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dissertation entitled

An Investigation of the Feasibility of Using 13 Situ ATR
FTIR Spectroscopy in the Measurement of Crystallization
Phenomena for Research and Development of Batch
Crystallization Processes

presented by
Dilum D. Dunuwila

has been accepted towards fulﬁllment
of the requirements for

Ph.D. degree in _Ch_emi_c_él_Engineering

 

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AN INVESTIGATION OF THE FEASIBILITY OF USING HV SI TU ATR
FTIR SPECTROSCOPY IN THE MEASUREMENT OF
CRYSTALLIZATION PHENOMENA FOR RESEARCH AND
DEVELOPMENT OF BATCH CRYSTALLIZATION PROCESSES.

By

Dilum D. Dunuwila

A Dissertation

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

Doctor of Philosophy

Department of Chemical Engineering

1996

ABSTRACT

AN INVESTIGATION OF THE FEASIBILITY OF USING IN SI TU ATR
FTIR SPECTROSCOPY IN THE MEASUREMENT OF
CRYSTALLIZATION PHENOMENA FOR RESEARCH AND
DEVELOPMENT OF BATCH CRYSTALLIZATION PROCESSES.

By
Dilum D. Dunuwila

Bulk Crystallization from solution is one of the most widely used unit
operations in the food, pharmaceutical and chemical industries. However, a
systematic approach to process development and control of crystallization
processes has not been presented due to the lack of a technique capable of
meastning crystallization phenomena such as solubility and
supersaturation, in situ. ATR FI‘IR (Attenuated Total Reﬂection Fourier
transform infrared) spectroscopy provides a 1mique conﬁguration in which
theinﬁ'aredspectrum ofaliquidphase canbeobtainedina sltn'ry without
phase separation. Initially, the feasibility of the technique itself was

investigated using a Micro CIRCLE® Open Boat Cell equipped with a ZnSe
(zinc selenide) ATR rod. Experiments conducted with aqueous citric acid
proved that ATR FTIR spectroscopy can be successfully employed to
determine solubility and supersaturation.

Subsequently, establishing the technical feasibility of in situ ATR
FTIR spectroscopy for the measurement of crystallization phenomena was

undertaken. The viability of the technique for in situ measurements was

investigated using a DIPPER® 210 immersion probe manufactured by
Axiom Analytical, Inc., of Irvine, California. Initial experiments conducted
using aqueous maleic acid proved that ATR FTIR spectroscopy can be
successfully employed to measure supersaturation, solubility and the
metastable limit, in situ, with suﬁcient accuracy and precision.

Infrared spectra provide information about the chemical nature and
the molecular structure of chemical systems. Changes in molecular
structure are reﬂected in numerous ways in the IR spectrum.
Consequently, the full potential of FTIR spectroscopy as a tool to both
understand crystallizing systems and measm'e crystallization parameters
was explored. As such the broad scape of in situ ATR FTIR spectroscopy in
the ﬁeld of crystallization is demonstrated.

In this investigation, the versatility of in situ ATR FTIR spectroscopy
is demonstrated by its applicability in research and development of batch
crystallization processes and by its use for the elucidation of molecular
structures in supersaturated solutions in aid of understanding
crystallization phenomena. However, its potential for implementation in
control of crystallization processes, although promising, remains to be
proven. A methodology for the development of a control strategy is provided
along with other recommendations for further investigations.

iv

To Savi

Hydrocortisone crystallization
A practice in sleep deprivation
It tested his grit

But, he now fears to sit

Lest he sleeps through his own presentation

- Peter W. Burke
Pharmacia & Upjohn Company (1995)

ACKNOWLEDGMENTS

I would like to thank my advisor, Dr. Kris A. Berglund, for the
opportunities, the freedom and the guidance he provided toward my
professional growth during my tenure as a graduate student.

I am grateful to my wife, Savi, for her patience and support. I am also
grateful to my parents, Mallika and Robert Keerthi, and my sister, Vishani, for
all the encouragement I received over the years.

A special acknowledgment is due to my sister-in-law, Shirani Perera, her
husband, Dr. Priyantha Perera, and their daughter, Dilshani Perera, for their
hospitality and help extended to me during my early years in the United States
of America.

Many thanks to my colleagues, Dr. David Gagliardi, Dr. Everson
Miranda, Dr. Borlan Pan, Leslie Carroll II, Sanjay Yedur, Marketta Uusi-
Penttila, Chris Esswein, Klaus Weisphenig, Yilan Ling, Arvind Mathur, Laurie
Ruiz, Dr. Tom Carter, Dr. Beatrice Torgerson, Mark Torgerson and Dr. Hasan
Alizadeh, for making my tenure as a graduate student easier in numerous ways.

I would like to thank the members of my dissertation committee, Dr. Kris
A. Berglund, Dr. Alec Scranton, Dr. Robert Y. Ofoli, Dr. Stanley Crouch and Dr.
Clark Radcliﬂ'e for their time and eﬁ'ort. A special word of thanks to Dr. Clark
Radcliﬁ‘e for his participation in this venture.

I acknowledge the ﬁnancial support from the United States Department
of Agriculture and the Crop and Food Bioprocessing Center - Research
Excellence Fund at Michigan State University.

Finally, I would like to thank Dr. Mike Doyle, the President of Axiom
Analytical, Inc., for his continuing support for this venture.

TABLE OF CONTENTS

LIST OF TABLES .................................................................................................... ix

LIST OF FIGURES .................................................................................................. x
CHAPTER 1

INTRODUCTION ............................................................................................... 1

1. 1 Identiﬁcation and Signiﬁcance of the Investigation ......................... 1

1.2 References ................................................................................................ 8
CHAPTER 2

AN INVESTIGATION OF THE APPLICABILITY OF ATR FTIR
SPECTROSCOPY FOR MEASUREMENT OF SOLUBILITY AND

SUPERSATURATION IN SLURRIES ....................................................... 10
2.1 Background ............................................................................................ 10

2.2 Materials and Methods ........................................................................ 13

2.2.1 Construction of the Calibration Curves .................................. 15

2.2.2 Measm'ement of Solubility Using Slurries .............................. 16

2.3 Results and Discussion ........................................................................ 17

2.4 Conclusions ............................................................................................ 30

2.5 References .............................................................................................. 3 1

CHAPTER 3

AN INVESTIGATION OF THE FEASIBILITY OF ATR FTIR
SPECTROSCOPY FOR IN SI TU MEASUREMENT OF

CRYSTALLIZATION PHENOMENA. ......................................................... 32
3.1 Background ............................................................................................ 32
3.2 Materials and Methods ........................................................................ 33

3.2.1 Measurement of Solubility In Situ ........................................... 35
3.2.2 Measurement of Supersaturation In Situ .............................. 35
3.2.3 Measurement of CSD ................................................................. 35
3.2.4 Construction of the Calibration Curves .................................. 36

3.3 Results and Discussion ........................................................................ 36

3.3.1 Measurement of Solubility In Situ ........................................... 38

3.3.2 Measurement of the Metastable Limit In Situ ..................... 39

3.3.3 Measurement of Supersaturation In Situ .............................. 44

3.3.4 Calibrations .................................................................................. 52

3.4 Conclusions ............................................................................................ 54

3.5 References .............................................................................................. 55
CHAPTER 4

IDENTIFICATION OF FTIR SPECTRAL FEATURES
RELATED TO SOLUTION STRUCTURE FOR UTILIZATION IN

MEASUREMENT OF CRYSTALLIZATION PHENOMENA ................ 56

4.1 Background ............................................................................................ 56

4.1.1 Identiﬁcation of the Vibrations of the Carboxyl Group ........ 58

4.2 Materials and Methods ........................................................................ 59

4.2.1 Measurement of Solubility in Slurries ..................................... 60

4.2.2 Construction of the Calibration Curves .................................. 60

4.2.3 Data Processing ........................................................................... 60

4.3 Results and Discussion ........................................................................ 6 1

4.4 Conclusions ............................................................................................ 93

4.5 References .............................................................................................. 93
CHAPTER 5

CONTINUING INVESTIGATIONS ............................................................ 95

5. 1 Background ............................................................................................ 95

5.1.1 Control Strategy .......................................................................... 95

5.1.2 Solution Structure .................................................................... l 10

5.1.3 Effect of impurities ................................................................... 1 12

5.2 Conclusions ......................................................................................... 1 14

5.3 References ........................................................................................... 1 l4

APPENDD( ............................................................................................................ 116

LIST OF TABLES

Table 2.1 Comparison of experimental solubility measurements of
citric acid in water to literature values [5]. The given
solubilities are based on % (w/w). ............................................. 28
Table A1 Data for Figure 2.4 ................................................................... 1 16
Table A2 Data for Figures 2.5 and 2.6 .................................................. 1 17
Table A3 Data for Figures 2.7 and 2.8 .................................................. 1 18
Table A4 Data for Figures 3.3 and 3.5 .................................................. l 19
Table A5 Data for Figure 3.6 ................................................................... 120
Table A6 Data for Figure 3.7 ................................................................... 121
Table A7 Data for Figure 3.8 ................................................................... 122
Table A8 Data for Figure 3.9 ................................................................... 123
Table A9 Data for Figure 3.10 ................................................................ 124
Table A10.1 Data for Figure 3.11 ................................................................ 125
Table A10.2 Data for Figure 3.11 ................................................................ 126
Table A10.3 Data for Figure 3.11 ................................................................ 127
Table A10.4 Data for Figure 3.11 ................................................................ 128
Table A10.5 Data for Figure 3.11 ................................................................ 129
Table A10.6 Data for Figure 3.11 ................................................................ 130
Table All Data for Figure 4.5 ................................................................... 131
Table A12 Data for Figure 4.6 ................................................................... 132
Table A13 Data for Figme 4.10 ................................................................ 133
Table A14 Data for Figm'e 4.11 ................................................................ 134
Table A15 Data for Figure 4.12 ................................................................ 135
Table A16 Data for Figure 4.13 ................................................................ 136
Table A17 Data for Figure 4.17 ................................................................ 137
Table A18 Data for Figure 4.18 ................................................................ 138
Table A19 Data for Figure 5.4 .................................................... A ............... 1 39

Figm'e 1.1

Figure 1.2

Figure2.1

Figure 2.2

Figtn'e 2.3

LIST OF FIGURES

Comparison of cooling proﬁles for batch crystallization. These
proﬁles are not speciﬁc to any system. They are presented to
demonstrate the distinction between the three operating
policies .................................................................................................. 6
Projected supersaturation proﬁles as a consequence of
applying cooling proﬁle given for batch crystallization. ............. 7

A schematic diagram of the operation of internal reﬂection
spectroscopy. Infrared radiation is totally reﬂected at the
media interface and is propagated as a transverse wave. The
evanescent ﬁeld generated by infrared radiation penetrates
into the rarer medium in the z-direction as an exponentially
decaying wave. It is composed of electric vector components in
all spatial directions. IRE stands for internal reﬂection
element [1] . ....................................................................................... 1 1

The cross section of the Micro CIRCLE® Open Boat Cell
(Spectra-Tech) and its optical schematic. ATR stands for
attenuated total reﬂection [4]. ...................................................... 14
IR spectra of citric acid in water compared to the IR spectrum
of water. The arrows indicate the directions of change of the
spectrum as the concentration of citric acid in water is
increased. Spectra recorded here were taken at 35 °C.
Spectra at both 10 °C and 30 °C also followed the same

trend. .................................................................................................. 1 9

Figure 2.4

Figme 2.5

Figure 2.6

Figure 2.7

Figure 2.8

Calibration of RT,. RT1 is the transmittance ratio of the
transmission band at 3277 cm'1 to that at 2610 cm". The
solubilities indicated in the ﬁgure are literature values [5].
They were superimposed on the experimental calibrations to
demonstrate the extension of RT! into the supersaturated
region. ................................................................................................. 2 1
Calibration of RT2 at 10 °C. RT2 is the transmittance ratio of
the transmission band at 3277 cm‘1 to that at 1220 cm". The
solubility indicated in the ﬁgure is the literature value [5]. It
was superimposed on the experimental calibration to
demonstrate the extension of RT2 into the supersaturated
region ................................................................................................. 22
Calibration ofRT2 at 30 °C. RT2 is the transmittance ratio of
the transmission band at 327 7 cm'1 to that at 1220 cm”. The
solubility indicated in the ﬁgure is the literature value [5]. It
was superimposed on the experimental calibration to
demonstrate the extension of RT2 into the supersaturated
region. ................................................................................................. 23
Plot of RTl of slurries at equilibrium as a ﬁmction of
temperature. RT, is the transmittance ratio of the
transmission band at 3277 cm‘1 to that at 2610 cm“. Each
data point represents the average of measurements made
using three different samples. ....................................................... 25
Plot ofRTz of slurries at equilibrium as a function of
temperature. RT2 is the transmittance ratio of the
transmission band at 327 7 cm'1 to that at 1220 cm". Each
data point represents the average of measurements made
using three different samples. ....................................................... 26

Figure 3.1

Figure 3.2

Figtn'e 3.3

Figure 3.4

Figure 3.5

Figm'e 3.6

A schematic of the experimental setup.

a = spectrometer, b = ATR immersion probe, c = Crystallizer,
d = Chiller, e = Crystallizer temperature relay,

f = Product holding tank, g = Temperature controlled bath,

h = Buchner funnel, I = vacuum ................................................... 34
ATR FTIR spectra of aqueous maleic acid as the maleic acid
concentration (% w/w) was increased (a=50%, b=60%, c=65%
maleic acid in water). The arrows indicate the direction of peak
intensity movement with increase in maleic acid concentration.
The thick arrows indicate the peaks chosen for the
transmittance ratio, TR.

__ transmittance at 3394 cm’1

— transmittance at 1172 cm'1
Solubility of maleic acid with respect to TR measured in Situ, in
a slurry.

_ transmittance at 3394 cm'1
— transmittance at 1172 cm'1
Simulated desupersaturation proﬁles, (a), of cooling batch
crystallization. The desupersaturation proﬁles 1, 2 and 3
correspond to parabolic, linear and natural cooling proﬁles, (b),
respectively ....................................................................................... 4 1
The metastable limit of maleic acid, (Y,), measured at a cooling
rate of 1.3 °C/min. and a stirring rate of 420 rpm. The result of
one experiment is given for illustration purposes. For the given

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 3i

 

TR

................................................ 4O

 

TR

experiment, point X denotes the initial conditions and point Y1
denotes spontaneous nucleation. All points, Y,, were extracted
from similar experiments.

- -1
TR = transm‘ttance at 3394 cm 1 ................................................ 43

transmittance at 1172 cm'

 

Experimental cooling proﬁles. Proﬁles 1 and 2 are parabolic
cooling proﬁles and proﬁle 3 is a linear cooling proﬁle ............... 46

Figm'e 3.7

Figure 3.8

Figure 3.9

Figure 3.10

Figure3.11

Figtn‘e 4.1
Figure 4.2

Figure 4.3

The desupersaturation proﬁle corresponding to cooling proﬁle 1
given in Figure 3.6.

transmittance at 3394 cm'1
TR = 1 1 ................................................ 47
transmittance at 1172 cm'

The desupersaturation proﬁle corresponding to cooling proﬁle 2
given in Figure 3.6.

transmittance at 3394 cm’1
1 ................................................

 

 

TR = 48

transmittance at 1172 cm'
The desupersaturation proﬁle corresponding to cooling proﬁle 3

given in Figure 3.6.

transmittance at 3394 cm'1

TR = 1 ‘1 ................................................ 49
transmittance at 117 2 cm

Mass based product crystal size distributions (CSD). The

CSDs 1, 2 and 3 correspond to desupersaturation proﬁles 1, 2

 

and 3, respectively. The arrows indicate the mass based
average sizes of each size distribution. ....................................... 5 1
Calibrations of the transmittance ratio, TR, with respect to
temperature and maleic acid concentration (% w/w maleic acid
in water). The constant concentration lines were extracted
from the given experimental data.

 

transmittance at 3394 cm'1
TR = . _1 ................................................ 53
transmittance at 117 2 cm
Self association of carboxylic acids via H-bonding .................... 5 7
First, second, third and fourth derivatives of a Gaussian
peak ................................................................................................... 63
In situ, slurry ATR FTIR spectra of aqueous maleic acid at
saturation in the low frequency region. ....................................... 64

Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figm'e 4.8

Figure 4.9

Figure 4.10

First derivative proﬁles of the v(C=O) vibrational mode from

Figure 4.3. BL1=0.005 and BL2=-0.012 were the baselines
used for PIR1 and PIR2, respectively.

PIR,=(DA at 1740 cm'1 - a)/(DA at 1720 cm‘1 - a)

PIR2=(DA at 1740 cm’1 + b)/(DA at 1692 cm'1 + b)

a=0.005 and b=0.012 are the baseline adjustments,
DA=derivative absorbance ............................................................ 66
Solubility and concentration lines of maleic acid with respect to
PIR, measured in situ. In addition, solubility was measured in
a slurry.

PIR1=(DA at 1740 cm'1 - a)/(DA at 1720 cm‘1 - a)
DA=derivative absorbance

a=0.005 is the baseline adjustment ............................................. 67
Solubility and concentration lines of maleic acid with respect to
PH?2 measmed in situ. In addition, solubility was measured in
a slurry.

Pm,=(DA at 1740 cm’1 + b)/(DA at 1692 cm'1 + b)
DA=derivative absorbance

b=0.012 is the baseline adjustment ............................................. 69

Isolated second derivative proﬁles of the v(C=O) vibrational
mode of aqueous maleic acid at saturation. ............................... 7 1
First derivative proﬁles of the 5(O-H) in-plane deformation

vibrational mode from Figure 4.3. ................................................ 73
Bond distances and angles for the maleic acid molecule.

Bond distances are given in A and the angles are italicized for
clarity. ................................................................................................ 74
Solubility and concentration lines of maleic acid measured with
respect to the peak shift of the v(C=O) vibrational mode, in
situ. In addition, solubility was measured in a slurry. Absolute
peak positions at two conditions are shown for reference

purposes. ........................................................................................... 7 7

xiv

Figure4.11

Figure 4.12

Figm'e 4.13

Figure 4.14

Figtn'e 4.15

Figure 4.16

Figure 4.17

Figure 4.18

Solubility and concentration lines of maleic acid measured with
respect to the peak shift of the v(C-O) vibrational mode, in situ.

In addition, solubility was measured in a slurry. Absolute peak
positions at two conditions are shown for reference

purposes. ........................................................................................... 7 8
Solubility and concentration lines of maleic acid measured with

respect to the peak shift of the v(C=C) vibrational mode, in

situ. In addition, solubility was measm'ed in a slurry. Absolute
peak positions at two conditions are shown for reference

purposes. ........................................................................................... 79
Solubility and concentration lines of maleic acid measured with

respect to the peak shift of the 5(O-H) vibrational mode, in situ.

In addition, solubility was measured in a slurry. Absolute peak
positions at two conditions are shown for reference

purposes. ........................................................................................... 8 1
In situ, slun'y ATR FTIR spectra of aqueous maleic acid at
saturation in the high frequency region ....................................... 82

Gaussian components of the v(O—H) region. Due to the

closeness of the ﬁt the original spectral proﬁle (normalized and
baseline corrected spectrum at saturation at 30.75 °C from
Figure 4.14) and the six component Gaussian function used for

the ﬁt are superimposed ................................................................. 84
Peak shift of the component near 3150 cm'1 from
Figure 4.15. ....................................................................................... 86

Solubility and concentration lines of maleic acid measured with
respect to the peak shift of the v(O-H) vibrational mode, in situ.

In addition, solubility was measmed in a slurry. ....................... 87
Solubility of maleic acid in water with respect to % maleic acid
(w/w). .................................................................................................. 91

XV

Figure 5.1

Figure 5.2

Figure 5.3

Figm'e 5.4

Control policy projected to maximize the mean size of a crystal
size distribution from a cooling batch crystallization process.
The policy is based on maintaining a constant supersaturation

deﬁned by the IR parameters given by A(Pm) or 8(Pm).
Amy?) = Pm '- Pm,sol and
P112

50311;) =
PIR,sol

 

where Pm is any parameter discussed in Chapters 2, 3 and 4 in
the context of measurement of supersaturation and solubility
and Pm”, is the solubility with respectto Pm. ............................. 98
A simple schematic of a batch crystallizer and the primary
components of the envisioned control system.

T, = Inlet coolant temperature of the jacketed crystallizer,

To = Outlet coolant temperature, w = Coolant ﬂow rate,

A(P,R) = Supersaturation, E = Primary controller,
B = Heat removal system, D = Secondary controller,
H = Heat ﬂux from the crystallizer measured by

T,, To and w. ....................................................................................... 99
Block diagrams of the cascade control system. The normalized
heat removal secondary loop is illustrated in (b) .................... 10 1

A supersaturation proﬁle of aqueous citric acid represented in
terms of TIR.

. -1
TIR = transmittance at 3284 cm .......................................... 103

transmittance at 1190 cm'1

 

xvi

CHAPTER 1

INTRODUCTION

 

1.1 Identification and Significance of the Investigation

Crystallization from solution is a widely used unit operation in the
food, pharmaceutical, and chemical industries. Along with separation and
puriﬁcation, production of a speciﬁed crystal size distribution (CSD) is one of
the primary goals of a crystallization process. The CSD affects the cost of
operation of down-stream units such as ﬁltration equipment and dryers.
These are often the limiting steps in chemical manufacturing processes and
signiﬁcant cost reductions can be realized by creating CSDs that have
favorable ﬁltration and drying properties. Supersaturation is the driving
force for both crystal nucleation and growth and, as such, controls the rate
of crystallization and the resulting CSD [1, 2]. Therefore, control of
crystallization processes requires in situ measurement and subsequent
control of supersaturation. However, a technique that is suitable for in Situ
measurements has not been fully developed.

In today’s competitive environment, there is a need to implement
control strategies that provide a quantitative output that can be either used
by an operator or implemented in an automatic control scheme. A primary
impetus for improved control comes from the pharmaceutical industry
wherein nearly all products are crystallized at some point in their
production. Pharmaceutical processing is usually done in a batch mode,

which is often more diﬁicult to control than continuous processes primarily
because batch processes are nonsteady state operations. Another
consideration is batch-to-batch ﬂuctuations, which can cause considerable
variation in the crystallization process resulting in ﬁnal product divergence.
Reworking a batch that does not meet speciﬁcations incurs additional costs
and opens the opportunity for contamination.

Clearly, there is a need for the development of an in situ measuring
device for the dynamic parameters of crystallization processes. Numerous
analytical techniques for the measurement of solubility and supersaturation
of solutes in liquids have been proposed [3]. They range ﬁ'om simple residual
weight determinations to radioactive tracer methods. The primary difﬁculty
in using conventional analytical techniques (reﬁ'actometry, interferometry,
viscometry, density calibrations, etc.) is the procurement of a sample which
truly reﬂects the dynamic process composition at process conditions.
Generally, the separation of the saturated or the supersaturated solution
from the crystals is required prior to analysis. Percolation, decantation and
ﬁltration are common methods used for this separation. During separation
and subsequent transportation and analysis special care must be taken to
maintain process conditions, primarily temperature, and to avoid adsorption
of solute on any of the sampling and analytical equipment. In addition, the
analytical techniques themselves pose some difﬁculties. For example, in
reﬁ'actometry, changes in the refractive index as a function of temperature
and/or composition are small and often occur in the fourth decimal point.
Interferometry, on the other hand, poses considerable procedural

complexities.

