.159 0.145
Thomas 0.685 0.266 0.213 0.168 0.150

 

 

 

 

 

 

* Steady state achieved

122

Simulation conditions given in Figure 2.9.

 

with the stochastic simulation method. In this simulation. the effects of column
length, linear velocity, stationary-phase diffusion coefficient, interfacial mass
transfer coefficient, and equilibrium constant have been evaluated. Overall, the
retention factors are the most reliable from the statistical moment method.
relatively reliable from the EMG and Giddings models. and exhibit the greatest
error from the Thomas model. For the kinetic rate constants, the different
parameters that influence mass transport appear to have different effects on the
relative accuracy of the different methods. When increasing the column length.
rate constants from the statistical moment, Giddings, and Thomas models are
quite constant while those from the EMG model increase. Decreasing the linear
velocity has the same effect as increasing the column length. After spending a
similar amount of time on the column, the same zone profiles are achieved.
When decreasing the stationary-phase diffusion coefficient or decreasing the
interfacial mass transfer coefficient. rate constants for all models decrease and
the zone profiles become broader with more asymmetry. In all of these
simulations. the rate constants from the statistical moment. EMG, Giddings. and
Thomas models are all similar to the true kinetic value. However. when
increasing the equilibrium constant, the rate constants deviate from the true
kinetic data for all models. This deviation may arise from poor fit of the
simulation data to the single exponential decay in the true kinetic method.
Heterogeneous surfaces with equally or unequally distributed interaction
sites are also generated to compare the kinetic rate constants with different

methods. While the statistical moment, EMG. Giddings, and Thomas models

123

yield comparable results. significant deviation is observed from the true kinetic
method due to poor fit in the true kinetic method. In these cases, the statistical
moment, EMG, Giddings. and Thomas models may be more reliable in extracting
kinetic rate constants. It is apparent that tailing of zone profiles is a transient
phenomenon for homogeneous surfaces and for heterogeneous surfaces with a
limited number of interaction sites. But the tailing can be maintained longer and

stronger with unequally distributed heterogeneous surfaces.

124

26
[H

B]
B]
M]
[S
[W

W]
W]
[9
NW
“0
“H

UN

1141
1151
[161
1171

um
um
mm
90

REFERENCES

J.C. Giddings, Dynamics of Chromatography. Marcel Dekker. New York,
NY, 1960.

J.C. Giddings. J. Chromatogr. 2 (1959) 44-52.

J.C. Giddings, J. Chem. Phys. 31 (1959) 1462-1467.
J.C. Giddings, J. Chromatogr. 3 (1960) 443-453.
J.C. Giddings. J. Chromatogr. 5 (1961) 61-67.

S. Golshan-Shirazi. G. Guiochon. in: F. Dondi. G. Guiochon (Eds),
Theoretical Advancement in Chromatography and Related Separation
Techniques. Kluwer, Amsterdam, 1992, 61-92.

J.C. Giddings. H. Eyring, J. Phys. Chem. 59 (1955) 416-421.
J.C. Giddings. J. Chem. Phys. 26 (1957)169-173.

D.A. McQuarrie, J. Chem. Phys. 38 (1963) 437-445.

F. Dondi. M. Remelli. J. Phys. Chem. 90 (1986) 1885-1891.
C.P. Woodbury, J. Chromatogr. Sci. 32 (1994) 339-348.

A. Felinger. A. Cavazzini. F. Dondi. J. Chromatogr. A 1043 (2004) 149-
157.

A. Cavazzini. F. Dondi. A. Jaulmes. C. Vidal-Madjar. A. Felinger, Anal.
Chem. 74 (2002) 6269-6278.

V.L. McGuffin, P. Wu, J. Chromatogr. A 722 (1996) 3-17.
D.L. Hopkins, V.L. McGuffin, Anal. Chem. 70 (1998) 1066-1075.
P.E. Krouskop, V.L. McGuffin. J. Chromatogr. A 959 (2002) 49-64.

V.L. McGuffin. P.E. Krouskop, D.L. Hopkins, American Chemical Society
(2000) Chapter 4, 37-66.

C. Horvath, H.J. Lin, J. Chromatogr. 126 (1976) 401 -420.
C. Horvath, H.J. Lin, J. Chromatogr. 149 (1978) 43-70
A.M. Lenhoff, J. Chromatogr. 384 (1987). 285-299.

K. Miyabe. G. Guiochon. J. Sep. Sci. 26 (2003) 155-173.

125

[22]

[23]
[24]
[25]
[26]
[27]
[28]
[29]

8.8. Howerton. C. Lee. V.L. McGuffin. Anal. Chim. Acta, 478 (2003) 99-
110.

V.L. McGuffin, C. Lee, J. Chromatogr. A 987 (2003) 3-15.

8.8. Howerton. V.L. McGuffin. Anal. Chem. 75 (2003) 3539-3548.

8.8. Howerton, V.L. McGuffin. J. Chromatogr. A 1030 (2004) 3-12.

V.L. McGuffin, S.B. Howerton, X. Li, J. Chromatogr. A 1073 (2005) 63-73.
J.C. Giddings, Anal. Chem. 35 (1963) 1999-2002.

G.H. Weiss, Sep. Sci. Technol. 16 (1981) 75-80.

G.H. Weiss. Sep. Sci. Technol. 17 (1982-1983) 1609-1622.

126

CHAPTER 3
EXPERIMENTAL METHODS

3.1 EXPERIMENTAL SYSTEM

3.1.1 Column Packing

In order for the quantification of thermodynamics and kinetics. capillary
columns are employed throughout the study. A well-behaved column is crucial
for our research. In this section, the methods for column packing are described.

An optically transparent, fused-silica capillary is used for the column (200-
um i.d., Polymicro Technologies). With 5-pm particles, the number of particles
across the column is around 40. The number of particles across the column is
important because a larger number of particles across the column results in a
minimization of wall effects, which contribute to asymmetrical tailing (vide infra).
The column detection window needs to be made before packing by burning off
the polyimide coating. The columns are terminated by quartz wool frits that
prevent leakage of the stationary phases from the packed column.

The stationary phase used in chiral separation are native B—cyclodextrin
(Cyclobond l 2000. Astec) characterized by a 5.2-um particle size. 0.89-ng
pore size. and 305-m2/g surface area. In order to pack the stationary phase, the
slurry method is utilized [1]. Columns prepared by this method have very uniform
packing across the diameter and along the length. This method involves
suspension of the stationary phase in a solvent that prevents immediate
precipitation. For the B-cyclodextrin stationary phase, methanol is chosen as the

solvent. Once suspended. the material is transferred to a stainless steel

127

reservoir that is connected in series with a single-piston reciprocating pump
(Model 114M, Beckman Instruments) and a fused-silica capillary. The reservoir
is pressurized rapidly, thus injecting the stationary phase into the open capillary.
The highest pressure at 4000 psi packs the column in a matter of minutes. The
highest pressure is maintained for three hours and lowered to 1500 psi gradually.
The pressure is maintained at 1500 psi overnight. This lower pressure allows the
packed bed to compress, thus removing any voids that could be left during the
initial packing step. The column has a plate height (H) of 99 pm and reduced
plate height (h) of 19.03.
3.1.2 Chromatographic System
3. 1.2. 1 One detector system for the mobile phase study

As illustrated in Figure 3.1, this system is used for the mobile-phase study
(Chapter 4). The solutes are separated on a capillary liquid chromatography
system. The mobile phases are delivered by a single-piston reciprocating pump
(Model 114M, Beckman Instruments), operated in the constant-pressure mode.
The pump allows for the mobile phase to be supplied continuously without the
need for depressurization during the refill cycle. After injection (Model ECI4W1,
Valco Instruments), the samples are split between the column and a fused-silica
capillary (SO-um i.d., Polymicro Technologies) that served as a splitter. The
length of the splitter is varied to change the amount of sample that is introduced
into the column so as to prevent an overload of the stationary phase. Under

normal conditions. the injection volume is around 15 nL.

128

Figure 3.1 Schematic diagram of the experimental system for capillary liquid
chromatography with one on-column laser-induced fluorescence detector for
mobile phase study. I: injection valve. 8: splitting tee. F: filter. PMT:

photomultiplier tube. AMP: current to voltage amplifier.

129

 

 

Laser

 

 

 

 

 

 

 

 

 

 

 

 

5:200
in

paéa

n=>_< $58800

 

 

 

 

 

 

 

130

The polyimide coating is removed from the capillary column at 99-cm
length to facilitate on—column detection by laser-induced fluorescence. A helium-
cadmium laser (Model 3074-20M. Melles Griot) provides excitation at 325 nm.
The fluorescence emission is isolated by a liquid filter (1% aqueous NaNOa) and
two interference filters (420 nm. S10-410-F. Corion), and is detected by a
photomultiplier tube (Centronic Model Q42498A. Bailey Instruments). The
resulting photocurrent is amplified, converted to the digital domain (Model PCI-
MlO-16XE-50, National Instruments), and stored by a user-defined program
(Labview v5.1, National Instruments).

3. 1.2.2 Four-detector system for temperature and pressure study

As illustrated in Figure 3.2, this system is used for the temperature and
pressure study (Chapter 5 and 6). The design and validation of this system were
conducted by Dr. Shu-hui Chen [2]. There are three major differences between
this system and the system discussed in 3.1.2.1.

At the end of the column. another capillary (20-prn i.d., Polymicro
Technologies) is attached to serve as restrictor. The length of the restrictor is
reduced as the inlet pressure is decreased in order to maintain a constant
pressure drop along the column of (~10 psi/cm). By reducing the length of the
restrictor and splitter proportionally, the split ratio could be maintained at a
constant value.

The injector, splitter, column, and restrictor are all housed within a

cryogenic oven (Model 3300. Varian Associates) that maintains a constant

131

Figure 3.2 Schematic diagram of the experimental system for capillary liquid
chromatography with four on-column laser-induced fluorescence detectors for
temperature and pressure study. I: injection valve. S: splitting tee, R: restrictor,
FOP: fiber-optic positioner, F: filter, PMT: photomultiplier tube, AMP: current to

voltage amplifier.

132

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. Scan.

 

 

 

 

 

 

:2... _e.2n._ :22 So
222. n..2< n..2< n..2<
r , _ _ _
T

 

 

28232800

 

 

133

temperature (1 0.1 K) through the use of liquid nitrogen aspiration and resistive
heating coils.

Four detector windows are available for this system to monitor solute zone
profiles along the column. The laser beam Is carried via UV-grade optical fibers
(100 um, Polymicro Technologies) to four locations along the column where the
polyimide coating has been removed. The laser power at each location is
balanced using fiber optic positioners and a fluorophore at the inception of each
experiment. At each location, the fluorescence is collected orthogonal to the
incident beam by optical fibers (500 um, Polymicro Technologies) and is
transmitted to a photomultiplier tube (Model R760. Hamamatsu), which has a
420-nm interference filter (S10-420-F, Corion). The resulting photocurrent is
amplified using a gain of 100 nA/V and a time constant of 10 ms. The signal is
then converted to the digital domain (PCI-MlO—16XE-50. National Instruments)
and stored by a user-defined program (Labview v5.1. National Instruments). The
acquisition rate of the program can be manually adjusted. and is typically set

between 1 and 4 Hz.
3.2 DATA ANALYSIS

After collection. the zone profile for each solute is extracted from the
chromatogram. Each profile is fit by nonlinear regression to the exponentially
modified Gaussian (EMG) equation by using a commercially available program
(Peakfit v4.14, SYSTAT Software). The EMG equation is chosen because the
statistics of fit are better than for any other model that has been demonstrated to

have physical meaning. Specifically speaking. the statistical fit parameter R2

134

from the EMG model is usually higher than that from the Thomas [3,4] or
Giddings [5] models. The residuals from the EMG model are more random and
smaller than those from the Thomas or Giddings models as well. The EMG
model has already been validated for extracting thermodynamic and kinetic
information by the simulation works in Chapter 2. The EMG equation is the

convolution of Gaussian and exponential functions, with the resulting form

_A 02 tg-t t-tg a
C(t)—z—texpl:2t2+ T ][erf[‘/2_o-J§t]+1] (2.1)

where C(t) is the concentration as a function of time, A is the peak area. to is the

 

 

retention time of the Gaussian component. a is the standard deviation of the
Gaussian component, I is the exponential component. and erf is an statistical
error function. Symmetrical zone broadening, which arises from diffusion and
mass transfer processes that are fast relative to the separation time. is quantified
by a. Asymmetrical broadening, which arises from volumetric sources (i.e..
injectors, unions, etc.), electronic sources (i.e., amplifiers. etc.), nonlinear
isotherm, and diffusion and mass transfer processes that are slow relative to the
separation time, is quantified by 1. By deliberate design of the system. the
asymmetrical broadening from volumetric and electronic sources can be
minimized and kept small relative to those from slow mass transfer processes.
The nonlinear isotherm contribution to asymmetric broadening can be totally
eliminated by injecting solutes at sufficiently low concentrations. Thus. the slow

mass transfer will dominate the asymmetrical broadening. The resultant fitting

135

parameters of the EMG equation are used to calculate thermodynamic and

kinetic values [6] as discussed in Chapters 1.4 and 2.3.3.
3.3 CONCLUSIONS

In order to accurately characterize the liquid chromatographic process.
both a judiciously designed experimental system and an accurate data analysis
method are necessary. This chapter describes the system as well as the

mathematic function for analysis.

136

3.4 REFERENCES

[1] J.C. Gluckman. A. Hirose, V.L. McGuffin, M. Novotny. Chromatographia
17 (1983) 303-309.

[2] S.-H. Chen, in Chemistry, Michigan State University, East Lansing.
Michigan 1993

[3] H.C. Thomas. J. Am. Chem. Soc. 66 (1944) 1664-6.
[4] J. L. Wade, A.F. Bergold, P.W. Carr, Anal. Chem. 59 (1987) 1286-95.

[5] J. C. Giddings, Dynamics of Chromatography; Marcel Dekker: New York,
NY, 1965.

[6] 8.8. Howerton, V.L. McGuffin, Anal. Chem. 75 (2003) 3539-48.

137

CHAPTER 4

EFFECT OF MOBILE PHASE COMPOSITION TO CHIRAL
SEPARATIONS WITH B-CYCLODEXTRIN STATIONARY PHASE

4.1. INTRODUCTION

In liquid chromatography, once a specific stationary phase is chosen,
mobile phase composition is the factor that will most significantly affect the
separation. With native cyclodextrin CSPs, reversed-phase separation is the
most popular and successfully used mobile phase [1.2]. Many publications are
available on the effect of mobile phase composition in the reversed-phase mode
[3-16]. Systematic studies have been performed on the effect of organic modifier
type. modifier concentration, buffer type, buffer concentration and ionic strength.
More recently, polar-organic phase separation has also become widely utilized.
Armstrong et al. [17] first utilized polar-organic mobile phases with native [3-
cyolodextrin CSP to separate some B-blocker pharmaceuticals. Since then.
many other enantiomers have been separated in the polar-organic mode [18-21].
However, limited information is available on the effect of polar-organic mobile
phase composition. especially detailed and systematic characterization studies.
Notably. there have been investigations of mobile phase effects on p-blockers
[22] and amino acids [23]. In these studies. the thermodynamic effects on
retention factor and chiral selectivity are carefully investigated. however, the
kinetic effects on mass transfer rates are usually overlooked. Both
thermodynamic and kinetic information are equally important for elucidation of

the retention mechanism.

138

In addition to the effect of mobile phase composition, the memory effect is
another interesting issue that needs to be addressed. The existence of memory
effects with acid and amine modifiers has been demonstrated with
polysaccharide columns by Stringham et al. [24,25]. In their work. acids and
amines showed persistent effects after their removal. indicating strong interaction
with the polysaccharide CSP. However, there has been no report on these
effects with cyclodextrin CSPs. Considering that cyclodextrin has the same
building blocks (glucose units) as polysaccharides, the memory effect is worthy

of investigation.
4.2. EXPERIMENTAL METHODS

4.2.1 Chemicals

As depicted in Figure 4.1, five coumarin-based solutes are chosen based
on their structural similarities. Warfarin is a well-known pharmaceutical
compound that serves as an anti-coagulant. It inhibits the synthesis of clotting
factors, thus preventing blood clot formation. Coumachlor, coumafuryl, and
coumatetralyl are three anti-coagulant pesticides to kill rodents. They take effect
by blocking vitamin K-dependent synthesis of the blood clotting substance
prothrombin. thus causing wide-spread internal bleeding [26]. All four
compounds are chiral and they are marketed in racemic form. The chirality of
these compounds arises from the sp3 - alpha carbon. Another achiral compound.
4-hydroxycoumarin, is an important intermediate for coumarin-related
pharmaceuticals. It is a subunit contained in all four chiral compounds. thus. a

separate view of this particular group to the retention process is possible. The

139

Figure 4.1 Structure of coumarin-based solutes.

 

Coumafuryl Coumatetralyl

O 0
CL;
OH

4-Hydroxycoumarin

140

solutes are obtained from Sigma-Aldrich as solids and are dissolved in high-
purity acetonitrile (Burdick and Jackson, Baxter Healthcare) to yield standard
solutions at 10“ M. Nitromethane is used as non-retained marker and is added
to each solution at a concentration at 15% (vlv). High purity acetonitrile.
methanol (Burdick and Jackson. Baxter Healthcare). acetic acid (Sigma-Aldrich).
and triethylamine (Sigma-Aldrich) are used for mobile phase preparation.
4.2.2 Experimental System

The solutes are separated on a capillary liquid chromatography system as
illustrated in Figure 3.1. The silica packing (Cyclobond l 2000, Astec) is
characterized by a 5.2-um particle size. 0.89-ng pore volume. and 305-m2/g
surface area, reacted with B—cyclodextrin at a bonding density of 0.39 umollm’.
The data are analyzed by exponentially modified Gaussian (EMG) function. as
described in Chapters 1.4.3.2.2 and 2.3.3.

4.3. RESULTS AND DISCUSSION

4.3.1. Memory Effect

In the first series of experiments, warfarin is utilized as the solute to
investigate memory effects on a B-cyclodextn‘n CSP. Two polar-organic mobile
phase compositions are used: the first mobile phase contains only acetonitrile
and methanol at a 90%:10% ratio by volume; the second mobile phase contains
acetonitrile and methanol (90%:10%) together with acetic acid (0.30%) and
triethylamine (0.20%) modifiers. Warfarin is initially injected at the first mobile
phase composition. This result serves as the “original" retention data (t.) for

comparison when acid and amine are not present in the mobile phase. Then the

141

second mobile phase is introduced with another warfarin injection. Finally. the
first mobile phase is switched back, and warfarin is injected over successive days
to monitor the peak shape and retention time. Representative chromatograms
are illustrated in Figure 4.2. The original peaks have a broad and fronting shape.
with a retention time of approximately 35 min (Figure 4.2A). When acid and
amine are added to the mobile phase, the elution time of warfarin is greatly
reduced and the peak shape becomes narrow and Gaussian (Figure 4.28).
When acid and amine are subsequently removed from the mobile phase. the
retention time of warfarin increases. with increased peak broadening as well
(Figures 4.2C and 4.20). until 3 days later when the retention time reaches a
maximum (Figure 4.2E). Thereafter. the retention time begins to decrease and
the peak shape becomes broader and more fronting (Figure 4.2F). But even
after 10 days, the retention time does not return to the original value shown in
Figure 4.2A. These data indicate two possibilities: either a memory effect of the
acid and amine exists in the cyclodextrin CSP, or the equilibration time for the
acetonitrile:methanol mobile phase is extremely long. The second possibility can
also be considered as the existence of a memory effect of methanol.

