View metadata, citation and similar papers at core.ac.uk brought to you by CORE
provided by Digital Repository @ Iowa State University
Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations
1988 Solute clustering and crystallization from solution Irwan Tjahjadi Rusli Iowa State University
Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Chemical Engineering Commons
Recommended Citation Rusli, Irwan Tjahjadi, "Solute clustering and crystallization from solution " (1988). Retrospective Theses and Dissertations. 9723. https://lib.dr.iastate.edu/rtd/9723
This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS The most advanced technology has been used to photo graph and reproduce this manuscript from the microfilm master. UMI films the original text directly from the copy submitted. Thus, some dissertation copies are in typewriter face, while others may be from a computer printer. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyrighted material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are re produced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each oversize page is available as one exposure on a standard 35 mm slide or as a IT x 23" black and white photographic print for an additional charge. Photographs included in the original manuscript have been reproduced xerographically in this copy. 35 mm slides or 6" X 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order.
•lUMIAccessing the World's Information since 1938 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA
Order Number
Solute clustering and crystallization from solution
Rusli, Irwan Tjahjadi, Ph.D.
Iowa State University, 1988
UMI 300N.ZeebRd. Ann Arbor, M 48106
Solute clustering and crystallization from solution
by
Irwan Tjahjadi Rusli
A Dissertation Submitted to the
Graduate Faculty in Partial Fulfillment of the
Requirements for the Degree of
DOCTOR OF PHILOSOPHY
Major: Chemical Engineering
Approved:
Signature was redacted for privacy. In Charge of Major Work
Signature was redacted for privacy. For the Mafor Department
Signature was redacted for privacy. For the Graduate College
Iowa State University Ames, Iowa
1988 ii
TABLE OF CONTENTS PAGE
DEDICATION ix
ABSTRACT X
INTRODUCTION 1
LITERATURE REVIEW 7 Crystallization from Solution 7 Solubility and supersaturation 7 Nucleation 10 Homogeneous nucleation 11 Heterogeneous nucleation 14 Secondary nucleation 14 Crystal growth 16 Statistical surface models 16 Two-dimensional growth models 18 Continuous step models 19 Ion-Ion and Ion-Solvent Interactions and Solution Structure . . 21 Ion-ion and ion-solvent interactions 21 Raman spectroscopy and solution structures 24 Raman spectra of nitrates 25 Recent Studies 28 Raman study 28 Column experiment 29
EXPERIMENTATION AND RESULTS 37 Laser Raman Spectroscopic Study 37 Conventional Raman experiment 38 Experimentation 38 Sample cell for solution 38 Sample cell for melt 38 Raman spectrometer 40 Raman spectra acquisition 40 Results 42 Microprobe Raman experiment 53 Experimentation 59 Results 61 Column Experiment 63 Experimentation 63 Results 68 Microscopic Observation of Nucleation 72 Experimentation ..... 72 Sample cell 72 Procedure 72 Results 75
DISCUSSION 78 iii
PROPOSED MECHANISMS OF CRYSTALLIZATION FROM SOLUTION 89 Solute Clustering in Solution 89 Effect of supersaturation 90 Thermodynamic considerations of solute clustering 91 Cluster interface 100 Solute concentration within the cluster 101 Nucleation from Solution 101 Nucleation under metastable condition 105 Nucleation under unstable condition ..... 109 Metastable versus unstable nucleation mechanisms Ill Crystal Growth from Solution 115
CONCLUSIONS 118
RECOMMENDATIONS FOR FUTURE WORKS 121
BIBLIOGRAPHY 123
ACKN0WLEDQ4ENTS 127
APPENDIX: RESULTS OF CURVE-FITTING ANALYSIS 128 iv
LIST OF TABLES
PAGE
TABLE A.l. Results of curve-fitting analysis 128 LIST OF FIGURES
PAGE
FIGURE 1. Solubility curve 9
FIGURE 2. Free energy diagram (AG versus size) for homogeneous nucleation 13
FIGURE 3. Kossel's model for a growing crystal surface. Attachment of growth units (shown as cubes) at (A) flat surface (B) step (C) kink site 17