This investigation presents a novel method for the measurement of
crystallization phenomena. The proposed technique, which is ATR FTIR
(Attenuated Total Reﬂection Fomier transform inﬁ'ared) spectroscopy [4] ,
provides a unique sampling conﬁgm'ation in which the infrared spectrum of
the liquid phase of a slurry (a mixture composed of a solution saturated or
supersaturated with a solute in contact with a dense suspension of the
undissolved particles of the solute) can be obtained without phase
separation. In ATR FTIR spectroscopy, the spectrum is characteristic of
the vibrational structure of the material in intimate contact with the ATR
apparatus. With regard to a slurry, the proposed approach is predicated on
the assumption that effective contact can be limited to that between the
liquid phase of the slurry and the ATR apparatus, thus allowing the
spectroscopic investigation of the liquid phase without its separation from
the suspended particles. The method has the potential to minimize
diﬁculties encountered in sampling and analysis through in Situ
measurement. Separation of the solution from the crystals is completely
avoided.

Initially, the feasibility of the technique itself was investigated using a

Micro CIRCLE® Open Boat Cell equipped with a ZnSe (zinc selenide) ATR
rod. Experiments conducted with aqueous citric acid proved that ATR FTIR
spectroscopy can be successfully employed to determine solubility and
supersaturation in slurries. The results are presented in Chapter 2.
Subsequently, establishing the technical feasibility of in situ ATR
FTIR spectroscopy for the measurement of crystallization phenomena was
undertaken. The approach was aimed at exploiting recent developments in

ATR FTIR spectroscopy for in situ measurement of supersaturation for the
purposes of analysis and control of crystallization processes. The results of
in situ measurement of supersaturation, solubility and the metastable limit
of aqueous maleic acid are presented in Chapter 3. In addition, a simple way

to extract the transient slurry density is outlined. The ATR apparatus used

in this study was the DIPPER® 210 immersion probe manufactured by
Axiom Analytical, Inc. of Irvine California, USA

Infrared spectra provide information about the chemical nature and
the molecular structure of chemical systems [5]. Infrared active molecular
vibrations absorb inﬁared radiation, thus generating a characteristic IR
spectrum. Reactions, changes in composition, introduction of new species
and temperature affect the molecular vibrational structure of a chemical
system. These changes are reﬂected in numerous ways in the IR spectrum,
the most prominent being peak intensity changes generally associated with
composition [6, 7]. Changes in molecular vibrational structure are
manifested in more subtle spectral features such as shifts in peak positions
[8]. These features, in addition to providing valuable insight to the
organization of solute and solvent molecules in supersaturated solutions,
can be extremely useful as a tool for measuring crystallization parameters.
This is particularly true with systems that have overlapping IR bands
where intensity changes are diﬁcult to isolate.

The discussion in Chapter 4 focuses on methods available to identify
and isolate subtle effects of IR spectra toward elucidation of solution
structure in supersaturated solutions and toward utilization in

measurement of crystallization parameters. Both derivative spectroscopy

[9] and deconvolution [9] of overlapping bands were used to isolate IR
absorption bands arising ﬁ'om various vibrational modes of maleic acid
sensitive to reorganizations in solution structure. Several parameters
suitable for measurement of solubility and supersaturation were identiﬁed
and the results are presented. In addition, some insight to the organization
of aqueous maleic acid in supersaturated solutions is provided.

Batch crystallizers operated under natural cooling are known to
produce a supersaturation peak at the onset of nucleation leading to high
rates of nucleation and excessive ﬁnes formation [1, 10]. This phenomenon
leads to fouling problems, reduced product yields and problems in
downstream product handling and processing that can be extremely
detrimental to the productivity of the process. The conventional method for
circumventing this phenomenon is to use programmed cooling methods [1,
10, 11], as illustrated in Figure 1.1, where the crystallizing system responds
to a programmed cooling proﬁle. The predicted time course of the
corresponding supersaturation proﬁles are given in Figure 1.2 [10].
However, this is an open-loop control method, in that, it does not allow
intervention to optimize the output through control of supersaturation,
which is the driving force for crystal nucleation and growth In large scale
industrial processes, batch-to-batch variations notwithstanding,
supersaturation can undergo random ﬂuctuations due to minor changes in
operating conditions. What is desired is a closed-loop control scheme that
responds to ﬂuctuations in supersaturation by adjusting the rate of cooling
and/or the rate of evaporation to maintain optimal conditions during the

operation. ATR FTIR spectroscopy provides an opportunity to investigate

Temperature (°C)

Figure 1.1

 

I
I iii I

 

 

 

 

 

 

 

60 +Parabolic
55 .’. .1 . +Linear
' +Natural

50 {-

45 4.

40 {-

35 {-

30 i

25 {-

0 36 72 108 144 180
Time (min)
Comparison of cooling proﬁles for batch crystallization. These

proﬁles are not speciﬁc to any system. They are presented to
demonstrate the distinction between the three operating
policies.

l 1
I j ' U I I ' ' '

+Parabolic cooling ‘
‘11— Linear cooling

0,012 ~- +Natural cooling

 

.4-

0.016'v-:-..

 

 

 

 

 

0.008

Supersaturation

0.004 '

 

 

 

 

Figure 1.2 Projected supersaturation proﬁles as a consequence of
applying cooling proﬁle given for batch crystallization.

the possibility of using in situ measurement of supersaturation in closed-
loop control schemes for industrial crystallizers. An outline for a possible
control strategy is presented in Chapter 5.

At this time development of a control strategy for batch
crystallization is recommended. The impetus for the focus on batch
crystallization is derived from the following considerations; the unsteady
state operation of batch crystallizers requires more robust control, current
trends in the competitive specialty chemical industry call for the
development of batch crystallization and the lack of attention batch
crystallization has received in general over time.

The scope of in situ ATR FTIR spectroscopy in crystallization is not
limited to its use in measurement of crystallization parameters. IR spectra
can provide valuable information to deduce the solution structure of
supersaturated solutions of various systems. A discussion on this topic is
given in Chapter 4 and is continued in Chapter 5. In addition, its potential to

study effects of impurities on various systems is discussed.

1 .3 References

1. Mullin, J. W., “Crystallization”, Butterworth-Heinemann, Oxford,
England, (1993).

2. Randolph, A D.; Larson, M. A, “Theory of Particulate Processes”,
Academic Press, New York, USA., (1988).

3. Zimmerman, H. K, Chemical Reviews, 51 (1952) 25.

4. Mirabella, Jr., F. M., Ed., “Internal Reﬂection Spectroscopy”, Marcel
Dekker, Inc., New York, USA, (1993).

5. Ingle Jr., J. D., Crouch, S. R., “Spectrochemical Analysis”, Prentice Hall,
Englewood Cliffs, New Jersey, (1987).

10.
11.

Dunuwila, D. D., Carroll II, L. B., Berglund, K A, J. Cryst. Growth,
137, (1994), 561.

Dunuwila, D. D., Berglund, K. A, Revised for publication in Ind. Eng.
Chem. Fundamentals, (1995).

Avram, M., Mateescu, GH. D., “Infrared SpectroscopyApplications in
Organic Chemistry”, Wiley-Interscience, New York, New York,
(1966), Ch.7.

Perkin Elmer IR Data Manager, User’s Manual, (1991).

Jones, A G., Mullin, J. W., Chem. Eng. Sci, 29, (1974), 105.

Mullin, J. W., Nyvlt, J ., Chem. Eng. Sci, 26, (1971), 369.

*
CHAPTERZ

AN INVESTIGATION OF THE APPLICABILITY
OF ATR FTIR SPECTROSCOPY FOR
MEASUREMENT OF SOLUBILITY AND
SUPERSATURATION IN SLURRIES

 

2.1 Background

Attenuated total reﬂection spectroscopy is based on the presence of
an evanescent ﬁeld in an optically rarer medium (lower reﬁ'active index) in
contact with an optically denser medium (higher refractive index) within
which radiation is propagated due to total internal reﬂection [1]. Figure
2.1 is a schematic of this phenomenon. The placement of an absorbing
optically rarer medium in contact with the denser propagating medium
facilitates the interaction between the evanescent ﬁeld and the absorbing
medium. The evanescent wave is a component of the propagating
electromagnetic radiation. Electromagnetic radiation conveys information
characteristic of matter interacting with its components. This is the basis
of most spectroscopic techniques regardless of the mode of operation
(transmission, internal reﬂection, etc.). Consequently, information
characteristic of the absorbing medium is conveyed by the propagating
radiation. For the current application, propagating infrared radiation
generates the characteristic infrared spectrum of the absorbing medium.

 

’ Dunuwila, D. D., Carroll 11, 1.3., Berglund, K. A, J. Cryst. Growth, 137, (1994), 561.

10

11

a"
I
.....
.-
o'.’
o.-
9"
n.-

 

    
 

 

 

 

; Reﬂected
IRE .; ------- 5 Wave
r: .. """
Z
Rarer Medium 1 Evanescent
(Sample) Wave

 

.-
.o
’0
O
.0
.0
o
I
a...
.o
I
.o
.-
.-
I
.-

D
.-
I.
I.-
.....
..
a"
I
O
n...

 

Figure 2.1 A schematic diagram of the operation of internal reﬂection
spectroscopy. Infrared radiation is totally reﬂected at the
media interface and is propagated as a transverse wave. The
evanescent ﬁeld generated by infrared radiation penetrates
into the rarer medium in the z-direction as an exponentially
decaying wave. It is composed of electric vector components
in all spatial directions. IRE stands for internal reﬂection
element [1].

12

The evanescent ﬁeld decays exponentially in the z-direction and

therefore its effect is conﬁned to the immediate vicinity of the media

interface (2-5 um). It follows that intimate contact between the medium

subjected to analysis and the propagating medium is essential for reliable
spectral analysis. The penetration of the exponentially decaying energy
ﬁeld is assessed by a parameter called the depth of penetration (dp) [2].

The depth of penetration is related to the angle of incidence (0) of the

propagating radiation on the internal reﬂection element (IRE), the

wavelength (A) and the refractive index of the analyte medium relative to

the denser propagating medium (am) as follows;

(1,, decreases as Oincreases

dp decreases as 2. decreases

dp decreases as n1,1 decreases (n2,< 1)

The extension of this technology for the measurement of
crystallization phenomena in slurries was based on the expectation that
there will be minimal contact between the crystals of a slurry and the IRE.
Minimal contact between the crystals of a slurry and the IRE minimizes
the interaction between the crystals and the evanescent ﬁeld allowing the
accumulation of solution phase properties without phase separation with
little or no interference from the crystals. It could be postulated that the
interaction of the evanescent ﬁeld is limited to the solution phase that
wets the IRE which in turn serves as a minute solution phase barrier that
hinders close contact between the crystals and the IRE. In this scenario,

13

the thickness of the wetting solution phase ﬁlm is expected to be greater
than the depth of penetration of the evanescent ﬁeld. In addition, d}D can

be decreased by manipulating 9, land n21. For example, an alternate ATR

conﬁguration that has a more favorable angle of incidence can be used.
Also spectral analysis can be conducted at lower wavelengths and/or an
IRE with a higher refractive index can be utilized.

2.2 Materials and Methods

The applicability of ATR technology toward determination of

solubility and supersaturation of solutes in solution using slurries was

investigated using a Micro CIRCLE® Open Boat Cell equipped with a
ZnSe ATR rod manufactured by Spectra Tech Inc, Stamford, CT, USA. A

schematic of the CIRCLE® cell is given in Figure 2.2. This conﬁguration
was particularly suited for preliminary experiments due to its open boat
construction into which solutions or slurries can easily be dispensed.
Temperature control was accomplished using a stainless steel heating
jacket designed to speciﬁcations that provide best contact between the

CIRCLE® cell and the jacket. The heating jacket was incorporated into
the structure of the Perkin-Elmer base plate designed speciﬁcally for the

use of the CIRCLE® cell. The jacket was constructed at the machine shop
of the Division of Engineering Research, Michigan State University. The
heating jacket was connected to a Lauda Brinkmann Refrigerating
Circulator R06. The infrared spectrometer was a Perkin-Elmer 1750

14

 

 

 

 

 

/ EE‘.--- \ A $ ‘ \;---)
Cone T

Micro Circle Open Boat Cell

Figure 2.2 The cross section of the Micro CIRCLE® Open Boat Cell
(Spectra-Tech) and its optical schematic. ATR stands for
attenuated total reﬂection. [4].

15

Infrared Fourier Transform Spectrometer connected to a Perkin-Elmer
7700 Professional Computer.

The solute-solvent system of choice was citric acid in water.
Crystalline citric acid monohydrate was obtained from Columbus Chemical
Industries Inc., Columbus, WI, USA.

2.2.1 Construction of the Calibration Curves

Appropriate amounts (weight) of citric acid monohydrate and
distilled water were placed in 20 ml Kimble disposable scintillation vials.
The mixtures were gently heated with a Master Heat Gun and stirred with

a Vortex Genie 2 Mixer, alternately, to homogeneous solutions. The

CIRCLE® cell was heated to the set temperature (10 °C and 30 °C) in the
heating jacket. The cell and the light transfer optics were aligned to obtain
an optimum energy throughput. The spectrum due to the empty cell was
scanned and stored as the background. Consequently, the sample
spectrum appears free of the background spectral information. The
solutions were dispensed into the cell using Pasteur pipettes. Solutions
were left standing in the cell for about 10 minutes to allow the solution
temperature to equilibrate with the set temperature (jacket temperature).
It was noted however, that less than 5 minutes was required for the
temperatures to come in to equilibrium. It was also noted that, at thermal
equilibrium, for all practical purposes, there was no difference in
temperature between the sample contained in the cell and the heating
jacket. The temperature within the cell was measured using an Omega
OL-703 linear response thermistor probe connected to an Omega Digicator
digital readout.

16

Sample spectra were recorded at the set temperature. The percent
transmittance at 327 7 cm“, at 2610 cm'1 and at 1220 cm‘1 were recorded
over a wide range of citric acid concentrations in water (approximately 0 -
70 % (w/w)). Data were collected at set temperatures 10 °C and 30 °C.
Between analysis of different samples the cell was rinsed ﬁrst with
distilled water and then with HPLC grade acetone (obtained from
Mallinckrodt Specialty Chemical 00., Paris, KY, USA). The acetone rinse
was to facilitate faster drying of the cell in preparation for the next sample
analysis.

2.2.2 Measurement of Solubility Using Slurries
A 150 ml batch reactor equipped with a heating jacket connected to

the Lauda Brinkmann circulator (same as that connected to CIRC LE® cell
heating jacket) was used to prepare slurries of citric acid and water. The
slurries were stirred with a Curtin Matheson Scientiﬁc 244-793 magnetic
stirrer. Slurries at solubility were prepared by dissolving an excess
amount of citric acid (an amount exceeding the anticipated solubility at a
given temperature) in distilled water, heating the mixture to a
homogeneous solution, cooling the solution to the set temperature to
facilitate nucleation and stirring for 24 hours to provide sufﬁcient time for
growth and equilibration. The temperature settings ranged ﬁum 10 °C to

35 °C. The preparation of the FTIR spectrometer and the CIRCLE® cell
was identical to the procedure described under the preceding subtitle. The
slurries at equilibrium were transported to the cell with a syringe (a 10 ml

disposable syringe was cut at the neck to provide a wider aperture that

l7

facilitated easy uptake and disposal of the slurry). Three slurry samples
were analyzed at each temperature.

2.3 Results and Discussion

According to the absorption law [3] the absorptance, a, can be
written as;

a = (1—T) = 1—e""’ (2.1)
where T is the transmittance, k is the absorption coeﬁcient and b is the
thickness of the absorbing medium. Note that Equation 2.1 is valid for
both absorption at an interface or surface and absorption within a medium.
Equation 2.1 can be solved to give;

T = e’“ (2.2)
In ATR spectroscopy the equivalent expression for the path length, b, for
absorption across an IRE interface is given by the product [4];

b = Nd p (2.3)
where N is the number of reﬂection points on the surface in contact with
the sample and d, is the depth of penetration.

A parameter that is often used for quantitative measurements when
using spectroscopic techniques for analysis is a ratio between peaks that
reﬂect the relative changes of the system. Peak-ratioing provides an
internal standard that can effectively eliminate errors due to imprecise
alignment of optical coupling attachments in analyzing subsequent
samples. Errors due to instrumental drifts are also minimized. There is

evidence to suggest that when peak-ratioing techniques are employed for

l8

analysis, calibrations developed using a particular IRE and a particular
angle of incidence of the radiation on the IRE, are equally valid for an
alternate IRE and an angle of incidence [1].

Let Tl be the transmittance of a characteristic infrared transmission
band of a solute dissolved in a given solvent. Let T2 be the transmittance
of a characteristic infrared transmission band of the solvent. Equations
2.2 and 2.3 yield;

T2 _ Ndpikl-kz)
— — 8
T1

(2.4)
where Itl and 122 are the absorption coefﬁcients of the solute and solvent
bands respectively. The dependence of d p on wavelength has been
neglected for the purpose of demonstration. The relative transmittance,
RT = Tle,, given by Equation 2.4, predicts an exponential gain in RT as
the concentration of the solute is increased (k1 is proportional to the solute
concentration). Therefore, RT is particularly suitable for measurement of
crystallization parameters since linear changes in concentration are
expressed by exponential gains in RT providing substantial signal gain for
the measurement. In addition, a measurement with minimum error is
provided by the peak-ratio.

In order to determine the solubility of citric acid in water it was
necessary to develop a calibration curve of RT vs. concentration of citric
acid in water. The calibration parameters were selected by observing the
relative spectral dynamics of the solute/solvent system.

FTIR spectra of aqueous citric acid solutions are given in Figure 2.3.

The decrease in intensity of inﬁared transmission bands of citric acid

19

 

 

 

 

100'....5....!....5....£-....L....
o % (w/w) Citric Acid 3
80 i I.
Q)
Q .
“ 1
c6
4.)
ECO-1H ii-
m b d
S: 1 .
CU . 1 .
@401 1 .-
50 D d
1 70% 1 j
20-. ] '._.
‘4 1
o ------------------- u ~ ,

 

 

l l l r A i n ‘ i ‘
3700 3200 2700 2200 1700 1200 700

Wavenumber (cm‘l)

Figure 2.3 IR spectra of citric acid in water compared to the IR spectrum
of water. The arrows indicate the directions of change of the
spectrum as the concentration of citric acid in water is
increased. Spectra recorded here were taken at 35 °C.
Spectra at both 10 °C and 30 °C also followed the same trend.

20

relative to that of water (in the vicinity of 3300 cm": OH stretching) is
clearly evident. Spectra at 10 °C and at 30 °C resemble those at 35 °C
given in Figure 2.3. Using the observed infrared spectra two calibration

parameters, RT, and RT,, were deﬁned;

transmittance of the water band at 3277 cm'1
transmittance of the citric acid band at 2610 cm’

RT _ transmittance of the water band at 3277 cm‘1
2 transmittance of the citric acid band at 1220 cm’1

 

RTl = 1

(2.5)

 

As previously discussed, the depth of penetration of the evanescent
ﬁeld into the sample is proportional to the wavelength of the radiation. As
a result, the possibility exists for the deeper penetrating energy ﬁelds at
higher wavelengths to interact with the undissolved particles. Therefore,
analysis at higher wavelengths could produce erratic data due to spectral
contributions from the solid state. To test the consequences of the
wavelength dependence of dp, the calibration parameters given in Equation
2.5 were deﬁned; one at a shorter wavelength, RT,, and the other at a
longer wavelength, R T2.

The plots of RT, vs. concentration of citric acid in water are given in
Figure 2.4. The temperature dependency of RT is expected due to
intermolecular and intramolecular interactions such as hydrogen-bonding.
The ﬁlled circles in Figure 2.4 represent literature solubilities of citric acid
in water [5] and they were incorporated into the ﬁgure to illustrate the
extension of the calibration curves into the supersaturated region. Figure
2.4 conﬁrms the exponential gain in RT predicted by Equation 2.4.

Plots of RT2 vs. concentration of citric acid in water are given in

Figures 2.5 and 2.6. The two calibrations, at 10 °C and at 30 °C, are not

21

 

 

 

0.6 .ﬁ+..ﬂt....:m14-11”“, e
+10°C ti
051: +30°C 1. “_
' . C Solubility 11' .
J

I 1
n '4 1
. '{I 1
0.4.: '1. .1.
. :loo .
E: 0.3-1 .- .‘.
m i- ..r‘ '0 i
J
:- :'.’. ‘
0.211 . .. i.

F . '

l D .p.

. .o 1
0.1-1: "0; ._
" 'IOO. .
r: :. '0 1
0 was

 

 

 

0 10 20 30 40 50 60 70
% (w/w) Citric Acid in Water

Figure 2.4 Calibration of RT,. RT, is the transmittance ratio of the
transmission band at 3277 cm‘1 to that at 2610 cm". The
solubilities indicated in the ﬁgure are literature values [5] .
They were superimposed on the experimental calibrations to
demonstrate the extension of RT, into the supersaturated
region.

22

 

L I l l L l
ftuv'vuuv—IWYVY'YTVII'VVIII-fiv'v

 

0 10 °C
C Solubility

 

 

 

-.-.l.---

RT

 

 

 

 

0 10 20 30 40 50 60 70
% (w/w) Citric Acid in Water

Figure 2.5 Calibration of RT, at 10 °C. RT, is the transmittance ratio of
the transmission band at 3277 cm‘1 to that at 1220 cm". The
solubility indicated in the ﬁgure is the literature value [5]. It
was superimposed on the experimental calibration to
demonstrate the extension of RT, into the supersaturated
region.

23

 

 

_ —e—30°C I °f
6 -_- 1 C Solubility

 

RT

 

 

 

 

% (w/w) Citric Acid in Water

Figure 2.6 Calibration of RT, at 30 °C. RT, is the transmittance ratio of
the transmission band at 3277 cm'1 to that at 1220 cm". The
solubility indicated in the ﬁgure is the literature value [5]. It
was superimposed on the experimental calibration to

demonstrate the extension of RT, into the supersaturated

region.

24

presented in the same ﬁgure due to considerable overlap of data. Here too,
the data conﬁrms the predicted exponential behavior of RT.

The reproducibility and the consistency of both calibration
parameters near and above the solubility of citric acid in water makes
them viable candidates for the measurement of solubility and
supersaturation. In addition, the exponential gain in RT provides more
gain for the measurement of supersaturation than concentration-based
approaches.