In the approach used by Stringham et al. [24,25] to remove the memory
effect of acid or amine on a polysaccharide CSP, the column was washed with
alcohols or water. Since methanol is already a component of the polar-organic
mobile phase. methanol alone is used herein to remove any possible memory
effect of acid or amine. The B-cyclodextrin column is washed with methanol for

one day, then the mobile phase is switched back to acetonitrile:methanol

142

Figure 4.2 Representative chromatograms of memory effect from acetic acid
and triethylamine. Column: B-cyclodextrin. Solute: racemic warfarin. Mobile
phase composition: acetonitrile:methanol (90%:10%) (A) original data before acid
and amine modifier added; (8) acetic acidztn'ethylamine (0.30%:0.20%) added; (C)

removal of acid and amine modifier at hour 4; (D) day 1; (E) day 3; (F) day 10.

143

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(90%:10%), followed by the injection of warfarin over successive days.
Representative chromatograms are shown in Figure 4.3. After one day, the
retention time for warfarin is extremely long at around 150 min (Figure 4.3A).
Moreover, the peak shape is tailing instead of fronting as seen previously in
Figure 4.2. After two days, the retention time is reduced to around 65 min with a
fronting peak shape (Figure 4.38). The retention time of warfarin continues to
decrease over several days. but does not return to the original value even after
10 days (Figure 4.3D). However, these retention times are closer to the original
values than those obtained after removal of acid and amine (Figure 4.2). These
data indicate fllat washing with methanol provides some improvement, but
cannot completely eliminate the memory effect of acid or amine. On the contrary,
methanol itself exhibits an even stronger memory effect over short periods of
time (e.g., less than 1 day). These results suggest that more detailed
investigation of the effect of the individual components in the polar-organic
mobile phase is warranted. Prior to these experiments, the B-cyclodextrin
column is washed with pure acetonitrile for several weeks to remove any residual
memory effect of the previous mobile phases.
4.3.2. Two-Component Mobile Phase

In these experiments, acetonitrile and methanol are the only components
in the mobile phase, no acid or amine is added. The percent of methanol is
varied at 3%, 5%, 10%, 15%, and 20%. Each composition of the mobile phase is
maintained for several days in order to observe the rate of achievement of

equilibrium conditions.

145

Figure 4.3 Representative chromatograms of memory effect from methanol.
Column: B-cyclodextrin. Solute: racemic warfarin. Mobile phase composition:
acetonitrile:methanol (90%:10%) after removal of pure methanol mobile phase at

(A) day 1; (8) day 2; (C) day 3; (D) day 10.

146

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The retention time of warfarin over successive days is reported in Table
4.1. Using the second day as an example, the retention time decreases as the
mobile phase composition changes from 3% to 10% methanol. From 10% to
20% methanol, however, the retention time shows an increasing trend. For each
composition, the retention time is not stable even after several days.
Interestingly, the trends in retention time over days are not the same for each
concentration. At lower concentrations (3% and 5%) of methanol, the retention
time decreases over successive days. At higher concentrations (15% and 20%),
the retention time increases over successive days. At an intermediate
concentration of 10% methanol, the retention time shows an initial decrease
followed by an increase. By careful observation, the trend over successive days
is noted to be the same as the trend for the next higher concentration of
methanol. Using 3% methanol mobile phase as an example, the retention time
of warfarin increases over successive days, and retention time also increases
when changing from 3% to 5% methanol. Using 15% methanol as an example,
the retention time of warfarin decreases over successive days, and retention time
also decreases when changing from 15% to 20% methanol. These observations
suggest that methanol may accumulate on the B—cyclodextlin column. While a
low concentration of methanol can compete with the solute warfarin and serve as
a displacing agent to decrease its retention time, higher concentrations may build
up a layer of methanol on the cyclodextrin surface. This layer can serve as a
partitioning medium and can increase retention time because the effective

volume of the stationary phase increases with increasing methanol concentration.

148

 

Table 4.1

two-component mobile phase

Retention time of 1‘t warfarin enantiomer over successive days in a

 

 

 

 

 

 

 

 

 

 

 

 

Mobile Phase Retention Time (min)
Composition
(acetonitrile:methanol) Day 1 Day 2 Day 3 Day 4
97%:3% 183.5 174.8 174.1 NIA'
95%:5% 93.4 81 .3 76.1 NIA
90%:10% 28.1 22.9 27.8 31.6
85%:15% NIA 48.0 50.9 55.3
80%:20% 100.3 96.1 105.4 108.3
a not available

149

 

Another interesting observation is the change in warfarin peak shape with
concentration of methanol. At concentrations of 3% to 15% methanol, all the
peaks are fronting. At 20% methanol, however, different peak shapes appear
over successive days as shown in Figure 4.4. The peaks on the second day are
fronting (Figure 4.4A), those on the third day are slightly tailing (Figure 4.48),
while those on the sixth day are strongly tailing (Figure 4.4C). This change in
peak shape suggests a change in the interaction between warfarin and the
cyclodextrin CSP. A tailing shape is usually considered as a sign of a Langmuir
or BET type I isotherm, where there exists a limited number of interaction sites
on the stationary phase. As the concentration of solute increases, these sites
become completely occupied and the remaining solute molecules are not
retained. A fronting shape usually suggests an anti-Langmuir or BET type III
isotherm, where there is weak interaction between the solute and stationary
phase. As the concentration of solute increases, it has stronger interactions with
other solute molecules bonded to the stationary phase than with the stationary
phase alone. It is certainly possible that the retention mechanism changes with
increasing methanol concentration due to the formation of a methanol layer, as
discussed above. However, it is also possible that a single mechanism exists
with a more complicated isotherm, such as BET type V, which combines the
features and behavior of the BET type I and Ill isotherms. More detailed studies
are needed to elucidate the underlying reason for the change in peak shape with

methanol concentration.

150

Figure 4.4. Comparison of chromatograms in two-component mobile phase.
Column: B-cyclodextrin. Solute: racemic warfarin. Mobile phase composition:

acetonitrile:methanol (80%:20%) (A) day 2; (8) day 3; (C) day 6.

151

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4.3.3 Three-Component Mobile Phase

In these experiments, acetic acid or triethylamine is added to an
acetonitrile:methanol (90%:10%) mobile phase to prepare a three-component
mobile phase. The retention time, equilibration time, peak shape, and isothenn
effect are compared for the different mobile phase conditions.

4. 3. 3. 1 Retention Time and Equilibration Time investigation

As in the previous study, warfarin is injected over successive days to
observe the trends in retention time and equilibration time. Three different
mobile phase compositions are reported. The first mobile phase is a two-
component mobile phase containing acetonitrile and methanol (90%:10%). The
second mobile phase added 0.30% acetic acid to the first mobile phase, while
the third mobile phase added 0.20% triethylamine to the first mobile phase.

The retention time of warfarin measured over successive days at each
mobile phase composition is reported in Table 4.2. The average retention time,
standard deviation, and percent relative standard deviation (RSD) are reported
as well. In the two-component mobile phase, equilibrium is not reached even
after four days, which can be discerned from the large RSD of 13%. In fact, the
retention time is still changing even after one week (results not shown). When
acid or amine modifier is added to the mobile phase, equilibrium is reached much
faster (one day or less) and the RSD is reduced to 1 - 2%. This indicates that
acid or amine modifier can help greatly to shorten the equilibration time of the

mobile phase.

153

Table 4.2 can also be used to compare the retention time for different
mobile phase compositions. When compared to the two-component mobile
phase, the addition of 0.30% acetic acid modifier does not have a significant
effect upon retention time, which increases only slightly. On the contrary, the
addition of 0.20% triethylamine modifier greatly shortens the retention time. The
suspected reasons for this behavior will be discussed in the next section.
4.3.3.2. Peak Shape and lsothenn Investigation

As the mobile phase composition is changed, not only do the retention
time and equilibration time change, but also the peak shape. Unusual fronting
and tailing shapes are frequently encountered, as discussed in Sections 4.3.1
and 4.3.2. Since these peak shapes are usually associated with nonlinear
isotherms, this possibility is examined by injecting warfarin at different
concentrations ranging from 5x10‘5 to 8x104 M.

As discussed previously, fronting peaks are observed in the two-
component mobile phase composition with acetonitrile:methanol (90%:10%). But
when both acid and amine modifiers are added, symmetric Gaussian peaks are
observed. To determine which modifier is responsible for the Gaussian peak
shape, two different mobile phases are investigated. One contains 0.30% acetic
acid modifier and the other contains 0.05% triethylamine modifier.
Representative chromatograms of warfarin are illustrated in Figures 4.5 and 4.6.
Wlth acid modifier alone, the retention time is virtually unchanged and the peak
shape is Gaussian until the highest warfarin concentration (8x104 M), where the

retention time decreases slightly and is accompanied by slight tailing. This

154

Table 4.2

two-component and three-component mobile phases

Retention time of 1‘t warfarin enantiomer over successive days in

 

 

 

 

 

 

Mobile Phase Retention Time (min)
Composition
St. %
Average
(acetonitrile:methanol: Day Day Day Day Dev. RSD‘I
1 2 3 4
acidzamine)
90%:10%:0%:0% 28.1 22.9 27.8 31.6 27.6 3.7 13
90%:10%:0.30%:0% 28.6 29.1 28.9 NIAb 28.9 0.3 1
90%:10%:0%:0.20% 12.3 12.3 11.9 NIA 12.2 0.3 2

 

 

 

 

 

 

 

 

a % RSD = (Average / St. Dev.) x 100 %

Not available

155

 

suggests that a linear isotherm is obtained in the mobile phase with acid modifier
over most of the solute concentration range in this study. However, with amine
modifier alone, fronting peaks are observed even at the lowest warfarin
concentration. The solutes become more retained and the peaks become more
asymmetric with increasing concentration. Although the maxima are shifted to
longer retention time, all the peaks for the first enantiomer appear to arise from
the same initial position. The peaks for the second enantiomer do not arise from
the same initial position, but are shifted to longer retention time with increasing
warfarin concentration. This behavior is indicative of a competitive nonlinear
isotherm, where both enantiomers are competing for the same adsorption sites
on the cyclodextrin CSP.

The change in peak shape with mobile phase composition is interesting
and informative. Fronting peaks are observed when no modifier or only amine
modifier is present in the mobile phase. As noted above, fronting shape is
usually indicative of an anti-Langmuir or BET type III isotherm. When no acid or
amine modifier is present, the methanol may accumulate on the cyclodextrin
surface, as discussed above. This may be the reason why warfarin cannot
interact directly with cyclodextrin, but tends to interact with other warfarin
molecules. When triethylamine is present, it has a tendency to interact with the
acidic hydroxyl group on warfarin (pK. = 4.5) to facilitate its elution, which
corresponds to the much shorter retention time. However, triethylamine probably
cannot compete with and displace warfarin from the cyclodextrin sites or from the

sites where the solute molecules interact with each other, thus it does not affect

156

:i
l

Figure 4.5 Warfarin peak shape in the presence of acetic acid. Column: 8-
cyclodextrin. Mobile phase composition: acetonitrile:methanol:acid
(90%:10%:0.30%). Warfarin concentration from highest to lowest: 8x10“ M;

4x10:t M; 2x104 M.

157

 

 

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hm

 

 

158

Figure 4.6 Warfarin peak shape in the presence of triethylamine. Column: [3-
cyclodextrin. Mobile phase composition: acetonitrile:methanol:amine
(90%:10%:0.05%). Warfarin concentration from highest to lowest: 8x104 M;

4x104 M; 2x104 M; 1x10:t M ; 5x10'5 M.

159

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the fronting shape. In contrast, acetic acid (PK. = 4.76) can effectively compete
and replace warfarin and methanol from similar sites on cyclodextrin. In this
manner, the linear range of the isotherm is increased and the fast acid-base
kinetics improve the peak shape.
4.3.4. Four-Component Mobile Phase

When all four components are present in the mobile phase, the peak
shapes are within the linear isotherm range to provide reasonable
thermodynamic and kinetic information. Thus, as the concentration of each
mobile phase component is changed, a detailed examination of its individual
effect on the thermodynamic and kinetic behavior of the coumarin-based solutes
is possible. The mobile phase composition of acetonitrile:methanol:acid:amine
(99%:1%:0.15%:0.10%) is chosen as the reference composition, from which all
variations are measured. Methanol is varied at 0%, 1%, 3%, and 5%; acetic acid
is varied at 0.05%, 0.10%, 0.15%, 0.20%, and 0.30%; triethylamine is varied at
0.05%, 0.10%, 0.15%, and 0.20%.
4. 3.4. 1. Comparison of Salutes

At the reference mobile phase composition, the retention factor, chiral
selectivity, and rate constants are reported in Table 4.3. The trend in retention
factor has a close relationship with the solute structure in Figure 4.1. As
generally believed, retention in the polar-organic mode with the B-cyclodextrin
CSP is mainly due to hydrogen bonding. The achiral compound, 4-
hydroxycoumarin, has the largest retention factor due to its strong intermolecular

hydrogen bonding with the stationary phase. The interactions of two sites, the

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hydroxyl and carboxyl groups of 4-hydroxycoumarin, contribute predominantly to
the retention. The relatively planar structure of 4-hydroxycoumarin facilitates the
simultaneous interaction of both sites with the hydroxyl groups on the rim of
cyclodextrin. All of the chiral solutes have smaller retention than 4-
hydroxycoumarin because of the bulky groups inserted between the hydroxyl and
carboxyl groups, which block their simultaneous interaction. Coumafuryl,
warfarin, and coumachlor have a similar structure but differ slightly in one
substituent on the chiral carbon. For coumafuryl, the oxygen of the furan ring
has the ability to hydrogen bond with the hydroxyl group. Due to this
intramolecular hydrogen bonding, the intermolecular hydrogen bonding of the
hydroxyl group with the stationary phase is decreased. Thus, coumafuryl has the
smallest retention factor. By replacement of the furan ring with a benzene ring,
warfarin and coumachlor do not have the same intramolecular hydrogen bonding
as coumafuryl. Thus, they have slightly larger, but similar retention factors due to
their similar structures. Coumatetralyl has a much larger retention factor than the
other three chiral solutes. The hydroxyl group can also form intramolecular
hydrogen bonds with the carbonyl group, which is present in coumafuryl, warfarin,
and coumachlor, but not present in coumatetralyl. Thus, coumatetralyl has the
least intramolecular hydrogen bonding and, hence, the largest intermolecular
hydrogen bonding with the stationary phase. Moreover, the substituent group of
coumatetralyl is relatively nonpolar, which enhances its interaction Wifl'l the
nonpolar cyclodextrin cavity. All of these effects contribute to its largest retention

factor among the chiral compounds.

163

Chiral selectivity, also summarized in Table 4.3, can help to explain the
difference between the two enantiomers and their interactions with the
cyclodextrin CSP. Under all conditions, warfarin has the largest chiral selectivity,
around 1.30. Coumachlor has a slightly smaller chiral selectivity, around 1.25,
due to the chlorine group on the benzene ring. The aromatic substituents of
warfarin and coumachlor have the ability to draw the molecule to hydrogen bond
closer to the chiral center by interacting with the cyclodextrin cavity. In fact, the
chlorine group on coumachlor further enhances this process and weakens the
much stronger hydrogen bonding interaction of the carboxyl group in the cyclic
ester. The presence of chlorine enhances retention, but not the chirally selective
interaction of hydrogen bonding. Thus, the chiral selectivity of coumachlor is
actually less than that of warfarin. Coumafuryl has a chiral selectivity around
1.20. Again, this is related to the smaller chirally selective interaction of
hydrogen bonding, as discussed above. Coumatetralyl has the least selectivity
among all the chiral molecules at around 1.05. This is related to the different
structure of coumatetralyl. Its chiral carbon is within a ring structure, which
restricts motion and makes it more difficult to discriminate between the two
enantiomers. Also, the substituents on the chiral carbon do not have hydrogen-
bonding ability. These substituents are relatively nonpolar, and have a better
chance to interact with the cavity of cyclodextrin. In other words, the groups with
stronger inclusion effects contribute more greatly to retention, but are not chirally

selective.