FIGURE 4. Two-dimensional growth models (Ohara and Reid, 1973) . . 20
FIGURE 5. Various forms of ionic solutes in an aqueous solution (Frank and Wen, 1957) 23
FIGURE 6. Raman amd infrared vibrational frequencies of free nitrate ions 26
FIGURE 7. Integrated intensities of component bands as functions of concentration for the NaNOg system (Hussmann et al., 1984) 30
FIGURE 8. Integrated intensities of component bands as functions of concentration for the KNO3 system (McMahon, 1984) 31
FIGURE 9. Integrated intensities of component bands as functions of distance from a growing crystal—NaNOg system (Hussmann et al., 1984) 32
FIGURE 10. Free energy change for cluster and nuclei formation (Larson and Garside, 1986a) 35
FIGURE 11. Effect of supersaturation on free energy curve (Larson and Garside, 1986b) 36
FIGURE 12. Schematic diagram of sample cell in Raman study of bulk solution 39
FIGURE 13. Schematic diagram of sample cell used in Raman study of melt 41
FIGURE 14. Raman spectrum of NaNOg powder 43 vi
FIGURE 15. Raman spectra of NaNOg crystal, melt, and solution ... 45
FIGURE 16. Raman spectra of solid, melt, and solutions at low wavenumber region 46
FIGURE 17. Comparison of spectra at different concentrations ... 47
FIGURE 18. Comparison of spectra of a solution at 35*C and at 70*C 49
FIGURE 19. Comparison of spectra of solution at saturation (30°C) and at 7*>C undercooled 50
FIGURE 20. Difference spectra between spectra at various undercoolings and the spectrum at saturation 51
FIGURE 21. Decomposition of a spectrum into a summation of a Cauchy and a Gauss distribution functions. The data and the sum of the two functions are also shown .... 54
FIGURE 22. Locations of peaks of the Cauchy and the Gauss component bands at various undercoolings 55
FIGURE 23. Relative areas of the Cauchy and the Gauss component bands at various undercoolings 56
FIGURE 24. Comparison of spectra of 2M solution systems: NaNOg-H^O and MaN03-D20 systems 57
FIGURE 25. Comparison Of spectra of 7M solution systems: NaN03-H20 and NaNOj-C^O systems 58
FIGURE 26. Schematic diagram of sample cell in micro Raman study of crystal-solution interface—stagnant solution system 60
FIGURE 27. Schematic diagram of sample cell in micro Raman study of crystal-solution interface—flowing solution system 62
FIGURE 28. Comparison of the spectra of solution at and near the crystal-solution interface—stagnant solution system . . 64
FIGURE 29. Comparison of the spectra of solution at and near the crystal-solution interface—flowing solution system . . 65
FIGURE 30. Schematic diagram of the column used in the column experiment 67 vii
FIGURE 31. Data for density differences between the bottom and top of the 40-cm column 69
FIGURE 32. Data for density differences between the bottom and top of columns for different column heights 70
FIGURE 33. Density gradient data along the column height. The height ratio of one corresponds to the bottom of column 71
FIGURE 34. Data for density differences between the bottom and top of the column in the presence of one or more growing crystals at the bottom of column 73
FIGURE 35. Schematic diagram of cell used in microscopic observation of nucleation 74
FIGURE 36. Crystal size versus time data for the microscopic observation experiment 76
FIGURE 37. Estimated cluster sizes as calculated from equation (18) 86
FIGURE 38. Concentration profile at and near crystal-solution interface of a growing crystal 88
FIGURE 39. Free energy versus solute mole fraction diagram for systems with (a) negative H and (b) positive H 93
FIGURE 40. Free energy versus mole fraction diagram for solution phases with solute clustering. The relative position of the solid phase is also shown 95
FIGURE 41. Free energy diagram of solute cluster system with a relatively small degree of change 98
FIGURE 42. Free energy diagram of solute cluster system with a relatively large degree of change 99
FIGURE 43. Free energy diagram of a cluster system 102
FIGURE 44. Concentration profile of the interface between the lower-ordered species amd the cluster phase 103