The traditional solubility and supersaturation measurement
techniques (refractometry, interferometry, viscometry, density
calibrations, etc.) measure a single calibrated parameter. However, IR
spectroscopy, which reﬂects the vibrational structure of the analyte, can
provide more than one piece of information. For example, in addition to
solubility or supersaturation, the presence of additives or impurities can be
monitored. Reaction dynamics of reactive
crystallization systems can be monitored. The advantage is that necessary
information can be obtained simultaneously using the same technique
without resorting to multiple techniques that are variable speciﬁc. The
broader scope of IR spectroscopy in crystallization is taken up in the
chapters to follow.

RT, and R T, of slurries at equilibrium were plotted against
temperature in Figures 2.7 and 2.8, respectively. They are the solubility
curves of aqueous citric acid with respect to RTs. The solubility of aqueous
citric acid with respect to % MW at 10 °C and at 30 °C was determined
using RT, and RT, of slurries at equilibrium and the respective calibration

25

 

-1-

 

 

 

0.55 n W, 1
0.5
0.45
sic-4
0.35
0.3
0.25;----;+1--,--U,UH:,_H: 1-- 1
5 10 15 20 25 30 35 40
Temperature (°C)

Figure 2.7 Plot of RT, of slurries at equilibrium as a function of
temperature. RT, is the transmittance ratio of the
transmission band at 3277 cm" to that at 2610 cm“. Each
data point represents the average of measurements made
using three different samples.

26

 

 

 

 

11 1 . ;. iw :1 1‘
10 J- 1.
Q'E :11-
81:. ..
e" -- 1.
a: 7 1 1
6.: ..
4:-b 1.
3’ A: u: U: A : A: -1 ‘

5 10 15 20 25 30 35 40

Temperature (°C)

Figure 2.8 Plot of RT, of slurries at equilibrium as a function of
temperature. RT, is the transmittance ratio of the
transmission band at 3277 cm“1 to that at 1220 cm". Each
data point represents the average of measurements made
using three different samples.

27

curves at the respective temperatures. Solubilities thus determined are
compared to literature values [5] in Table 2.1.

The percent deviation of the solubility determined using RT, from
the literature value is relatively small. These deviations are most likely
due to inadequate control in experimental procedure rather than due to
the analytical technique. Since this investigation, at this stage, was
primarily concerned with proving the viability of the concept, precise
control of the experiment was not implemented. For example,
disturbances due to temperature ﬂuctuations and solute adsorption on the

sampling apparatus during sampling of slurries were not controlled. A

difference of 1 °C between the reactor temperature and the CIRCLE® cell
temperature was observed. For these experiments the digital temperature
readout of the Lauda Brinkmann circulator and the digital readout
connected to the thermistor probe were not calibrated against a standard
thermometer.

Such procedural inadequacies were most likely responsible for the minor
deviations in measurement.

The measurement using RT, overestimates solubility by 3.7 % at 10
°C and by 10 % at 30 °C. It is apparent ﬁ‘om Figure 2.8 that the solubility
measured using RT, increasingly overestimates the solubility at higher
temperatures. As discussed before, RT, is a parameter that probes deeper
into the slurry compared to RT,. It is possible that signiﬁcant
contributions ﬁ-om the crystals of the citric acid slurry to the solution state
spectrum could result in an overestimation. However, it is not clear why

overestimation is increasingly higher at higher temperatures. Scattering

28

Table 2.1 Comparison of experimental solubility measurements of

citric acid in water to literature values. [5]. The given
solubilities are based on % (w/w).

 

 

Solubility - Solubility
Measurement “1115,65?th ExSp ($133,116,331 Given in the % Deviation
Parameter Literature
RT, 10 55.8 54.0 + 3.3
RT, 30 63.6 64.3 - 1.1
RT, 10 56.0 54.0 + 3.7

RTz 30 70.7 64.3 + 10.0

 

29

of data is also increasingly higher at higher temperatures. A likely cause
is not clear at this moment.

If the deeper penetration of the evanescent ﬁeld into the sample was
in some way responsible for the overestimation of solubility and scattering
of data, the employment of a greater angle of incidence for the radiation on
the IRE and an IRE with a higher refractive index (Ge and AMTIR-l ATR
elements) could help overcome such problems through the reduction of the
depth of penetration. Such parametric manipulations may be absolutely
necessary for solute-solvent systems that have transmission bands of
utility only at higher wavelengths.

Concentrations of supersaturated solutions of citric acid in slurries

were not measured using the CIRCLE® cell. The degree of control in the
crude sampling procedure followed in these experiments were deemed
inadequate to study the labile supersaturated region. It was a limitation
imposed by the procedure and certainly not by the technology. However, in
recognition of the feasibility of the technique for the measurement of
supersaturation, a few comments follows. Supersaturation, S, is deﬁned
by the following equation [6];

S=nln{ YC } (2.6)

quCeq

 

where 7 is the activity coefﬁcient, C is the concentration and n is the
number of ions in a molecular unit. The subscript "eq" denotes the solute-
solution equilibrium. The activity coefﬁcient, 7, reﬂects nonideality of

solutions. Generally, nonideal behavior is due to extensive intermolecular

30

and intramolecular interactions between the solute and the solvent. These
interactions in turn conﬁgure the solution structure of the system. Then,
it follows that the activity coefﬁcient is reﬂective of the solution structure
at a molecular level. Therefore, a method for determining supersaturation
that is reﬂective of the solution structure would be inherently more
accurate. However, due to practical restraints in measuring activities,
conventional techniques such as refractometry, interferometry, viscometry
and densitometry that measure the respective bulk properties are used
along with simplifying assumptions. However, IR spectroscopy, which
probes the vibrational and rotational structure of molecules is reﬂective of
the solution structure and therefore is a more viable technique to measure
supersaturation that is more reﬂective of activities. Recently, other
solution structure based methods such as ﬂuorescence spectroscopy have

been used to measure supersaturation in aqueous systems [7, 8].

2.4 Conclusions

This investigation clearly demonstrates the feasibility of ATR FTIR
spectroscopy toward measurement of solubility and supersaturation in
slurries. The exponential gain of the deﬁned parameters, RT, and RT,,
with increasing solute concentrations provides increased signal gain for
more accurate data analysis. The capability to carry out measurements
using slurries certainly eliminates the separation of phases required by
other measurement techniques. The feasibility of extending ATR FTIR
spectroscopy for in situ measurement of crystallization phenomena such as
solubility and supersaturation is explored in the following chapter. The

31

noted inconsistency in solubility measured using RT, and RT, is addressed

in Chapter 4.

2.5 References

1.

Mirabella, Jr., F. M., in: “Internal Reﬂection Spectroscopy”, Ed. F. M.
Mirabella, Jr., Marcel Dekker, Inc., New York, USA, (1993), ch. 2.
Harrick, N. J ., duPre, F. K., Appl. Opt, 5, (1966), 1739.

Ingle, Jr., J. D., Crouch, S. R., “Spectrochemical Analysis”, Prentice
Hall, Englewood Cliffs, USA, (1988), ch. 3.

Coates, J. P., in: “Internal Reﬂection Spectroscopy”, Ed. F. M.
Mirabella, Jr., Marcel Dekker, Inc., New York, USA, (1993), ch. 3.
The Merck Index, Ed. S. Budavari, Merck and Co., Inc., Rahway, USA,
(1989), 11th edition.

Garside, J ., Chem. Engng. Sci, 40:1, (1985), 3.

Chakraborty, R., Berglund, K. A, AIChE Symp. Ser., 88:284, (1991),
114.

Chakraborty, R., Berglund, K A, J. Cryst. Growth, 125, (1992), 81.

*
CHAPTER3

 

AN INVESTIGATION OF THE FEASIBILITY OF
ATR FTIR SPECTROSCOPY FOR IN SI TU
MEASUREMENT OF CRYSTALLIZATION
PHENOMENA

3.1 Background

Numerous analytical techniques for the measurement of
supersaturation of solutes in liquids have been proposed [1, 2, 3, 4, 5, 6].
They range from simple residual weight determinations to radioactive tracer
methods. The primary difﬁculty in using most conventional analytical
techniques for the measurement of supersaturation is the requirement of
phase separation for analysis. Both the presence of a slurry and the shiny
density can adversely affect the measurement. Consequently, such
techniques are not adequately suited for in situ measurement.

ATR FTIR spectroscopy [7] provides a unique sampling conﬁguration
in which the inﬁ'ared spectrum of the liquid phase of a slurry can be
obtained without phase separation. The approach was predicated on the
assumption that effective contact can be limited to that between the liquid
phase of the slurry and the ATR apparatus. The validity of the assumption
was veriﬁed in the study presented in Chapter 1 [8]. Substantial evidence
for the feasibility of ATR FTIR spectroscopy for the measurement of

 

' Dunuwila, D. D., Berglund, K. A, (in review) Ind. Eng. Chem. Fundamentals, (1995).

32

33

solubility and supersaturation was provided. However, the Micro CIRCLE®
Open Boat Cell used in the study presented in Chapter 2 was not conﬁgured
for in situ measurements. Therefore, the focus of this chapter is
establishing the technical feasibility of ATR FTIR spectroscopy for in situ
measurement of crystallization phenomena. This continuing effort was
inspired by recent developments in ATR FTIR technology in the form of
various ﬂexible radiation transfer systems and ATR conﬁgurations

particularly suited for in situ measurements. One such device is the

DIPPER® 210 immersion probe manufactured by Axiom Analytical, Inc. of
Irvine California, USA that was used in this investigation.

3.2 Materials and Methods

In situ measurements of supersaturation, solubility and the

metastable limit were performed using a DIPPER® 210 ATR FTIR
immersion probe equipped with an AMTIR- 1 conical internal reﬂection
element manufactured by Axiom Analytical, Inc. of Irvine, California, USA.
A simple schematic of the experimental setup is given in Figure 3.1.
Temperature control of the 2L baﬂled and jacketed glass crystallizer was
accomplished by a Lauda Brinkmann Refrigerating Circulator, model RC6.
The crystallizer was pln'chased from Lab Glass, Inc. Stirring was provided
by a 2" polystyrene marine impeller powered by a Fisher Scientiﬁc
StedFastn‘ stirrer, model SL600. The infrared spectrometer was a Perkin-
Elmer 1750 Infrared Fourier transform spectrometer connected to a

34

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figtn‘e 3. 1 A schematic of the experimental setup.
a = spectrometer, b = ATR immersion probe,
c = Crystallizer, d = Chiller, e = Crystallizer temperature relay,
f = Product holding tank, g = Temperature controlled bath,
h = Buchner funnel, I = vacuum

35

Gateway 2000 486DX2-50V micro computer and the spectrometer was
supported by Perkin-Elmer IRDM software. The slmry temperature was
recorded using an Omega RD-TEMP-XT temperature logger and monitored

umng an Omega OL-7 03 linear response thermistor probe connected to a

Omega DIGICAT0R® digital readout.

The solute-solvent system studied was maleic acid in water and
maleic acid was purchased from the Aldrich Chemical Company.
3.2.1 Measurement of Solubility In Situ

Solubility was measured in a slurry at temperatures ranging ﬁ'om
50°C to 67°C. At each temperature, solubility was approached both ﬁ'om
supersaturation and undersaturation in order to insure accuracy of the
measm'ements. At least ﬁve spectra were scanned per setting (i.e., at least
10 spectra at each temperature setting since solubility was approached
both from supersaturation and undersaturation).
3.2.2 Measurement of Supersaturation In Situ

A 63% (w/w) maleic acid solution (total weight was 2 kg) was slightly
supersatm'ated by cooling to 63°C, seeded and cooled by applying
predetermined cooling proﬁles. Two grams of 463 micron seeds were used.
Three distinct cooling proﬁles were used. The product crystals were collected
at 56°C. ATR FTIR spectra were accumulated every 20 seconds.
8.2.3 Measurement of CSD

The product crystals were vacuum ﬁltered and washed with ethyl
ether under vacuum immediately. The product was dried overnight at 45°C
in a Fisher Scientiﬁc ISOTEMP programmable oven, model 818F, before
subjecting to sieve analysis. Sieve analysis was done using a Tyler RX-86

36

sieve shaker.
3.2.4 Construction of the Calibration Curves

Appropriate amounts (weight) of maleic acid and distilled water were
placed in the crystallizer and heated to a homogeneous solution. The
solution was cooled while accumulating solution ATR FTIR spectra, in situ,
every 2 minutes until maleic acid spontaneously nucleated. A series of such
experiments ranging from 59 to 65 % (w/w) maleic acid was conducted. At

each weight percent, experiments were conducted in duplicate.

3.3 Results and Discussion

ATR FTIR spectra of aqueous maleic acid solutions are given in
Figm'e 3.2. The decrease in intensity of inﬁared transmission bands of
maleic acid relative to that of water (in the vicinity of 3400 cm*1: OH
stretching) as the maleic acid concentration is increased ﬁ‘om 50 to 65
%(w/w) is clearly evident.

In Chapter 2, the merits of using a transmittance intensity ratio
between a solvent band and a solute band as the entity that reﬂects
crystallization parameters were discussed and results that justify the use of
a transmittance ratio were presented [8]. Accordingly, we used, a
transmittance intensity ratio for in situ measurement of supersatm'ation,
solubility and the metastable limit. Technically, it is plausible to use any of
the maleic acid bands that appear in Figure 3.2 as the denominator of the
transmittance ratio. However, upon closer observation it was noted that
the band at 1 172 cm'1 is more sensitive to changes in solute concentration
than are the bands at 1222 cm'1 and 1707 ch. Therefore, the

37

80‘

70

 

60

50

% Transmittance

 

 

40‘
3800 3400 3000 2600 1700 1500 1300 1100

Wavenumber (cm-1)

Figure 3.2 ATR FTIR spectra of aqueous maleic acid as the maleic acid
concentration (% w/w) was increased (a=50%, b=60%, c=65%
maleic acid in water). The arrows indicate the direction of peak
intensity movement with increase in maleic acid concentration.
The thick arrows indicate the peaks chosen for the
transmittance ratio, TR.

_ transmittance at 3394 cm'1

TR " . -1
transmittance at 1172 cm

38

transmittance ratio, TR, was deﬁned as;

_ transmittance at 3394 cm'1

_ (3.1)
transmittance at 117 2 cm'1

 

TR

In the following discussion, we have chosen to represent solubility,

supersaturation and the metastable limit in terms of TR since TR, which is a

function of concentration and temperature, reﬂects these parameters
implicitly. Alternatively, crystallization parameters can be represented in
terms of concentration. In doing so, however, the useful signal gain provided
by the exponential gain in T, is sacriﬁced.
3.3.1 Measurement of Solubility In Situ

Achievement of equilibrium poses a signiﬁcant problem in
measurement of solubility. Often, prolonged agitation at constant
temperatme is necessary for systems to reach equilibrium. Contact for
days and weeks is not uncommon for some highly viscous solutions and
systems at relatively low temperatures. Substances of low solubility may
also require long contact times. Thus, the most convenient method for
measurement of solubility would be one that is suitable for in situ
measurements since a system approaching equilibrium can be monitored,
minimizing expended time and effort. As alluded to in the previous chapter,
conventional techniques do not meet these requirements. For example, it is
inconvenient to monitor a system steadily approaching equilibrium using
these techniques since portions of solutions have to be sampled ﬁequently
for analysis. However, continuous observation can be easily accomplished
through in situ utilization of ATR FTIR spectroscopy. In order to check the

accuracy of solubility determinations, it is recommended to approach

39

equilibrium from both the undersaturated and supersaturated states. The
capability of an in situ measuring device to continuously monitor the system
dynamics make such checks easier.

The solubility of maleic acid in water measured in a shiny, in situ, is
given in Figure 3.3. The data represent the average of T, obtained upon
approaching solubility from both the supersaturated state and the
undersaturated state. In both approaches, when there was no signiﬁcant
change in T,, the system was considered to be at or close to equilibrium.
Since the measured solubility can be the average of measurements ﬁ'om
both approaches, it is not necessary to prolong experiments lmtil
thermodynamic eqm'librium is reached. Thus, the technique is convenient
and time-saving. The experimental solubility data clearly demonstrate that
ATR FTIR spectroscopy can be used to measure crystallization parameters
in situ, in slurries, with a tolerable noise level. Certainly, these features of in
situ ATR FTIR spectroscopy manifests the viability of the technique for
application in process development of crystallization processes.

3.3.2 Measurement of the Metastable Limit In Situ

The metastable limit along with the solubility deﬁnes the operating
zone of bulk crystallization ﬁ'om solution as illustrated in Figure 3.4. The
metastable limit is the critical supersaturation at which point the system
nucleates spontaneously (primary nucleation) [9]. Therefore, the
dominating event of a system operating in the vicinity of the metastable

limit is primary nucleation. Primary nucleation generates an excessive

40

 

 

 

 

 

4.5 . . . - AT
52 54 56 58 60
Temperature (°C)

I U

62 64 66 68

Figm'e 3.3 Solubility of maleic acid with respect to T, measmd in situ, in
a slurry.

transmittance at 3394 cm'1

TR = . -1
transmittance at 1172 cm

41

 

 

Concentration
Temperature

 

 

 

 

 
 

Undersaturation

 

 

V

 

 

Temperature

(a)

 

Figure 3.4 Simulated desupersaturation proﬁles, (a), of cooling batch
crystallization. The desupersaturation proﬁles 1, 2 and 3
correspond to parabolic, linear and natural cooling proﬁles,
(b), respectively.

42

number of nuclei. Consequently, the average sizes of CSDs resulting from
desupersaturation proﬁles that approach the metastable limit are very
small. Such distributions can be overly taxing 0n ﬁltration and drying units,
driving up operation costs. Away ﬁom the metastable limit and close to the
solubility line, secondary nucleation (nuclei formed ﬁom collisions and shear)
and growth events are prominent. In this circumstance, due to the lack of
driving force, the limited number of nuclei grow slowly resulting in coarser
CSDs. Therefore, to meet CSD speciﬁcations, the level and the rate of
supersaturation should be maintained appropriately. The level of
supersaturation corresponding to target product speciﬁcations depend on
the width of the operating zone deﬁned by the metastable limit and
solubility. Therefore, the knowledge of the location of the metastable limit
will give engineers a better grasp on system behavior, allowing more
effective operations.

The metastable limit of a particular system depends on the
supersaturation rate and the hydrodynamic conditions of the crystallizer [9] .
Since the metastable limit depends on the hydrodynamic conditions of the
crystallizer, it is imperative that it be measured under the same conditions
that the material will be crystallized. ATR FTIR spectroscopy is a
particularly convenient technique that provides the opportunity to measure
the metastable limit in situ. The metastable limit can be measm'ed easily
as illustrated by experimental data in Figure 3.5. A homogeneous solution
at point X can be cooled while accumulating ATR FTIR spectra (T,
accumulated every 20 seconds) of the supersaturation proﬁle. At point Y,,

the system nucleates spontaneously and rapidly desupersaturates due to

43

 

      

 

 

 

 

 

 

8 i i iﬁ -
i
C
7.5 "': \ :1-
7 .1 X ,‘.
6.5 .E.
En: i i
6 .1 -'
1 .
5,5 .1:- 1
° Data 3
5 .L Solubility J.
C 5 + Metastable limit I
4.5’-~-:--~+~--:--~
50 55 60 65 70

Temperature (°C)

Figure 3.5 The metastable limit of maleic acid, (Y,), measured at a cooling
rate of 1.3 °C/min. and a stirring rate of 420 rpm. The result of
one experiment is given for illustration purposes. For the given
experiment, point X denotes the initial conditions and point Y,
denotes spontaneous nucleation. All points, Y,, were extracted
from similar experiments.

__ transmittance at 3394 cm'1
transmittance at 1172 cm'1

 

TR

44

excessive nucleation and growth. Thus, point Y, is one point of the periphery
of the operating zone for the given system under the implemented cooling
and stirring conditions. In this case, the cooling rate was 1.3 °C/min. and the
stirring rate was 420 rpm. The cooling rate implemented was the maximum
allowed by the capacity of the chiller. A series of experimental points, Y,,
constructs the metastable limit for the system under the given operating
condition.
3.3.3 Measurement of Supersaturation In Situ

The primary impetus for measurement of supersaturation, in situ, is
that it allows the estimation of kinetic parameters under hydrodynamic
conditions governed by viscous properties of the system, heat and mass
transfer properties and mixing patterns. The system kinetics in ttn'n
determine the process conditions. Crystallization process models indicate
that, to maintain a desupersaturation proﬁle as the one represented by
proﬁle number 1 of Figure 3.4, the temperature proﬁle implemented should
be parabolic in time [10, 11]. The initial rate of cooling corresponding to a
parabolic cooling proﬁle is very low and it increases progressively over the
course of the batch time. On the other extreme, a natural cooling proﬁle
(uncontrolled cooling) leads to a supersaturation proﬁle (proﬁle number 3)
that approaches the metastable limit resulting in extremely ﬁne CSDs. The
desupersaturation proﬁle corresponding to the linear cooling proﬁle may
follow a course as the one depicted by proﬁle number 2. The challenge in
process development of batch crystallization is to ascertain the appropriate
controlled cooling proﬁle. The proﬁle cannot be any parabolic or linear proﬁle
because the coemcients of the proﬁle depend signiﬁcantly on the kinetics of

45

the particular system under operating conditions. Therefore, a consistent
set of kinetic parameters that adequately describe process behavior is
necessary for process development leading to efﬁcient operation of
crystallization processes. Models to extract growth kinetics ﬁ'om batch
crystallizers and models to analyze batch crystallizers have been developed
[12]. However, the use of kinetic models or the application of behavior
models for industrial batch crystallizers has been stymied by the
unavailability of an in situ measuring device for supersaturation which is
the driving force for all crystallization phenomena. In essence, the
prerequisite for the determination of coeﬁcients of controlled cooling proﬁles
satisfying product speciﬁcations based on system kinetics is the ability to
measure supersaturation in situ.

In order to demonstrate the importance of in situ measurement of
supersaturation for process development and control purposes and the
effect of small changes in supersaturation on the product CSDs, the results
of three experiments are presented. Results of each of the three
experiments consist of a cooling proﬁle, the corresponding desupersaturation
proﬁle and the resulting product CSD.

The three cooling proﬁles are given in Figure 3.6. They are identiﬁed
as parabolic, intermediate parabolic and linear cooling proﬁles. The
corresponding desupersaturation proﬁles are given in Figures 3.7 (parabolic),
3.8 (intermediate parabolic) and 3.9 (linear). The differences in the course of
desupersaturation corresponding to the cooling proﬁles are clearly evident.
The generation of a supersaturation peak as in the case of the
desupersaturation proﬁles corresponding to the intermediate parabolic and

46

 

64 .1 . . : . . r +Parabolic
-5- Intermediate parabolic
+Linear

 

  

 

 

 

 

Temperature (°C)

  

 

 

 

O 360 720 1080 1440 1800

Time (sec.)

Figure 3.6 Experimental cooling proﬁles. They are identiﬁed as parabolic,
intermediate parabolic and linear cooling proﬁles.