164

The kinetic rate constants also have a direct relationship with the solute
structure. The rate constants for 4-hydroxycoumarin are one to two orders-of-
magnitude smaller than those of the chiral molecules, as shown in Table 4.3.
Because of the two strong and simultaneous hydrogen bonding sites, the
adsorption and desorption processes for 4-hydroxycoumarin on the cyclodextrin
surface are extremely slow. For the chiral solutes, the restricted accessibility of
the hydrogen bonding sites also influences their rates of mass transfer. In
general, the longer the solutes are retained, the smaller are their rate constants.
However, within each chiral pair, the second enantiomer has a higher rate of
mass transfer than the first enantiomer, even though it is more retained. This
behavior suggests that the chiral and achiral selective sites have different kinetic
contributions, with the chiral sites having surprisingly higher mass transfer rates.
Warfarin, coumachlor, coumatetralyl, and 4-hydroxycoumarin all have a higher
adsorption rate (k...) than desorption rate (km). Hence, the limiting mass transfer
process is from stationary to mobile phase for these solutes. However, for
coumafuryl, the limiting mass transfer process is from mobile to stationary phase.
4.3.4.2. Effect of Methanol

The effect of methanol on thermodynamics is shown in Table 4.4. As
mentioned previously, methanol is able to hydrogen bond with the B-cyclodextrin
CSP. Thus, as the concentration of methanol is increased from 0% to 5%, the
retention factor of all solutes is decreased. The decrease in retention factor for
all chiral compounds is similar at 44% to 48%. However, the decrease in

retention factor for 4-hydroxycoumarin is the largest at 55%, which suggests that

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methanol is affecting 4-hydroxycoumarin more than the other compounds. This
behavior also supports the previous discussion of the strong hydrogen bonding
interaction between 4-hydroxycoumarin and the stationary phase. The effect of
methanol concentration on chiral selectivity is relatively small. Warfarin,
coumachlor, and coumatetralyl show a slight decrease, but coumafuryl shows a
slight enhancement. The effect of methanol on kinetics is shown in Table 4.5.
As the concentration of methanol is increased, all the solutes show an increase
in the desorption rate constant for transfer from stationary to mobile phase (k...)
But the adsorption rate constant for transfer from mobile to stationary phase is
relatively constant. In other words, because methanol acts as a displacing agent,
it influences the desorption rate rather than the adsorption rate.
4.3.4.3. Effect of Triethyiamine

Tables 4.6 and 4.7 demonstrate the effect of triethylamine on
thermodynamics and kinetics when the acetic acid concentration is held constant
at 0.15%. As the concentration of triethylamine is increased from 0.05% to
0.20%, the retention factor of all solutes is decreased. However, chiral
selectivities are simultaneously increased for warfarin, coumachlor, and
coumatetralyl. As noted above, it is most likely that triethylamine is interacting
with the acidic hydroxyl group of the solute molecules. As these interactions do
not directly involve the chiral center. they are probably decreasing the achiral
interactions such that the chiral selectivities are actually enhanced. As the
concentration of triethylamine is increased, the rate constants for mass transfer

(k... and k...) are increased as well. This indicates that triethylamine increases

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170

both adsorption and desorption rates for all solutes, but the desorption rate
increases faster.
4.3.4.4. Effect of Acetic Acid

Tables 4.8 and 4.9 demonstrate the effect of acetic acid on
thermodynamics and kinetics when the amine concentration is held constant at
0.10%. As the concentration of acetic acid is increased from 0.05% to 0.20%.
the retention factor of all chiral solutes increases. However, a further increase
from 0.20% to 0.30% actually decreases the retention factor for warfarin,
coumachlor, and coumatetralyl. Coumafuryl shows a continual increase over the
concentration range. On the contrary, 4-hydroxycoumarin shows a continual
decrease with an increase in acid concentration. While the acid serves as a
displacing agent for 4-hydroxycoumarin. it may have a different effect for the
chiral solutes. It is noteworthy that the chiral selectivity decreases for the chiral
solutes. which suggests that acetic acid may be interacting with chiral selective
sites of the stationary phase. The rate constants for mass transfer (k... and k...)
decrease for the chiral solutes, but are relatively constant for the achiral solute.
4—hydroxycoumarin.

To understand this behavior more fully, a three-component mobile phase
is examined to determine whether acetic acid acts in the same manner without
the amine. Table 4.10 shows the effect of acetic acid on thermodynamics and
kinetics of a single solute, warfarin, when no amine is present. The data in this
table are used as a direct comparison to those in Tables 4.8 and 4.9.

Interestingly, the trends in retention are completely opposite and suggest a

171

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174

difference in mechanism. When the amine is absent, an increase in the acetic
acid concentration alone decreases the retention factor of warfarin. Under these
conditions, acetic acid probably behaves as a displacing agent for the acidic
solute. When triethylamine is present in the mobile phase, the acetic acid tends
to interact with the amine first to minimize the amine effect. That is why the
retention factor of the chiral solutes increases initially for 0.05% to 0.20% acid in
Table 4.8. But for acid concentration in range of 0.20% to 0.30%. where the
amine has been completely consumed. the system behaves in the same manner
as acid present alone and the retention factor decreases. The chiral selectivity
exhibits the same trend and decreases regardless of whether triethylamine is
present. This behavior indicates that acetic acid is interacting with the chirally
selective sites of the stationary phase. Thus, as the retention factor is decreased,
chiral selectivity is reduced as well. Although both acid and amine can affect
retention. they are actually interacting with different positions of the stationary
phase or with the solutes. The acid interacts with chiral selective sites, whereas
the amine interacts with achiral selective sites. As to the kinetics, in the absence
of amine, acetic acid serves only to increase the desorption mass transfer rates
(km), but not the adsorption rates (k....).
4.4 CONCLUSIONS

In this study, the effect of mobile phase composition on thermodynamics
and kinetics of chiral separation is examined. Mobile phase composition affects
the equilibration time, retention time, as well as peak shape. Both acid and

amine modifier shorten the equilibration time greatly from weeks to one day or

175

less. Whereas the acetic acid modifier can increase the linear isotherm range
and ensure a Gaussian peak shape, the triethylamine modifier can dramatically
decrease the retention time while still enhancing chiral selectivity. In four-
component mobile phases. the elution order of all solutes is strongly dependent
on the hydrogen bonding ability between the solutes and the stationary phase.
The kinetic rate constants typically decrease with an increase in retention factor.
For the chiral solutes, the second enantiomer has a surprisingly higher mass
transfer rate than the first enantiomer although it is more retained. This behavior
suggests a difference in the kinetic contributions for chiral and achiral selective
sites. In a four-component mobile phase. methanol can hydrogen bond with the
stationary phase, thus decreasing retention and increasing the kinetics for all
solutes. Triethylamine decreases retention. but enhances chiral selectivity, but
acetic acid increases retention and reduces chiral selectivity. Both acid and
amine modifiers increase adsorption and desorption rate constants. When both
acid and amine are present in the mobile phase. they tend to interact with each

other and complicate the separation process.

176

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REFERENCES

W.L. Hinze, T.E. Riehl, D.W. Armstrong, W. DeMond, A. Alak, T. Ward,
Anal. Chem. 57 (1985) 237-242

H.Y. Aboul-Enein, MR. Islam, S.A. Bakr, J. Liq. Chromatogr. 11 (1988)
1485-1493

D.W. Armstrong, G.L. Bertrand, K.D. Ward, T.J. Ward, H.V. Secor, J.l.
Seeman, Anal. Chem. 62 (1990), 332-338

K. Fujimura, T. Ueda, T. Ando, Anal. Chem. 55 (1983) 446-450

K.G. Feitsma, J. Bosman, B.F.H. Drenth, R.A. De Zeeuw, J. Chromatogr.
333 (1985) 59—68

C.A. Chang, Q. Wu, D.W. Armstrong, J. Chromatogr. 354 (1986) 454-458
C.A. Chang, Q. Wu, M.P. Eastman, J. Chromatogr. 371 (1986), 269-282

J.l. Seeman, H.V. Secor, D.W. Armstrong, K.D. Timmons, T.J. Ward, Anal.
Chem. 60 (1988) 2120-2127

P. Macaudiere, M. Caude, R. Rosset, A. Tambute, J. Chromatogr. 450
(1988) 255-269

I.Z. Atamna, G.M. Muschik, H.J. lssaq, J. Chromatogr. 499 (1990) 477-
488

J.T. Andersson, G. Kaiser, Fresenius' Zeitschrift fuer Analytische Chemie
334 (1989) 749-751

S. Li, W.C. Purdy, J. Chromatogr. 543 (1991) 105-112
C.A. Chang, H. Ji, G. Lin, J. Chromatogr. (1990) 522 143-152

S. Piperaki, A. Perakis, M.‘ Parissi-Poulou, J. Chromatogr. A 660 (1994)
339-350

R.J. Soukup, R.V. Rozhkov, R.C. Larock, D.W. Armstrong,
Chromatographia 61 (2005) 219-224

X. Han, T. Yao, Y. Liu, R.C. Larock, D.W. Armstrong, J. Chromatogr. A
1063 (2005) 111-120

D.W. Armstrong, S. Chen, C. Chang, 8. Chang, J. Liq. Chromatogr. 15
(1992), 545-556

177

[13]

[19]

[20]

[21]

[221
[231
[241
[251
[261

SC. Chang, G.L. Reid, S. Chen, C.D. Chang, D.W. Armstrong, TrAC,
Trends Anal. Chem. 12 (1993) 144-153

C. Pham—Huy, B. Radenen, A. Sahui—Gnassi, J. Claude, J. Chromatogr. B,
665 (1995) 125-132

J. Zukowski, M. Pawlowska, M. Nagatkina, D.W. Armstrong, J.
Chromatogr. 629 (1993) 169-1 79

E. Lipka, V. Glacon, G. Mackenzie, D. Ewing, C. Len, D. Postel, M.
Vaccher, J. Bonte, C. Vaccher, Anal. Lett. 37 (2004) 385-398

M.W. Matchett, S.K. Branch, T.M. Jefferies, Chirality 8 (1996) 126-130
S. Chen, T. Ward, Chirality 16 (2004) 318-330

R.W. Stringham, K.G. Lynam, B.S. Lord, Chirality 16 (2004) 493-498
Y.K. Ye, B. Lord, R.W. Stringham, J. Chromatogr. A 945 (2002) 139-146

S.E. Hygnstrom, D.R. Virchow, Controlling rats, Ed. Wildlife Management
University of Nebraska-Lincoln, 2001

178

CHAPTER 5

EFFECT OF TEMPERATURE AND PRESSURE TO CHIRAL
SEPARATIONS WITH fi-CYCLODEXTRIN STATIONARY PHASE

5.1. INTRODUCTION

As demonstrated in Chapter 4, the effect of mobile phase composition is
important to the thermodynamics and kinetics of chiral separation. In this chapter,
temperature and pressure effects are illustrated to quantitate more detailed
thermodynamic and kinetic information.

In previous research, temperature studies are utilized most for
thermodynamic characterization. However, most of the investigations were in
reversed-phase mode [1.2]. Cabrera et al. [3] reported the different temperature
effects on chiral selectivity on two pharmaceuticals, oxazepam and prominal.
Mon'n et al. [4] reported van’t Hoff plots at different mobile phase compositions.
A change in the retention mechanism was accompanied by a change in pH value.
Pressure effects are also utilized for thermodynamic characterization. Most
investigations have been carried out by the Evans group with positional isomers
[5] and a few barbiturate chiral compounds [6-8]. Compared to the
thermodynamic characterizations, kinetic characterizations on 8—cyclodextn'n
stationary phase are limited.

Thus, the goal here is to conduct a systematic investigation on chiral
separation, to observe temperature and pressure effects on both thermodynamic
and kinetic behavior, to report specific thermodynamic and kinetic parameters,

and to elucidate chiral separation mechanisms.

179

5.2 EXPERIMENTAL METHODS

5.2.1 Chemicals

As depicted in Figure 4.1, five coumarin-related solutes are chosen as
model compounds: warfarin, coumachlor, coumafuryl, coumatetralyl and 4-
hydroxycoumarin. The solutes are obtained from Sigma-Aldrich as solids and
dissolved in high-purity acetonitrile (Burdick and Jackson, Baxter Healthcare) to
yield standard solutions at 10" M. Nitromethane is used as non-retained marker
and is added to each solution at a concentration at 15% (vlv). High purity
acetonitrile, methanol (Burdick and Jackson, Baxter Healthcare), acetic acid
(Sigma-Aldrich), and triethylamine (Sigma-Aldrich) are used for mobile phase
preparation.
5.2.2 Experimental System

The solutes are separated on a capillary liquid chromatography system as
illustrated in Figure 3.2. The silica packing (Cyclobond l 2000, Astec) is
characterized by a 5.2-pm particle size, 0.89-ng pore volume, and 305-mzlg
surface area, reacted with B-cyclodextrin at a bonding density of 0.39 pmollmz.
The temperatures for these experiments are 273, 278, 283, 288 and 293 K. The
inlet pressures for these experiments are 1200, 1800, 2400, 3000 and 3600 psi.
These values correspond to the average pressure of 700, 1300, 1900 and 3100
psi. The data are analyzed by exponentially modified Gaussian (EMG) function,
as described in Chapters 1.4.3.2.2. and 2.3.3.

180

5.3 RESULTS AND DISCUSSION

In Chapter 4, the mobile phase effect on chiral separation with B-
cyclodextrin stationary phase has been carefully investigated. A standard mobile
phase composition is chosen at 99:1:0.15:O.1 (acetontrilezmethanolzacetic
acidztriethylamine). In this chapter, all of the investigations are carried out in this
standard mobile phase composition.

5.3.1 Thermodynamic Behavior
5. 3. 1. 1 Retention Factor

Retention factors for all compounds are reported in Table 5.1. The
retention follows the same general order as in Chapter 4 for coumafuryl, warfarin,
coumachlor, coumatetralyl, and 4-hydroxycoumarin. Their retention orders are
greatly affected by their hydrogen-bonding abilities. Coumafuryl has the greatest
intra-molecular hydrogen bonding, thus the least inter-molecular hydrogen
bonding between solute and stationary phase. Warfarin and coumachlor have
similar retention factors, smaller intra-molecular hydrogen bonding, and slightly
larger inter-molecular hydrogen bonding. Coumatetralyl has even less intra-
hydrcgen bonding ability. Finally, 4-hydroxycoumaim has the largest inter-
molecular hydrogen bonding because of the free hydroxyl group, free carboxyl
group, and its relatively planar structure.

The effects of temperature and pressure on retention are demonstrated in
Table 5.1. Retention factors for all the solutes decrease dramatically with an

increase in temperature. With an increase in pressure, the retention factors

181

Table 5.1:

Retention factors for the coumarin-based solutes.

 

 

 

 

 

 

 

 

233 K‘ 303 K‘ 700 psib 3100 psib
Solute
k1c k2° R1 R2 k1 R2 R1 R2
Coumafuryl 0.85 1.00 0.59 0.68 0.72 0.84 0.66 0.76
Warfarin 1.07 1.42 0.76 0.96 0.92 1.19 0.85 1.09
Coumachlor 1.07 1.35 0.70 0.86 0.89 1.11 0.80 1.01
Coumatetralyl 3.20 3.39 2.11 2.18 2.60 2.73 2.44 2.55
4-Hydroxy-
4.89 NIA“ 4.15 N/A 4.59 NIA 4.29 NIA
coumarin

 

 

 

 

 

 

 

 

 

“ Retention factor (k) calculated at P = 1300 psi

0'

Retention factor calculated at T = 293 K

c R1 and k2 are retention factors for the first and second enantiomers

Q

Not available

182

 

decrease as well. The detailed reasons for these phenomena are discussed
below.
5. 3. 1.2 Molar Enthalpy

A representative graph of the logarithm of the retention factor versus the
inverse temperature (van’t Hoff plot) is shown in Figure 5.1. The graph for each
solute is linear (R2 = 0.993 - 0.999) with a positive slope. A linear graph
indicates that the change in molar enthalpy is constant, which suggests that there
is no significant change in retention mechanism and no phase transition over the
temperature range of 283 — 303 K. A positive slope is indicative of a negative
change in molar enthalpy, which suggests that the transfer from mobile to
stationary phase is an enthalpically favorable process. The change in molar
enthalpy is calculated from the slope of this graph according to Equation 1.6 and
is reported in Table 5.2. The standard deviation is coming from linear regression.

Although 4-hydroxycoumarin is the most retained solute among the
coumarin series, it has the least negative change in molar enthalpy. In other
words, the energy between the solutes and stationary phase is the smallest. If
the van’t Hoff plots were extrapolated to calculate the intercepts, 4-
hydroxycoumarin has the largest intercept. A large intercept usually implies that
the change in molar entropy for 4-hydroxycoumarin is larger or, alternatively. that
the phase ratio 4-hydroxycoumarin experienced by is smaller. 4-
Hydroxycoumarin has multiple positions for inter-molecular hydrogen bonding
with cyclodextrin. Every hydrogen bonding process will displace solvent

molecules from the cyclodextrin and introduce a change in molar entropy. Thus,

183

Figure 5.1 Representative graph of the retention factor versus inverse
temperature used to calculate the change in molar enthalpy. Mobile phase:
acetonititrilezmetl'ianolzacetic acidztn'ethylamine 99%:1%:0.15%:0.1% (v/v/vlv).
1300 psi, Solutes: coumafuryl ( <> ), warfarin (O ), coumachlor ( O ).
coumatetralyl ( I ). 4-hydroxycouman’n ( A ). Other experimental details are

given in the text.

184

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the more interaction sites, the more solvent molecules are displaced, and the
higher the change in molar entropy. In addition, the smaller size and the
relatively planar structure of 4-hydroxycoumarin facilitate its binding with
cyclodextrin with more possible configurations, which could potentially increase
the change in molar entropy as well. The phase ratio 4-hydroxycoumarin
experienced by might be different from that of the other chiral molecules.
depending on the adsorption sites. For example, if 4-hydroxycouman'n can
access unreacted silanol sites on the silica surface due to its small size, whereas
others cannot, then the phase ratio for 4-hydroxycoumarin is different.

When the changes in molar enthalpy are compared between the two
enantiomers, the second enatiomer always has a more negative change in molar
enthalpy than that of the first enantiomer. This difference indicated that the
second enantiomer is more enthalpically favorable in the transfer from mobile to
stationary phase.

When the changes in molar enthalpy are compared among all chiral
solutes in Table 5.2, no apparent trend can be found. In the reversed-phase
separation with octadecylsilica stationary phase, the change in molar enthalpy is
usually more negative as the retention factor increases. However, this trend is
not observed for cyclodextrin column with our series of compounds. This
behavior suggests that the change in molar entropy is an important parameter for
retention, and the trend of the change in molar entropy is not consistent with the
trend of retention. When we take a close look at warfarin and coumachlor, they

have similar structures and similar retention at ambient temperature, but their

186

Table 5.2

Changes in molar enthalpy and molar volume for coumarin-based

 

 

 

 

 

 

 

solutes
AH1a AHza AV1b AVzb
Solute
(kcallmol) (kcallmol) (cmalmol) (cmalmol)

Coumafuryl -3.21 :t 0.04 -3.33 i 0.03 13.8 :t 0.5 15 :t 1
Warfarin -2.91 i 0.07 -3.28 1: 0.07 14 :l: 1 13 i 1
Coumachlor -3.65 :l: 0.09 -3.8 :l: 0.1 16 :l: 2 15 :l: 2
Coumatetralyl -3.54 :t 0.02 -3.78 :t 0.02 11 :t 1 11 1: 1

4-
-1.5 :t 0.1 N/A° 18 :t 2 NIA
Hydroxycoumarin

 

 

 

 

 

" Molar enthalpy (AH) for the first and second enantiomer calculated at P =

1300 psi

b

° Not available

187

Molar volume (AV) for the first and second enantiomer calculated at T = 293 K

 

changes in molar enthalpy are surprisingly different from each other.
Coumachlor has a more negative molar enthalpy than warfarin. Although both
compounds have a similar response to mobile phase composition, their
differences in the change of molar enthalpy enable their separation with the
change of temperature. At lower temperature, warfarin will elute before
coumachlor, while at higher temperature. the elution order will be reversed.

5. 3. 1.3 Molar Volume

A representative graph of the logarithm of the retention factor versus
pressure is shown in Figure 5.2. The graph for each solute is linear (R2 = 0.98 -
0.99) with a negative slope. A negative slope is indicative of a positive change in
molar volume, which suggests that the solute occupies more volume in the
stationary phase than in the mobile phase. The change in molar volume is
calculated from the slope of mis graph according to Equation 1.9. and reported in
Table 5.2. The standard deviation is coming from linear regression.