FIGURE 45. Free energy diagram of the solution phases of a solute clustering system 106
FIGURE 46. Free energy diagram of a metastable solution system . . 108
FIGURE 47. Free energy diagram of an unstable solution system . . . 110 vlil
FIGURE 48. Free energy curve showing the nucleatlon and the splnodal decomposition 112
FIGURE 49. Comparison between metastable and unstable nucleatlon mechanisms 114
FIGURE 50. Free energy diagram of solution and solid phases during crystal growth process 117 ix
DEDICATION
This work is dedicated to:
• author's parents, Mr. and Mrs. Lukmam Rusli, and author's
brother and sisters
• author's wife, Kiem (Leny)
• author's daughters, Melissa and Evelyn
• Mr. and Mrs. Theodore H. Lachelt of Carmel, California
• Mr. Horace (Randy) J. Randazzo of Carmel Valley, California and in memoriam to:
• author's brother, Rudy Rusli
• former Mrs. Yvonne (Bonnie) Randazzo of Carmel Valley,
California. ABSTRACT
Three experimental studies, consisting of a laser Raman
spectroscopic study, a vertical column experiment, and a microscopic
observation, were carried out to evaluate the structures and
characteristics of solute clustering in NaNO^ solution systems and the
relations between solute clustering and crystallization from solution.
The results of these experimental studies suggest that solute clustering occurs in NaNOg solution systems. These solute clusters are apparently solvated clusters that have no solid-phase structure, and they may exist in saturated and supersaturated, as well as in undersaturated, solutions. The relative number of the solute clusters and the degree of clustering increase with solution concentration. The results also suggest that with an observation field of about 20 microns, there is no significant difference between the solution structures at and near the crystal-solution interface of a growing crystal and that in the bulk solution.
For a given solution concentration, as the solution becomes supersaturated, a dynamic rearrangement occurs between lower-ordered ionic species and clusters. The present study explains this rearrangement process in terms of the coalescence of some of the clusters at the expense of other clusters and the dilution of the lower-ordered species.
Thermodynamic considerations and analyses of this solute clustering are described in terms of relationship of free energy versus xi the solute mole fraction. Models for the nucleation and the crystal growth mechanisms are proposed. These models are based on the fluctuations and changes in structures and properties of solvated solute clusters.
The proposed nucleation models consider two types of mechanisms: the mechanism that occurs under metastable conditions, and the mechanism that occurs under unstable conditions. The latter mechanism is associated with the spinodal-type decomposition. The proposed crystal growth model suggests a dynamic arrangement between the lower- ordered species and the clusters at and near the crystal-solution
Interface of a growing crystal. The model also suggests a depletion of the clusters as the solution concentration decreases during the growth process. 1
INTRODUCTION
Crystallization from solution is an important process operation in
many chemical process industries, such as the food, pharmaceutical,
mineral, and fertilizer industries. It is generally used as a method
for separation, purification, or both. Although historically it is one
of the oldest process operations and has been practiced extensively,
the understanding of the fundamental nature of industrial
crystallization processes has been very limited. As a consequence, the
development of many industrial crystallization processes has been based
only on a limited utilization of fundamental crystallization theory.
One of the main objectives in the crystallization process is the
production of crystals of desirable quality, shape, and/or size. The
quality of a crystal may include such features as its purity, strength,
and molecular structure. In many cases, careful control of the
crystallization process is critical in obtaining optimal crystal
characteristics.