47

 

   

 

 

 

 

 

 

 

 

7.5-; ,-; -:e'-
+ I,
7 "’ .1 )-
Elm 6.5 "' I,” .-
, I," 0 Experimental Data
6 -~,I’ — Smoothed Data
f
, —Solubi].ity
’ """ Metastable Limit
5.5 I If . - - 1' - 4 - 1
56 58 60 62 64
Temperature (°C)

Me 3.7 The desupersaturation proﬁle corresponding to the parabolic
cooling proﬁle given in ﬁgure 3.6.
_ transmittance at 3394 cm’1

TR - . _1
transmittance at 1172 cm

 

48

 

 

 

 

 

 

 

 

7.5 . i . . . i . . . : , i, , g . . ' .
b ’I
D i” &
t I," g 36.3"... C}? j
7 .. .,' . 0 4P
1 0 o .
a; . ' i
a: ’ ’1’ .." t
E 6'5 -- 'I’ ”’10 'l'
P 1’ 00.1 1
. ’1” o ..,' 0 Experimental Data
6 '2" . 1’ —Smoothed Data
' _./ —Solubil.ity
, 7"" """ Metastable L1m' it
56 58 60 62 64
Temperature (°C)

Figure 3.8 The desupersatmation proﬁle corresponding to the
intermediate cooling proﬁle given in Figure 3.6.
_ transmittance at 3394 cm'1
transmittance at 117 2 cm'1

 

TR

49

 

 

 

 

 

 

 

 

7.5 i t : r; . : . - -
L x
L "I . o 0 °
I, O
7 . x. .
Em 6'5 ‘ ’X o o ‘
b I 1
; I," , - 0 Experimental Data
6 u," . — Smoothed Data
f —Solubi1ity
/‘ ----- Metastable Limit
55- “‘:r“:‘*‘:“‘1.
56 58 6O 62 64
Temperature (°C)

Figure 3.9 The desupersaturation proﬁle corresponding to the linear
cooling proﬁle giveninFigin'e3.6.

_ transmittance at 3394 cm'1

TR - . -1
transmittance at 1172 cm

 

50

the linear cooling proﬁles or the lack thereof as in the case of the
desupersaturation proﬁle corresponding to the parabolic cooling proﬁle,
essentially determines the characteristics of the ﬁnal product CSD [1 1].
The magnitude of the supersaturation peak depends on the implemented
cooling proﬁle. Thus, we emphasize the importance of extracting kinetic
information from in situ measurements in order to determine the
appropriate cooling proﬁle. Consequences of implementing the wrong cooling
proﬁle can be detrimental. A faster rate of cooling will drive the system
closer to the metastable limit resulting in a ﬁner CSD than that speciﬁed
causing operation problems at ﬁltration and drying steps. On the other
hand, unnecessarily slow cooling rates can stagnate the operation due to
inadequate driving force resulting in unreasonably long batch times.

The experimental cooling proﬁles in Figure 3.6 were not based on
system kinetics, rather they were chosen and implemented based on prior
experience with the system to demonstrate the eﬁ‘ect of diﬂ'erences in
supersaturation on product CSDs. However, as part of this ongoing eﬁ'ort,
the corresponding desupersaturation proﬁles will be used to extract kinetic
parameters that will enable the determination of cooling proﬁles appropriate
for speciﬁed CSDs. The subject is taken up in Chapter 5.

The mass based product CSDs resulting from desupersaturation
proﬁles corresponding to the three cooling policies are given in Figm'e 3.10.
The average size of the CSD resulting from the parabolic cooling proﬁle is
about 760 microns. The average size of the CSD resulting ﬁom the linear
cooling proﬁle is about 440 microns. The average size of the product
resulting from the parabolic proﬁle is nearly double in comparison to that

CSD (% weight)

Figure 3.10

51

l
I

 

 

 

 

 

 

 

 

 

50 i 4 5 i I
. a +Parabolic
. f E. "I- Intermediate paraboli
4o -_- 5 ]440 --0-Linear
L i' l i
. g i 760
. i 1
3o .. f i
* i i
L g g
’
20 .. :1
. .5 a,”
i ,l.‘
10 q- '0' ‘
, 3' f
If 0'
to
0 ' t
200 400 600 800 1000

Size (microns)

Mass based product crystal size distributions (CSD). The
CSDs 1, 2 and 3 correspond to desupersaturation proﬁles 1, 2
and 3, respectively. The arrows indicate the mass based

average sizes of each size distribution.

52

resulting ﬁom the linear proﬁle. The changes in CSD characteristics are
signiﬁcant. This evidence underscores the importance of implementing the
cooling proﬁle beﬁtting the speciﬁed CSD. Thus, it is anticipated that the
ability to measure crystallization parameters, especially supersaturation,
in situ, will have a considerable impact on the efﬁciency of process
development and control of batch crystallization processes.

3.3.4 Calibrations

Calibrations can serve two purposes. First, they demonstrate that
ATR FTIR spectroscopy, TR, provides a true reﬂection of system variables.
More importantly, calibrations provide the basis to extract the transient
crystal slurry density. The slim-y density is an explicit parameter in most
batch crystallization process models [12, 13].

The calibrations of TR for aqueous maleic acid with respect to
temperature and concentration (% w/w maleic acid in water) are given in
Figure 3.11. The plot consists of a three parameter grid comprising TR,
temperatme and concentration on which the experimental solubility has
been superimposed. Each point where the solubility line crosses the
concentration lines indicates the solubility of maleic acid in water with
respect to the solution concentration which is the more conventional way of
representing solubility. This data is within 3% of the solubility data given in
[9] . The accuracy of the current experimental data conﬁrms that ATR
FTIR spectroscopy is well suited to measure crystallization parameters.

Secondary nucleation depends on the slurry density. Therefore, slurry
density is an explicit parameter in most batch crystallization process
models. It is important to be able to measure the transient slurry density to

53

Ill-
-
)

8--r--g----;-,-- "T‘"'.%(w/w)
.. . .
Solubihty v 165%

i 64%
63%
j- 62%

‘. 61%

j_ 60%

 

 

70

Temperature (°C)

Figure 3.11 Calibrations of the transmittance ratio, T3, with respect to
temperatm'e and maleic acid concentration (% w/w maleic acid
in water). The constant concentration lines were extracted
from the given experimental data.

_ transmittance at 3394 cm’1
transmittance at 117 2 cm’1

 

TR

54

extract kinetic parameters and to accurately emulate system behavior.

The equation;

C=(a1+a2xT+a3xT2)(bz+b2xTR+b3xT3) (3.2)

where T is the temperature, 01=l.079, a2=-1.6989x10“3, a3=5.7812x10“,

b1=40.39, b2=5.4039 and b3=-2.77O4x10'°1, gives the solution concentration
of maleic acid in water at any point in the three parameter grid of Figure
3.11. Using this equation, the mass balance, the initial conditions and the
batch volume, the transient slurry density can be easily calculated.

There is a noticeable increase in the noise level of the calibration data
compared to the solubility data. This is due to the accumulation of air
bubbles on the sensing head of the internal reﬂection element of the
immersion probe. Air bubbles were a problem in the 2L crystallizer used for
these experiments since its built-in baﬂle design is not adequate to
completely avoid vortex formation. In the presence of a slurry, however, the
crystals of the slurry inhibit the accumulation of air bubbles on the sensing
head. Consequently, the noise level is dramatically reduced. This is clearly
demonstrated by the low noise level in the solubility data that were
measured in slurries. It is anticipated that air bubbles will not cause
signiﬁcant problems since the true measuring environment for

crystallization parameters is a slurry.

3.4 Conclusions

The primary objective of this effort was to investigate the feasibility

of ATR FTIR spectroscopy for in situ measurement of crystallization

55
parameters, especially supersaturation. To this end, the data have not only

demonstrated that in situ ATR FTIR spectroscopy is well suited to measure
supersaturation, the data have also demonstrated that ATR FTIR
spectroscopy is sensitive enough to measure small changes in
supersaturation that lead to signiﬁcant changes in product CSDs. It is
anticipated that the technique will be useful in process development and
control of batch crystallization, providing for improved product

quality/reproducibility and reduced energy utilization and cost of operation.

3.5 References

1. Zimmerman, H. K., Chem. Rev., 51, (1952), 25.

2. Liszi, I., Halasz, S., Bodor, B., in: “Industrial Crystallization 87:
Process Technology Proceedings, 6”, Ed. Nyvlt, J. ; Zacek, S., Elsevier,
New York, USA., (1989), 399.

3. Ymamoto, H., Sudo, S., Yano, M., Harano, Y., in: “Industrial
Crystallization 87 : Process Technology Proceedings, 6”, Ed. Nyvlt, J .;
Zacek, S., Elsevier, New York, USA, (1989), 403.

4. Myerson, A S., Rush, S., Schork, F. J ., Johnson, J. L., in: “Industrial
Crystallization 87: Process Technology Proceedings, 6”, Ed. Nyvlt, J .;
Zacek, S., Elsevier, New York, USA, (1989), 407.

5. Miller, S., Rawlings, J. B., AIChE J, 40:8, (1994), 1312.

6. Nyvlt, J ., Karel, M.; Pisarik, S., Cryst. Res. Technol., 29, (1994), 409.

7. Mirabella, F. M., Ed., “Internal Reﬂection Spectroscopy”, Dekker,
New York, USA., (1993).

8. Dunuwila, D. D., Caroll 11, L. B.; Berglund, K. A., J. Cryst. Growth, 137,
(1994), 561.

9. Mullin, J. W., “Crystallization”, Butterworth-Heinemann, Oxford,
England, (1993).

10. Mullin, J. W., Nyvlt, J ., Chem. Eng. Sci., 26, (1971), 369.

11. Jones, A. G., Mullin, J. W., Chem. Eng. Sci., 29, (1974), 105.

12. Tavare, N. S., Separation and Puriﬁcation Methods, 22:2, (1993), 93.

13. Randolph, A. D., Larson, M. A, “Theory of Particulate Processes”,
Academic Press, New York, USA., (1988).

*
CHAPTER4

 

IDENTIFICATION OF FTIR SPECTRAL
FEATURES RELATED TO SOLUTION
STRUCTURE FOR UTILIZATION IN
NIEASUREMENT OF CRYSTALLIZATION
PHENONIENA

4.1 Background

Carboxylic acids are generally characterized by vibrational modes of

the carboxyl group [1]. Of the six vibrational modes of the carboxyl group,
the v(C=C), v(C-O) and v(O-H) stretching vibrations and the 5(O-H) in-plane

deformation vibration produce prominent fundamental IR absorbtion bands
in the 1100-3000 cm" region of the mid-IR spectrum. The nomenclature is
discussed in [2]. The distinctive structure of the carboxyl group facilitates
association of carboxylic acids through hydrogen bonding [1]. Association of
carboxylic acids is illustrated in Figure 4.1. Formation of these dimers
lowers the force constant of the v(C=C) and the v(O-H) vibrations and the
frequency of the vibrations [3, 4]. The large decrease in ﬁequency as a
result of the transition ﬁom the monomeric to the associated form is

evidence for the exceptional strength of hydrogen bonds. Hydrogen bonds,

due to their strength, are largely responsible for the solution and crystal

 

' Dunuwila, D. D., Berglund, K. A., Submitted to Trans. I. ChemE., (1995).

56

Figure 4.1

57

/O----H—O\
R—C /C —R
\O—H-n-O/

Self association of carboxylic acids via H-bonding.

58

structure of carboxylic acids. Consequently, any change in solution
structure due to reactions, changes in composition, introduction of new
species and temperature is reﬂected by spectral features produced by
molecular vibrations affected by hydrogen bonding.

Carboxylic acids can form complexes with polar solvents via hydrogen
bonds [1, 5, 6, 7]. Depending on the proton donor/acceptor strengths of polar
solvents, carboxylic acids can form hydrogen bonds either by the
participation of the carbonyl oxygen or the hydroxy group. However,
intermolecular hydrogen bonding of dissimilar species is signiﬁcantly weak
compared to that of the same species.

4.1.1 Identiﬁcation of the Vibrations of the Carboxyl Group

The v(O-H) Stretching Vibration: The v(O-H) vibration for monomeric
carboxylic acids is observed around 3500-3570 cm'1 [1, 8, 9]. The
monomeric form occurs only in the vapor phase and in dilute solutions of
nonpolar solvents. The broadened v(O-H) band of the associated form is
observed over the range 2700-3100 cm‘1 [1, 3, 4, 10, 11]. The associated
form, either dimeric or polymeric [9, 12] , occurs almost exclusively in solid
state, liquid state and in concentrated solutions. The shift of the v(O-H)
band to lower ﬁ'equencies upon association is characteristic of carboxylic
acids. In addition, the broad band generally appears as a convoluted band

made up of several bands. A simple interpretation is that the overlapping

bands are due to a number of hydrogen bonds of varying lengths resulting
ﬁom the complexity of associations [1]. An alternate interpretation is that

this is due to coupling of the v(O-H) fundamental with several other low

59

frequency vibrational modes of the associated form [1, 13]. Other

explanations are available [10].
The v(C=O) Stretching Vibration: The v(C=O) vibration for monomeric
saturated aliphatic carboxylic acids is observed around 17 80:15 cm‘1 [1, 3,

9]. The v(C=O) vibration for the associated form of saturated

monocarboxylic acids (liquid and solid state) is found around 1710i10 cm'1
[1, 3, 9, 10, 11] demonstrating the shift to lower frequencies upon
association. Both the monomer (around 1760 cm") and the dimer (around
1710 cm“) are observed in the case of many carboxylic acids in nonpolar

solvents [1, 14].

The v(C-O) Stretching and the 5(O-H) In-Plane Deformation

Vibrations: Coupling of the v(C-O) stretching and the 5(O-H) in-plane

deformation vibrations occurring in the plane of the ring formed by the
association of carboxylic acids result in two bands around 1420i20 cm'1 and

1300:]:15 cm'1 [1, 10, 11, 15]. The band at 1420 is assigned to v(C-O) and the

band at 1300 is assigned to 5(O-H) [3]. These bands are reported to appear

only under conditions that promote association via hydrogen bonding [1, 15].
These two bands are reported to shift in the opposite direction to that of

v(C=O) and v(O-H) upon association [3, 9].

4.2 Materials and Methods

All details regarding the experimental setup and instrumentation are
given in Chapter 3 and [16]. The protocols for the accumulation of solubility

60

data and data corresponding to the constant concentration lines are outlined
below. Further details are given in Chapter 3 and [16].
4.2.1 Measurement of Solubility in Slurries

Solubility was measured in a slurry, in situ, at temperatures ranging
from 30°C to 70°C. At each temperature, ten spectra were scanned.
Therefore, the plotted data represent the average of ten measurements. An
equilibration time of about one hour was allowed for the slurry at each
temperature setting. A slurry equilibration time of one hour was determined
to be sufﬁcient by monitoring the system approaching equilibrium both ﬁ‘om
supersaturation and undersaturation.
4.2.2 Construction of the Calibration Curves

Appropriate amounts (weight) of maleic acid and distilled water were
placed in a 2 L crystallizer and heated to a homogeneous solution. The
solution was cooled while accumulating solution ATR FTIR spectra, in situ,
every 2 minutes until it spontaneously nucleated. A series of such
experiments ranging ﬁ'om 50 to 65 percent maleic acid by weight was
conducted.
4.2.3 Data Processing
Deconvolution: The spectral region between 2750-3700 cm“1 was decon-
voluted as follows. The given region was isolated ﬁ‘om rest of the spectrum.
The baseline of the absorbtion spectra was ﬁxed at 37 00 cm'1 (that is,
absorbance at 3700 cm'1 was set to zero). Spectra were normalized at 3490
cm". All spectral proﬁles were ﬁtted to a function consisting of six Gaussian
components using the “leastsq” least squares minimization function
available in the professional version of the MATLAB optimization toolbox.

61

The six-component Gaussian function provided the best ﬁt for the spectral
proﬁle. The contribution of each component to the spectral proﬁle was
generated using the adjustable parameters (peak position and standard
deviation (peak width at half maximum» of the corresponding Gaussian
distribution.

Derivative Spectra: The derivative spectra of ATR FTIR absorbtion
spectra were obtained. The peak positions of all the identiﬁed maleic acid
vibrational modes and the useful peak intensities (intensities used to
compute PIR1 and PIRZ) were extracted from the derivative spectra and
tabulated. This otherwise tedious task was simpliﬁed by using the user
programmable OBEY programming utility available in the Perkin-Elmer
IRDM software.

4.3 Results and Discussion

As discussed earlier, the primary focus of this paper was to
investigate the methods available to identify and isolate the subtle features
of IR spectra, that are susceptible to changes in solution structure, for
utilization in measurement of crystallization parameters. Changes in
molecular vibrational structure are manifested in spectral features such as
shifts in peak positions and peak widths that may not be readily apparent
[1] . Both derivative spectroscopy [17] and deconvolution [17] of overlapping
bands can be used to isolate peak position and peak width shifts of IR
absorbtion bands arising from reorganizations in solution structure.
Derivative spectroscopy, which is a standard menu option in FTIR software,
is the more straightforward method of the two and thus will be discussed

62

ﬁrst. Although, some FTIR instrument manufacturers include a
deconvolution algorithm as a standard menu option, these algorithms are
designed only for peak enhancement and thus cannot resolve highly
convoluted broad bands.

Spectral data can be cluttered by interferences and artifacts that
appear in the form of polynomial shapes such as sloping lines or quadratic
curves [17]. The derivative of the spectrum, which is one order higher than
the polynomial shape, resolves some of the ﬁner details concealed by the
polynomial shapes. For example, the ﬁrst derivative removes sloping lines
and the second derivative removes quadratic curves and adds clarity to the
spectrum. As such, derivative spectra can reveal a host of information
otherwise hidden or not readily apparent in the original spectra and can be
used to extract both qualitative and quantitative information. Figure 4.2
illustrates the derivative curves of a Gaussian band. The ﬁrst and the third
derivative curves give the precise peak position while the second and the
forth derivative curves generate the inverted and the original curves,
respectively. The illustrations are not intended to demonstrate the
particular advantages of derivative spectroscopy, rather they demonstrate
the results of taking the derivative of an ideal hand up to the fourth
derivative. Their utility in analyzing real spectra will be apparent shortly.

Figure 4.3 gives the ATR FTIR spectra (lower frequency window) of
saturated aqueous maleic acid at various temperatm‘es. Band assignments
are indicated by the arrows [1, 3, 9, 10, 11, 14, 15]. These spectra are used

to illustrate the advantages of derivative spectroscopy.

63

---- Gaussian

---- Gaussian

— Second derivative

— First derivative

 

 

 

 

A

"fVWVﬁjw-

A

A
Vii v v v va v

 

 

 

“"‘l‘l‘“"“““

 

 

---- Gaussian

---- Gaussian

 

— Fourth derivative

[‘1‘ ‘ ‘ ‘ F‘ i ‘ ‘ ‘ 1

d ‘ ‘ I ‘ ‘ ‘ I

A A A A A A A A A A A A A A

 

 

— Third derivative

 

 

 

1650

 

 

1600 1650

1550

1600

1550

Wavenumber (ch)

Figure 4.2 First, second, third and fourth derivatives of a Gaussian peak.

 

 

 

 

 

 

 

 

 

 

 

(172 - ‘ 4. 4+4 . .. i. .. . E. .1». 5. -. . t. ..
+3075 °C
(164‘#
+50.25 °C
D + O
0.56 . 65.00 C
a)
o .
g 0.48 -
4: .
H
8 04 '
.Q ' '
<2
(132 i /
(L24
0.16’ll A: ‘ ‘ 1:1411: L

 

1700 1600 1500 1400 1300 1200

Wavenumber (cm'1 )

Figm'e 4.3 In situ, slurry ATR FTIR spectra of aqueous maleic acid at
sattn'ation in the low frequency region.

65

Consider the v(C=O) peak that occurs in the vicinity of 1700 cm". It

appears to be a single peak devoid of any other feature such as shoulders.
However, the ﬁrst derivative proﬁle given in Figure 4.4 reveals information
plausibly hidden by an artifact in the form of a polynomial shape. The most
striking feature is the enhancement of a shoulder on the high frequency side

of the v(C=O) peak that is manifested in the form of two peaks in the

positive component of the derivative proﬁle. A parameter can be deﬁned
based on a ratio (PIR1) between the derivative absorbance peak intensity at
1740 cm'1 to that at 1720 cm’1 for the measurement of crystallization
phenomena. A higher gain in PIR (peak intensity ratio) can be achieved by
using an appropriate baseline as the one denoted by BLl at 0.005. The
solubility and the concentration lines of maleic acid with respect to PIR1
measured in situ are given in Figure 4.5. This parameter is clearly a
function of temperature and independent of concentration. Therefore, the
concentration lines coincide with the solubility line. Consequently, this
parameter is not suitable for the measurement of supersaturation of
aqueous maleic acid. However, the results are presented to demonstrate the
power of derivative spectroscopy in bringing out spectral features that may
be used to measure crystallization parameters of many other systems.
Alternatively, a second parameter can be deﬁned using the features

of the ﬁrst derivative of the v(C=O) mode. The deﬁned parameter is the ratio
(PIR2) between the derivative absorbance peak intensity at 1740 cm‘1 to

that at 1692 cm'1 with the baseline adjusted to -0.012 (BL2) as indicated in
Figm'e 4.4. Essentially, this parameter reﬂects the relative changes

66

 

 

 

 

 

 

 

0.015P-v-ivv-l ............. l
t A +3075 00
001 . " -B-50.25°C.
Q) ' . ‘2
8 ’ " +65.00°C
é EL 1 T A\’ _
o 0.005 ’ I \\
m ’ \
e + _ 1
e 0.. 1740 cm'1 \‘ 692 cm' .
.2 : \\ .
45 » \\ ,
.> ' _1\“ /
5'0-005'1 1720 cm .. Z/ .
r:
-0.01 13L 2 .

 

 

 

 

17 80 1760 1740 17 20 1700 1680

Wavenumber (cm'l)

Figure 4.4 First derivative proﬁles of the v(C=O) vibrational mode ﬁom

Figtn'e 4.3. BL1=0.005 and BL2=-0.012 were the baselines
used for P112, and Pm.” respectively.

PIR,=(DA at 1740 cm‘1 - a)/(DA at 1720 cm’1 - a)

Pm2=(DA at 1740 cm'1 + b)/(DA at 1692 cm’1 + b)

a=0.005 and b=0.012 are the baseline adjustments
DA=derivative absorbance

4.5

PIRl
00

2.5 ‘f

l

 

3 .5
’ -O- Solubilityl

 

50%
53%
56%
59%
62%
65%

ZBDODO

 

 

2t

 

1.5

 

30 35 40 45 50 55 60 65 70

Temperature (°C)

Figtn'e 4.5 Solubility and concentration lines of maleic acid with respect to
PIR1 measured in situ. In addition, solubility was measured in

a slurry.
PIR,=(DA at 1740 cm‘1 - a)/(DA at 1720 cm'1 - a)

DA=derivative absorbance

a=0.005 is the baseline adjustment

68

between the high ﬁ'equency side of the v(C=O) peak and that of the low

frequency side. The solubility and the concentration lines of maleic acid with
respect to PIR2 measured in situ are given in Figure 4.6. PIRg, unlike PD?”
is a function of concentration and only slightly dependent on temperature as
demonstrated by slightly sloping concentration lines. The fact that P11?2 is a
strong ftmction of concentration renders it a highly suitable candidate for
measurement of supersaturation as demonstrated in Figure 4.6.