In reversed-phase separations with cyclodextrin stationary phase, the
solute will be included into the cyclodextrin cavity, where a negative change in
molar volume is usually observed. In the polar-organic mode as described here,
the change in molar volume is positive. which is a clear sign that no inclusion
occurs. The change in molar volume is the smallest for coumatetralyl. larger and
statistically similar for warfarin, coumachlor and coumafuryl, and largest for 4-
hydroxycoumarin. Coumatetralyl has the most rigid structure, which might partly
explain its smallest change in molar volume in the coumarin series. When the

changes in molar volume are compared for the two enantiomers, they are

188

Figure 5.2 Representative graph of the retention factor versus pressure used
to calculate the change in molar volume. Mobile phase:
acetonititrilezmethanolzacetic acidztriethylamine 99%:1%:0.15%:0.1% (vlvlv/v),
293 K, Solutes: coumafuryl ( <> ), warfarin (O ), coumachlor( O ), coumatetralyl

( I ), 4-hydroxycoumarin ( A ). Other experimental details are given in the text.

189

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190

Figure 5.3. Representative graph of the chiral selectivity versus inverse
temperature used to calculate the chiral difference in molar enthalpy and molar
entropy. Mobile phase: acetonititrile:methanol:acetic acid:triethylamine
99%:1%:0.15%:0.1% (v/v/v/v), 1300 psi, Solutes: coumafuryl ( <> ). warfarin (O ),
coumachlor( O ), coumatetralyl ( I ). Other experimental details are given in the

text.

191

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192

statistically similar. This indicates that pressure will have a similar effect on both
enantiomers, and chiral selectivity will not be significantly affected by pressure.
5. 3. 1.4 Chiral Difference ln Molar Enthalpy and Molar Entropy

A representative graph of the logarithm of the chiral selectivity versus the
inverse temperature is shown in Figure 5.3. The graph for each chiral solute is
linear (R2 = 0.982 - 0.997) with a positive slope. Positive slope is indicative of a
negative differential change in molar enthalpy for the enantiomer.

The differential change in molar enthalpy and molar entropy are calculated
from Equation 1.7, and are reported in Table 5.3. The standard deviation is
coming from linear regression. Because the mobile phase is an achiral
environment, the two enantiomers will have the same molar enthalpy and molar
entropy in the mobile phase. Thus. the differential change in molar enthalpy is
solely concerned with the chiral interactions with the stationary phase. The
difference in molar enthalpy is negative. which indicates that the second
enantiomer is enthalpically more favorable in the stationary phase. The
difference is molar entropy is also negative. which indicates that the first
enantiomer is actually entropically more favorable in the stationary phase. This
is the first indication that the chiral separation of the coumarimbased solutes is
an enthalpy-controlled process.

5. 3. 1.5 Enthalpy-Entropy Compensation
A graph of the natural logarithm of retention factor versus the
change in molar enthalpy is shown in Figure 5.4. Each point represents one of

the coumarin-based solute. The scattering of these points clearly shows that no

193

Table 5.3 Differential changes in molar enthalpy and molar entropy for the

chiral coumarin-based solutes

 

 

 

 

 

 

Solute AAHa (kcallmol) AAS‘I (callmol K)
Coumafuryl - 0.122 :I: 0.005 - 0.12 :t 0.02

Warfarin - 0.369 :l: 0.002 - 0.751 a: 0.005
Coumachlor - 0.17 :t 0.02 - 0.14 :t 0.05
Coumatetralyl - 0.23 :l: 0.02 - 0.71 :t 0.08

 

 

 

a Chiral differences in molar enthalpy (AAH) and molar entropy (AAS)

calculated at P = 1300 psi

194

 

Figure 5.4 Representative graph of the retention factor versus change in molar
enthalpy used to observe enthalpy-entropy compensation. Mobile phase:

acetonititrile:methanolzacetic acid:triethylamine 99%:1%:0.15%:0.1% (v/v/v/v),

1300 psi

195

 

 

 

 

10

196

0.1

-10

-15

-20

AH

enthalpy-entropy compensation is achieved. Different retention mechanisms are,
thus, responsible for the retention of the individual solutes.

The co-elution temperatures, Tho, are also calculated from Equation 1.10
and reported in Table 5.4. The values are higher than ambient temperature.
which suggests that the separation of all chiral solutes is an enthalpy-driven
reaction. A different Tm for all solutes is another sign that enthalpy-entropy
compensation does not occur. But the T.» values are similar for coumafuryl and
coumachlor, and for warfarin and coumatetralyl. This suggests that the retention
mechanism is similar for these pair of solutes. The Tao values for coumafuryl and
coumachlor are significantly greater than those for warfarin and coumatetralyl.
For coumafuryl and coumachlor, AAH mainly controls their chiral separation. But
for warfarin and coumatetralyl, AAS plays a more important role for their chiral
separation.

5.3.2. Kinetic Behavior

While thermodynamics can elucidate the steady-state information and is
concerned with the change between the initial (mobile phase) and final
(stationary phase) states, it does not fully explain the retention mechanism. By
considering a transition state, the pseudo-first-order rate constants, activation
energies, and activation volumes can be calculated with the equations developed
above. These values help to quantify the kinetic aspects of mass transfer
between the mobile and stationary phases as a function of solute structure.
These data provide information about the retention mechanism that would not be

available from thermodynamic data alone.

197

Table 5.4 Co—elution temperature (T ..o) for the chiral coumarin-based solutes

 

 

 

 

 

 

Chiral Solute The (K)
Coumafuryl 1000 :t 170
Warfarin 491 :I: 4
Coumachlor 1200 i 460
Coumatetralyl 320 :l: 46

 

 

198

 

5.3.2.1 Rate Constants

Representative kinetic rate constants, including the desorption rate
constant km and the adsorption rate constant km, are summarized in Table 5.5.
As noted previously. 4-hydroxycoumarin has notably smaller kinetic rate
constants than the other chiral molecules due to its small size and multiple
positions for strong hydrogen bonding. When the chiral solutes are compared.
the kinetic rate constants decrease as the retention factors increase. But for
each chiral pair, the second eluted enantiomer always has a surprisingly higher
mass transfer rate constant than the first enantiomer. This variation might be
attributed to the different contribution from chiral selective sites and achiral
selective sites. The kinetic rate constants generally show an increasing trend
with an increase in temperature.
5.3.2.2 Activation Energy

A representative graph of the logarithm of the desorption rate constants
versus the inverse temperature is illustrated in Figure 5.5. The standard
deviation is coming from linear regression. The rate constant for 4-
hydroxycoumarin is relatively constant with temperature, so it is not included in
the graph. The graph for each chiral solute is linear, (R2 = 0.942 - 0.999) with a
negative slope, which indicates a positive change in activation energy. The
activation energy is calculated from the slope of this graph according to Equation
1.15, and is shown in Table 5.6. The activation energy for the transfer from

stationary phase to transition state (AEq) is larger than that from mobile phase to

the transition state (AEm). These data indicate that it is easier for the solutes to

199

Table 5.5. Kinetic rate constants for the coumarin-based solutes

 

 

 

 

 

 

 

 

283 K“ 303 K'
Solute 11....“ kn...“ km: km; km km k..." km
(8") (8") (6") (8“) (8") (8“) (3") (8")
Coumafuryl 13 12 11 12 33 b 39" 23” 32"
Warfarin a 8 3 11 18 26 13 25
Coumachlor 7 7 8 10 15° 30 12” 26
Coumatetralyl 2 4 7 13 3 14 9° 31
4-Hydroxy-
_ 0.05 NIA' 0.23 NIA 0.03 NIA 0.14 NIA
coumann

 

 

 

 

 

 

 

 

 

Kinetic rate constants calculated at P = 1300 psi

Kinetic rate constants calculated at T = 293 K

° Kinetic rate constants calculated at T = 298 K

km and km are desorption mass transfer rate constants from stationary to
mobile phase for the first and second enantiomers

k..." and km are adsorption mass transfer rate constants from mobile to
stationary phase for the first and second enantiomers

Not available

200

 

Figure 5.5 Representative graph of the kinetic rate constant km" versus
inverse temperature used to calculate the change in activation energy. Mobile
phase: acetonititrile:methanol:acetic acid:triethylamine 99%:1%:0.15%:0.1%
(v/vlv/v), 1300 psi, Solutes: coumafuryl ( O ), warfarin (O ), coumachlor ( O ).

coumatetralyl ( I ). Other experimental details are given in the text.

201

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ooooo mmooo 38o moooo «mooo

 

202

SW”

10..

 

 

 

00..

 

Table 5.6 Activation energy for the coumarin-based solutes

 

 

 

 

 

 

 

item.“ Aem" AEmb AEm"
Solute
(kcallmol) (kcallmol) (kcallmol) (kcallmol)
Coumafuryl NIA 16.3 :1: 0.4 NIA 19.6 :1: 0.4
Warfarin 3.6 :l: 0.8 7 i 1 6.5 :1: 0.8 10 :I: 1
Coumachlor 4.5 i 0.8 8 j: 1 8.0 i: 0.9 11 t 1
Coumatetralyl 5 i 2 8 i 2 9 i 2 12 t 2
4-Hydroxy-
N/A° N/A N/A N/A
coumarin

 

 

 

 

 

a AEW and AEmg are the activation energy from mobile to transition state for

the first and second enantiomers calculated at P = 1300 psi

the first and second enantiomers calculated at P = 1300 psi

Not available

203

AEw and AB,” are the activation energy from stationary to transition state for

 

enter the stationary phase than to exit. A comparison between the two
enantiomers demonstrates that the second enantiomer always has higher
activation energy than the first enantiomer. Thus, the energy diagram can be
constructed as follows: both enantiomers start in the mobile phase at the same
energy state. then the second enantiomer needs to overcome an even higher
activation energy (AEm) than the first enantiomer, but finally reaches a lower
energy state in the stationary phase than the first enantiomer.

5.4 CONCLUSIONS

In this study, the thermodynamic and kinetic behavior is examined with the
8-cyclodextrin stationary phase in polar-organic mode. Increasing temperature
from 283 to 303 K decreases the retention for all solutes dramatically. The
change in molar enthalpy can be calculated through the slope of the van't Hoff
plot. 4-Hydroxycoumarin has the largest retention, but the least negative change
of molar enthalpy. For the chiral solutes, the trend of their change in molar
enthalpy doesn’t always match the trend of their retention. Apparently. the
change in molar entropy takes an important role in the separation. The second
enantiomer has a more negative change in molar enthalpy than the first
enantiomer, indicating an enthalpically more favorable process for the second
enantiomer. But the second enantiomer does not experience an entropically
favorable process in the transfer. which can be seen from the negative chiral
difference in molar entropy (AAS). All the separations are enthalpically controlled.
But there is no enthalpy-entropy compensation observed with five model solutes.

Increasing pressure decreases the retention for all solutes. The positive change

204

in molar volume indicates no inclusion happened in this mobile phase. As for
kinetics, increasing temperature increases kinetic rate constants. Activafion
energies are positive for chiral solutes, with the second enantiomer having higher

activation energy than the first enantiomer.

205

5.5 References

[1] W.L. Hinze, T.E. Riehl, D.W. Armstrong, W. DeMond, A. Alak, T. Ward,
Anal. Chem. 57 (1985) 237-242.

[2] H.Y. AbouI-Enein, M.R. Islam, S.A. Bakr, 1 1 (1988) 1485-1493.

[3] K. Cabrera, D. Lubda, J. Chromatogr. A 666 (1994) 433-438.

[4] N. Morin, Y.C. Guillaume, E. Peyrin, J.C. Rouland, Anal. Chem. 70 (1998)
2819-2826.

[5] MC. Ringo, C.E. Evans, Anal. Chem. 69 (1997) 643-649.

[6] MC. Ringo, C.E. Evans, J. Phys. Chem. B 101 (1997) 5525-5530.

[7] MC. Ringo, C.E. Evans, Anal. Chem. 69 (1997) 4964-4971.

[8] MC. Ringo, C.E. Evans, J. Microcolumn Sep. 10 (1998) 647-652.

206

CHAPTER 6

THERMODYNAMIC AND KINETIC CHARACTERIZATION OF
NITROGEN-CONTAINING POLYCYCLIC AROMATIC
HYDROCARBONS IN REVERSED-PHASE LIQUID
CHROMATOGRAPHY

6.1. INTRODUCTION

Polycyclic aromatic hydrocarbons (PAHs) are a class of compounds that
present a recognized health hazard. As a result, many studies have been
conducted to investigate the biological and chemical properties of these
substances [1-3]. When formed at elevated temperatures, PAHs may contain
substituent moieties that alter their toxicity. Two substitutions that lead to highly
toxic analogues involve the exchange of a carbon atom with nitrogen to form an
azaarene, and the replacement of a hydrogen atom with an amino or nitro group.
These solutes are collectively known as nitrogen-containing polycyclic aromatic
hydrocarbons (N-PAHs). N-PAHs are commonly found in fossil fuels and their
derivatives. although some may also form during combustion processes.

Relative to their parent PAHs, N-PAHs are more soluble in aqueous
environments. Increased water solubility results in an increased potential for
harm. For example, 1-aminopyrene demonstrates a fifty-fold increase in
mutagenic activity when compared to that of the parent PAH, pyrene [4].
Similarly, azaarenes demonstrate increased carcinogenicity when compared to
their parent PAHs [5-7].

Studies have been carried out to determine the presence of N-PAHs in

fossil fuels [8-12], coal substitutes [13], lake sediment [14]. urban aerosols [15],

207

as well as in the degradation products of polymers [16]. In order to identify and
differentiate N-PAHs, many investigators have used chromatographic techniques
because of their high resolving power. These techniques have included gas
[12.17.18], thin layer [19], supercritical fluid [20], and liquid chromatography [8-
11.16.17.21-26]. In nearly all instances. the chromatographic applications have
focused upon the optimization of the separation or upon qualitative and
quantitative analysis, rather than a detailed examination of the molecular
contributions to retention. The most noteworthy study by Colin et al. [21]
examined the retention of 26 mono-substituted and 5 di-substituted aza-PAHs in
reversed-phase liquid chromatography as a function of the mobile and stationary
phase compositions. They reported that the aza-PAHs are separated on the
basis of carbon number with aqueous methanol mobile phases and
octadecylsilica stationary phases. whereas the position of the nitrogen atom(s)
has a greater effect with aqueous tetrahydrofuran or acetonitrile mobile phases
and octylsilica stationary phases. They observed dramatic tailing, which was
attributed to interactions with unreacted silanol groups and/or the slow
equilibrium between the neutral and protonated forms of the aza—PAHs.
Although these observations suggest unusual thermodynamic and kinetic
behavior, to the best of our knowledge, no results of quantitative explorations of
this behavior have been published.

To overcome this dearth of information, the thermodynamics and kinetics
of retention for a series of N-PAHs are presented herein. Using theory and

methodology developed in Chapter 1, the retention factors and rate constants for

208

the N-PAHs are determined as a function of temperature and pressure. The
effect of mobile phase is examined by using methanol as a model of protic
solvents and acetonitrile as a model of aprotic solvents. From the retention
factors, the changes in molar enthalpy and molar volume are quantitated. From
the rate constants, the activation energy and activation volume are quantitated.
This analysis provides insight into the retention mechanism of N-PAHs in

reversed-phase liquid chromatography.
6.2. EXPERIMENTAL METHODS

6.2.1 Chemicals

As depicted in Figure 6.1. five N-PAHs are chosen to study the effect of
nitrogen position, ring number. and annelation structure on the thermodynamics
and kinetics of retention. 1-Aminopyrene (Sigma-Aldrich), 1-azapyrene. 4—
azapyrene, benz[a]acridine, and dibenz[a,jjacridine (lnstitilt f0r PAH Forschung)
are obtained as solids and dissolved in high-purity methanol and acetonitrile
(Burdick and Jackson, Baxter Healthcare) to yield standard solutions at a
concentration of 10“ M. A nonretained marker, 4-hydroxymethyl-7-
methoxycoumarin, is added to each solution at a concentration of 10" M.
6.2.2 Experimental System

The solutes are separated on a capillary liquid chromatography system
that has been described in Figure 3.2. The mobile phases are methanol and
acetonitrile. and the stationary phase is polymeric octadecylsilica. The silica
packing is characterized by a 5.5-pm particle size, 190-A pore size, and 240-m2lg

surface area (IMPAQ 200, PO Corp.), and reacted with trifunctional

209

Figure 6.1 Structures of PAHs and N-PAHs for liquid chromatographic study.

210

 

1-azapyrene 4-azapyrene

1-aminopyrene

benz(a)acridine dibenz(a¢)acridine

211

octadecylsilane to produce a polymeric phase with bonding density of 5.4
pmol/mz. Although this stationary phase is not commercially available, it may be
considered representative of high-density, polymeric octadecylsilica phases. The
column has a plate height (H) of 15 pm, reduced plate height (h) of 2.73. total
porosity (81') of 0.84, and flow resistance parameter (4») of 500. The column is
operated at a nominal flow rate of 1.05 lemin, linear velocity (v) of 0.055 cmls,

and reduced velocity (v) of 2.75. The temperatures for these experiments are
283, 288, 293, 298 and 303 K for methanol, and 298, 303. 308. 313, and 323 K
for acetonitrile. The inlet pressures for the methanol experiments are 1000,
1750. 2500, 3250 and 4000 psi. These values correspond to average pressures
of 585, 1335, 2085, 2835, and 3585 psi, respectively, which were calculated
assuming a linear pressure drop along the column. The inlet pressure for the
acetonitrile experiments was 2500 psi, which corresponds to an average
pressure of 2175 psi, which was calculated assuming a linear pressure drop
along the column. The data were analyzed using the exponentially modified
Gaussian (EMG) and the Thomas (NLC) equations, which are described in

Section 2.3.3 and 2.3.4

6.3. RESULTS AND DISCUSSION

Based on previous experience with the parent PAHs [27.28], the EMG
function was chosen for regression of the N-PAH zone profiles in initial studies.
The zone profiles in methanol mobile phase, shown in Figure 6.2A, are similar to
those observed in previous studies. The overall quality of fit is high. exhibiting

random residuals and large values for the square of the correlation coefficient (R2

212

Figure 6.2 Representative chromatograms of 4-azapyrene in reversed-phase
liquid chromatography. Column: polymeric octadecylsilica. Mobile phase: (A)
methanol, 303 K, 2085 psi. 0.08 cmls; (B) acetonitrile, 303 K, 2185 psi, 0.08
cmls. Column: polymeric octadecylsilica. Other experimental details are given in

the text.