During the past fifteen years, significant progress has been made
in the research and development of industrial crystallization
processes, most notably in the areas of crystal size distribution (CSD)
analysis and control. Much of this progress was made possible through
the use of the population-balance concept (Randolph and Larson, 1971)
that relates CSD and the kinetic parameters. Although the technique
has certain limitations, it has been successfully implemented in the development, design, and control of many industrial crystallization systems. 2
Advances in particle counting instrumentation have made it
possible to measure the CSD down to few-micron and submicron size
ranges. Most of the systems studied showed unexpectedly high
populations at these small size ranges (Estrin, 1976; Garside and
Davey, 1980). It was observed that many of these nuclei apparently do
not grow initially or do grow at immeasurably slow rates (Garside et
al., 1979). Recent studies suggest that some of the growing nuclei
undergo growth rate dispersion (Berglund, 1981; Ebrahim Khan, 1981;
Kaufman, 1980). Other reasons suggested for the high populations of
small crystals include excessive secondary nucleation and size-
dependent growth rates. These explanations, however, have not yet been
satisfactorily elaborated and they likely depend on the crystallizing
systems being considered. The anomalous behavior of high population- density numbers for the small size ranges causes some problems in the analysis of CSD, especially in the derivation of nucleation kinetics.
Additional information on the fundamental nature of the formation of these nuclei êuid of their subsequent growth behaviors is needed for optimal CSD control and analysis.
Understanding the process fundamentals and how they are affected by the operating parameters is essential for the optimal operation and control of the crystallization process. There are basically two phenomena governing the crystallization process: nucleation and crystal growth kinetics. These phenomena may closely compete with each other, or one may be dominant, depending on the degree of 3
supersaturation. Thus, one way to control the CSD of a crystallization
process is to control the relative supersaturation of the crystallizing
system. An understanding of nucleation and growth kinetics will
require knowledge of the nature of the supersaturated solutions and how
these solutions are affected by the operating conditions.
In a crystallizing system, the nucleation process may occur as a
result of different mechanisms. In industrial crystallization
processes that require optimal conditions for crystal growth, it is necessary to operate the system at a relatively low supersaturation level in order to avoid excessive nucleation. Under this condition, it is believed that secondary nucleation, defined as nucleation due to the presence of crystals of materials being crystallized, is the dominant source of nuclei. One of the most important forms of secondary nucleation is the contact nucleation that occurs when a crystal collides with other crystals or with other objects in the crystallizer, such as agitators, baffles, or walls. It is not surprising that many of the recent studies on nucleation processes have been directed toward understanding secondary nucleation processes, especially of contact nucleation (Botsaris, 1976; Clontz and McCabe, 1971; Johnson et al.,
1972).
It is likely that one of the important sources of secondary nuclei in contact nucleation is the parent crystals, through the micro- and macro-attrition mechanisms in which crystal breakages are dislodged by the contact process and subsequently become individual nuclei. Other 4
sources of secondary nuclei that have been suggested include the bulk
supersaturated solution and the so-called "semi-ordered" layer next to
the crystal-solution interface of the growing parent crystal (Botsaris,
1976). Direct experimental evidence of this "semi-ordered" layer is
not well established, and the identification of the bulk supersaturated
solution as a source of nuclei has been based on indirect observations.
The fundamental evaluation of the secondary nucleation process will
require an understanding of the structure of the supersaturated
solution at or near a growing crystal.
One of the spectroscopic techniques that can be used to evaluate
the characteristics of ionic interaction in an aqueous solution is
laser Raman spectroscopy. It is based on the light scattering
phenomena associated with molecular vibrational and rotational
energies. Most of the Raman studies of aqueous solutions, however,
have been of undersaturated solutions and have not been directed toward
the understanding of the crystallization process. Some of these
studies (Chang and Irish, 1973; Frost and James, 1982; Hussmann, 1984;
Irish, 1971; Irish and Brooker, 1976) present evidence of the formation of solute clusters or aggregates in ionic solutions. It has been
suggested that this ordering of the solute molecules occurs even before
saturation. Data concerning supersaturated solutions are very limited and are needed in order to evaluate the solution structures and their relation to crystallization from solution. 5
Using micro-Raman spectroscopy, Hussmann (1984) also evaluated the
solution structure at a distance of about 20 microns from the crystal-
solution interface of a growing crystal. It would be of interest to observe the solution characteristics at distances much closer than 20 microns.