Previously [16, 18] , it has been established that band ratioing
techniques such as PIRs or area intensity ratios are the most appropriate
for quantitative measurements. This is because ratioing gives rise to an
internal standard that eﬁ'ectively eliminates errors due to instrumental
drifts. Instrumental drifts usually occur due to energy ﬂuctuations that
arise as a result of radiation source instabilities and alignment problems of
optical coupling attachments. In many systems, it may be diﬂicult to
identify features that can be used for ratioing in the original spectra.
Features of infrared spectra of crystallization systems can be masked by
the presence of various species such as impurities, byproducts and additives
that have strongly absorbing vibrational modes making the identiﬁcation of
features suitable for ratioing diﬁcult. In addition, most solvents have
characteristic IR spectra. As demonstrated above, derivative spectroscopy
can be successfully used to bring out features that are well suited for

ratioing. In this case, the v(C=O) peak used for demonstration is devoid of

any identiﬁable feature in the original spectra. Nevertheless, the features
that the ﬁrst derivative proﬁle reveals are quite remarkable. This is ample

69

 

 

 

 

 

 

12 "Hi --1‘....: i. -+,, :'j1: r
’ o 50% .
D 53% ‘~‘ .5523:
’ o 56% - a
10 4. b 59% " t.
’ a 62% .
. a 65% .,::..:_-::_.B.31': ::

8 ._ +Solubility| " - -- " _
on" , ‘
H
m _ A

6 .. 1,.

’ 4

4 . . 'l.‘ ‘ ‘-

 

30 35 40 45 50 55 60 65 70
Temperature (°C)

Figure 4.6 Solubility and concentration lines of maleic acid with respect to
PH?2 measured in situ. In addition, solubility was measured in
a slurry.
Pm2=(DA at 1740 cm" + b)/(DA at 1692 cm‘1 + b)
DA=derivative absorbance
b=0.012 is the baseline adjustment

70

evidence for the power of derivative spectroscopy and in general for the far
reaching utility of ATR FTIR spectroscopy for use in measuring and
understanding crystallization phenomena.

As illustrated in Figm'e 4.4, the second derivative proﬁle of a peak
generates the inverted peak. It can be used to isolate the individual

components of a convoluted band. Consider the v(C-O) peak at 1430 cm‘1

that is accompanied by three other shoulder peaks that may be due to
vibrational mode coupling or overtones. The second derivative can be used

to isolate the v(C-O) peak from the shoulder peaks. The inverted second

derivative of the v(C-O) stretch at saturation is given in Figme 4.7 . The

relative changes of this peak in the original spectrum are identiﬁable.
However, the same changes are more recognizable and convincing in the
second derivative proﬁle which is the isolated peak. The changes can readily
be used for measurement of crystallization parameters. For example, a PIR
between peak intensities at 1430 cm'1 and 1442 cm'1 is suitable.

Parameters discussed thus far for quantitative measurements were
based on hand ratioing techniques. Although they are highly suitable for
quantitative measurements their relationship to solution structure may be
ambiguous. A parameter that is suitable for quantitative measurements
and capable of providing some insight to the solution structure of
crystallizing systems is the peak shift of numerous vibrational modes. Just
as H-bonding is responsible for causing the transition of monomeric
carboxylic molecules in dilute solutions to associated forms in more
concentrated solutions [1, 19] , they are responsible for the crystal structure

71

 

 

 

 

 

 

   
  

(105 - -- -5 -- -- 5- -, -5 fjgv- e- -- -1 --
{ +30% °C j
_ —B—40.50 °C
, +5050 °C A t
0.04 .. +6000 °C . ..
r +6500 °C .
r .
g 0.03 -. 0.
“Q I 1
H 1
O r
3 002 -’ / J
<1 ' , /,~
0-01 ~ 1430cm'1 ‘-
.. 1442 cm'1 1
» y’)-
0 . :2} AAAAAAAAAAAAAAAAAAAAAA ‘5

 

 

 

1460 1450 1440 1430 1420 1410
Wavenumber (cm'l)

Figure 4.7 Isolated second derivative proﬁles of the v(C=O) vibrational
mode of aqueous maleic acid at saturation.

72

and the preceding solution structure in supersaturated solutions. As the
forces such as H-bonds that are responsible for the organization of
molecules in supersaturated solutions gain in strength, the force constants
of the vibrational modes adjacent to the site affected by H-bonding are
reduced. The consequent reduction in vibrational frequency is reﬂected in
the IR spectrum [3, 4]. Due to the presence of electronic phenomena such
as inductive effects and conjugation [1] , peripheral vibrational modes may
be affected and the resulting structure is reﬂected in the IR spectrum.
Derivative spectroscopy is a convenient method for extracting peak
shift information. The same information can be obtained from the original

spectrum. However, the shifts are more discernible in derivative spectra
(lst and 3rd derivative). Consider the 8(O-H) in-plane deformation vibration
of maleic acid given in Figure 4.3. The red shift of the peak upon increasing
saturation temperature conditions is evident. The same shift is more

convincingly demonstrated by the derivative proﬁles of the peaks in Figure

4.8. The parameter Av denotes the total shift of the peak in going from the

solubility condition at 30.75 °C to that at 65 °C. The peak shift information
was extracted using the user programmable OBEY programming utility
available in the Perkin-Elmer IRDM software. A discussion of the use of
maleic acid vibrational modes for the measurement of crystallization
parameters of aqueous maleic acid and some insight to the organization of
maleic acid in supersaturated solutions follows.

The covalent bond lengths and the interbond angles for maleic acid
derived ﬁom the crystal structure are shown in Figure 4.9 [20]. The IR peak

 

 

73

 

0.0053 "

0.0027

 

 

 

 

0

-0.0027

 

Derivative Absorbance
O

I +3075 °C
'0'0053 , —a—50.25 °C *‘ 74

I +6500 °C ‘ /
-0.008"

 

 

 

 

 

 

1260 1248 1237 1225 1213 1202
Wavenumber (cm'l)

Figme 4.8 First derivative proﬁles of the 5(0-H) in-plane deformation
vibrational mode from Figure 4.3.

1.218
\~

118.9"

1.04

1.337
113° — - 7

131.6°

1.488

121.4°

.304

110° 171°

0.91

74

1.0
, ® 116°
128.2° 1.475
1 3 108° 0.99

125.1 ° 6 '
122.6°

1.222

®

110°

un—
g,

1.595

ﬁgme 4.9 Bond distances and angles for the maleic acid molecule. Bond
(ﬁstancesrnnagﬁvenuhillaundtineauuﬁku;areitahcinadfbrcﬂarﬁmn

75

positions of the numerous vibrational modes of crystalline maleic acid are as

follows [1, 9, 21]. The v(C=O) stretching mode appears at 1705 cm". The
v(C—O) stretching mode appears at 1437 cm“. The v(C=C) stretching mode
appears at 1635 cm". The v(O-H) stretching vibration appears over the
range 2500 - 3000 cm". This band is modiﬁed by the v(C-H) stretching
hands that occur over the 2800 - 3100 cm‘1 range. The 6(O-H) in-plane

deformation appears at 1272 cm". Evidence suggests that the folded
structure of the maleic acid molecule in the crystalline state - due to
intramolecular H-bonding - stays intact upon dissolution in concentrated
solutions (0.3M) [5]. Therefore, it is plausible to expect a high level of
similarity between the crystalline state IR spectra and the solution state IR
spectra of maleic acid. A close comparison of the two conﬁrms this
rationalization. Upon supersaturation of aqueous maleic acid - that is when
a solution is cooled and as a consequence it approaches the onset of
nucleation - it is also expected that the solution state peaks will approach
the solid state peak positions, given the similarity between the solid and
solution state molecular structure. An absolute convergence is unlikely due
to the higher level of organization in the crystal lattice. The following
paragraphs examine the events that are expected to accompany the
convergence of solid and solution state structures in terms of peak shifts
and the utility of these shifts toward measurement of crystallization

parameters.

76

Solubility and concentration lines of aqueous maleic acid with respect
to the peak shift of the v(C=O) vibration measured in situ are shown in
Figure 4.10. Solubility, in addition to being measured in situ, was measured
in a slurry. When solutions at all concentrations are cooled, the v(C=O)
stretching vibration red shifts to lower frequencies. This is clearly indicative

of the strengthening H-bond. Upon cooling, H—bonds gains in strength.
Consequently, the strength of the adi acent C=O bond or the force constant

of the v(C=O) stretching vibration is reduced. This phenomenon is

manifestedinthe IRspectrumas ared shiftinthev(C=O)peak as shown in
Figure 4.10.
Solubility and concentration lines of aqueous maleic acid with respect

to the peak shiit of the v(C-O) vibration measured in situ are shown in

Figure 4.11. Upon cooling, \mlike the v(C=O) peak, the v(C-O) peak

demonstrates a blue shift. This is consistent with previous studies on
association of carboxylic acids [3, 9]. The complexity of electronic effects
such as inductive forces and conjugation that are affected by H—bonding

may be responsible for the blue shift of the v(C-O) peak.

Solubility and concentration lines of aqueous maleic acid with respect
to the peak shift of the v(C=C) vibration measured in situ are shown in
Figure 4.12. When solutions at all concentrations are cooled, the v(C=C)

stretching vibration red shifts to lower frequencies. Since most studies on

association have been done using saturated carboxylic acids, peak shifts of

 

77

 

 

 

 

 

 

0 -__-,----;,---;----;,,,-;----;,--T+--,-
* 0 50% ‘
r U 54%
1 o 58%
-2 .. 0.“, ‘. A 62% ..
El . B 65% J
a " ;_. - + Solubility ,
5 .ui" o
5. '4 ' l
ﬂ ' 1706 cm'l ‘
'M I- o -1 1
8 .~ 1708 cm .
O-t -6 .b A
‘h ‘
-8 a. “nil" un-
“ﬂﬁ

 

 

 

30 35 40 45 50 55 60 65 70
Temperature (°C)

Figure 4. 10 Solubility and concentration lines of maleic acid measured with
respect to the peak shift of the v(C=O) vibrational mode, in

situ. In addition, solubility was measured in a 31m. Absolute
peak positions at two conditions are shown for reference

purposes.

 

78

 

 

 

 

 

 

 

 

 

 

14 :r -; .4, - : :vm-n—r
t t
t o 50% ﬁ .
12 .. n 54% B -==.: ..
: o 58% ,3 .
' A 62% ‘ “.
1° '3 a 65% n ‘ Ba 1‘
A Z+Solubility o ' 1
8 3.. ° ..
t: A 4
E ED ,0. 3
LE 6 L o n ° ° 1427 cm'1j_ s.
m t D" Q o ‘ l:
'33 ’ . ° ,
q) 4.. 1.
DH r O ‘ ‘
; o '. n n ;
2.. o ..
.. . '3 1429cm'l :
0 1" El
° 1
-2 111.
30 35 40 45 50 55 60 65 70
Temperature (°C)

Me 4.11 Solubility and concentration lines of maleic acid measured with
respect to the peak shift of the v(C-O) vibrational mode, in situ.

In addition, solubility was measm'ed in a slurry. Absolute peak
positions at two conditions are shown for reference purposes.

79

 

 

 

 

 

 

 

14 4

C 9
12. . ..
103 I.
’5‘ o -°°° 1
v 8 -- 1627 cm’1 4
:1 - - 9
CD 6 “ l3"’ 1:5: 4
1 9 .
m . o 50% I
4- n 54% v
°" ° 58% .
2 d; A 62% :_
-1 B 65% .
<———1630.5 cm _ Solubility~
0 -

3O 35 4O 45 5O 55 60 65 70
Temperature (°C)

Figure 4.12 Solubility and concentration lines of maleic acid measm'ed with
respect to the peak shift of the v(C=C) vibrational mode, in

situ. In addition, solubility was measured in a slrn'ry. Absolute
peak positions at two conditions are shown for reference

purposes.

 

80

the v(C=C) vibration are not documented. Nevertheless, this data suggest

that the strength of the C=C bond or the force constant of the v(C=C)

stretching vibration is reduced upon approaching the onset of nucleation.

Solubility and concentration lines of aqueous maleic acid with respect

to the peak shift of the 5(O-H) in-plane deformation vibration measured in

situ are shown in Figrn-e 4.13. The behavior of the 5(O-H) peak shift upon

approaching conditions that favor a higher degree of association, in this case

lower temperatures, is similar to that of the v(C-O) peak as has been

documented [3, 9]. The v(C-O) and the 5(O-H) modes are mutually coupled
and blue shifts upon association via H-bonding [3, 9].

The peak shifts of v(C=O), v(C-O), v(C=C) and 5(O-H) vibrations were
isolated using derivative spectroscopy. A common feature of these bands is

that they have relatively narrow band widths that give rise to informative
derivative proﬁles. However, the derivative proﬁles of the highly convoluted,

broad v(O-H) stretching vibration region are not conducive to meaningful
analysis. In the case of aqueous maleic acid, the v(O-H) stretching region

constitutes of contributions from both water and acid. In addition, the v(C-

H) stretching mode coincide in this region [9]. The relative changes in this
region are shown in Figure 4.14. However, subtle features such as peak
shifts are not quite detectable. Isolation of the contributing components via
deconvolution of the broad, convoluted band can reveal the concealed
information.

81

 

 

 

 

 

 

 

 

70 7 7 7 r: ......... i ......... i ........ r3
, at“ 13
Z 0 50% :9 f “ " 1
60,; :1 54% , . A/ 1
; ° 58% . . ‘
: ‘5 62% ' ' a
50.. B 65% .7, --
a I O Solubility 4.’
G .1 .
g 40 : . o" 1221 cm'13
6‘5 30.: 3.
":3 i :
Q) ., .
Dd . ' 'l- J
20 7.: . r 455: 1'
10 .E .‘7
- 1232 cm'1 :
0 1 ' ‘
30 35 40 45 50 55 60 65 70
Temperature (°C)

Figure 4. 13 Solubility and concentration lines of maleic acid measured with
respect to the peak shift of the 5(O-H) vibrational mode, in situ.

In addition, solubility was measured in a drum. Absolute peak
positions at two conditions are shown for reference purposes.

82

 

 

 

 

 

0.4 ..... .....
I —e—30.75°C .
: ‘ —B—50.25 °C 1

03 .. ‘ +65.00°C ._

0.2 «i ,7 ' ‘5 ..

\ 1

" "x .

v ' \V?’ \ ‘
v(O-H)water ' ' '

 

Absorbance

 

 

 

 

 

 

v(C-H) acid ' '
v(O-H) acid
3300 3000 2700 2400

Wavenumber (cm'1 )

Figure 4.14 In situ, slrn'ry ATR FTIR spectra of aqueous maleic acid at
saturation in the high frequency region.

83

Deconvolution algorithms are available in some FTIR instrument
software packages. However, they are designed to enhance existing peaks.
They are not adequate for resolving highly convoluted, broad bands. An
alternative is to ﬁt the spectral proﬁle in this region to a multicomponent
Gaussian function using a least squares minimization algorithm. A rule of
thumb that is generally applicable in utilizing this technique is to use the
least number of Gaussian components that provide the best ﬁt for the
spectral proﬁle. Consider the spectrum at solubility at 30.7 5 °C over the
2700 - 3700 cm‘1 range (Figure 4.14). The normalized and baseline adjusted
spectrum was ﬁt to a function consisting of six Gaussian components. The
results are given in Figme 4.15. Due to the closeness of the ﬁt, the
spectrum and the six component function used for the ﬁt are not distinctly
identiﬁable in the ﬁgm'e. The six isolated components are also shown. The

components toward the high ﬁ'equency side of the band can be loosely
assigned to the v(O-H) stretching bands of water. Conversely, the
components toward the low frequency side of the band can be loosely

assigned to the v(O-H) stretching bands of maleic acid. The assignments are
not meant to be deﬁnitive because the contributions from the v(C-H)

stretching vibration of maleic acid to both v(O-H) stretching band intensities

cannot be discounted. However, the general trends of the components can
be used within the scope of this investigation. For example, it is reasonable
to associate most of the peak shifts observed in individual components to

the inﬂuence of H-bonding on the v(O-H) stretching vibrations. As a result of

84

 

14 1 1 1 1 1 1
. i I I I I I I U 1 Tﬁ' V I j I V V Y I’ Y Y‘rj V

v(O-H) water

 

1.2 .L I I .1.
3150 cm"

 

Absorbance

 

 

 

3800 3600 3400 3200 3000 2800 2600

Wavenumber (cm '1 )

Figure 4.15 Gaussian components of the v(O—H) region Due to the

closeness of the ﬁt the original spectral proﬁle (normalized and
baseline corrected spectrum at saturation at 30.7 5 °C from
Figure 4.14) and the six component Gaussian ﬁmction used for
the ﬁt are superimposed.

85

the transition from the monomeric to the associated form, a large decrease

in frequency of the v(O-H) vibration of carboxylic acids is observed due to the

exceptional strength of hydrogen bonds [3, 4]. The same trend is expected to
continue in highly concentrated solutions where strengthening H-bonds play
a critical role in the organization of carboxylic acid molecules.

Consider the component identiﬁed at 3150 cm'1 in Figme 4.15. Its
peak shift is shown in Figm'e 4.16. As discussed in the previous paragraph,

the peak shift was associated with the v(O-H) stretching vibration of maleic

acid. The peak shift of the low frequency side of the v(O-H) band is clearly

demonstrated by the considered component whereas it is not evident in the

original spectra. Solubility and concentration lines of aqueous maleic acid

with respect to the peak shift of the v(O-H) vibration measured in situ are

shown in Figm‘e 4.17. When solutions at all concentrations are cooled, the

v(O-H) stretching vibration is expected to demonstrate a red shift toward

lower frequencies under the inﬂuence of strengthening H-bonds. The
concentration lines appear to have slight negative gradients as expected.
However, due to the complexity of this region it is not possible to provide a
deﬁnitive interpretation.

Overall, all the peaks characteristic of maleic acid shift in the
direction that suggests a greater degree of association of the molecules (via
H-bonding) upon cooling. These trends observed in supersaturated solutions
in approaching the onset of nucleation, is consistent with the trends

observed in the transformation from the monomeric form to the associated

86

 

 

 

 

(13 77-9 .7..:. -7 77 --49-- -9 -- -9 1
—9— 30.75 °C 3

0.7 —a— 50.25 °C -j
+ 60.00 °C

 

 

0.6

0.5

0.4

Absorbance

0.3

0.2

0.1

 

 

3383 3267 3150 3033 2917 2800

Wavenumber (cm '1 )

Figure 4.16 Peak shift of the component near 3150 crn'l from Figure 4.15.

87

 

 

 

 

 

 

 

 

 

100 7....:....:....:....:.--.:....:....9-.
I o 50% v ~.
, D 53% ‘
.L ° 56% ..
80 . A 59% B ” -- == ,
B 62% .
a El 65% ,
5 60 .. +Solubility ._ " . ..
5:3 .
.2 1
U)
.14
g 40 '1' o ..
0.. r
20 "' 4p
0.0
0 #1--:----:-1--:----
3O 35 40 45 50 55 60 65 70
Temperature (°C)

Figure 4.17 Solubility and concentration lines of maleic acid measured with
respect to the peak shift of the v(O-H) vibrational mode, in situ.
Inaddﬁnursdubﬂﬁvaunmmamnednnashury

88

form in more dilute solutions. In addition, all peaks approach the peak
positions of the solid state spectrum. While recognizing that this evidence
alone is not sufﬁcient to provide conclusive remarks regarding the similarity
of the solid state and the solution (supersaturated) state molecular
structure, it is not unreasonable to suggest that the molecular structure in
the two states are most likely similar considering the convergence of peak
positions and the evidence [5] for the folded conﬁguration of maleic acid in
solution.

A concrete analysis on the nature of the solution state structure of
aqueous maleic acid in supersaturated solutions is beyond the scope of this
investigation. This analysis is a prelude to a more in-depth study that will
involve both Raman and NMR spectroscopy in addition to FTIR
spectroscopy. The different techniques can reveal complementary
information. Frn'ther, utilization of the deutero analogues of both water and
maleic acid in experiments similar to ones discussed above can provide a
host of conﬁrmatory information [10, 11, 22] . The deuteration of a
particular bond results in a signiﬁcant red shift in its vibrational frequencies

due to the heavy atom effect. For example, the v(O-D) vibration of the
deuterated acetic acid is observed at 2299 cm'1 in comparison to the v(O-H)
vibration of acetic acid that occurs at 3140 cm‘1 [10]. The 5(O-D) vibration

is observed at 1046 cm‘1 compared to the 5(O-H) vibration at 1294 cm“.

Consequently, experimentation with selectively deuterated maleic acid and
deuterated water in judiciously chosen combinations can help resolve many
of the ambiguities of the current analysis. For example, use of maleic acid in

89

heavy water will clear the v(O-H) stretching region of any contribution from
the v(O—H) vibration of water thus making it much easier to identify

dynamics of the v(O-H) vibration of maleic acid.

Thus far, a discussion of the utility of the peak shifts of maleic acid
vibrational modes for the measurement of crystallization parameters of
aqueous maleic acid, which incidentally is the primary objective of this
investigation, has been neglected. The discussion has been centered on
providing some insight to the organization of maleic acid in supersaturated
solutions. However, maleic acid vibrational modes suitable for

measurement of supersaturation and solubility are quite evident. The
v(C=C) mode (Figure 4.12), the 5(O-H) mode (Figm'e 4.13) and the v(O-H)

mode (Figure 4.17), that demonstrate a strong dependence on concentration,
are the ones suitable for this purpose. The other modes that are
independent of concentration, although reﬂective of the solution structure,
are clearly not useful for quantitative measurements.

Between the band ratioing techniques investigated in Chapters 1 and
2 [16, 18] and discussed herein and the peak shifts of numerous vibrational
modes, it is anticipated that it will not be a diﬂicult task to identify a
parameter appropriate for measurement of crystallization phenomena of
most inorganic and organic systems. As indicated above, features of
infrared spectra otherwise suitable for quantitative measurements of many
other crystallization systems can be masked by the presence of various
species such as impurities, byproducts, additives and solvents that have,
strongly absorbing vibrational modes. Upon encountering such a system,

90

the techniques discussed herein can be used to help enhance features toward
identifying a parameter suitable for measurement of solubility and
supersaturation. In the case of maleic acid many options that are equally
eﬂ'ective are available. The solubility measured with respect to each of the
options discussed above is shown in Figure 4.18. The precision of the data is
quite reasonable considering the diversity of the parameters used to extract
them.