213

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214

> 0.98) and F-statistic (F > 1000). However, the zone profiles in acetonitrile
mobile phase. shown in Figure 6.28. are quite different and demonstrate a much
higher degree of asymmetry. This asymmetry may arise from a change in
retention mechanism from partition to either adsorption or mixed-mode partifion
and adsorption. As a result, the zone profiles in acetonitrile were analyzed by
using the Thomas model, which was thought to be more appropriate for the
adsorption mechanism. However, the Thomas model failed to produce any
improvement in the quality of fit (R2 > 0.95, F > 1000). Moreover, the zone
profiles did not change as a function of concentration. which suggests that the
isotherm is linear rather than nonlinear. Consequently. the EMG model was
used throughout this study to provide consistency in the thermodynamic and
kinetic results.
6.3.1 Methanol Mobile Phase
6. 3. 1. 1 Thermodynamic Behavior
6.3.1.1.1 Retention Factor

Representative values of the retention factor for the N-PAHs in methanol
mobile phase are summarized in Table 6.1. The retention factors for the N-PAHs
are notably smaller than those for the parent PAHs on the same stationary phase
[27,28]. 1-Aminopyrene, 1-azapyrene, and 4-azapyrene have retention factors
that are smaller by 73%, 38%, and 43%, respectively, than pyrene (k = 0.84 at
303 K). Similarly, the retention factor for benz[a]acridine is 60% smaller than that
for benz[a]anthracene (k = 1.46 at 303 K). This decreased retention is due to the

increased polarity of the N-PAHs relative to that of the PAHs. Because the

215

Table 6.1 Retention factors for N-PAHs in methanol mobile phase.

 

 

 

 

 

 

 

 

k a k "
Solute
288 K 303 K 585 psi 3585 psi

1-Aminopyrene 0.35 0.23 0.35 0.35
1-Azapyrene 0.94 0.52 0.95 0.94
4-Azapyrene 0.78 0.48 0.79 0.78
Benzlalacridine 1 .03 0.58 0.97 1 .03
Dibenz[a, ]acridine 3.26 1.52 2.96 3.26

 

 

 

 

 

" Retention factor (k) calculated at P = 3585 psi

b Retention factor calculated at T = 288 K

216

 

partition mechanism is governed by differences in relative solubility in the polar
mobile phase and nonpolar stationary phase [29], the more polar N-PAHs are
less retained. It is noteworthy that the trends in retention factor for the N-PAHs
are the same as those identified previously for the PAHs. Retention increases
with the number of aromatic rings [27] and decreases with more condensed
annelation structure [28] or length-to-breadth ratio [30]. These trends are
consistent with the partition mechanism.

As shown in Table 6.1, the retention factor for all solutes decreases
significantly (34 — 53%) with increasing temperature. The retention factor
increases slightly (6 - 10%) with increasing pressure for benz[a]acridine and
dibenz[a4]acridine, but remains statistically invariant for the amino- and aza-
pyrenes. The reasons for this behavior are discussed below in further detail.

6. 3. 1. 1. 2 Molar Enthalpy

A representative graph of the logarithm of the retention factor versus the
inverse temperature (van’t Hoff plot) is shown in Figure 6.3. The data for the
methanol mobile phase are represented using solid lines. The graph for each
solute is linear (R2 = 0.986 - 0.999) and the slope is positive. A linear graph
indicates that the change in molar enthalpy is constant, which suggests that there
is no significant change in retention mechanism over the temperature range of
283 — 303 K. A positive slope is indicative of a negative change in molar
enthalpy, which suggests that the transfer from mobile to stationary phase is
enthalpically favorable. The change in molar enthalpy is calculated from the

slope of Figure 6.3, according to Equation 1.6.

217

Figure 6.3 Representative graph of the retention factor versus inverse
temperature used to calculate the change in molar enthalpy. Mobile phase:
methanol, 2085 psi, 0.08 cmls (—); acetonitrile, 2185 psi, 0.08 cmls (- - -).
Solutes: 1-aminopyrene ( O ), 1-azapyrene (O ), 4—azapyrene ( O ),
benz[a]acridine ( I ), dibenz[a,j]acridine ( A ). Other experimental details are

given in the text.

218

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219

As shown in Table 6.2, the changes in molar enthalpy are the least
negative for 1-aminopyrene, are comparable for 1-azapyrene and 4-azapyrene,
and become progressively more negative for benz[a]acridine and
dibenz[a,j]acridine. These changes in molar enthalpy follow the same trends as
observed for the parent PAHs [27,28]. These trends indicate that the change in
molar enthalpy becomes more negative with increasing ring number and with
less condensed annelation structure. The reasons for these trends have been
discussed previously [28] and may be attributed to the depth to which each PAH
can penetrate into the stationary phase. The proximal regions, where the alkyl
group is bound to the silica surface, are highly ordered with all trans carbon-
carbon bonds. As the distance from the surface increases there are more
gauche bonds and greater disorder [31,32]. The more condensed PAHs, such
as pyrene, probe only the distal regions, whereas less condensed PAHs, such as
benz[a]anthracene, can penetrate more deeply into the ordered regions of the
stationary phase. Consequently, the change in molar enthalpy becomes more
negative the farther the PAH penetrates into the stationary phase.

When compared to the molar enthalpy of the parent PAH, pyrene (AH =
4.4 kcallmol [28]), the change in molar enthalpy is 0.6 kcallmol more negative for
1-aminopyrene and 1.2 — 1.3 kcallmol more negative for the azapyrenes on the
same stationary phase. Interactions with the octadecyl groups are relatively
similar for these solutes. Hence, the differences may arise from interactions with
silanol groups, either on the silica surface or on incompletely reacted and

hydrolyzed molecules of the trifunctional octadecylsilane [21,33]. The PAHs

220

Table 6.2 Changes in molar enthalpy and molar volume for N-PAHs in

methanol mobile phase.

 

 

 

 

 

 

 

Solute AH (kcallmol) ‘ AV (mUmol) "
1-Aminopyrene ° —5.0 :l: 0.2 -2 :I: 2
1-Azapyrene —5.7 :l: 0.3 I —0.1 :l: 4
4-Azapyrene -5.6 i 0.2 -2 :l: 5
Benz[a]acridine —6.6 :I: 0.1 --7 i 1
Dibenz[a,/]acridine —8.9 :I: 0.1 —11 :t 1

 

 

 

° Molar enthalpy (AH) calculated at P = 2085 psi
b Molar volume (AV) calculated at T = 288 K, except as otherwise noted

° Molar volume calculated at T = 283 K

221

 

interact very weakly with the silanol sites by hydrogen bonding through the
aromatic (1:) system. The nitrogen atom imparts a more basic character to the N-
PAHs, relative to that of the parent PAHs, and this feature allows for stronger
interaction with the acidic silanol sites [34,35]. This interaction is stronger than a
simple hydrogen bond, but not as strong as proton transfer [35]. The amine
group is less basic than the aza group, as evidenced by the acid-base
equilibrium constants of aniline (Mo = 4.63) and pyridine (pKe = 5.25) [36]. Thus,
the change in molar enthalpy for 1-aminopyrene is expected to be less than that
for the azapyrenes, as observed in Table 6.2. The molar enthalpy for 4—
azapyrene is less than that for 1-azapyrene because diffusion through the
octadecyl groups to the silanol sites is more facile along the short axis than along
the long axis of the molecule. It is also evident that the change in molar enthalpy
for benz[a]acridine is 0.5 kcallmol less negative than that for the parent PAH,
benz[a]anthracene (AH = 7.1 kcallmol [28]). Given the position of the nitrogen
atom, diffusion must occur along the long axis of the molecule in order to bind
with the silanol groups. This is much less favorable for the linear structure of
benz[a]acridine than for the condensed structure of the azapyrenes. Similar
steric effects are expected for dibenz[a,j]acridine, whose molar enthalpy is 6.9
kcallmol less negative than the structurally similar five-ring PAH, picene [28].
Although there have been no published studies on the thermodynamics of
retention for N-PAHs in reversed-phase liquid chromatography, supporting
evidence is provided from other separation techniques. Woodrow and Dorsey

examined the partitioning of acridine in micellar electrokinetic chromatography

222

[37]. They report an enthalpy of transition between the alkyl group of the
surfactant and water as -6.75 kcallmol for acridine. Matzner and Bales
examined the retention of acridine on silica in aqueous media [38,39]. They
report an enthalpy of transition between silica and water as —8.05 kcallmol.
These results support our suggestion that the more negative values of enthalpy
for the four-ring N-PAHs relative to that of their parent PAHs are due to
interactions with the silica surface.

Finally, it is important to note that the retention factors for the N-PAHs are
smaller than those of the parent PAHs, even though the changes in molar
enthalpy are more negative. There are two potential reasons for this
phenomenon. First, there may be a significant entropic effect that offsets the
enthalpic contributions to retention. For example, Matzner and Bales report
values for the entropy term (TAS) as -5.09 kcallmol compared with the enthalpy
term of —8.05 kcallmol for adsorption of acridine on silica [38,39]. Second, the
phase ratio for the silanol sites may be very small relative to that of the octadecyl
groups because of the high bonding density (5.4 umol/mz). According to
Equation 1.6, either a significant change in the entropy term or the phase ratio
would allow the retention factors for the N-PAHs to remain smaller than those of
the parent PAHs, despite the greater changes in molar enthalpy. As both of
these contributions are contained in the intercept of the van’t Hoff plot, they are

difficult to distinguish by chromatographic methods alone.

223

6. 3. 1. 1.3 Molar Volume

A representative graph of the logarithm of the retention factor versus
pressure is shown in Figure 6.4. Although the graph for each N-PAH is linear,
the square of the correlation coefficient is highly variable (R2 = 0.594 - 0.998)
because of the small influence of pressure on retention. It should be noted that
the smallest correlation coefficients are exhibited by the azapyrenes, which are
affected the least by changes in pressure. The slope of the graph is positive for
all solutes, which is indicative of a negative change in molar volume. This
suggests that the solute occupies less volume in the stationary phase than in the
mobile phase. The change in molar volume is calculated from the slope of this
graph, according to Equation 1.9.

As shown in Table 6.2, 1-aminopyrene, 1-azapyrene, and 4-azapyrene
have values that are statistically indistinguishable and close to zero. In contrast,
benz[a]acridine and dibenz[a,j]acridine exhibit changes in molar volume that are
statistically nonzero, with the four-ring N-PAH demonstrating a less negative
change in molar volume than the five-ring analogue. The values for the
azapyrenes and benz[a]acridine are similar to those for the parent PAHs, pyrene
(2.3 mUmol) and benz[a]anthracene (8.4 mUmol) [28]. As noted previously,
these changes in molar volume may be attributed to the depth that each PAH
can penetrate into the stationary phase [27,28]. The more condensed PAHs,
such as pyrene, probe only the distal regions, whereas less condensed PAHs,

such as benz[a]anthracene, can penetrate more deeply into the ordered region

224

Figure 6.4 Representative graph of the retention factor versus pressure used
to calculate the change in molar volume. Mobile phase: methanol, 283 K, 0.08
cmls. Symbols defined in Figure 6.3. Other experimental details are given in the

text.

225

 

 

 

 

 

 

 

 

 

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3000

2000

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4000

1000

of the stationary phase. Consequently, the change in molar volume becomes
more negative the farther the PAH penetrates into the stationary phase.
6. 3. 1.2 Kinetic Behavior

Although the thermodynamic data demonstrate the steady-state aspects
of chromatographic behavior, they do not fully explain the retention mechanism.
Using the equations and methods developed in Section 1.4.2, the pseudo-first-
order rate constants, activation energies, and activation volumes were
calculated. These values help to quantify the kinetic aspects of mass transfer
between the mobile and stationary phases as a function of solute structure.
These data provide information about the retention mechanism that would not be
available from thermodynamic data alone.
6.3. 1. 2.1 Rate Constants

Representative values of the rate constants, calculated using Equation
1.38, are summarized in Table 6.3. 1-Aminopyrene undergoes the highest rate
of transfer, followed by 4-azapyrene, benz[a]acridine, and dibenz[a,1]acridine. 1-
Azapyrene has the lowest rate of transfer, with rate constants that are one order-
of-magnitude less than 4-azapyrene and two orders-of-magnitude less than 1-
aminopyrene. The rate-limiting step for 1-aminopyrene, 1-azapyrene, 4-
azapyrene, and benz[a]acridine is the transfer from mobile to stationary phase,
because the retention factor (k = kart/km.) is less than unity. In contrast, the rate-
limiting step for dibenz[a4]acridine is the transfer from the stationary to the mobile

phase, since the retention factor is greater than unity.

227

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The rate constants for the four-ring N-PAHs are notably smaller than those
for their parent PAHs on the same stationary phase [28]. 1-Aminopyrene, 1-
azapyrene, and 4-azapyrene have rate constants that are smaller by 71%,
99.8%, and 97%, respectively, than pyrene (k.... = 2300 s'1 at 303 K). Similarly,
the rate constant for benz[a]acridine is 91% smaller than that for
benz[a]anthracene (km. = 850 s‘1 at 303 K). In contrast, the rate constant for the
five-ring N-PAH, dibenz[a,j]acridine, is more comparable to that for the five-ring
PAH, picene [27]. These results suggest that 1-azapyrene is most greatly
affected, 4-azapyrene and benz[a]acridine are moderately affected, and
dibenz[a,j]acridine is relatively unaffected by the slow kinetics of adsorption at
silanol sites.

As shown in Table 6.3, the rate constants for all solutes increase
significantly (240 - 720% for k...) with increasing temperature. This behavior is a
consequence of the increased diffusion coefficients and the enhanced fluidity of
the stationary phase. As more kinetic energy is imparted, the alkyl chains
become more labile and can more readily undergo rotation of the carbon-carbon
bonds from the trans to gauche conformation. In fact, an order—disorder phase
transition has been reported previously for this stationary phase at approximately
318 K. The rate constants decrease significantly (58% for It...) with increasing
pressure for 1-aminopyrene, but decrease only slightly or remain invariant for the
other solutes. This behavior is a consequence of the compression of the alkyl

chains, which impedes diffusion into and out of the stationary phase.

229

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230

6. 3. 1.2.2 Activation Energy

A representative graph of the logarithm of the rate constant versus the
inverse temperature is shown in Figure 6.5. The data for the methanol mobile
phase are represented using solid lines. The graph for each solute is linear (R2 =
0.968 — 0.995) and the slope is negative. A negative slope is indicative of a
positive energy barrier. The activation energy is calculated from the slope of this
graph, according to Equations 1.15. As shown in Table 6.4, the activation
energies are positive for all solutes. The activation energy for the transfer from
stationary phase to transition state (AEu) is greater than that from mobile phase
to transition state (AEm). These data indicate that it is easier for the solutes to
enter the stationary phase than to exit. The energy barriers A533, and AEm seem
to be similar for all solutes and, indeed, there is no statistically significant
difference. These values are comparable to those reported previously for the
parent PAHs [28].
6.3. 1.2.3 Activation Volume

A representative graph of the natural logarithm of the rate constant versus
pressure is shown in Figure 6.6. The activation volume is calculated from the
slope of this graph, according to Equations 1.17. As shown in Table 6.4, 1-
aminopyrene has the largest activation volume while those of the other solutes
are somewhat smaller. The values for the azapyrenes appear to be similar to
those for the parent PAH, pyrene (Av... = 47 :l: 7 mL/mol, AV” = 43 :l: 7 mUmol)
[28]. However, the activation volumes for many of the N-PAHs are statistically

indistinguishable from zero, given the small effect of pressure and the

231

Figure 6.5 Representative graph of the rate constant (k...) versus inverse

temperature used to calculate the activation energy. Mobile phase: methanol,
2085 psi, 0.08 cmls (-—); acetonitrile, 2185 psi, 0.08 cmls (— — -). Symbols

defined in Figure 6.3. Other experimental details are given in the text.

232

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233

Figure 6.6 Representative graph of the rate constant (k...) versus pressure
used to calculate the activation volume. Mobile phase: methanol, 283 K, 0.08

cmls. Symbols defined in Figure 6.3. Other experimental details are given in the

text.

234

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235

correspondingly large standard deviation. Hence, no definitive conclusions can
be drawn about the volumetric barrier for these solutes.
6.3.2 Acetonitrile Mobile Phase

In the previous study, the N-PAHs showed evidence of a partition
mechanism on the octadecylsilica stationary phase, similar to that of the parent
PAHs, with some additional contributions that are attributable to adsorption. The
methanol mobile phase used for this study is able to form hydrogen bonds with
the N-PAHs and thereby inhibit their ability to adsorb at silanol sites. At the same
time, methanol can form hydrogen bonds with the silanol sites to displace or
compete with the N-PAHs. By these two mechanisms, the protic mobile phase
can reduce interactions of the N-PAHs with silanol sites. Therefore, it is
beneficial to examine the effect of an aprotic solvent such as acetonitrile, which
cannot undergo such hydrogen-bonding interactions, on the combined partition-
adsorption mechanism.

The effect of temperature on the thermodynamic and kinetic behavior of
the N-PAHs in the methanol mobile phase is significant (Tables 6.1 and 6.3), so
that a large temperature range is also warranted in acetonitrile. A higher range
of temperatures (293 to 333 K) is selected because of the greater retention and
asymmetry of the zone profiles in acetonitrile (Figure 6.2). In contrast, the effect
of pressure on the thermodynamic and kinetic behavior is very small in the
methanol mobile phase (Tables 6.1 and 6.3). Hence, the study in acetonitrile is

conducted at a single average pressure of 2185 psi.

236

6. 3. 2. 1 Thermodynamic Behavior
6. 3. 2. 1.1 Retention Factor

Representative values of the retention factor for the N-PAHs in acetonitrile
mobile phase are summarized in Table 6.5. As shown, 1-aminopyrene is eluted
first, followed by 4-azapyrene, benz[a]acridine, and dibenz[e,j]acridine. 1-
Azapyrene is the most strongly retained solute and it exhibited such severe
asymmetry that it was excluded from the quantitative thermodynamic and kinetic
studies.

When compared to the results with the methanol mobile phase (Table
6.1), all solutes demonstrate an increase in retention factor in acetonitrile. Given
that acetonitrile is less polar than methanol, the retention factor would be
expected to decrease if the partition mechanism were predominant. Thus, the
observed increase in retention factor suggests that the adsorption mechanism is
contributing more greatly to retention in acetonitrile than in methanol. The
increase is slight (4%) for 1-aminopyrene but very substantial (320 - 850%) for
the aza-PAHs, which is consistent with the relative basicity of amine and aza
groups, as discussed previously. In fact, the retention factors for the four-ring
aza-PAHs are markedly larger than those for the parent PAHs [27,28], which
suggests that the adsorption mechanism is predominant for these solutes in
acetonitrile.
6. 3. 2. 1. 2 Molar Enthalpy

A representative graph of the logarithm of the retention factor versus the

inverse temperature is shown in Figure 6.3. The data for the acetonitrile mobile

237

 

phase are represented using dashed lines. It is evident that the retention data for
1-aminopyrene are nearly collinear in the acetonitrile and methanol mobile
phases. This suggests that there is no significant difference in the retenh’on
mechanism for this solute. In contrast, the retention factors for the aza-PAHs are
approximately an order-of-magnitude greater in acetonitrile than in methanol.
Although the graph for each N-PAH is linear, the square of the correlation
coefficient is highly variable (R2 = 0.724 - 0.986) because of the high degree of
asymmetry and resulting uncertainty in the retention factor. It should be noted
that the smallest correlation coefficients are exhibited by the aza-PAHs, which
have the greatest asymmetry. The slope of the graph is positive, which is
indicative of a negative change in molar enthalpy and suggests that the transfer
from mobile to stationary phase is enthalpically favorable. The change in molar
enthalpy is calculated from the slope of graph in Figure 6.3, according to
Equation 1.6.