An experimental study (Mullin and Leci, 1969) using citric acid solutions showed that when a column of. supersaturated solution was left undisturbed for about one day, a concentration gradient developed between the top euid bottom levels. A recent study (Larson and Garside,
1985a) confirmed this observation for several other systems and attributed this effect to the establishment of a quasi-equilibrium condition within the system. Furthermore, the study also suggested that the difference in solution concentrations at the top and at the bottom levels was associated with the effect of gravitational force on molecular clusters.
The above Raman studies and column experiments show evidences of molecular cluster formations in ionic solution systems. Further studies are needed in order to evaluate the nature of these clusters as the solution becomes supersaturated. The present study was undertaken in an effort to evaluate the structures and characteristics of solute clustering in NaNOg solution systems and the relations between solute clustering and crystallization from solution. Three experimental studies were performed: a laser Raman spectroscopic study, a vertical column experiment, and a microscopic observation. On the basis of the 6 results of these studies, the characteristics of the solute clusters in a crystallizing system and the models for nucleation and crystal growth mechanisms are proposed and discussed. 7
LITERATURE REVIEW
Crystallization from Solution
Crystallization from solution can be defined as the formation or
the deposition of solute material in its crystalline form from its
mother liquor. A solid phase will crystallize from its mother liquor
when its chemical potential is less than that of the dissolved solid.
Although in principle this difference in chemical potential is the
driving force for the crystallization process, in practice the
supersaturation level is used to express this driving force. The
establishment of a supersaturated condition with respect to the
crystallizing solute Is essential in order for the crystallization
process to occur. Once supersaturation has been established, the crystallization process can occur in two ways: (a) through the
formation of new nuclei or (b) through the growth of crystals.
Depending on process conditions, the nucleation and crystal growth processes may closely compete with each other, or one may dominate.
Solubility and super saturation
A saturated solution is a solution that is in equilibrium with the solid phase of the solute. When a solution contains more dissolved solute than its saturation concentration, it is said to be supersaturated. The saturation concentration is a function of temperature, and the curve of saturation concentration versus temperature is referred to as the solubility curve (Figure 1). The 8
characteristics of the solubility curve for a crystallizing system is
an important factor in determining the best method to attain
supersaturation. It has been recognized that supersaturation can be
obtained by three methods: by the evaporation of a saturated solution;
by the cooling of a saturated solution; and by the addition of another
substance that will reduce the solubility of the dissolved solids.
Lines AB and AC in Figure 1 illustrate the cooling and the evaporation
routes. The combination of these two methods may also be carried out as shown by line AD.
There are several ways to describe the supersaturation level.
These include:
1. the concentration difference,
C = C - C* (1)
where C* is the saturation concentration, and C is the
solution concentration
2. the supersaturation ratio
S = C/C* (2)
3. the relative supersaturation
a a (C - C*)/C* (3)
4. the undercooling
T a T* - T (4) 9
Su
STABLE
TEMPERATURE
FIGURE 1. Solubility curve 10
where T* is the saturation temperature, and T is the
solution temperature.
Unless otherwise stated, this report will use the undercooling term to
express the supersaturation level.
Ostwald (1897) introduced the concepts of metastable and labile
supersaturations as the supersaturation regions in which spontaneous
nucleation in the absence of solid particles will and will not occur,
respectively. In the metastable region, the supersaturation level is
not high enough to produce spontaneous nucleation, and crystallization
will occur only when the solid particles or seed crystals are available
for solute deposition.