In Chapter 1, an inconsistency between the solubility data extracted
from two different ratios (RT1 and RT,,) was attributed to the optical

properties and the material of the ATR conﬁguration of the Micro CIRC LE®
Open Boat Cell. It was postulated that the deeper penetration of the
evanescent ﬁeld into the sample at longer wave lengths (RTz) may have
been responsible for this anomaly. It was also pointed out that the depth of
penetration can be reduced by using alternate ATR conﬁgurations and ATR
elements that have higher refractive indices such as AMTIR- 1 crystals. In
the feasibility study presented in Chapter 1, the ATR element used was a
cylindrical, ZnSe rod that has a low refractive index. In addition, the Micro

CIRCLE® Open Boat Cell is a sampling device that may allow settling of
slurries over the ATR rod leading to inconsistencies in accumulated data. In
the studies undertaken subsequently and presented in Chapter 2 and here,
the ATR element used was a conical, AMTIR-l ATR crystal that has a
higher refractive index conﬁgured for in situ measurements. It is very likely
that the combination of in situ measurements, the conical ATR
conﬁguration and the AMTIR- 1 ATR element with a higher refractive index

91

 

66-

05
DD

% (w/w) Maleic Acid
01
q

'ﬁrv

 

 

 

lammnlmlnllmnnnlnmn l annlnnmnlnnn

30 35 40 45 50 55 60 65 70

 

Temperature (°C)

Figure 4.18 Solubility of maleic acid in water with respect to % maleic acid
(w/w).

92

contributed to the consistency of the data extracted from the diverse set of
IR parameters.

Not all parameters considered were suitable for measurement of
supersaturation as a result of some being independent of concentration. The
existence of a clear distinction between parameters in terms of the
dependence on concentration may be indicative of the unique structure of

aqueous maleic acid. For example, consider PIR1 and PIIi‘2 that were

extracted from the v(C=O) peak. PIRl is independent of concentration.

Conversely, PIR2 is dependent on concentration. This may be indicative of
the carbonyl bond being inﬂuenced by two types of H-bonds as illustrated in
Figm'e 4.9. Evidence suggests that the folded structure of the maleic acid
molecule in the crystalline state - due to intramolecular H-bonding - stays
intact upon dissolution in concentrated solutions (0.3M) [5]. Consequently,
the two carbonyl bonds of maleic acid in solution are most likely affected by
both intramolecular and intermolecular H-bonding. Therefore, it can be
postulated that the nature of the carbonyl bonds is manifested in the
spectra as two mutually exclusive features, one independent (PEI) and the
other dependent (PIRZ) on concentration. Again, such phenomena cannot be
conﬁrmed without other corroborative evidence by way of Raman and NMR
spectroscopic data and experimental data using deuterated analogues of
water and maleic acid. However, the broad scope of ATR FTIR
spectroscopy for measurement of vital crystallization parameters and
understanding crystallization systems is indisputable.

93

4.4 Conclusions

The primary focus of this paper was to investigate the methods
available to identify and isolate subtle features of IR spectra for utilization
in measurement of crystallization parameters. Both derivative
spectroscopy and deconvolution were successfully used to reveal features
otherwise obscured by spectral artifacts. These features were primarily
useful for quantitative measurements. The precision of the solubility
measurements extracted from numerous IR parameters established the
consistency of IR spectroscopy toward measurement of crystallization
parameters. It is our ﬁrm belief that the techniques discussed herein can be
used to help enhance features of many organic or inorganic crystallization
systems toward identifying a parameter suitable for measurement of
solubility and supersaturation. In addition to the versatility of ATR FTIR
spectroscopy as a measurement tool, the spectra can be abundant with
information that would provide some insight to the chemical natm'e of

various systems.

4.5 References

1. Avram, M., Mateescu, GH. D., “Infrared Spectroscopy'Applications in
Organic Chemistry”, Wiley-Interscience, New York, New York,
(1966), Ch.7.

2. Hadzi, D., Bratos, S., in: “The Hydrogen Bond”, Eds. Schuster, P.,
Zundel, G., Sandorfy, C., North-Holland, New York, New York, (1976),
Ch.12.

3. Davies, M., Sutherland, G. B. B. M., J. Chem Phys, 6, (1938), 755.

4. Hadzi, D., Chimia, 26, (1972), 7.

17.
18.

19.
20.
21.

22.

94

Hadzi, D., Novak, A, Spectrochim. Acta., 18, (1962), 1059.
Lascombe, J ., Haurie, M., Josien, M. L., J. Chim. Phys, (1962), 1233.
Flett, M. St. 0., Trans. Faraday Soc., 44, (1948), 767.

Weltner Jr., W., J. Am. Chem. Soc, 77, (1955), 3941.

Flett, M. St. C., J. Chem. Soc, (1951), 962.

Kishida, S., Nakamoto, K., J. Chem. Phys, 41:6, (1964), 1558.
Fukushima, K., Zwolinski, J ., J. Chem. Phys, 50:2, (1969), 737.
Millikan, R. C., Pitzer, K S., J. Am. Chem. Soc, 80, (1958), 3515.
Davies, M., Evans, J. C, J. Chem Phys, 20, (1952), 342.

Grove, J. F., Williams, H. A., J. Chem. Soc, (1951), 877.

Hadzi, D., Sheppard, N., Proc. Roy. Soc, London , A216, (1953), 247.
Dunuwila, D. D., Berglund, K. A., Revised for publication in Ind. Eng.
Chem. Fundamentals, (1995).

Perkin Elmer IR Data Manager, User’s Manual, (1991).

Dunuwila, D. D., Carroll II, L. B., Berglund, K. A., J. Cryst. Growth,
137, (1994), 561.

Badger, R. M., Bauer, S. H., J. Chem. Phys, 5:11, (1937), 839.
James, M. N. G., Williams, G. J. B.,Acta. Cryst, 330, (1974), 1249.
The Aldrich Library of FP-IR Spectra, Vol. 1, Aldrich Chemical
Company, Inc., Milwaukee, USA

Bratoz, S., Hadzi, D., Sheppard, N ., Spectrochim. Acta., 8, (1956), 249.

CHAPTER5

CONTINUING INVESTIGATIONS

 

5.1 Background

5.1.1 Control Strategy
Deﬁnition of Supersaturation: It has been observed that
maintenance of constant supersaturation during a crystallization process
leads to improved crystal size distributions [1]. Supersaturation is deﬁned in
terms of the fundamental properties of solutions as given in Equation 2.6 of
Chapter 2. However, for all practical purposes, supersaturation is
approximated by the concentration difference or ratio with respect to the
solubility with the underlying assumption of ideality [2]. This assumption is
valid for sparingly soluble systems. For highly soluble systems, the
approximation can lead to substantial misrepresentation of supersaturation
due to increased nonideality of the solution.

Generally, nonideal behavior of concentrated solutions, reﬂected by

the activity coeﬁcient (7), is due to extensive intermolecular and

intramolecular interactions between the solute and the solvent. These
interactions in turn conﬁgure the solution structure of the system. Then, it
follows that the activity coeﬂicient is reﬂective of the solution structure at a
molecular level. Therefore, a method for determining supersaturation that is
reﬂective of the solution structure would be inherently more accurate.
Conventional techniques such as refractometry, interferometry, viscometry

95

96

and densitometry, in addition to being unsuitable for in situ measurements,
can measure only their respective bulk properties which are not sensitive to
solution structure at a molecular level. In addition, conventional methods
are not sensitive enough and their use can lead to gross misrepresentation of
supersaturation. Conversely, infrared spectroscopy, which probes the
vibrational structure of molecules is reﬂective of the solution structure and
therefore is a viable technique to measure supersaturation reﬂective of
solution activity. In Chapter 4, parameters sensitive to solution structure
and supersaturation were distinguished from those that were sensitive to
solution structure and not supersaturation, highlighting the speciﬁcity of IR
spectroscopy. Further, the sensitivity of IR parameters (reﬂected by the
signal gain) over a broad operating region was demonstrated in Chapter 4.
Therefore, conceivable deﬁnitions for supersaturation include;

Adam) = Pm -Pm,”l and

mm) = Pm (5‘1)
Pm,sol

 

where Pm is any parameter discussed in Chapters 2, 3 and 4 in the context
of measurement of supersaturation and solubility and Pm”, is the solubility

with respect to P13. Since P3; is a parameter that reﬂects the fundamental
structure of the solution, A(Pm) and 8(Pnz) will most likely contribute to a
more accurate measurement of supersaturation. The sensitivity and the
potential accuracy provided by ATM and 5(Pm) is anticipated to contribute

toward the performance of a control scheme. It is also a direct
measurement of supersaturation that does not require calibrations and
therefore more practical. In eﬁ'ect, a set point for a control scheme designed

97

to obtain a crystal size distribution (CSD) with a large average size can be

envisioned as;
A(Pm) = constant, or (5.2)
5(Pm) = constant

which is illustrated in Figure 5.1.

One of the primary objectives in controlling a crystallization process
is to obtain a speciﬁed CSD. Excessive nucleation occurs when the system
approaches its metastable linrit [3] resulting in CSDs with smaller average
sizes. Therefore, if a larger average size is desired, it is imperative that the
system is maintained well within the metastable zone; i.e., away from the
limit. However, it is counterproductive to operate very close to the solubility
line since this does not provide suﬁcient driving force for growth resulting in
unacceptably long batch times.

Closed Loop Batch Crystallizer Control: A simple schematic of a batch
crystallizer and the primary components of the envisioned control system is
shown in Figure 5.2. The system consists of a jacketed crystallizer where a
coolant ﬂuid enters its jacket at temperature T,- and exits at T0. The ﬂow

rate is denoted by w. Supersaturation in the crystallizer measured by in

situ ATR FTIR spectroscopy - A(Pm) or 5(Pm) - is measured and transmitted

to the primary controller, E, which in turn adjusts the heat removal system,
B, accordingly. In order to compensate for ﬂuctuations in the heat removal
system, a secondary controller, D, is suggested [4]. In this conﬁguration, the
heat ﬂux, H , from the crystallizer measured by T,, T, and w is transmitted
to the secondary controller which compensates for the ﬂuctuations.

Without a secondary controller, any ﬂuctuation in the heat removal system

98

 

 

)
>

Supersaturation

>

————_———_——1

 

 

 

A(Pm) 0" 6(Pm)

 

 

 

 

 

 

 

o Supersaturation, A(Pm)
)
(mam ‘uonemresredns

 

.9
t"
o

Temperature Time
> 9

 

 

Figure 5.1 Control policy projected to maximize the mean sizeof a crystal
size distribution from a cooling batch crystallization process.
The policy is based on maintaininga constant supersaturation
deﬁned by the IR parameters given by A(Pm) or 5(Pm).

A(Pm) = Pm - Pat”; and

P
6(P )= m
IR P H3301

where Pm is any parameter discussed in Chapters 2, 3and 4 in

 

the context of measurement of supersaturation and solubility
and Pm”, is the solubility with respect to Pm.

 

* A(Pm)

 

 

 

/.

 

 

I

 

 

 

 

 

 

 

 

[_________

 

Figure 5.2 A simple schematic of a batch crystallizer and the primary
components of the envisioned control system.
T, = Inlet coolant temperature of the jacketed crystallizer,
To = Outlet coolant temperature, w = Coolant ﬂow rate,

MPH.) = Supersaturation, E = Primary controller
B = Heat removal system, D = Secondary controller
H = Heat ﬂux from the crystallizer measured by T,, To and w.

100

can lead to a prolonged excursion in supersaturation from its setpoint. The
reason for this is that the primary controller,without the aid of a secondary
controller, does not take any corrective action until the distrn'bance is
transmitted through the system consisting of several resistances. In the
secondary control loop, heat ﬂux ﬁ'om the crystallizer is used as the
measured variable as opposed to measuring the temperatm'e in the
crystallizer since heat ﬂux control has been proven to provide more stable
control systems [5]. The block diagram of the cascade control system is
given in Figure 5.3 (a).

Although, a good heat removal system is tantamount to the stable
operation of the overall control scheme, its design is not expected to be a
limiting factor considering the resources available for its design [6].
Therefore, the heat removal system is not speciﬁed. The task more
substantial in terms of relevancy and more challengingwillbe the design of
the primary loop controlling supersatm'ation. In order to consummate the
goal of designinga stable supersaturation control scheme (primary loop), it
is not necessary to know the dynamics of the secondary loop, since the two
loops can be analyzed independent of each other. The standard procedure in
designing cascade control systems is to ﬁrst establish the control dynamics
for a stable secondary loop. Subsequently, the secondary loop can be
normalized to determine the stability of the primary loop. This is
demonstrated between Figures 5.3 (a) and 5.3 (b). However, in this case its
reasonable to consider normalizingthe secondary loop for heat ﬂux control
without specifying the heat removal system taking comfort in the resources
available for its design in terms of hardware, literature and specialists.

101

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853.555 .558

 

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388m 55580 9 .5380
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8.323 I ewe mam aweﬁﬁﬁeusw L 5.58

102

Thus, the hitherto unventmed, yet promising aspect of crystallizer design
and control, which is design and control based on in situ measurement of
supersaturation, can be promptly attended to as it is more relevant to and
more substantial in the ﬁeld.

One concern in using in situ ATR FTIR spectroscopy for control of
batch crystallization processes may be whether the frequency of
measurement would be sufﬁcient for implementation in control of a highly
labile process such as batch crystallization. The scan rate of the
supersaturation proﬁles presented in Chapter 3 (Figures 3.5 and 3.7) was
0.05 sec". In fact, the desupersaturation of aqueous citric acid, which is one
of the fastest growing systems known, was measured with remarkable point
to point resolution and is shown in Figure 5.4. Desupersaturation of aqueous
citric acid was measured using a protocol similar to that used with maleic
acid at a scan rate of 0.008 sec". The citric acid solution was not seeded. In
view of a control scheme with high performance, a scan rate of 0.1 sec'1 is
realizable. Clearly, the data suggest that the frequency of measurement will
not be a limiting factor in the development of a control scheme.
Crystallization Modeh The particle number-size distribution theory
introduced by Randolph and Larson [7] and the fundamental
supersaturation balance discussed by Mullin and Nyvlt [8, 9, 10] provide
powerful models to evaluate crystallization processes. The model derived
from the particle number-size distribution theory is based on the population
balance (number of particles per unit volume per length range) and takes
nucleation and growth of crystals into account. The fundamental
supersaturation balance is derived taking into consideration that the driving

103

 

 

3'1'." O TIRproﬁle

 

+ Solubility

 

TIR

 

 

144 m1 1
I

a] nnnnnn Ill nnnnn IAAAJIAJLLILJJJ

5 10 15 20 25 30 35 40 45

 

 

Temperature (°C)

Figure 5.4 A supersaturation proﬁle of aqueous citric acid represented in
terms of TIR.

transmittance at 3284 cm'1

TIR = , 1
transmittance at 1190 cm'

 

104

force for all crystallization phenomena such as nucleation and growth is
supersaturation. Thus, kinetic parameters for nucleation and growth are
nested in these models giving them both predictive and descriptive
capabilities. Another valuable set of equations commonly used in
crystallization analysis is the moments of the particle number-size
distribution [7]. The moments have been utilized to circumvent a basic
dimensional incompatibility between the population balance and the
transport equations for mass, momentum and energy.

The particle phase space consists of a set of internal coordinates in
adchtion to the three spatial dimensions. This incompatibility complicates
the simultaneous solution of the population balance with the transport
equations. The most signiﬁcant internal coordinate in the particle phase
space is the particle size. Therefore, the population density distribution is
integrated over the particle size internal coordinate reducing the
dimensionality of the population balance to that of the transport equations.
The moments that give the total particle properties (presented shortly)
upon integrating the population balance over the particle size coordinate are
given by;

m ,0) = Tn(L,t)LjdL, j = 0, 1,2, (5.3)
0

where n is the population density distribution and L is the particle size.

The application of these models in engineering simulations and
process analysis and control has been limited by the unavailability of a
reliable and sensitive technique to obtain kinetic data in situ. In

crystallization processes, in situ measurement is extremely important since

105

the hydrodynamic conditions set by the crystallizer dimensions, ﬂow
patterns induced by the propeller and the suspended crystal slurry can
signiﬁcantly alter kinetic parameters from that obtained under controlled
laboratory experiments [1 1]. Theoretically, kinetic parameters can be
extracted from the desupersaturation rate of the solution monitored by in
situ ATR FTIR spectroscopy. An attempt was made to extract the
crystallization kinetic parameters of aqueous maleic acid by least squares
minimization between the measured supersaturation proﬁle and the
supersaturation proﬁle calculated using the supersaturation balance which
has a structure similar to the moment equations. Crystallization is a
particulate process where the number of particles generated over the batch
time plays a signiﬁcant role in affecting the course of the process.
Therefore, it was extremely diﬁcult to obtain a consistent set of
crystallization kinetic parameters using supersaturation alone since it does
not provide number related information. It is anticipated that in situ
measurement of supersatm'ation using ATR FTIR spectroscopy and
measurement of the transient CSD using a light scattering device in
combination will be a more promising approach for the estimation of kinetic
parameters. The model most convenient for the extraction of kinetic
parameters using supersaturation measurements and CSD measurements
is the set of moment equations [7].

The population balance for a well mixed, constant volume batch
crystallizer is given by,

913(6):) _
3: 6L ’

 

O (5.4)

106

where G is the linear growth rate of crystals. In order to obtain the
moments of the distribution, the population balance is integrated over the

particle size coordinate as follows;

T[%”+ 32%") = 0]LJ'dL, j = 0,1, 2, (5.5)
0

 

The resulting set of moments are given by;
iti—OJB" = JGmJ-_1, j =0,],2,... (5.6)

where 0’ = 0 for j at O. The time dependent moments are as follows;

=__dNn = 30

m
dt

dm

'3?"

d3. : lg : mlG (57)
dt

is;
dt

dm.

'21?

where the number rate of nucleation, B”, the number of seeds, N,, and the
linear crystal growth rate, G, are deﬁned in terms of the frequently used

power model as;

3°: kuplL ———[k,,,pA(Pm)" wk, ,,-M’"A(PIR)”]
c n,0

kc,

3495‘
M__,__o%

N3:
. 10.0.12
where N, is the total number of nuclei, L is the total length of crystals, A is
thetotalareaofcrystaIs,Misthetotalmassofcrystalsinsuspension, k, is

G: k ,A(Pm)g (5.8)

 

107

the area shape factor, k, is the volume shape factor, p, is the crystal

density, Lmo is the size of nuclei at birth, Lw is the initial size of seed
crystals, W“, is the initial mass of seed crystals, k”, is the primary
nucleation rate constant, k M is the secondary nucleation rate constant, k g is
the growth rate constant, 11,, is the order of primary nucleation, n, is the
order of secondary nucleation and g is the order of growth. In order to solve
the moment equations, the operating conditions should be deﬁned and the

mass balance should be speciﬁed. The mass balance is speciﬁed as;

“(1332) = _ dPIR,sol _ M

5.9
dt dt dt ( )

 

The time dependent population density distribution can be recovered by the
following approximation [7];
n(L) = A'lm (5.10)
where m is the moment vector and the elements of the matrix A is given by;
a j, = LiALk (5.11)
where L, is the midpoint of a size range AL, It has been shown that four to

ﬁve moments satisfactorily reproduce an original distribution [7]. The
higher moments unduly weight the distributions toward the larger sizes.

Control System Equations; State Variable Form: State variable form
is particularly convenient for the description of complicated systems for
which a standard, compact notation is especially helpful [12]. The state
representation of systems, that uses integrators, is useful not only in control
system analysis, but for simulation and analysis of systems of all kinds. A

state variable description of an nth-order system, in the Laplace domain,

108

involves n integrators and the corresponding outputs which are the state

variables. The inputs of each of the integrators is given as a linear
combination of the state signals, X", and the system inputs, 12,-;

“1(8) = 011X1(S) + 012X2(8) + ... + (1th (8) + b11R1(S) + ... + “1.121(8)

8X2(S) = a21X1(S) + 022X2(3) + + 02an (S) + b21R1(8)+ + bZiRl(s) (5 12)

Ex" (3) = an1X1(S) + an2X2(8) + + 0,,an (3) + bn1R1(S) + ... ‘1" built! (8)

In the time domain these are a set of n ﬁrstorder linear differential
equations;

“(l—t1 = (11111 + a12x2 + ...+ ahxn + bur, + +b1lrl-

dxz

dt = amxl +a22x2 + ...+a2,,x,, +521r, +...+ 52,1;-

 

 

 

 

 

 

 

 

 

 

(5.13)
-d—tn = anlxl +an2x2 + ...+a,,,,x,, + bnlr, + ...+b,,,-r,-
In matrix notation the state variable can be compiled as;
"’51- “‘1- F011 012 aln-le- P511 blinrl-
ixz=izzazl 022 021 x2+b21 “bzirz
dt 5 E 1 3 '- i i E ' i E
_xnj _in_ _anl an2 ann__xnd _bnl bni‘_ri_,
or (5.14)
dx
—=i=Ax+Br
dt

The system outputs are related to the state variables through the output
equations;

3’1 011 012 Cb: x1

ym cm] cm2-
or
y :0:

cmn xn

(5.15)

109

The time course of the state variables are described by the state
equations. This is a standard form of representing any system described by
linear constant-coefﬁcient integrodiﬂ‘erential equations. Often, systems
consisting of a mixed collection of simultaneous system equations, some of
ﬁrst order, some of second order, some involving running integrals, etc., are
manipulated to place them in this standard form. The primary advantage is
that systematic methods of analysis such as frequency response analysis
can be implemented on involved problems quite efﬁciently. For example, it
may be desirable to determine the contributions of each of the state
variables to the overall process gain of the system. In this exercise, the
more signiﬁcant state variables can be isolated from those that are much
less signiﬁcant Thus, more insigniﬁcant state variable can either be
neglected or considered as a disturbance input to the system. The latter
scenario is described by the following equation assuming that the
contribution of the state variable x, is negligible.

{-551- Parr “13 arnvxrl [bu bit-7'11 ’0127

x3 031 033 031 J"3 bar b3i "3 + “223:2 (516)

 

 

 

 

 

 

 

 

 

 

in, _anl an3 annJ_xn_ Lbnl bnid_ri_ _an24
This analysis gives process development engineers an insight to the process
parameters most important toward design and development.

In crystallization the process state variables include,
supersaturation, CSD, slurry density, total crystal surface area, nucleation
rate, growth rate and heat ﬂux State variable analysis brieﬂy outlined
above will help identify the relative importance of process parameters
related to each of the state variables at various operating conditions. The

110

relative merits of in Situ measurement of supersaturation and in situ
measurement of CSD can be analyzed.

The set of equations that describe a well mixed constant volume
batch crystallizer is given by Equations 5.7, 5.8, 5.9 and 5.10. The
differential equations are highly nonlinear. However, a methodology for the
systematic characterization of dynamic systems by state variable analysis
has been developed only for linear systems as presented above. Thus, the
convenience of state variable analysis is signiﬁcant motivation for
approximating nonlinear systems with linear ones. One technique
commonly used is linearization around a judiciously chosen operating point
using a Taylor series expansion [4]. The success of the linear approximation
depends on the deviation of the system ﬁ‘om the chosen operating point.
The smaller the deviation the better the approximation. Therefore, process
simulations will have to be used in aid of choosing the most appropriate
operating point. In the rare event that linearization around an operating
point fails to provide a reasonable approximation, more diﬁcult methods of
nonlinear analysis may have to be used [4].