As shown in Table 6.5, the changes in molar enthalpy are the least
negative for 1-aminopyrene and dibenz[a,j]acridine, and become progressively
more negative for benz[a]acridine and 4-azapyrene. This order does not show
the trends expected for the partition mechanism, i.e., more negative changes in
molar enthalpy with increasing ring number and less condensed annelation
structure. Rather, this order is consistent with the hydrogen bonding strength
and steric effects at silanol groups, as discussed previously for the methanol
mobile phase. The changes in molar enthalpy for the four-ring N-PAHs are

slightly more negative in acetonitrile than in methanol. 1-Aminopyrene, 4-

238

Table 6.5 Thermodynamic data for N-PAHs in acetonitrile mobile phase.

 

 

 

 

 

 

 

ka AH'
Solute
303 K 313 K (kcallmol)
1-Aminopyrene 0.24 0.16 6.3 :l: 0.7
4-Azapyrene 4.55 2.74 10 :l: 1
Benz[a]acridine 4.48 4.15 8 :l: 2
Dibenz[a.j]acridine 6.43 5.49 6 :l: 2

 

 

 

 

a Retention factor (k) and change in molar enthalpy (AH) calculated at P = 2185

psi

239

 

azapyrene, and benz[a]acridine exhibit values that are 1.3, 3.7, and 1.7 kcallmol
more negative in acetonitrile than in methanol (Table 6.2). This change in molar
enthalpy is consistent with the greater role of adsorption in the aprotic solvent,
particularly for azapyrene. In contrast, the value for dibenz[a,1]acridine is 2.8
kcallmol less negative in acetonitrile than in methanol. This suggests that the
partition mechanism is still relatively important for this solute, such that the less
polar mobile phase, acetonitrile, competes more effectively than methanol with
the nonpolar stationary phase.

Although there are small but important differences, it is noteworthy that the
changes in molar enthalpy are very similar in the acetonitrile and methanol
mobile phases. Yet the retention factors for the aza-PAHs differ by nearly an
order of magnitude in these mobile phases. From Figure 6.3, it is evident that
the difference lies in the intercept of the van’t Hoff plot. Again, according to
Equation 1.6, there are two possible origins of this difference. The entropy term
may be substantially more negative in methanol because of the solvent release
from both solute and silanol sites upon binding. A smaller entropy term in
acetonitrile would lead to a larger value for the intercept. Alternatively, a change
in the phase ratio may arise because of the greater number of free silanol groups
in acetonitrile. In methanol, many of the silanol groups may be hydrogen bonded
and not available for binding with the solute. The larger phase ratio in acetonitrile
would also lead to a larger value for the intercept. As noted previously, it is
difficult to discern which of these origins prevails by chromatographic methods

alone.

240

6.3.2.2 Kinetic Behavior
6. 3. 2. 2.1 Rate Constants

Representative values of the rate constants are summarized in Table 6.6.
1-Aminopyrene undergoes much higher rates of transfer than 4-azapyrene,
benz[a]acridine, and dibenz[a,j]acridine, which are two to three orders-of-
magnitude lower. As in the methanol mobile phase, the rate-limiting step for 1-
aminopyrene is the transfer from the acetonitrile mobile phase to the stationary
phase. However, the aza-PAHs demonstrate the inverse trend, with the transfer
from stationary to mobile phase serving as the rate-limiting step. When
compared to the methanol mobile phase, the rate constants in acetonitrile are
two to four orders-of-magnitude smaller. The differences in the rate constants
result from the increased ability of the N-PAHs to interact with the silica support.
As noted previously, the aprotic solvent acetonitrile does not hydrogen bond to
the solutes or to the silanol sites as does the protic solvent methanol. Hence, the
rate constants from mobile to stationary phase and from stationary to mobile
phase are substantially smaller.
6. 3. 2. 2.2 Activation Energy

A representative graph of the logarithm of the rate constant versus the
inverse temperature is shown in Figure 6.5. The data for the acetonitrile mobile
phase are represented using dashed lines. It should be noted that the data for 1-
aminopyrene are not depicted in this graph. The zone profiles for 1-aminopyrene
are nearly Gaussian and, as such, exhibit very small values of the asymmetric

variance (:2). The small values of 12 result in calculated values for the rate

241

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242

constants that are highly variable as a function of temperature.

As shown in Figure 6.5, the graph for each N-PAH is linear and the slope
is negative. Unlike the graph for the methanol mobile phase, acetonitrile shows
correlation coefficients for the linear regression that vary significantly (R2 = 0.038
- 0.960). As such, the reported values should be used only to draw general
conclusions. The activation energy is calculated from the slope of this graph,
according to Equations 1.15. As shown in Table 6.6, the activation energies are
positive for all of the N-PAHs. The activation energy for the transfer from
stationary phase to transition state (AEa) is generally larger than that from mobile
phase to transition state (AEm). These data indicate that it is easier for the
solutes to exit the stationary phase than to enter. In spite of the large standard
deviations, the activation energy appears to be smallest for 1-aminopyrene,
slightly greater for benz[a]acridine and dibenzla,j]acridine, and greatest for 4-

azapyrene.
6.4. CONCLUSIONS

In this study, the thermodynamic and kinetic behavior of N-PAHs was
examined in reversed-phase liquid chromatography. The parent PAHs are
separated primarily by a partition mechanism with the octadecyl groups, but
some minor interaction with the silanol groups can occur through the aromatic (1:)
system. In methanol mobile phase, the retention factors for the N-PAHs are less
than those for the parent PAHs. This is consistent with the partition mechanism,
where retention decreases as the polarity of the solute increases. In addition, the

trends of retention with ring number and annelation structure are consistent with

243

the partition mechanism. However, the changes in molar enthalpy for the N-
PAHs indicate that adsorption at the silanol groups is more significant than for
the parent PAHs. The observed changes reflect the relative basicity of the amine
and aza groups, but also indicate that steric effects are important. The more
condensed amino- and azapyrenes can diffuse more easily to the silanol groups
than the more linear benz[a]acridine and dibenz[a,j]acridine. The importance of
adsorption is also reflected in the kinetic rate constants, which are significantly
smaller for the NPAHs than for the parent PAHs.

The trends in thermodynamic behavior in the protic solvent methanol
become even more pronounced in the aprotic solvent acetonitrile. Methanol is
able to hydrogen bond with the NPAH solutes as well as with the silanol groups,
thereby reducing their mutual interactions. Acetonitrile is not able to shield
interactions in this manner, hence the retention factors for the aza-PAHs are
substantially greater than those in methanol. Moreover, the retention factors for
the four-ring aza-PAHs are greater than those for the parent PAHs, which
suggests that the adsorption mechanism is predominant for these solutes. The
changes in molar enthalpy are slightly more negative for these solutes, but not
sufficient to account for the large change in retention factor. Hence, we suggest
that a significant change in entropy or the phase ratio is responsible for the
thermodynamic behavior. The kinetic behavior also reflects the increased role of
adsorption, with rate constants that are two to four orders-of-magnitude smaller

than those in methanol. This thermodynamic and kinetic information provides a

244

 

much clearer description of the retention mechanism of N-PAHs in reversed-

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245

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REFERENCES

T. Vo-Dinh, Ed., Chemical Analysis of Polycyclic Aromatic Hydrocarbons,
John Wiley 8. Sons, New York, NY, 1988.

M. Cooke, A.J. Dennis, G.L. Fisher, Eds., Polynuclear Aromatic
Hydrocarbons: Physical and Biological Chemistry, Battelle Press,
Columbus, OH, 1982.

RF. Hertel, G. Rosner, J. Kielhom, Eds., Selected Non-Heterocyclic
Polycyclic Aromatic Hydrocarbons, World Health Organization, Geneva,
Switzerland, 1998.

CH. Ho, B.R. Clark, M.R. Guerin, B.D. Barkenbus, T.K. Rao, J.L. Epler,
Mutat. Res. 85 (1981) 335-345.

G.M. Seixas, B.M. Andon, P.G. Hollingshead, W.G. Thilly, Mutat. Res. 102
(1982) 201-212.

A. Matsuoka, K. Shudo, Y. Saito, T. Sofuni, M. lshidae, Mutat. Res. 102
(1982) 275-283.

E.A.J. Bleeker, S. Wlegman, P. de Voogt, M. Kraak, H.A. Leslie, E. de
Haas, W. Admiraal, Rev. Environ. Contam. Toxic. 173 (2001) 39-83.

J.M. Schmitter, H. Colin, J.L. Excoffier, P. Arpino, G. Guiochon, Anal.
Chem. 54 (1982) 769-772.

8.0. Ruckmick, R.J. Hurtubise, J. Chromatogr. 321 (1985) 343-352.
C. Borra, D. Wiesler, M. Novotny. Anal. Chem. 59 (1987) 339-343.

N. Motohashi, K. Kamata, R. Meyer, Environ. Sci. Technol. 25 (1991) 342-
346.

J.M. Schmitter, l. lgnatiadis, G. Guiochon, J. Chromatogr. 248 (1982) 203-
216.

MR. Guerin, C.H. Ho, T.K. Rao, B.R. Clark, J.L. Epler, Environ. Res. 23
(1980) 42-53. ‘

S.G. Wakeham, Environ. Sci. Technol. 13 (1979) 1118-1123.
H.Y. Chen, M.R. Preston, Environ. Sci. Technol. 32 (1998) 577-583.

M. Wilhelm, G. Matuschek, A. Kettrup, J. Chromatogr. A 878 (2000) 171-
181.

246

 

[17] K. Kamata, N. Motohashi, J. Chromatogr. 319 (1985) 331-340.

[18] K. Kamata, N. Motohashi, R. Meyer, Y. Yamamoto, J. Chromatogr. 596
(1992) 233-239.

[19] K. Kamata, N. Motohashi, J. Chromatogr. 396 (1987) 437-440.
[20] M. Ashraf-Khorassani, L.T. Taylor, J. Chromatogr. Sci. 26 (1988) 331-336.
[21] H. Colin, J.M. Schmitter, G. Guiochon, Anal. Chem. 53 (1981) 625-631.

[22] AM. Siouffi, M. Righezza, G. Guiochon, J. Chromatogr. 368 (1986) 189-
202.

 

[23] TR. Steinheimer, M.G. Ondrus, Anal. Chem. 58 (1986) 1839-1844.

[24] J.W. Haas, W.F. Joyce, Y.J. Shyu, P.C. Uden, J. Chromatogr. 457 (1988)
215-226.

[25] K. Kamata, N. Motohashi, J. Chromatogr. 498 (1990) 129-135.

[26] H. Carlsson, C. Ostman, J. Chromatogr. A 715 (1995) 31 -39.

[27] SB. Howerton, V.L. McGuffin, Anal. Chem. 75 (2003) 3539-3548. 1
[28] SB. Howerton, V.L. McGuffin, J. Chromatogr. A 1030 (2004) 3-12.

[29] J.H. Hildebrand, R.L. Scott, The Solubility of Nonelectrolytes, 3rd ed.,
Reinhold Publishing, New York, NY, 1950.

[30] SA. Wise, W.J. Bonnett, F.R. Guenther, W.E. May, J. Chromatogr. Sci. 19
(1981 ) 457-465.

[31] MW. Ducey, C.J. Orendorff, J.E. Pemberton, L.C. Sander, Anal. Chem.
74 (2002) 5576-5584.

[32] MW. Ducey, C.J. Orendorff, J.E. Pemberton, L.C. Sander, Anal. Chem.
74 (2002) 5585-5592.

[33] A. Nahum, C. Horvath, J. Chromatogr. 203 (1981) 53-63.

[34] RA. Matzner, R.C. Bales, J.E. Pemberton, Appl. Spectrosc. 48 (1994)
1043-1053.

[35] SC. Ringwald, J.E. Pemberton, Environ. Sci. Technol. 34 (2000) 259-265.

[36] DR. Lide, Handbook of Chemistry and Physics, 71st Ed., CRC Press,
Boca Raton, FL, 1990.

247

[37] B.N. Woodrow, J.G. Dorsey, Environ. Sci. Technol. 31 (1997) 2812-2820.
[38] R. Matzner, R.C. Bales, Chemosphere 29 (1994) 1 755-1773.
[39] R. Matzner, R.C. Bales, J. Colloid Interface Sci. 168 (1994) 61 -66.

248

 

 

CHAPTER 7

SPECTROSCOPIC STUDY OF NITROGEN-CONTAINING
POLYCYCLIC AROMATIC HYDROCARBONS BY
FLUORESCENCE QUENCHING

7.1 INTRODUCTION

7.1.1 Nitrogen-Containing Polycyclic Aromatic Hydrocarbons (N-PAHs)

As described in Chapter 6, polycyclic aromatic compounds are well known
for their potent biological effects, forming the largest known group of chemical
carcinogens and mutagens [1-3]. While much attention has been paid to
polycyclic aromatic hydrocarbons (PAHs), comparatively less information is
available for nitrogen-containing polycyclic aromatic hydrocarbons (N-PAHs).
The N-PAHs fall into two categories: amino-PAHs and aza-PAHs (azaarenes).
By another classification scheme, they can also be divided into altemant and
nonaltemant N-PAHs. Representative altemant N-PAH (1-azapyrene) and
nonaltemant N-PAH (3-azafluorencene) are shown in Figure 7.1. After labeling
every other atom in the aromatic ring system, skipping one atom between,
altemant N-PAHs will have no labeled atoms adjacent. Nonaltemant N-PAHs will
have at least one pair of adjacent labeled or unlabeled atoms [4].

7.1.2 Fluorescence Quenching

Fluorescence is a luminescence technique that is quite suitable for the
study of PAHs and N-PAHs because of their high quantum efficiency, which is
associated with the delocalized electrons present in conjugated double bonds.
While high sensitivity can easily be obtained from fluorescence, high selectivity is

not always assured. Synchronous scanning techniques, in which both the

249

'J

?.3 ......‘m
I .
.

 

 

Nonaltemant N-PAH

Figure 7.1 Representative examples of altemant N-PAH and nonaltemant

N-PAH

250

 

excitation and emission monochromators are scanned by maintaining a constant
wavelength or energy interval, can provide greater selectivity [5]. However,
synchronous scanning may not be sufficient to distinguish structurally similar
PAHs and N-PAHs. The use of fluorescence quenchers may significantly
increase the selectivity. Fluorescence quenching refers to any process that
decreases the fluorescence power of a sample [6,7]. Among the different
mechanisms, dynamic quenching is the most useful tool for analytical purposes
[3].

In dynamic quenching, an excited-state fiuorophore collides and forms a
transient complex with a ground-state quencher. This excited-state complex
dissociates upon radiative or nonradiative deactivation, leaving both the
fluorophore and quencher in the ground state. Dynamic quenching can be

described by the Stem-Volmer equation:

fl — 1 +k 0c —1 K c

pf“ d‘i q- + d q (7.1)
where 1°. is the fluorescence lifetime of the fluorophore without quencher, kd is
the bimolecular rate constant, and K. is the Stem-Volmer constant. A graph of
the fluorescence power ratio (PP/Pr) versus the quencher concentration (Cq) is
linear, with a slope equal to the Stem-Volmer constant and an intercept of unity.
The Stem-Volmer constant is characteristic of each fluorophore—quencher pair
and serves as a measure of the quenching efficiency. The ratio of Stem-Volmer
constants for two fluorophores with the same quencher, or two quenchers with

the same fluorophore, serves as a measure of the selectivity.

251

Although a large number of quenchers have been identified for polycyclic
aromatic compounds, very few have been studied in sufficient depth to permit
their routine application. Most of these quenchers are concerned with
discrimination between altemant and nonaltemant PAHs. These quenchers
include nitromethane [8-11], pyridium chloride [12], cetylpyridinium chloride [13],
and dodecylpyridinium chloride [14]. Among these quenchers, nitromethane is
the most well-known and well-characterized dynamic quencher. After Sawicki et
al. first demonstrated that nitromethane, an electron acceptor, could selectively
deactivate the fluorescence of altemant PAHs [15], Acree et al. performed
systematic studies that elucidated the so-called “nitromethane selective
quenching rule" [8-10]. Subsequently, Ogasawara et al. performed a quantitative
study to show that the Stem-Volmer constants of nitromethane are 33 - 100
times larger for altemant than nonaltemant isomers [11]. Recently, Goodpaster
and McGuffin performed an investigation of aliphatic amines as new potential
quenchers [16]. Diisopropylamine can quench nonaltemant PAHs 15 - 45 times
more effectively than their altemant isomers. To date, most of the investigations
have been limited to PAHs. For the N-PAHs, only one quencher, nitromethane,
has been studied by Acree et al. [4]. But no quenching rule for altemant N-PAH
is clearly elucidated, and no quantitative figures have been obtained. In the
present study, aliphatic amines will be used to investigate the selective
quenching rules applicable to N-PAHs and to evaluate their potential for

analytical applications.

252

 

7.2 EXPERIMENTAL METHODS

7.2.1 Chemicals

Reagent-grade hexylamine, diisopropylamine, and triethylamine (Aldrich)
are used as received. The PAHs, shown in Figure 7.2, include pyrene, 1-
aminopyrene, fluoranthene, and 3-aminofluoranthene (Aldrich). In addition, 1-
azapyrene, 4-azapyrene, 3-azafluoranthene, benzo[a]pyrene, 10-
azabenzo[a]pyrene, benz[a]anthracene, benz[a]acridine, benz[a]acridine,
dibenz[a,j]acridine, and dibenz[c,h]acridine are obtained from lnstitilt f0r PAH-
Forschiing, Greiffenberg, Germany. The PAHs are dissolved in acetonitrile to
prepare stock solutions of approximately 1.0 mM concentration. These stock
solutions are diluted 100-fold in acetonitrile and mixed with quencher solutions of
different concentrations to prepare the sample solutions, which are analyzed with
the system described below. High purity, spectroscopic-grade acetonitrile
(Burdick and Jackson, Baxter Healthcare) is used to prepare all solutions. No
effort was made to remove dissolved oxygen from these solutions. The results of
these fluorescence quenching studies are intended for routine practical
applications, where scrupulous removal of oxygen may be difficult and the
resulting variability in residual oxygen concentration may limit the quantitative
accuracy.
7.2.2 Fluorescence Quenching Measurements

A laser-induced fluorescence spectrometer is used for the determination
of quenching constants. Solutions composed of fluorophores and quenchers of

different concentrations are introduced to a fused-silica capillary flow cell (75-um

253

‘7'“.

ii;

Figure 7.2 Structures of PAHs and N-PAHs for fluorescence quenching study.