Nucleation
The formation of crystal nuclei or the nucleation process can be
schematically categorized as follows:
Nucleation / \ Primary Secondary / \ Homogeneous Heterogeneous
The main criterion for this division is whether nucleation occurs
spontaneously in the absence of solute crystals (primary nucleation) or occurs because of the presence of solute crystals (secondary nucleation). Primary nucleation is further categorized into two types: homogeneous nucleation, which occurs spontaneously in the absence of 11
any foreign particles, and heterogeneous nucleatlon, which occurs
because of the presence of foreign particles.
Homogeneous nucleatlon The classical theory of homogeneous nucleatlon suggests the formation of solute molecules according to the following scheme (for example, as discussed by Mullin, 1972):
A + A = Ag
A2'*' A ® Ag
An-l+'A = An, (5) where A is an individual molecule and A^ is the critical-size clusters.
Further addition of molecules to the critical cluster A^^ would result in nucleatlon and subsequent growth. These molecular additions presumably occur in locally high supersaturation regions. Many of these clusters fail to reach critical size and simply dissolve because they are unstable.
The thermodynamic evaluation of the classical nucleatlon theory was first presented by Gibbs (1928), who described the formation of liquid droplets during condensation. This theory has been assumed to be applicable analogously to homogeneous nucleatlon from a solution.
During the formation of a more ordered structure, such as the molecular clusters in a solution, there is a change in Gibbs free energy that can 12
be represented by the negative contribution due to phase change (AGy)
and the positive contribution due to interface formation (AGg). Thus,
AG = AGy + AGg, (6)
or, for a spherical cluster of size r,
AG = 4/3 ff r^ AGv + 4 JT r^y, (7)
where AG^ is the free energy change per unit volume and y is the
surface tension. Figure 2 shows typical curves representing each term in equation (7). The maximum value, AGg, corresponds to the free energy change associated with the formation of a critical-size cluster having a radius r^. The formation of clusters of sizes r < r^ will increase the free energy of the system, and the clusters will therefore become thermodynamlcally unstable and tend to decrease in size (to dissolve). The formation of clusters of sizes r > r^ will be thermodynamlcally favorable, and the clusters will therefore tend to increase in size (to grow) and to become stable nuclei. The size of the critical-size nuclei can be estimated by setting d(AG)/dr = 0, in order to obtain
r^ = - 27/AGy. (8)
Note that the classical nucleation theory predicts continuous dissolution of the unstable clusters of sizes less than r^. 13
SIZE OF NUCLEUS (r)
FIGURE 2. Free energy diagram (AG versus size) for homogeneous nucleation 14
Heterogeneous nucleation The heterogeneous nucleation process,
which occurs because of the presence of foreign particles (e.g., dust
particles), will generally occur at relatively lower supersaturation
than will the homogeneous nucleation process. The foreign particles
presumably provide sites at which the nucleation can occur. The
presence of these sites will cause a decrease in the free energy change
for the formation of critical nuclei from that required for the
homogeneous nucleation process. Thus,
AGg (heterogeneous) = (homogeneous) (9)
where \i> is less than unity. This \l/ factor has been discussed in terms of the contact angle (angle of wetting) at the liquid-solid interface.
Secondary nucleation Because of its importance in industrial crystallization processes, secondary nucleation has received considerable attention. Strickland-Constable and Mason (1973) suggested several possible mechanisms by which the secondary nuclei may be produced. One of the most important forms of secondary nucleation is the contact nucleation that occurs when a crystal collides with another crystal or with other objects in the crystallizer (agitator, baffles, and walls). It is believed that this contact nucleation is the dominant source of nuclei in many of the industrial crystallization processes. Botsaris (1976) has suggested that the main sources of secondary nuclei can be classified as follows: 15
1. sources from the surface of the crystal (i.e., crystal
breakage),
2. sources in the bulk supersaturated solution, and
3. sources in the so-called "semi-ordered" layer next to the
crystal-solution interface.