5.1.2 Solution Structure

In Chapter 4 a reasonable amount of evidence was presented in the
context of inferring the solution structure of aqueous maleic acid in
supersaturated solutions. The presented evidence suggest that the folded
structure of crystalline maleic acid remains intact in highly concentrated
solutions. However, a concrete analysis on the nature of the solution state
structure of aqueous maleic acid in supersaturated solutions was beyond the
scope of the investigation discussed in Chapter 4.

111

The depth of the investigation can be extended using both Raman and
NMR spectroscopy in addition to FTIR spectroscopy. The diﬁ‘erent
techniques can reveal complementary information. Further, utilization of
the deutero analogues of both water and maleic acid in experiments similar
to those discussed in Chapter 4 can provide a host of conﬁrmatory
information [13, 14, 15]. The deuteration of a particular bond results in a
signiﬁcant red shift in its vibrational frequencies due to the heavy atom

effect. For example, the v(O-D) vibration of the deuterated acetic acid is
observed at 2299 cm‘1 in comparison to the v(O-H) vibration of acetic acid
that occurs at 3140 cm’1 [13]. The 6(O-D) vibration is observed at 1046 cm’1

compared to the 5(O-H) vibration at 1294 cm". Consequently,

experimentation with selectively deuterated maleic acid and deuterated
water in judiciously chosen combinations can help resolve many of the
ambiguities of the analysis provided in Chapter 4. For example, use of

maleic acid in heavy water will clear the v(O-H) stretching region of any
contribution hour the v(O-H) vibration of water thus making it much easier
to identify dynamics of the v(O-H) vibration of maleic acid.

In Chapter 4, the peak near 1629 cm'1 was assigned to the v(C=C)

stretching mode. However, the strength of the peak is not consistent with
the vibrational mode. The strength of the IR active vibrational modes
depend on the strength of the permanent dipole moment of the mode.
Eventhough the maleic acid molecule is not perfectly symmetric around the

112

(C=C) bond, its relative symmetry prevents extensive polarization of the

(C=C) bond. Therefore, the peak intensity of the v(C=C) mode is expected to

be week. In fact, the v(C=C) mode is nonexistent in the IR spectrum of

fumaric acid, which is the trans conﬁguration of maleic acid, since it has a
center of symmetry around the (C=C) bond. Consequently, the most likely
event is that the strong band around 1629 cm‘1 is constituted by

contributions from the v(C=C) mode and other modes of maleic acid. The

other contributors could be overtones of lower ﬁ'equency modes of maleic
acid. The origins of these overtone bands can be scrutinized by
experimentation with selectively deuterated maleic acid and deuterated
water in judiciously chosen combinations. Separation of this convoluted
band using deuterated species can provide additional information toward
deducing the solution structure of aqueous maleic acid. Ambiguities
resulting from band convolution of other identiﬁed modes can be resolved in
similar fashion. In addition, assignments can be made on unidentiﬁed band
and shoulders. Studies with complementary spectroscopic techniques such
as Raman and NMR can be conducted with deuterated and non-deuterated
species adding to the wealth of information available to study the solution
structure.
5.1.3 Effect of impurities

In industrial crystallization, solutions invariably contain impurities
within detectable limits. In some crystallization schemes, impurities may
also be added to instigate desirable conditions. Impurities can signiﬁcantly
alter the solubility characteristics and crystallization kinetics of the

113

primary solute. In the presence of an impmity one of three situations is
likely to arise. The impmity may react with the primary solute and
completely alter the nature of the system, both chemically and physically.
The presence of an impurity may drive the primary solute into
supersaturation and thereby cause the primary solute to precipitate out of
solution. Lastly, the presence of an impurity may cause the system to be
undersaturated with respect to the primary solute. In the literature, the
latter two effects are identiﬁed as 'salting—out' and 'salting-in', respectively.
In addition, kinetics can be aﬂ‘ected by the adsorption of impurity molecules
on growing crystal surfaces. In industrial crystallization processes,
monitoring of impmity (either contained or added) levels and/or their effects,
is crucial for a successful operation.

ATR FTIR spectroscopy, in addition to having the capability to
measure solubility and supersaturation, can be used to monitor the
presence of additives or impurities and consequent reactions (reactive
crystallization schemes included). Infrared spectra, that reﬂect the
vibrational and rotational structure of the analytes, can provide more than
one piece of information unlike traditional solubility and supersaturation
measurement techniques that measure a single parameter calibrated for
the measurement of solubility and supersaturation. The advantage is that
necessary information can be obtained simultaneously using the same
technique, in situ, without resorting to multiple techniques that are variable
speciﬁc. The potential for the application of in situ ATR FTIR spectroscopy
to study impurity eﬂ‘ects remain to be explored.

114

5.2 Conclusions

The utility of in situ ATR FTIR spectroscopy for the measurement of
important crystallization parameters such as supersaturation, solubility
and metastable limit was demonstrated in the previous chapters. The
feasibility of the technique toward process development and eventually
control of batch crystallization processes that will provide for improved
product quality/reproducibility, time savings and cost containment was
established. However, its potential for implementation in control of
crystallization processes, although promising, remains to be proven. In
chapter 4 substantial evidence demonstrating the potential of in situ ATR
FTIR spectroscopy towards deducing solution structure in supersaturated
solutions was presented. Utilization of in situ ATR FTIR spectroscopy in
studying the effects of impurities on crystallization systems is yet another
avenue remaining to be explored. Therefore, it is recommended that the
implementation of control using in situ measurement of supersaturation
using ATR FTIR spectroscopy, utilization of IR spectroscopy for
understanding solution structure in supersaturated solutions and
investigation of eﬂ‘ects of impurities on crystallizing systems using ATR
FTIR spectroscopy be pursued in the futm'e.

5.3 References

1. Jones, A G., Mullin, J. W., Chem. Eng. Sci, 29, (1974), 105.
. Garside, J ., Chem. Eng. Sci, 40:1, (1985), 3.
3. Mullin, J. W., “Crystallization”, Butterworth-Heineman, Oxford,
England, (1993).

10.
11.
12.

13.
14.
15.

115

Coughanowr, D. R., “Process Systems Analysis and Control”,
McGraw-Hill, Inc., New York, USA

Radcliffe, 0., Professor, Mechanical Engineering, Michigan State
University.

Perry, R. , Chilton, Perry’s Handbook of Chemical Engineering,
McGraw Hill, New York, 6th Edition.

Randolph, A. D., Larson, M. A., “Theory of Particulate Processes”,
Academic Press, Inc., New York, USA, (1988), ch. 3.

Mullin, J. W., Nyvlt, J ., Chem. Eng. Sci, 26, (1971), 369.

Nyvlt, J ., Colin. Czech. Chem. Commun., 30, (1965), 2269.

Nyvlt, J ., Mullin, J. W., Chem. Eng. Sci, 25, (1970), 131.

N. S. Tavare, Separation and Puriﬁcation Methods, 22:2, 93, (1993).
Hostetter, G. H., Savant, Jr., C. J ., Stefani, R. T., “Design of Feedback
Control Systems”, Holt, Rinehart and Winston, New York, USA,
(1982), ch. 7.

Kishida, S., Nakamoto, K, J. Chem. Phys, 41:6, (1964), 1558.
Fukushima, K, Zwolinski, J ., J. Chem. Phys, 50:2, (1969), 737.
Bratoz, S., Hadzi, D., Sheppard, N., Spectrochim. Acta., 8, (1956), 249.

APPENDIX

APPENDIX

Table A1 Data for Figure 2.4

 

2.27 0.025 2.27 0.036
4.37 0.024 4.37 0.037
13.31 0.035 13.31 0.053
22.16 0.043 15.02 0.053
23.54 0.040 22.16 0.075
26.95 0.084 23.54 0.078
29.35 0.068 29.35 0.104
30.48 0.077 30.48 0.104
33.12 0.107 34.42 0.155
35.75 0.105 41.77 0.201
35.75 0.100 44.84 0.233
35.75 0.107 44.84 0.245
38.51 0.135 47.65 0.246
40.79 0.127 48.67 0.281
40.79 0.148 50.18 0.285
40.79 0.126 50.18 0.297
43.07 0.165 51.85 0.305
44.87 0.156 52.36 0.288
44.87 0.157 54.51 0.338
44.87 0.173 54.51 0.327
47.07 0.199 54.72 0.355
48.66 0.200 56.45 0.343
48.66 0.196 57.24 0.386
48.66 0.188 58.21 0.388
50.48 0.230 58.21 0.384
51.87 0.221 59.50 0.413
51.87 0.220 59.79 0.392
51.87 0.239 61.30 0.421
53.48 0.258 61.30 0.431
54.65 0.261 61.54 0.443
54.65 0.257 62.65 0.423
56.16 0.287 63.43 0.475
57.18 0.307 63.98 0.467
57.18 0.280 63.98 0.468
59.51 0.319 65.07 0.500
59.51 0.348 65.20 0.458
61.53 0.370 66.28 0.493
61.53 0.348 66.29 0.508

68.36 0 535

 

116

117

Table A2 Data for Figures 2.5 and 2.6

 

Temperature (°C) RT. at 10 °c Temperature (°C) RT. at 30 °C
2.27 0.043 2.27 0.056
4.37 0.051 4.37 0.064
13.31 0.089 13.31 0.117
22.16 0.160 15.02 0.127
23.54 0.113 22.16 0.239
26.95 0.277 23.54 0.289
29.35 0.328 29.35 0.405
30.48 0.403 30.48 0.472
33.12 0.436 34.42 0.641
35.75 0.547 41.77 1.069
35.75 0.528 44.84 1.483
35.75 0.551 44.84 1.301
38.51 0.675 47.65 1.632
40.79 0.888 48.67 1.719
40.79 0.927 50.18 2.165
40.79 0.853 50.18 1.900
43.07 0.983 51.85 2.006
44.87 1.284 52.36 2.316
44.87 1.265 54.51 2.501
44.87 1.289 54.51 2.974
47.07 1.380 54.72 2.559
48.66 1.768 56.45 3.047
48.66 1.847 57.24 3.043
48.66 1.803 58.21 3.336
50.48 1.821 58.21 3.946
51.87 2.405 59.50 3.568
51.87 2.333 59.79 3.826
51.87 2.390 61.30 4.642
53.48 2.321 61.30 4.091
54.65 2.965 61.54 4.255
54.65 3.031 62.65 4.527
56.16 2.797 63.43 4.791
57.18 3.915 63.98 5.611
57.18 3.771 63.98 4.792
59.51 4.871 65.07 5.326
59.51 4.801 65.20 5.454
61 .53 5.512 66.28 6.482
61.53 5.589 66.29 5.451

68.36 6.491

 

118

Table A3 Data for Figures 2.7 and 2.8
Temperature (°C) RT, etdev In RT. RT;
10 0.266 0.007 3.410
15 0.319 0.009 4.317
20 0.382 0.009 5.305
25 0.429 0.008 6.735
30 0.484 0.009 8.271
35 0.532 0.012 9.597

etdev in RT;

0.143
0.215
0.328
0.454
0.739
1.074

119

 

 

 

Table A4 Data for Figures 3.3 and 3.5
TR
TR Supersaturation
Temperature TR Temperature Supersaturation) Temperature proﬁle
(°C) Solubility (°C) proﬁle (°C) continued

52.70 4.821 66.50 7.508 62.21 7.296
56.60 5.611 66.44 7.425 62.05 7.378
60.51 6.443 66.38 7.529 61.90 7.252
64.51 7.408 66.32 7.611 61.74 7.345
66.47 7.874 66.24 7.501 61.59 7.332
TR 66.16 7.459 61.44 7.239
Temperature Metastable 66.08 7.531 61.29 7.354
° Limit 65.98 7.495 61.15 7.357
60.13 7.28 65.89 7.515 61.00 7.269
58.26 6.72 65.78 7.352 60.85 7.230
54.59 5.92 65.68 7.533 60.70 7.210
53.68 5.51 65.57 7.471 60.55 7.250
50.67 5.03 65.45 7.452 60.40 7.180
65.33 7.537 60.30 7.240
65.20 7.449 60.15 7.210
65.07 7.441 60.00 7.270
64.94 7.414 59.75 7.240
64.81 7.495 59.60 7.200
64.67 7.353 59.45 7.250
64.53 7.349 59.34 7.202
64.38 7.394 59.69 7.326
64.23 7.461 60.32 6.976
64.09 7.475 60.60 6.960
63.93 7.508 60.64 6.997
63.78 7.280 60.64 6.774
63.63 7.504 60.64 6.771
63.47 7.378 60.57 6.836
63.32 7.474 60.57 6.716
63.16 7.275 60.55 6.676
63.00 7.316 60.27 6.605
62.84 7.425 60.23 6.582
62.68 7.273 60.35 6.621
62.53 7.440 59.94 7.130
62.37 7.345 60.15 7.100

 

 

120

Table A5 Data for Figure 3.6

Temperature
Temperature (°C) Temperature Temperature
(°C) Parabolic (°C) (°C)
Time Parabolic Time cooling Time Int. parabolic Time Linear
(sec) cooling (sec) continued (sec) cooling (sec) cooling
0 63.04 1400 58.69 0 63.56 0 62.68
40 63.04 1440 58.42 40 63.45 20 62.26
80 63.03 1480 58.15 80 63.34 40 61.83
120 63.03 1520 57.86 120 63.21 60 61.40
160 63.02 1560 57.56 160 63.08 80 60.97
200 63.00 1600 57.26 200 62.94 100 60.54
240 62.98 1640 56.95 240 62.79 120 60.11
280 62.94 1680 56.63 280 62.64 140 59.68
320 62.90 1720 56.30 320 62.47 160 59.25
360 62.85 360 62.30 180 58.81
400 62.79 400 62.12 200 58.38
440 62.73 440 61.93 220 57.95
480 62.65 480 61.73 240 57.51
520 62.57 520 61 .53 260 57.08
560 62.48 560 61.31 280 56.64
600 62.38 600 61.09 300 56.21
640 62.27 640 60.86
680 62.16 680 60.62
720 62.04 720 60.38
760 61.90 760 60.12
800 61.76 800 59.86
840 61.62 840 59.59
880 61.46 880 59.31
920 61.30 920 59.02
960 61.13 960 58.72
1000 60.95 1000 58.42
1040 60.76 1040 58.10
1080 60.56 1080 57.78
1120 60.36 1120 57.45
1160 60.14 1160 57.11
1200 59.92 1200 56.77
1240 59.69 1240 56.41
1280 59.46 1280 56.05
1320 59.21 1320 55.68
1360 58.96 1360 55.30

 

 

 

 

 

 

 

121

Table A6 Data for Figure 3.7

 

 

TR
TR Supersaturation
Temperature Supersaturation Temperature Proﬁle
Proﬁle (°C) continued
56.13 5.526 61.54 6.988
56.30 5.609 61.62 6.954
56.47 5.667 61.69 6.931
56.63 5.716 61.76 6.837
56.79 5.714 61.84 6.922
56.95 5.730 61.90 6.970
57.11 5.809 61.97 6.854
57.26 5.758 62.04 6.960
57.41 5.823 62.10 7.048
57.56 5.826 62.16 6.944
57.71 5.918 62.22 7.070
57.86 5.926 62.27 7.065
58.00 5.926 62.33 7.070
58.15 6.033 62.38 7.089
58.29 6.039 62.43 7.079
58.42 6.021 62.48 7.099
58.56 6.079 62.52 7.201
58.69 6.190 62.57 7.036
58.83 6.195 62.61 7.191
58.96 6.212 62.65 7.159
59.09 6.270 62.69 7.137
59.21 6.255 62.73 7.261
59.33 6.309 62.76 7.203
59.46 6.312 62.79 7.160
59.58 6.386 62.82 7.210
59.69 6.347 62.85 7.226
59.81 6.501 62.88 7.307
59.92 6.517 62.90 7.287
60.03 6.486 62.92 7.312
60.14 6.517 62.94 7.286
60.25 6.522 62.96 7.114
60.36 6.447 62.98 7.194
60.46 6.482 62.99 7.366
60.56 6.707 63.00 7.278
60.66 6.599 63.01 7.340
60.76 6.619 63.02 7.215
60.85 6.729 63.02 7.176
60.95 6.770 63.03 7.316
61.04 6.753 63.03 7.282
61.13 6.858 63.03 7.294
61.21 6.757 63.03 7.289
61.30 6.883 63.04 7.322
61.38 6.765 63.04 7.270
61.46 6.910 63.04 7.228

122

 

 

Table A7 Data for Figure 3.8
Tn
Tn Supersaturation
Temperature Supersaturation Temperature Proﬁle
(°C) Profile (°C) continued

55.296 5.3865 60.744 6.6312
55.487 5.4195 60.862 6.7642
55.677 5.5388 60.978 6.8338
55.864 5.4821 61.092 6.7956
56.049 5.5299 61.204 6.8988
56.232 5.6675 61.314 6.8647
56.412 5.658 61.422 6.8572
56.591 5.7099 61.528 6.8928
56.767 5.7356 61.631 6.7263
56.942 5.7091 61.733 6.946
57.114 5.7315 61.833 7.1089
57.285 5.801 61.93 7.1234
57.453 5.8375 62.026 7.1212
57.619 5.8934 62.119 7.1956
57.783 5.9689 62.211 7.15
57.945 5.8844 62.3 7.196
58.104 6.0924 62.387 7.1268
58.262 6.0357 62.472 7.1791
58.418 5.9942 62.556 7.1612
58.571 6.1303 62.637 7.0954
58.722 6.0929 62.716 7.1826
58.872 6.1093 62.793 7.2122
59.019 6.1969 62.868 7.2826
59.164 6.3091 62.941 7.3143
59.307 6.3879 63.011 7.1401
59.448 6.336 63.08 7.1582
59.587 6.262 63.147 7.1531
59.724 6.3609 63.212 7.1343
59.859 6.4884 63.274 7.1327
59.991 6.4618 63.335 7.1691
60.122 6.4843 63.394 7.0479
60.25 6.4718 63.45 7.235
60.377 6.58 63.505 7.1843
60.501 6.5267 63.557 7.2077
60.624 6.6256

Data for Figure 3

Table A8
Ta
Temperature Supersaturation

(°C) Profile
56.207 5.6364
56.643 5.7073
57.078 5.7531
57.513 5.7942
57.947 5.9737
58.38 6.1093
58.813 6.1557
59.246 6.4522
59.677 6.4576
60.108 6.7233
60.539 6.7861
60.969 7.0622
61.398 7.1281
61.827 7.0984
62.255 7.1642
62.682 7.2312

123

124

Table A9 Data for Figure 3.10

CSD (Stweight)
CSD (Stweight) Intermediate CSD (Straight)
Parabolic parabolic Linear
Size cooling cooling cooling
(microns) proﬁle proﬁle proﬁle
180 0.00 0.52 0.44
265 0.40 1.40 2.08
373 4.10 13.16 45.84
463 4.90 9.58 15.88
550 9.20 14.80 14.78
655 13.10 13.62 5.28
780 23.70 21.84 1.90
925 18.00 12.88 0.00

1000 13.30 5.14 0.00

125

Table A10.1 Data for Figure 3.11

 

 

Tn TR
Concentration Concentration
Temperature line Temperature line
(°C) 60 % wlw (°C) 60 % wlw
56.89 4.827 56.90 4.795
56.86 4.778 56.86 4.833
56.82 4.764 56.81 4.811
56.76 4.838 56.76 4.856
56.71 4.801 56.70 4.853
56.64 4.807 56.64 4.882
56.57 4.774 56.57 4.864
56.50 4.772 56.50 4.822
56.42 4.750 56.43 4.784
56.33 4.762 56.35 4.758
56.24 4.694 56.27 4.794
56.15 4.739 56.19 4.839
56.05 4.762 56.10 4.790
55.95 4.783 56.01 4.785
55.84 4.714 55.91 4.773
55.74 4.772 55.81 4.850
55.63 4.768 55.71 4.735
55.52 4.738 55.61 4.770
55.41 4.795 55.50 4.738
55.29 4.744 55.39 4.791
55.18 4.779 55.28 4.840
55.06 4.729 55.16 4.859
54.94 4.823 55.04 4.814
54.82 4.830 54.92 4.792
54.70 4.761 54.80 4.779
54.58 4.774 54.68 4.745
54.46 4.727 54.55 4.738
54.34 4.753 54.42 4.813
54.22 4.790 54.29 4.705
54.09 4.787 54.16 4.672
53.97 4.706 54.03 4.798
53.84 4.770 53.89 4.736
53.71 4.797 53.76 4.736
53.59 4.780 53.62 4.753
53.46 4.685 53.48 4.806
53.33 4.682 53.34 4.729
53.20 4.751 53.20 4.705
53.06 4.712 53.06 4.693
52.93 4.739 52.91 4.736
52.79 4.703 52.77 4.745
52.65 4.826 52.62 4.710
52.51 4.698 52.47 4.715
52.36 4.760 52.33 4.761
52.21 4.701 52.18 4.727
52.06 4.686 52.03 4.749
51.90 4.715 51.88 4.728

126

Table A10.2 Data for Figure 3.11

 

TR TR
Concentration Concentration
Temperature line Temperature line
(°C) 61 7. WM (°C) 61 % wlw
58.52 5.200 58.54 5.266
58.52 5.228 58.53 5.387
58.51 5.283 58.51 5.270
58.48 5.250 58.49 5.167
58.45 5.221 58.46 5.184
58.42 5.252 58.42 5.303
58.37 5.314 58.38 5.258
58.32 5.224 58.33 5.224
58.26 5.299 58.28 5.221
58.20 5.207 58.23 5.307
58.13 5.196 58.17 5.246
58.05 5.238 58.10 5.251
57.97 5.247 58.03 5.217
57.89 5.313 57.96 5.198
57.80 5.291 57.88 5.245
57.70 5.288 57.80 5.234
57.60 5.184 57.71 5.202
57.50 5.169 57.62 5.191
57.39 5.221 57.53 5.260
57.28 5.153 57.43 5.248
57.16 5.188 57.33 5.094
57.04 5.271 57.23 5.239
56.92 5.243 57.12 5.255
56.80 5.142 57.01 5.168
56.67 5.137 56.89 5.278
56.55 5.131 56.78 5.228
56.41 5.180 56.66 5.211
56.28 5.149 56.53 5.183
56.15 5.226 56.41 5.161
56.01 5.211 56.28 5.224
55.87 5.148 56.15 5.242
55.73 5.180 56.01 5.201
55.59 5.181 55.88 5.156
55.45 5.197 55.74 5.180
55.31 5.163 55.60 5.177
55.16 5.163 55.46 5.194
55.02 5.195 55.32 5.191
54.87 5.182 55.17 5.152
54.73 5.140 55.03 5.104
54.58 5.075 54.88 5.173
54.43 5.182 54.73 5.127
54.28 5.181 54.58 5.203
54.13 5.106 54.43 5.219
53.99 5.121 54.28 5.116
53.84 5.127 54.13 5.200
53.69 5.064 53.97 5.168

 

127

Table A10.3 Data for Figure 3.11

 