254

 

a 8’: as

pyrene1-azapyrene1-aminopyrene

 

     

0‘0

fluoranthene 3-azafluoranthene 3-aminofluoranthene

255

benzo[a]pyrene 10-aza-benzolalpyrene
DOC O \O
N/ /
benz[a]anthracene benz[a]acridine benz[a]acridine
O \O 0 KO
N/ /
dibenz[ajjacridine dibenz[c,h]acridine

4-azapyrene

256

inner diameter, 375-pm outer diameter, 1.5-m length, Polymicro Technologies)
by a gas displacement pump. The capillary flow cell minimizes error arising from
primary and secondary absorption effects [17]. A continuous-wave He-Cd laser
(Melles Griot, Model 3074-40M, 325 nm, 32 mW) is used as the excitation source.
Fluorescence emission is collimated, filtered to remove laser scatter, and then
focused onto the entrance slit of a 0.34 m Czemy-Tumer monochromator
(Instruments SA, Model 340E, 300 groove/mm grating). Fluorescence power is
measured by a charge-coupled device (Instruments SA, Model (A)TECCD-
2000*800—7, 15-um pixels), which is cooled and maintained at 233 K. The
control of the system and the subsequent data acquisition are achieved by
commercially available electronic interfaces (Instrument SA, Model 081010 and
Model COO 2000) and the associated software (Instruments SA, Spectromax for
Windows, version 3.1).

Fluorescence power is measured for an integrated range of wavelengths,
rather than a single wavelength, because the relative intensity of the vibronic
bonds of PAHs may vary with solvent polarity [18,19]. The wavelength range for
different fluorophores is as follows: pyrene (360 - 460 nm). 1-azapyrene (350 -
450 nm), 4-azapyrene (355 -— 465 nm), 1-aminopyrene (385 — 530 nm),
fluoranthene (380 — 590 nm), 3-azafluoranthene (395 — 595 nm), 3-
aminofluoranthene (450 - 600 nm), benzo[a]pyrene (365 - 515 nm), 10-
azabenzo[a]pyrene (390 - 550 nm), benz[a]anthracene (365 - 515 nm),
benz[a]acridine (370 - 510 nm), benz[c]acn'dine (370 - 510 nm),

dibenz[afiacridine (380 - 495 nm), and dibenz[c,h]acridine (380 - 495 nm). The

257

ratio of fluorescence power with and without quencher is calculated and graphed
according to equation 7.1. After linear regression of the fluorescence power ratio
with respect to the concentration of quencher, the slope of the graph is
determined as the quenching constant (Kd).
7.2.3 Fluorescence Lifetime Measurements

Fluorescence lifetimes are measured by a time-correlated single photon
counting spectrometer [20]. In this system, the second harmonic of a
continuous-wave. mode-locked Nd:YAG laser (Quantronix, Model 416) is used to
excite a cavity-dumped, synchronously pumped dye laser (Coherent, Model 702-
2) at 325 nm. Fluorescence emission is collected and focused on a subtractive
double monochromator with a 10-nm bandpass. The emission is detected with a
cooled two-stage microchannel plate photomultiplier at 243 K. Single photon
counting is performed with commercially available electronic instrumentation
(Tennelec, Models T0454, TC864. TC412A, T0525. and PCA-II) and
commercially available software (Oxford Instruments, PCAME. Version 2.54).

Fluorescence lifetimes are determined at individual wavelengths
corresponding to the emission maximum for each PAH: pyrene (380 nm), 1-
azapyrene (375 nm), 1-aminopyrene (428 nm), fluoranthene (464 nm), 3-
azafluoranthene (468 nm), and 3-aminofluoranthene (525 nm). Three replicate
measurements of the fluorescence time decay are acquired by single photon
counting. The data deconvoluted from the instrumental response function (about
35 ps FWHM) are fit by nonlinear regression to a single exponential function to

determine the fluorescence lifetime [6].

258

 

 

 

7.3 RESULTS AND DISCUSSION

Aliphatic amines are dynamic fluorescence quenchers corresponding with
their electron-donating ability. They serve as electron donors through the
nonbonding electron pair of the nitrogen atom. In this study, aliphatic amines are
examined as fluorescence quenchers for fluorophores consisting of PAHs,
amino-PAHs, and aza-PAHs.

7.3.1 Effect of Water

During preliminary studies, it was observed that repeated measurements
with the same stock solution of triethylamine yielded a continuous decrease of
the Stem-Volmer constant. Because amines and polar solvents tend to be
hygroscopic, a detailed investigation of the effect of water was warranted. If the
primary source of water arises from the amine, then the net concentration of
water will vary with the quencher concentration. On the other hand, if the primary
source of water arises from the polar solvent, then the net concentration of water
will be relatively constant. Both of these effects are examined using the well-
investigated fluorophore, pyrene (105 M), and the quencher, triethylamine (0.01
— 0.05 M). For the first study, stock solutions of TEA containing 0%, 1%, and 5%
(vlv) of water are used to prepare the solutions. The resulting quenching
constants are summarized in Table 7.1. With increasing water concentration in
the TEA stock solutions, the quenching constants of pyrene and TEA are
systematically decreased. For the second study, the water concentrations in the
solvent acetonitrile remain constant at 0%, 1%, and 5%. The quenching

constants are summarized in Table 7.2. They show the same decreasing trend

259

 

 

with more water contained in the system. In both of these tables. good linearity
and intercepts approaching unity are achieved with all quenching constant
calculations. These features are indicative of a single quenching mechanism. In
order to understand this quenching mechanism, it is important to note that water
is not a fluorescence quencher but, according to our results, slightly enhances
the quantum yield of pyrene in acetonitrile. However, water can form hydrogen
bonds with the amine, comprising neutral complexes. ion pairs, or free ions
depending on the dielectric constant of the solvent. These complexes make the
nonbonding electrons of the nitrogen atom less accessible for quenching. Thus,
the effect of water is to decrease the concentration of the free amine, leading to a
decrease in the quenching constant. This is consistent with previous studies by
Goodpaster and McGuffln [16], who reported that amines exhibit smaller
quenching constants in methanol than in acetonitrile due to the existence of
hydrogen bonds. The results of the present study suggest that great care must
be taken to control water content in the amines and solvents in order to obtain
reproducible and reliable quenching constants. Water may be removed from the
amines by distillation with calcium hydride and storage with dry nitrogen.
7.3.2 Effect of Amino Structure

Two representative groups of alternant and nonaltemant PAHs and N-
PAHs are selected as fluorophores for this study. The altemant group includes
pyrene, 1-azapyrene, and 1-aminopyrene. The nonaltemant group includes
fluoranthene, 3-azafluoranthene, and 3-aminofluoranthene. The corresponding

altemant and nonaltemant PAHs or N-PAHs have the same molecular formula

260

Table 7.1 Stem-Volmer constants for pyrene with triethylamine in acetonitrile

at room temperature with different water concentration (v/v) in the amine

 

 

 

solution.a
water concentration K, (M") intercept R2
(vlv)
0% 49.2 :l: 0.8 1.08 :t 0.03 0.9992
1% 45 i 1 1.08 :l: 0.05 0.9981
5% 38 i 2 1.15 :l: 0.06 0.9934

 

 

a 10'5 M pyrene, 0.01 — 0.05 M triethylamine

261

 

Table 7.2 Stem-Volmer constants for pyrene with triethylamine in acetonitrile

at room temperature with different water concentration (vlv) in the solvent“.

 

 

 

water concentration
Kd (M-1) intercept R2
(WV)
0% 49210.8 1.08:0.03 0.9992
1% 41 .0:l:0.5 1.02:0.02 0.9996
5% 24.3:05 10210.02 0.9987

 

 

a 10’5 M pyrene. 0.01 — 0.05 M triethylamine

262

 

and the same number of aromatic rings. The fluorescence lifetime (1°f) of each
PAH and N-PAH is summarized in Table 7.3. Three aliphatic amines,
triethylamine, diisopropylamine, and hexylamine, which have the same molecular
weight but different structures, are chosen as quenchers. The Stem-Volmer
quenching constants for the two groups of fluorophores by different amines are
summarized in Table 7.3. In this table, all of the Stem-Volmer constant
calculations show good linearity and intercepts approaching unity. With the
information of fluorescence lifetime and Stem-Volmer constants. the bimolecular
rate constant for each fluorophore-quencher pair is calculated and is also
summarized in Table 7.3.

Comparing the quenching ability of the aliphatic amines, the quenching
constants systematically increase from primary to tertiary amine. The same
trend is observed for PAHs, aza-PAHs. and amino-PAHs, regardless of their
altemant or nonaltemant structure. The alkyl group can increase the electron-
donating ability of nitrogen. Thus, the greater the number of alkyl groups
connected to the nitrogen, the stronger the electron-donating ability, and the
higher the Stern-Volmer quenching constant. It is noteworthy that the
bimolecular rate constants for the tertiary amine. triethylamine, are approaching
the diffusion-limited values {101° — 1011 M" s"). This implies that almost every
collision between the fluorophore and quencher will induce quenching.

Selectivity can be defined as the ratio of quenching constants. In this
study, three different selectivities can be evaluated as follows:

a _ Kd(aza-PAH)
a Kd(amino-PAH)

 

(7.2)

263

Table 7.3 Stem-Volmer constants for PAHs and N-PAHs with three aliphatic
amines in acetonitrile at room temperature.

264

 

 

 

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265

_ Kd(aza -PAH)
' Kd(PAH)‘

 

(7.3)

a _ Kd(nonaltemant PAH)
c Kd (altemant PAH)

 

(7.4)

As evident from the Stem-Volmer constants in Table 7.3, aza-PAHs are easily
quenched by the aliphatic amines whereas amino-PAHs remain virtually
unquenched. The selectivity are between aza-PAHs and amino-PAHs is as high
as several hundred for diisopropylamine and triethylamine. Even the lowest
selectivity one for hexylamine is more than thirty-five. which is sufficiently high for
discrimination. It is important to note that the fluorescence lifetimes of the aza-
PAHs and amino-PAHs are on the same order of magnitude. Longer
fluorescence lifetimes will allow more opportunities for collision with the quencher,
thus increasing the Stem-Volmer constants according to equation 7.1. But this
difference in Stem-Volmer constant is due solely to the physical properties of the
fluorophores, which is not the case in the present system. In this system, the
difference in Stem-Volmer constant is due to the chemical properties, which
influence the bimolecular collision rate between excited-state fluorophore and
quencher. The high selectivity 0.; provides an easy means to discriminate
between aza-PAHs and amino-PAHs. While other techniques such as
thermionic detection [21] and mass spectrometry can be used to determine
whether nitrogen is present, they may fail to reveal whether the nitrogen is within
or outside the aromatic ring. 0n the other hand, some simple organic reactions
such as the Hinsberg test or sodium nitroprusside test [38] can differentiate

primary, secondary, and tertiary amines, however these methods are not suitable

266

for complex samples. The fluorescence quenching approach can easily address
these difficulties. .

Selectivity, orb, demonstrates the discrimination ability of amines for aza-
PAHs compared to that of their corresponding PAHs. It can easily be observed
that the selectivity ab decreases as the quenching constants increase from
primary to tertiary amines. The quenching constants for PAHs increase at a
much faster rate than those for the aza-PAHs. For the altemant group, the
quenching constants for 1-azapyrene are always larger than those of pyrene,
which demonstrates the trend that amines can serve as more effective
quenchers for altemant aza-PAHs than for PAHs. For the nonaltemant group.
however, no such trend is obeyed. Triethylamine is a more effective quencher
for fluoranthene, whereas diisopropylamine and hexylamine are more effective
quenchers for 3-azafluoranthene. However. when the fluorescence lifetimes are
taken into account, the bimolecular rate constants (kd) are always larger for aza-
PAHs than for their corresponding PAHs, regardless of altemant or nonaltemant
character.

Selectivity ac demonstrates the discrimination capacity of amines for
nonaltemant polycyclic aromatic compounds (PACs) compared to altemant
PACs, including both PAHs and aza-PAHs. The three amines can all serve as
more effective quenchers for nonaltemant PAHs than altemant PAHs. The
selectivity (1.; increases from primary to tertiary amines. For the aza-PAHs,
however, this trend is not observed. On the contrary, the three amines all serve

as more effective quenchers for altemant aza-PAHs. The selectivity do is

267

relatively small and constant. It is important to note that the nonaltemant PACs
have longer fluorescence lifetimes than do the altemant PACs. For example, the
lifetime of the nonaltemant PAH, fluoranthene, is approximately two times longer
than that of the altemant PAH, pyrene. For the nonaltemant and altemant
amino-PAHs, 3-aminofluoranthene and 1-aminopyrene, their fluorescence
lifetimes also differ by a factor of two. Thus, the selectivities based on
bimolecular rate constants for these two groups will be reduced by half. In
contrast, there is no significant difference between the lifetimes for nonaltemant
and altemant aza-PAHs, 3-azafluoranthene and 1-azapyrene. Hence, their
selectivity based on bimolecular rate constants will remain the same as that
based on Stem-Volmer constants.
7.3.3 Effect of Fluorophore Structure

Due to the consistent trends observed with the altemant PAHs and aza-
PAHs, a broader range of these solutes is chosen to investigate the structural
effects on fluorescence quenching. Ten solutes constitute the new study, being
divided into four groups with varying ring number and annelation structure.
Specifically, pyrene, 1-azapyrene, and 4-azapyrene have four aromatic rings
arranged in peri-condensed structure. Benz[a]anthracene, benz[a]acridine, and
benz[a]acridine also have four aromatic rings. but are ortho—condensed.
Benzo[a]pyrene and 10-azabenzo[a]pyrene have five rings, with one more ortho-
condensed ring than the pyrene group. Finally, dibenz[aflacridine and
dibenz[c,h]acridine have five rings, with one more ortho-condensed ring than the

benz[a]anthracene group. Furthermore, the position of nitrogen within the

268

aromatic ring is varied within some groups, for example, 1-azapyrene and 4-
azapyrene, benz[a]acridine and benz[a]acridine, dibenz[ay]acridine and
dibenz[c,h]acridine. The Stem-Volmer quenching constants for these 10
compounds are measured with diisopropylamine. In general, they show good
linearity and an intercept approaching unity. The Stem-Volmer quenching
constants and the selectivity ab. calculated according to equation 7.3, are
summarized in Table 7.4.

For each group, larger quenching constants are obtained for aza-PAHs
than for their corresponding PAHs, which is demonstrated by a selectivity on,
greater than one. This confirms the general rule shown previously that can be
applied to altemant aza-PAHs and altemant PAHs. This rule may help to
differentiate between aza-PAHs and PAHs with amine quenchers.

When there are two aza-PAHs in the same group, a close look at the
effect of nitrogen position is possible. In the pyrene group, 1-azapyrene and 4-
azapyrene have similar quenching constants, which implies that the nitrogen
atoms at the 1- and 4-positions show similar electron donor/acceptor ability and
similar accessibility. The same trend is observed for benz[a]acridine and
benz[a]acridine. In another group, however, dibenz[a,j]acridine has a quenching
constant almost two times greater than that of dibenz[c,h]acridine. Although
these two nitrogen atoms have similar electron donor/acceptor ability, the
nitrogen in dibenz[c,h]acridine is less accessible than that in dibenz[aJ]acridine.
Thus, steric hindrance may reduce contact between the fluorophore and

quenchen

269

Table 7.4

diisopropylamine in acetonitrile at room temperature.

Stem-Volmer constants for altemant PAHs and aza-PAHs with

 

 

 

Fluorophore Kd (M'f) Intercept R2 Selectivity ab
pyrene 1.76 i: 0.02 1.00 i 0.01 0.9995
1-azapyrene 47.7 i 0.6 1.08 1: 0.05 0.9995 27.10
4-azapyrene 44 j: 1 0.96 i 0.04 0.998 24.87
benz[a]anthracene 2.1 :t 0.2 0.92 :l: 0.05 0.986
benz[a]acridine 9.4 i 0.3 1.03 :l: 0.02 0.996 4.51
benz[a]acridine 9.6 :l: 0.2 1.01 :l: 0.01 0.999 4.58
benzo[a]pyrene 1.17 :l: 0.04 0.97 :l: 0.01 0.996
10-azabenzo[a]pyrene 1.67 i 0.03 1.00 :t 0.02 0.999 1.43
1.010 :l:
dibenz[a,j]acridine 10.42 :l: 0.05 0.9999
0.005
0.996 :1:
dibenz[c,h]acridine 6.68 i 0.08 0.9997
0.006

 

 

 

270

 

The effect of ring number on Stern-Volmer constants for PAHs is
demonstrated by comparison between pyrene and benzo[a]pyrene. Adding a
benzene ring from pyrene to benzo[a]pyrene decreases the Stern-Volmer
constant by 33%. For aza-PAHs, the effect of ring number can be demonstrated
in two groups. From 1- and 4-azapyrene to 10-azabenzo[a]pyrene, the Stem-
Volmer constants decrease dramatically by 96%. This difference might be
introduced by the extended ring number, similar to the trend for the parent PAHs,
pyrene and benzo[a]pyrene. It might also be related to the effects of steric
hindrance, due to reduced accessibility of the nitrogen atom in 10-
azabenzo[a]pyrene than in 1— or 4-azapyrene. Moreover, the electron
donor/acceptor ability might be different depending on the position of the nitrogen
atom. The nitrogen atom located within the pad-condensed four-ring system, as
1- or 4-azapyrene, might have stronger electron donor/acceptor ability than the
nitrogen atom located in the ortho-condensed benzene ring, as 10-
azabenzo[a]pyrene. Comparison can also be made between the benz- and
dibenz-acridines. Adding a benzene ring from benz[a]acridine to
dibenz[ay]acridine increases the Stem-Volmer constant by about 10%. The
accessibility and electron—donating/accepting ability of the nitrogen atom in these
two compounds are quite similar. However, adding a benzene ring from
benz[a]acridine to dibenz[c,h]acridine decreases the Stem-Volmer constant by
about 30%. This decrease in Stem-Volmer constant arises from the reduced

accessibility of the nitrogen atom in dibenz[c,h]acridine.