It is likely that one of the important sources of secondary
nucleation is the parent crystal itself, through micro- and macro- attrition mechanisms. Experimental evidence for other sources (the
bulk supersaturated solution and the "semi-ordered" layer) have not been well established.
Many studies have been conducted to evaluate the effect of operating parameters on secondary nucleation. Larson (1981) summarized some well-accepted generalizations and facts concerning secondary contact nucleation.
1. It occurs as a strong function of supersaturation.
2. A variety of nuclei sizes are produced directly, ranging
from less than 2 microns to about 40 microns.
3. Number and size distribution of the nuclei produced depend
on contact energy, supersaturation, and the hardness of
material being contacted.
4. Nucleation can be induced by fluid shear.
5. Most nuclei immediately exhibit the characteristic habit.
6. Intermediate size nuclei exhibit growth dispersion.
7. Very small nuclei tend not to grow or to grow very slowly. 16
Comprehensive reviews of the secondary nucleation mechanisms have been
presented by Botsaris (1976) and Garside and Davey (1980).
Crystal growth
The crystal growth process in a supersaturated solution can be considered as a two-step process: the diffusion of the solute molecules into the crystal surface and the incorporation of the solute molecules in the crystal surface. Although a unified crystal growth theory has not been developed, there are several crystal growth models that deal with certain aspects of the crystal growth process. These models may be considered as parts of a more general crystal growth theory. Some of these models will be briefly discussed in the following sections. A more detailed discussion on the subject may be obtained from references by Benema (1976), Ohara and Reid (1973),
Mullln (1972), and Buckley (1951).
Statistical surface models The statistical surface models suggest that the crystal surfaces of growing crystals are microscopically rough and consist of many steps and kink sites as modeled by Kossel (1927). Figure 3 illustrates the crystal surface postulated in this model. The geometric requirement for the formation of the interface area of the new growth at the crystal surface suggests that the flat surface is not energetically favorable for growth unit attachment as compared with the steps, while the kink site is the most favorable. 17
FIGURE 3. Kessel's model for a growing crystal surface. Attachment of growth units (shown as cubes) at (A) flat surface (B) step (C) kink site 18
Jackson (1958) defined a dimensionless factor of surface
characteristic a as:
a = 40/2kT (10)
where * is associated with the binding energy and k is the Boltzmann constant. Also, assuming that the driving force for the crystal growth can be represented by the difference in the chemical potentials Aw of growth units in the solution and in the solid phases, one can define
0 - Ait/kT (11)
Thus, the value of 0 is related to the degree of supersaturation in the solution system. In general, low values of a correspond to relatively rough crystal surface. Ohara and Reid (1973) and Benema (1976) used computer simulation studies to evaluate the theoretical growth rates for various values of a and 0.
Two-dimensional growth models The two-dimensional growth models are based on the formation and the development of two- dimensional nuclei on the surface of the crystal. These nuclei presumably have steps and kink sites at their outer edges, which will accommodate the incorporation of growth units for further advancement of crystal growth. Depending on the spreading velocity of these nuclei as compared with the formation rate of other nuclei, Ohara and Reid
(1973) discussed three models in terms of the relation between the growth rate R and the supersaturation a, which, in general, can be put in the following form: 19
R = Mcj^expC-M/a) (12)
where M, n, and p are the characteristic constants. These models
include:
1. Mononuclear model, which occurs when the spreading velocity
of the nuclei Is infinitely fast compared with the formation
of other nuclei. The value of p in Equation (12) for this
model is about 1/2. Figure 4a illustrate this case.
2. Polynuclear model, which occurs when the spreading velocity
is very slow. The crystal grows by accumulating many new
nuclei to cover the entire surface. The value of p is about
3/2 (Figure 4b).