Tn TR
Concentration Concentration
Temperature line Temperature line
(°C) 62 % wlw (°C) 62 % wlw
60.34 5.685 60.29 5.832
60.33 5.703 60.32 5.768
60.32 5.730 60.33 5.704
60.30 5.754 60.33 5.786
60.27 5.710 60.32 5.760
60.24 5.777 60.30 5.756
60.20 5.795 60.27 5.719
60.15 5.655 60.24 5.681
60.10 5.751 60.19 5.709
60.04 5.716 60.14 5.690
59.97 5.759 60.09 5.681
59.90 5.670 60.02 5.710
59.83 5.637 59.95 5.712
59.75 5.622 59.87 5.751
59.66 5.696 59.79 5.661
59.57 5.712 59.70 5.772
59.47 5.656 59.61 5.614
59.37 5.573 59.51 5.759
59.27 5.730 59.40 5.734
59.16 5.707 59.30 5.734
59.04 5.700 59.18 5.725
58.93 5.691 59.07 5.634
58.81 5.699 58.94 5.682
58.68 5.765 58.82 5.594
58.55 5.666 58.69 5.639
58.42 5.675 58.56 5.720
58.29 5.670 58.43 5.661
58.16 5.613 58.29 5.677
58.02 5.654 58.15 5.692
57.88 5.596 58.01 5.640
57.74 5.651 57.87 5.608
57.59 5.554 57.72 5.655
57.45 5.625 57.58 5.719
57.30 5.568 57.43 5.721
57.15 5.673 57.28 5.644
57.00 5.640 57.13 5.584
56.85 5.538 56.98 5.529
56.70 5.506 56.83 5.577
56.55 5.634 56.67 5.613
56.39 5.577 56.52 5.551
56.24 5.626 56.36 5.581
56.09 5.561 56.21 5.536
55.94 5.598 56.05 5.632
55.79 5.565 55.90 5.541
55.63 5.565 55.74 5.612
55.48 5.498 55.59 5.489

 

128

Table A10.4 Data for Figure 3.11

 

TR TR
Concentration Concentration
Temperature line Temperature line
(°C) 63 7. w/w (°C) 63 % wlw
62.20 6.059 62.22 6.138
62.21 6.269 62.23 6.211
62.21 6.159 62.22 6.247
62.21 6.195 62.21 6.191
62.19 6.068 62.19 6.287
62.16 6.180 62.16 6.141
62.13 6.108 62.12 6.134
62.08 6.216 62.07 6.084
62.03 6.205 62.01 6.153
61.97 6.141 61.95 6.141
61.91 6.173 61.88 6.181
61.83 6.134 61.80 6.193
61.75 6.123 61.72 6.063
61.66 6.139 61.63 6.190
61.57 6.145 61.53 6.122
61.47 6.060 61.43 6.106
61.37 6.139 61.33 6.087
61.26 6.045 61.22 6.231
61.15 6.146 61.10 6.163
61.03 6.265 60.99 6.153
60.91 6.130 60.86 6.089
60.78 6.144 60.74 6.216
60.65 6.117 60.61 6.107
60.51 6.075 60.48 6.252
60.38 6.143 60.35 6.148
60.24 6.114 60.21 6.164
60.09 6.158 60.07 6.185
59.95 6.198 59.94 6.098
59.80 6.082 59.79 6.173
59.65 6.049 59.65 6.095
59.49 6.056 59.51 6.063
59.34 6.100 59.36 6.028
59.18 6.050 59.22 6.126
59.03 6.014 59.07 6.041
58.87 6.140 58.92 6.106
58.71 6.091 58.77 6.038
58.55 6.038 58.62 6.002
58.38 6.026 58.47 5.990
58.22 6.062 58.32 6.036
58.06 5.930 58.17 6.029
57.90 5.974 58.02 5.952
57.73 6.023 57.87 6.043
57.57 6.090 57.71 6.052
57.40 5.980 57.56 6.045
57.24 5.930 57.41 6.003
57.08 5.954 57.26 6.057

 

129

Table A10.5 Data for Figure 3.11

 

TR TR
Concentration Concentration
Temperature line Temperature line
(°C) 64 7. WM (°C) 64 % wlw
64.94 6.699 65.57 6.965
64.95 6.753 65.54 7.016
64.95 6.801 65.51 6.932
64.95 6.741 65.46 6.925
64.93 6.780 65.40 6.919
64.90 6.683 65.34 7.044
64.87 6.881 65.27 6.957
64.83 6.746 65.19 6.848
64.78 6.636 65.11 6.924
64.72 6.952 65.02 6.859
64.66 6.811 64.92 6.836
64.59 6.796 64.82 6.967
64.51 6.927 64.71 6.878
64.42 7.053 64.60 6.980
64.33 6.696 64.48 6.969
64.24 6.886 64.36 6.960
64.14 6.843 64.24 6.901
64.03 6.680 64.11 6.845
63.92 6.786 63.98 6.945
63.80 6.794 63.85 6.894
63.68 6.811 63.71 6.925
63.55 6.639 63.58 6.968
63.42 6.756 63.44 6.811
63.28 6.719 63.29 6.787
63.15 6.949 63.15 6.916
63.00 6.740 63.01 6.878
62.86 6.806 62.86 6.930
62.71 6.850 62.71 6.929
62.56 6.702 62.56 6.889
62.41 6.756 62.41 6.864
62.25 6.700 62.26 6.903
62.10 6.836 62.11 6.797
61.94 6.983 61.95 6.904
61.78 6.595 61.80 6.838
61 .62 6.964 61.64 6.712
61.46 6.913 61.48 6.791
61 .30 6.568 61.33 6.905
61.14 6.806 61.17 6.865
60.98 6.717 61.01 6.856
60.81 7.370 60.84 6.852
60.65 6.733 60.68 6.848
60.49 6.772 60.51 6.830
60.33 6.526 60.35 6.850
60.17 6.528 60.18 6.722
60.02 6.673 60.00 6.771
59.86 6.711 59.83 6.857

 

130

Table A10.6 Data for Figure 3.11

 

TR TR
Concentration Concentration
Temperature line Temperature line
(°C) 65 % wlw (°C) 65 "I. wlw
66.30 7.508 66.34 7.519
66.31 7.425 66.33 7.395
66.31 7.529 66.31 7.526
66.29 7.611 66.28 7.471
66.26 7.501 66.24 7.619
66.22 7.459 66.19 7.524
66.17 7.531 66.14 7.533
66.10 7.495 66.08 7.581
66.03 7.515 66.01 7.440
65.95 7.352 65.93 7.381
65.86 7.533 65.85 7.609
65.76 7.471 65.76 7.535
65.66 7.452 65.67 7.477
65.55 7.537 65.57 7.514
65.44 7.449 65.46 7.401
65.32 7.441 65.35 7.456
65.19 7.414 65.24 7.537
65.07 7.495 65.12 7.501
64.94 7.353 64.99 7.593
64.80 7.349 64.86 7.587
64.67 7.394 64.73 7.483
64.53 7.461 64.59 7.405
64.39 7.475 64.45 7.480
64.24 7.508 64.31 7.465
64.10 7.280 64.17 7.391
63.95 7.504 64.02 7.473
63.81 7.378 63.86 7.507
63.66 7.474 63.71 7.268
63.51 7.275 63.55 7.477
63.36 7.316 63.39 7.323
63.21 7.425 63.23 7.432
63.06 7.273 63.07 7.418
62.90 7.440 62.90 7.339
62.75 7.345 62.74 7.313
62.59 7.296 62.57 7.342
62.43 7.378 62.40 7.381
62.27 7.252 62.23 7.339
62.11 7.345 62.05 7.342
61.95 7.332 61.88 7.344
61.78 7.239 61.71 7.357
61.61 7.354 61.53 7.297
61.44 7.357 61.36 7.395
61.26 7.269 61.18 7.324
61.07 7.295 61.00 7.434
60.89 7.120 60.83 7.348
60.69 7.245 60.65 7.359

 

131

Table All Data for Figure 4.5

 

 

 

 

 

PIR. PIR‘ PIR.
Concentration Concentration Concentration
Temperature line Temperature line Temperature line
°C
35.55 1.810 42.98 2.221 50.33 2.602
35.55 1.821 42.98 2.156 50.33 2.548
35.55 1.808 42.98 2.125 50.33 2.480
35.20 1.797 42.51 2.136 49.84 2.459
34.79 1.827 42.10 2.042 48.88 2.462
34.02 1.748 41.29 2.056 48.42 2.301
33.66 1.751 40.80 2.021 47.91 2.301
32.86 1.746 40.38 2.016 46.96 2.306
32.51 1.723 39.55 1.904 47.91 2.206
38.77 1.871 45.58 2.237
38.38 1.972 44.72 2.194
37.53 1.846 43.82 2.091
43.44 2.123
PlR. PIR. PIR.
Concentration Concentration Concentration
Temperature line Temperature line Temperature line
(°C 59 % wlw (°C 62 96 wlw (°C) 65 it wlw
57.75 3.105 64.65 3.852 67.35 4.200
57.75 3.090 64.65 3.813 67.35 4.099
57.75 3.074 63.91 3.849 66.82 4.043
57.18 3.018 63.31 3.869 66.82 4.015
56.10 2.931 62.63 3.628 65.27 3.833
55.48 2.861 61.95 3.581 64.65 3.628
54.89 2.707 60.75 3.406 63.91 3.674
53.89 2.634 60.13 3.339 62.63 3.420
53.41 2.641 59.00 3.328 61.95 3.388
52.40 2.501 58.32 3.055 60.75 3.362
51.26 2.472 57.18 2.922
50.33 2.454 56.10 2.858
49.84 2.391 55.48 2.806
48.88 2.311 54.46 2.811
53.41 2.618
54.46 2.596
PlR.
Temperature PIR1 Solubility
(°C) Solubility stdev
31.09 1.696 0.043
36.07 1.835 0.044
40.99 2.027 0.036
45.88 2.231 0.038
50.73 2.461 0.053
55.57 2.805 0.042
60.53 3.253 0.128
65.43 3.778 0.058

132

Table A12 Data for Figure 4.6

PIR. PIR. PIR.
Concentration Concentration Concentration
Temperature line Temperature line Temperature line

50 %wlw °C

 
     

 

 

 

 

35.55 4.269 42.98 4.990 50.33 6.157
35.55 4.251 42.98 5.031 50.33 6.097
35.55 4.246 42.98 4.927 50.33 5.984
35.20 4.255 42.51 4.930 49.84 6.070
34.79 4.175 42.10 4.962 48.88 6.015
34.02 4.250 41.29 4.886 48.42 5.847
33.66 4.163 40.80 4.938 47.91 5.986
32.86 4.272 40.38 4.998 46.96 5.976
32.51 4.231 39.55 5.047 47.91 5.991
38.77 4.946 45.58 5.917
38.38 4.978 44.72 5.869
37.53 4.892 43.82 5.899
43.44 5.827
PIR. PlR. PIR,
Concentration Concentration Concentration
Temperature line Temperature line Temperature line
°C 59%wlw °C 62%wlw °C 65%wlw
57.75 7.443 64.65 8.669 67.35 10.606
57.75 7.484 64.65 8.863 67.35 10.793
57.75 7.290 63.91 8.526 66.82 10.639
57.18 7.174 63.31 8.435 66.82 10.904
56.10 7.163 62.63 8.808 65.27 10.358
55.48 7.121 61.95 8.709 64.65 10.814
54.89 7.185 60.75 8.509 63.91 10.715
53.89 7.169 60.13 8.831 62.63 10.885
53.41 6.962 59.00 8.450 61.95 10.530
52.40 7.104 58.32 8.661 60.75 10.792
51.26 7.041 57.18 8.735
50.33 7.161 56.10 8.540
49.84 7.160 55.48 8.367
48.88 7.199 54.46 8.588
53.41 8.470
54.46 7.884
54.456 2.596
PIR.
Temperature PIR. Solubility
°C Solubil etdev
31.09 3.888 0.025
36.07 4.463 0.040
40.99 5.213 0.054
45.88 6.042 0.108
50.73 7.106 0.071
55.57 8.431 0.144
60.53 9.753 0.191
65.43 11.327 0.255

133

Table A13 Data for Figure 4.10

 

 

 

Peak shift Peak shift Peak shift
relative to relative to relative to
Temperature 5862 nm. Temperature 5862 nm. Temperature 5862 nm.
(°C) 50 % wlw (°C) 54 % wlw (°C) 58 % wlw
ﬂ
35.55 -2.248 45.58 -4.249 55.48 -5.501
35.55 -2.053 45.58 -3.881 55.48 -5.701
35.55 -2.213 45.17 -3.826 54.89 -5.520
35.20 -2.186 44.72 -3.774 54.46 -5.329
34.79 -2.073 44.32 -3.725 53.89 -5.312
34.02 -1.806 43.82 -3.757 53.41 -5.062
33.66 -1.960 42.98 -3.340 52.40 -4.741
32.86 -1.523 42.51 -2.938 51.86 -4.682
32.51 -2.053 41.65 -2.503 50.82 -4.740
41 .29 -2.981 50.33 -4.575
40.38 -2.961 49.36 -4.474
40.01 -2.370 48.42 -3.824
39.18 -2.695 47.91 -4.114
38.38 -1.953 46.96 -3.862
Peak shift Peak shift Peak shift
relative to relative to relative to
Temperature 5862 nm. Temperature 5862 nm. Temperature 5862 nm. Solubility
(°C) 62 % wlw (°C) 65 % wlw (°C) Solubility stdev
64.65 -8.398 67.35 -8.489 31 .09 -0.977 0.169
64.65 -8.617 67.35 -8.561 36.07 -2.043 0.202
63.91 -8.396 66.82 -8.368 40.99 -2.794 0.170
63.31 -8.330 66.82 -8.415 45.88 -3.838 0.239
62.63 -8.047 65.27 8.477 50.73 -4.749 0.209
61.95 -7.995 64.65 -7.981 55.57 -5.529 0.223
60.75 -7.905 63.91 -7.617 60.53 -6.688 0.228
60.13 -7.179 62.63 -7.243 65.43 -7.756 0.208
59.00 -7.213 61.95 -7.372
58.32 -6.801 60.75 -7.006
57.18 -6.181
56.10 -6.394
55.48 -6.249
54.46 -5.699
53.41 -5.792
54.46 -5.928

134

Table A14 Data for Figure 4.11

 

 

 

Peak shift Peak shift Peak shift
relative to relative to relative to
Temperature 6996 nm. Temperature 6996 nm. Temperature 6996 nm.
(°C) 50 % wlw (°C) 54 % wlw (°C) 58 “I. wlw
35.55 -1.151 45.58 6.328 55.48 9.552
35.55 3.566 45.58 5.331 55.48 7.308
35.55 1.166 45.17 6.405 54.89 8.231
35.20 6.267 44.72 2.868 54.46 7.141
34.79 1.903 44.32 5.754 53.89 8.816
34.02 1.086 43.82 7.244 53.41 9.692
33.66 3.527 42.98 7.188 52.40 7.168
32.86 0.290 42.51 2.859 51.86 6.497
32.51 2.845 41.65 1.680 50.82 5.362
41 .29 6.264 50.33 6.958
40.38 2.811 49.36 6.468
40.01 3.072 48.42 5.502
39.18 1.297 47.91 5.693
38.38 0.036 46.96 4.811
Peak shift Peak shift Peak shift
relative to relative to relative to
Temperature 6996 nm. Temperature 6996 nm. Temperature 6996 nm. Solubility
(°C) 62 % wlw (°C) 65 % wlw (°C) Solubility stdev
64.65 11.394 67.35 12.417 31 .09 1.335 1.9211
64.65 11.345 67.35 12.668 36.07 2.425 1.0928
63.91 12.179 66.82 13.988 40.99 4.618 1.2584
63.31 11.454 66.82 13.071 45.88 5.289 1.2916
62.63 11.045 65.27 12.056 50.73 7.644 1.56
61.95 10.350 64.65 12.310 55.57 8.506 1.2934
60.75 10.703 63.91 9.703 60.53 10.167 1.2655
60.13 10.673 62.63 9.761 65.43 11.315 0.624
59.00 9.926 61.95 12.237
58.32 10.654 60.75 9.477
57.18 9.074
56.10 7.857
55.48 8.644
54.46 7.821
53.41 9.656
54.46 7.131

135

Table A15 Data for Figure 4.12

Peak shift Peak shift Peak shift
relative to relative to relative to
Temperature 6132 nm. Temperature 6132 nm. Temperature 6132 nm.
(°C) 50%wlw 54%wlw 58%wlw

 

 

 

 

    

 

35.55 3.512 45.58 6.967 55.48 8.809
35.55 3.270 45.58 6.081 55.48 9.298
35.55 3.474 45.17 6.719 54.89 8.744
35.20 3.635 44.72 6.585 54.46 9.384
34.79 3.208 44.32 6.328 53.89 8.879
34.02 4.041 43.82 6.019 53.41 9.561
33.66 3.417 42.98 6.549 52.40 8.947
32.86 3.791 42.51 6.761 51.86 8.811
32.51 4.005 41.65 6.757 50.82 9.127
41.29 6.761 50.33 9.322
40.38 6.696 49.36 9.013
40.01 6.841 48.42 8.825
39.18 6.416 47.91 9.564
38.38 7.409 46.96 9.219

Peak shift Peak shift Peak shift

relative to relative to relative to

Temperature 6132 nm. Temperature 6132 nm. Temperature 6132 nm. Solubility

(°C) 62 7. WM (°C) 65 7. WM (°C) Solubility stdev

64.65 10.544 67.35 12.824 31.09 1.393 0.231
64.65 10.705 67.35 12.900 36.07 3.661 0.213
63.91 10.863 66.82 12.952 40.99 5.703 0.095
63.31 10.920 66.82 12.732 45.88 7.477 0.224
62.63 10.782 65.27 13.160 50.73 9.106 0.195
61.95 11.048 64.65 12.741 55.57 10.655 0.233
60.75 11.201 63.91 13.125 60.53 11.975 0.170
60.13 10.920 62.63 13.044 65.43 13.070 0.304
59.00 11.285 61.95 13.320

58.32 11.498 60.75 13.293

57.18 11.163

56.10 11.381

55.48 11.538

54.46 11.974

 

 

136

Table A16 Data for Figure 4.13

     
   
  

Peak shift Peak shift Peak shift
relative to relative to relative to
Temperature 8116 nm. Temperature 8116 nm. Temperature 8116 nm.

(°C) 50%wlw 54%wlw 58%wlw

    

 

  

     

 

 

 

 

 

35.55 6.819 45.58 20.491 55.48 38.830
35.55 4.485 45.58 19.741 55.48 38.320
35.55 5.930 45.17 22.158 54.89 37.229
35.20 3.135 44.72 19.635 54.46 39.925
34.79 5.184 44.32 20.274 53.89 39.178
34.02 6.295 43.82 18.960 53.41 36.583
33.66 4.825 42.98 20.863 52.40 38.129
32.86 4.792 42.51 19.793 51.86 35.421
32.51 5.742 41.65 18.537 50.82 34.888
41.29 18.327 50.33 32.548
40.38 15.997 49.36 34.933
40.01 16.935 48.42 34.745
39.18 16.618 47.91 35.662
38.38 17.829 46.96 31.451

Peak shift Peak shift Peak shift

relative to relative to relative to

Temperature 8116 nm. Temperature 8116 nm. Temperature 8116 nm. Solubility

 

 

(°C) 62 % wlw (°C) 65 % wlw (°C) Solubility stdev
64.65 53.528 67.35 69.036 31.09 1.131 1.136
64.65 56.172 67.35 68.751 36.07 7.816 1.636
63.91 56.863 66.82 67.874 40.99 17.108 1.437
63.31 56.867 66.82 66.194 45.88 26.476 1.253
62.63 59.180 65.27 65.671 50.73 35.933 1.640
61.95 54.014 64.65 67.824 55.57 46.750 1.564
60.75 54.919 63.91 66.519 60.53 58.742 1.904
60.13 53.250 62.63 67.325 65.43 68.751 2.166
59.00 53.760 61 .95 67.160
58.32 49.954 60.75 64.113
57.18 51.815
56.10 50.560
55.48 49.358
54.46 49.290
53.41 46.604
54.46 46.356

Table A17 Data for Figure 4.17

137

 

 

 

 

 

 

 

 

Peak shift Peak shift Peak shift
relative to relative to relative to
Temperature 3188 nm. Temperature 3188 nm. Temperature 3188 nm.
(°C) 50 % wlw (°C) 53 "/o wlw (°C) 56 % wlw
35.55 5.395 42.98 26.090 50.33 39.107
35.55 8.497 42.10 26.010 48.42 42.479
34.02 8.100 40.38 33.027 45.58 42.938
32.51 9.511 37.53 24.272 43.44 40.883
Peak sh? Peak“ Peak shift
relative to relative to relative to
Temperature 3188 nm. Temperature 3188 nm. Temperature 3188 nm.
(°C) 59 "/o wlw (°C) 62 % wlw (°C) 65 % w/w
E — —
57.75 60.487 64.65 75.847 67.35 91.172
55.48 59.729 61.95 76.282 65.27 91.234
52.40 62.326 58.32 78.015 62.63 92.522
48.88 60.050 54.46 74.498 60.75 95.901
Peak shifT
relative to
Temperature 3188 nm. Solubility
(°C) Solubility stdev
31.09 1.148 1.361
36.07 17.060 1.901
40.99 32.854 1.604
45.88 47.478 0.577
50.73 60.335 0.954
55.57 70.284 0.990
60.53 82.058 0.212
65.43 92.158 1.026

 

138

Table A18 Data for Figure 4.18
Temperature (°C) Temperature (°C) Temperature (°C) Temperature (°C)

 

 

64.60

0.73

Concentration at solubility at solubility at solubility at solubility
(it WM) from Figure 4.12. from Figure 4.13. from Figure 4.17. from Figure 4.6.
50 35.56 34.02 33.10 34.30
54 43.30 42.06 40.60 41.20
58 50.93 50.10 48.90 48.99
62 57.94 57.42 57.93 56.28
65 64.74 64.84 65.25 63.56
Average “meerature (°C)
Temperature (°C) stdev
34.25 1.02
41.79 1.17
49.73 0.97
57.39 0.78

Temperature

40.56
40.38
39.39
38.22
37.10
35.78
34.04
32.22
31.47
32.32
32.95
33.07
32.93
32.71
32.20
31.82
31.56
31.25
30.77
30.56
30.46
30.40
30.35
30.33
30.32
30.32
30.31
30.31
30.31
30.00
28.86
27.74
26.79
25.89
24.55
22.88
22.00
21.06
20.43
19.17
18.20
17.17
16.15
15.50
14.57
13.32
12.18
10.47

Table A19 Data for Figure 5.4

   

 

139

Temperature

35.30
30.26
25.17
20.05
15.01
9.92

TIR

2.869
2.511
2.229
1.956
1.738
1.468

 

 

H ’lv'c" x_"'-.' -xxdli ﬂ

 

MICHIGAN STQTE UNIV. LI
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31293014056‘