271

The effect of annelation structure for PAHs can be demonstrated by
comparison between pyrene and benz[a]anthracene. The more linear structure
of benz[a]anthracene increases the Stem-Volmer constant by 20%. However, for
the aza-PAHs, the Stem-Volmer constant decreases dramatically by 80% from
the compact structure of 1- and 4-azapyrene to the linear structures of
benz[a]acridine and benz[a]acridine. The accessibility of the nitrogen in these
four compounds should be similar to each other. However, the nitrogen atom in
the pen’-condensed pyrene system might have stronger electron donor/acceptor
ability than in the ortho-condensed benz[a]anthracene system. In the five-ring
system, the Stem-Volmer constant increases by 300% from 10-
azabenzo[a]pyrene to dibenz[a,j]acridine and dibenz[c,h]acridine, with more
linear structures. In this case, the nitrogen atoms are all located in the peri-
condensed ring and, thus, have similar electron donor/acceptor ability. The more
linear structures might increase the Stem-Volmer constants for these N-PAHs,
just as for the PAHs pyrene and benz[a]anthracene.

It is helpful to examine whether the observed trends in quenching
constants correlate with the gas-phase ionization potential of the fluorophore.
The smaller the ionization potential, the more readily the fluorophore can donate
rather than accept electrons, which should result in smaller quenching constants.
The available information on ionization potentials for selected fluorophores is
summarized, together with their quenching constants, in Table 7.5.

For PAHs, the ionization potential data show that benzo[a]pyrene < pyrene

s benz[a]anthracene < fluoranthene, which is in agreement with the trends in

272

Table 7.5 Ionization potentials for the fluorophores (PAHs and N-PAHs).

 

 

 

Ionization Quenching
PAHs and N-PAHs Reference
Potential Constant
pyrene 7.5, 7.41 [23,24] 1.76
fluoranthene 7.9 [25] 19.8
benz[a]anthracene 7.54, 7.43 [23,24] 2.1
benzo[a]pyrene 7.23 [23] 1.17
benz[a]acridine 8.02 [26] 9.4
benz[a]acridine 7.98 [26] 9.6
benzene 9.24 [27] NIA
pyridine 9.76 [28] NIA
aniline 7.72 [29] NIA

 

 

 

273

 

fluorescence quenching constants discussed above. For N-PAHs, the
information on ionization potential is only available for benz[a]acridine and
benz[a]acridine. Their similar ionization potentials are consistent with their
similar quenching constants. Meanwhile, both of their ionization potentials are
larger than their corresponding PAH, benz[a]anthracene. This is also consistent
with the trends for quenching constants.

To investigate the trend in quenching constants for altemant aza-PAH >
PAH > amino-PAH, the ionization potentials of benzene, pyridine, and aniline are
shown in Table 7.5. Although they are not the fluorophores investigated in this
paper, they compose a similar group for comparison with 1-azapyrene, pyrene,
and 1-aminopyrene. Aniline has an extremely small ionization potential, which
corresponds with the extremely small quenching constant for 1-aminopyrene.
Meanwhile, the ionization potential for benzene is smaller than that of pyridine,
which also corresponds to a smaller quenching constant for pyrene than that of
1 -azapyrene.

However, ionization potential alone cannot fully explain the trends in
Stern-Volmer quenching constant. For example, fluoranthene and the
benzacridines have similar ionization potential, yet their quenching constants
differ by a factor of two. More experimental and theoretical correlations need to

be investigated to fully explain these trends.
7.4 CONCLUSIONS

Fluorescence quenching has the potential to become a very practical and

useful technique due to its high sensitivity and selectivity. However, its

274

usefulness is still limited because of the small number of fluorophores and
quenchers that have been examined in sufficient detail. In this study, PAHs and
N-PAHs as fluorophores and aliphatic amines as quenchers are chosen for
investigation. The trends of increased quenching efficiency and decreased
selectivity are shown from primary to tertiary amine. Amino-PAHs remain
unquenched by aliphatic amines. Altemant aza-PAHs are quenched more
efficiently than their corresponding altemant PAHs. These two trends can be
very helpful in addressing the difficulty of identifying compounds in complex
samples in the future. However, the selectivity of diisopropylamine for some
systems in this study is not sufficiently high, which demands further research and

development.

275

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REFERENCES

M.L. Lee, M.V. Novotny. K.D. Bartle, Analytical Chemistry of Polycyclic
Aromatic Compounds, Academic Press, New York, 1981.

T. Vo Dinh, Chemical Analysis of Polycyclic Aromatic Compounds, Wiley,
New York, 1988.

V.L. McGuffin, J.V. Goodpaster, in RA. Meyers (Ed), Encyclopedia of

Environmental Analysis and Remediation, Wiley, New York, 1998, p. 3815.

SA. Tucker, W.E. Acree, M.J. Tanga, S. Tokita, K. Hiruta, H. Langhals,
Appl. Spectrosc. 46 (1992) 229-235.

6.6. Guilbault, Practical Fluorescence, Marcel Dekker, New York, 1990.

JR. Lakowicz, Principles of Fluorescence Spectroscopy. Plenum Press,
New York, 1983.

R. Badley, Fluorescence Spectroscopy, Plenum Press, New York, 1983.

SA. Tucker, J.M. Griffin, W.E. Acree, J.C. Fetzer, M. Zander, O. Reiser, A.
Meijere, l. Murata, Polycyclic Aromat. Compd. 4 (1994) 141-160.

S.A. Tucker, J.M. Griffin, W.E. Acree, M.J. Tanga, J.E. Bupp. T.K.
Tochimoto, J. Lugtenburg, K. Van Haeringen, J. Comelisse, P.C. Cheng,
L.T. Scott, Polycycl. Aromat. Compd. 4 (1994) 161-172.

W.E. Acree, S. Pandey, S.A. Tucker, J.C. Fetzer, Polycycl. Aromat.
Compd. 12 (1997) 71-123.

F.K. Ogasawara, Y. Wang, V.L. McGuffin, Appl. Spectrosc. 49 (1995) 1-7.
C. Mao, S.A. Tucker, J. Chromatogr. A 966 (2002) 53-61.
S. Pandey, W.E. Acree, J.C. Fetzer, Talanta 45 (1997) 39-45.

S. Pandey, L.E. Roy, W.E. Acree, J.C. Fetzer, Talanta 48 (1999) 1103-
1110.

E. Sawicki, T.W. Stanley, W.C. Elbert, Talanta 1 1 (1964) 1431-1439.
J.V. Goodpaster, V.L. McGuffin, Anal. Chem. 72 (2000) 1072-1077.

S. Chen, C.E. Evans, V.L. McGuffin, Anal. Chim. Acta 246 (1991) 65-74.
D.C. Dong, M.A. Winnik, Can. J. Chem. 62 (1984) 2560-2565.

276

‘

[1 9]
[20]

[21]

[22]

[23]
[24]

[25]
[26]

[27]
[23]

[29]

DC. Dong, M.A. Winnik, Photochem. Photobiol. 35 (1982) 17-21.

L. DeWitt, G.J. Blanchard, E. LeGoff, M.E. Benz, J.H. Liao, M.G.
Kanatzidis, J. Am. Chem. Soc. 115 (1993) 12158-12164.

M. Dressler, Selective Gas Chromatography Detectors, Elsevier Science
Publishing Co., New York, 1986.

J.C. Gilbert, S.F. Martin, Experimental Organic Chemistry: A Miniscale
and Microscale Approach, 2"d Ed., Saunders, New York, 1998.

Y. Sakamoto, S. Watanabe, Bull. Chem. Soc. Jpn. 59 (1986) 3033-3038.

I. A. Shkrob, M. C. Sauer, A. Liu, R. A. Crowell, A. D. Trifunac, J. Phys.
Chem. A 102 (1998) 4976-4989.

Y. Ling, C. Lifshitz, J. Phys. Chem. 99 (1995) 11074-11080.

W. Xue, D. Zapien, D. Warshawsky, Chem. Res. Toxicol. 12 (1999) 1234-
1239.

R. Billotto, R. J. Levis, J. Phys. Chem. A 103 (1999) 8160-8168.

P. D. Burrow, A. J. Ashe, D. J. Bellville, K. D. Jordan, J. Amer. Chem. Soc.
104 (1982) 425-429.

M. A. Smith, J. W. Hager, S. C. Wallace, J. Chem. Phys. 80 (1984) 3097-
3105.

277

CHAPTER 8

CONCLUSIONS AND FUTURE DIRECTIONS

Chiral separations have gained more and more attention over the past
twenty years. At present, there are more than 200 chiral stationary phases
(CSPs) commercially available for direct chiral separation. But most chiral
separations are still accomplished by “trial-and-error" approach. The underlying
reason is the uncertainty of the chiral separation mechanism. Thermodynamic
and kinetic investigations can provide insight into the retention mechanism and

demonstrate how solutes interact with the stationary phase at the molecular level.
8.1 Theoretical simulations

Chapter 2 details the stochastic simulation method to validate models for
extracting thermodynamic and kinetic information. Both homogeneous surface
and heterogeneous surfaces are simulated. The accuracy was compared
between different models and the “true” kinetic method. The reliability for
extracting the retention factors follows the order: statistical moment method,
exponentially modified Gaussian (EMG) model, Giddings model, and Thomas
model. For the extraction of kinetic information, different parameters will
influence the relative accuracy of the different methods. With an increase in
column length, the rate constants from the statistical moment, Giddings, and
Thomas models are constant, while those from the EMG model increase.
Decreasing the linear velocity has the same effect as increasing the column
length. With a decrease in the stationary-phase diffusion coefficient or a

decrease of the interfacial mass transfer coefficient, the rate constants for all

278

models decrease and the zone profiles become broader with more asymmetry.
All models provide reliable extraction of kinetic rate constants with a change in
column length, velocity, diffusion coefficient, and mass transfer coefficient.
However, the rate constants deviate from the true kinetic data for all models with
a change in equilibrium constant in the homogeneous simulations and in all
heterogeneous simulations. This deviation may arise from poor fit of the
simulation data to the single exponential decay in the true kinetic method.

Based on these results, all of the examined methods yield reasonably
accurate values for retention factors and rate constants by comparison to the true
kinetic method. However, this comparison was performed under the perfect
conditions of a stochastic simulation, i.e., well defined column geometry, well
defined interaction sites, no variability in flow rate, temperature, or other
parameters, no extra-column contributions, no background or noise, and so on.
As such, the stochastic simulation does not provide a realistic and
comprehensive consideration of all aspects of this comparison. Only a
comparison performed with experimental data can reveal the ability of these
different methods to extract retention factors and rate constants under practical
conditions, where column and extra-column contributions to broadening and
asymmetry are not as well established. The experimental investigation is
definitely important for a complete validation of the models.

Although this dissertation validates the different mathematical models for
extracting thermodynamic and kinetic information, all the simulations are based

on the absorption mechanism. Thus, other possible direction for the stochastic

279

simulation is to validate different mathematical models with the adsorption
mechanism or with a mixed-mode mechanism. Many separation processes are
complicated, where one single mechanism is not adequate to explain the
separations. A novel simulation method on the adsorption mechanism has been

successfully proposed by Dr. Peter Krouskop [1].
8.2 Chiral separations

Chapters 4 and 5 detail the then'nodynamic and kinetic investigation of
chiral separation with a B-cyclodextrin stationary phase. The EMG model is
utilized for all data analysis. Successful chiral separations of coumarin-related
compounds are demonstrated. Three different effects are investigated, which
include the mobile phase effect (Chapter 4), and the temperature and pressure
effects (Chapter 5).

Mobile phase composition is the most important parameter affecting liquid
chromatographic separations. In this work, the mobile phase affects the
equilibration time, retention time, as well as peak shape. In a preliminary
experiment, two-component mobile phases containing only acetonitrile and
methanol cannot reach equilibrium even after several weeks. But both acid and
amine modifiers shorten the equilibration time greatly from weeks to one day or
less. Whereas the acetic acid modifier can increase the linear isotherm range
and ensure a Gaussian peak shape, the triethylamine modifier can dramatically
decrease the retention time while still enhancing chiral selectivity. In four-
component mobile phases, all of the coumarin-based solutes are within their

linear isotherm range and give reasonable thermodynamic and kinetic

280

 

information. The elution order is strongly dependent on the hydrogen bonding
ability between the solutes and the stationary phase. 4—Hydroxycoumarin has
the largest retention due to simultaneous interactions at the hydroxyl and
carboxyl sites. The chiral solutes are retained less due to steric effects and
intramolecular hydrogen bonding. The kinetic rate constants typically decrease
with an increase in retention factor. The mass transfer kinetics for 4-
hydroxycoumarin are much slower than those for the chiral molecules because of
the simultaneous interactions. For the chiral solutes, the second enantiomer has
a surprisingly higher mass transfer rate than the first enantiomer, although it is
more retained. This behavior suggests a difference in the kinetic contributions
for chiral and achiral selective sites. The concentration of each component in the
four-component mobile phase is varied to observe its individual effects.
Methanol can hydrogen bond with the stationary phase, thus decreasing
retention and increasing the kinetics for all solutes. Triethylamine decreases
retention, but enhances chiral selectivity by interacting with the hydroxyl group of
the solutes and with achiral selective sites of the stationary phase. But acetic
acid increases retention and reduces chiral selectivity by interacting with the
amine and with chiral-selective sites. Both acid and amine modifiers increase
adsorption and desorption rate constants. When both acid and amine are
present in the mobile phase, they tend to interact with each other and complicate
the separation process.

Temperature and pressure effects are usually neglected in liquid

chromatographic separations. However, these two parameters showed great

281

effects in chiral separations in Chapter 5. More detailed thermodynamic and
kinetic information are demonstrated. Increasing temperature from 283 K to 303
K decreases the retention for all solutes dramatically. The change in molar
enthalpy can be calculated through the slope of the van’t Hoff plot. A linear slope
indicates a constant change in molar enthalpy over the temperature range. A
positive slope indicates a negative change of molar enthalpy. All the solutes
exhibit an enthalpically favorable transfer from mobile to stationary phase. 4-
Hydroxycoumarin has the largest retention, but the least negative change of
molar enthalpy. For the chiral solutes, the trend of their change in molar enthalpy
does not always match the trend of their retention. Apparently, the change in
molar entropy has an important role in the separation. The second enantiomer
has a more negative change in molar enthalpy than the first enantiomer,
indicating an enthalpically more favorable process for the second enantiomer.
But the second enantiomer does not experience an entropically favorable
process in the transfer, which can be seen from the negative chiral difference in
molar entropy (AAS). No enthalpy-entropy compensation is observed among all
solutes, indicated by the scattered points between logarithm of retention factor
versus the change in molar enthalpy, as well as by the different co-elution
temperatures (T...) of all solutes. All the chiral separations are enthalpically
controlled processes. Increasing pressure decreases the retention for all solutes.
A positive change in molar volume is calculated from the slope of the logarithm of
retention versus pressure. The positive change in molar volume indicates no

inclusion into the cyclodextrin cavity occurred in this polar-organic mobile phase

282

composition. As to kinetics, increasing temperature increases kinetic rate
constants. Activation energies are positive for chiral solutes, with the second
enantiomer having higher activation energy than the first enantiomer.

With the B-cyclodextrin chiral stationary phase, more mobile phase
additives can be investigated. Instead of methanol, other organic modifiers such
as ethanol, propanol, and isopropanol could be tried; instead of triethylamine,
other basic modifiers such as hexylamine, diethylamine and triethanolamine
could be tried; instead of acetic acid, other acidic modifiers such as citrate acid
could be tried as well. In this dissertation, all of the separations are investigated
in the polar-organic mode. Coumarin-related compounds can also be separated
in reversed-phase mode as well. Due to the distinct difference in retention
mechanism, dramatically different results could be expected with similar studies
of the effects of mobile phase, temperature, and pressure. For the system for
chiral separation, a circular dichroism detector would facilitate the identification of
each enantiomer [2].

[3-Cyclodextrin is only one representative type of CSP, other types of CSP
could also be investigated in a similar manner. With more systematic research
on different types of chiral stationary phase, chiral separation mechanism would
not be a mystery any more. More standard guideline procedures could be
established and followed. Thus, “trial-and-error" approach could be eliminated

and huge amount of resources could be saved.

283

8.3 Characterization of nitrogen-containing polycyclic aromatic

hydrocarbons (N-PAHs)

N-PAHs are a particular group of environmentally toxic polycyclic aromatic
hydrocarbons (PAHs) that contain nitrogen. Complete chromatographic (Chapter
6) and spectroscopic characterizations (chapter 7) are carried out in this
dissertation.

A series of N-PAHs is separated on an octadecylsilica (ODS) column in
methanol as well as in acetonitrile mobile phases. In methanol mobile phase, the
retention factors for the N-PAHs are less than those for the parent PAHs, which
is consistent with the partition mechanism. In addition, the trends of retention
with ring number and annelation structure are also consistent with the partition
mechanism. N-PAHs have significantly smaller kinetic rate constants than those
of the parent PAHs, indicating the co—existence of an adsorption mechanism. In
the aprotic solvent acetonitrile, this adsorption mechanism dominates the
separation. The underlying reason is the hydrogen-bonding ability of methanol
with the N-PAH solutes as well as with the silanol groups. However, acetonitrile
is not able to shield interactions in this manner, hence the retention factors for
the aza-PAHs are substantially greater than those in methanol. The changes in
molar enthalpy are slightly more negative for these solutes, but not sufficient to
account for the large change in retention factor. Hence, a significant change in
entropy or the phase ratio must be responsible for the thennodynamic behavior.
The kinetic rate constants are two to four orders-of-magnitude smaller than those

in methanol. This behavior also reflects the increased role of adsorption. The

284

thermodynamic and kinetic information provides a much clearer description of the
retention mechanism of N-PAHs in reversed-phase liquid chromatography.
However, further studies with aqueous mobile phases and additives are desirable
for more thorough characterization.

Selective fluorescence quenching is demonstrated in Chapter 7 to
differentiate PAHs and types of N-PAHs. Aliphatic amines are chosen as
selective quenchers. From primary to tertiary amine, the quenching efficiency
increases while the selectivity decreases. Amino-PAHs remain unquenched by
aliphatic amines. Thus, aliphatic amines are able to differentiate amino-PAHs
and aza-PAHs by their dramatically different quenching constants. Also,
altemant aza-PAHs are quenched more efficiently than their corresponding
altemant PAHs. These two trends can be very helpful in addressing the difficulty
of identifying compounds in complex samples in the future. Direct and indirect
identification of N-PAHs with liquid chromatographic technique could be applied

in a similar manner as reported by Goodpaster and McGuffin [3,4].

285

8.4

[1]
[2]

[3]
[4]

References

P. Krouskop, Ph.D. Dissertation 2002, Michigan State University

H. Takahashi, T. Kashima, S. Kimura, N. Muramoto, H. Nakahata, S.
Kubo, Y. Shimoyama, M. Kajiwara, H. Echizen, J. Chromatogr. B 701
(1997) 71 -80.

J.V. Goodpaster, V.L. McGuffin, Anal. Chem. 73 (2001) 2004-2011.

J.V. Goodpaster, S.B. Howerton, V.L. McGuffin, J Forensic Sci. 46 (2001)
1 358-1 371 .

286

   

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