3. Birth and spread model, which occurs when the spreading
velocity of the nuclei and the formation of new nuclei are
at finite rates. The value of p is approximately 5/6
(Figure 4c).
Continuous step models The continuous step models are based on the suggestion that at relatively low supersaturation levels, the growth of a crystal can be explained in terms of the advancement of structural imperfections (especially, the screw dislocations) that will provide steps for the attachment of growth units. Burton et al. (1951) developed a continuous step model for crystal growth at relatively low supersaturation levels. They derived a well-known BCF equation:
R = C {ffVffc tanh(ffj./ff)} (13) 20
(a) MONONUCLEAR MODEL
(b) POLYNUCLEAR MODEL
(c) BIRTH AND SPREAD MODEL
FIGURE 4. Two-dimensional growth models (Ohara and Reid, 1973) 21
where C and are the characteristic constants. Note that Equation
(13) is reduced to a parabolic equation for a « a^:
R a (CoZ/og) (14)
and is reduced to a linear relationship for a » 9^:
R = Co (15)
Ion-Ion and Ion-Solvent Interactions and Solution Structure
Ion-ion and ion-solvent interactions
The molecular structure of an ionic solution can be described in
terms of a dynamic equilibrium involving ion-solvent and ion-ion
interactions. The nature of the solvent molecules amd the types of
ions present determine the characteristics and extent of these
interactions (Bockris, 1949; Bockris and Reddy, 1970; Buckingham,
1957).
Depending on the nature of the interactions, solvent molecules, anions, and cations can associate in several configurations. Frank and
Wen (1957) modeled the various structural arrangements in which ionic species can exist in an aqueous solution (Figure 5). Figure 5a shows the conditions in which the anions and the cations are completely surrounded by solvent molecules. In a very dilute system most of the ions presumably exist under this condition. As the concentration of ions is increased, some of the ions may share a common solvation 22
(hydration) sphere, which results in solvent-shared or solvent-
separated ion pairs (Figure 5b). As fewer solvent molecules are
available for sharing, the ions may be brought into direct contact with
each other, resulting in the formation of ion pairs (Figure 5c). At an
even higher concentration it is possible to form ion aggregates, as
shown in Figure Sd. It is likely that in a dynamic equilibrium
condition, all of these ionic species exist to some extent.
The nature of ion-ion and ion-solvent interactions for
concentrated solutions has been modeled in terms of quasilattice
interactions. Based on an x-ray diffraction study of concentrated
NaNOj solutions (5M and 7M), Caminiti et al. (1980) explained the data obtained in terms of quasilattice structure. Samoilov (1965) described
several x-ray diffraction studies that suggest the existence of a short-range order of ion-ion interactions in concentrated solution systems. Howe et al. (1974) conducted a neutron diffraction experiment of NiCl and obtained some evidence of quasilattice arrangement. Ghosh
(1918) suggested the concept of expanded lattice structures in concentrated ionic solutions. Samoilov (1965) proposed a model in which the solution is considered as a nonhomogeneous phase consisting of regions of water molecules and regions of ion molecules in a quasilattice structure. Several studies using the Raman spectroscopic technique appeared to support the quasilattice structure model. A more detailed discussion of these Raman studies will be given in the following section. 23
FIGURE 5. Various forms of ionic solutes in an aqueous solution (Frsmk and Wen, 1957) 24
Raman spectroscopy and solution structures
Raman spectroscopy Is a form of vibrational and rotational
spectroscopy similar to infrared (IR) spectroscopy. Unlike IR
spectroscopy, which is based on the absorption phenomenon, Raman
spectroscopy is based on the light-scattering phenomenon. The Raman
effect is due to the change in the polarizability associated with the
vibrational modes of the molecules. The selection rules for Raman and infrared spectroscopies differ, but they are complementary in nature, in that some molecular vibrational modes are observed in Raman, some are observed in IR, and others may be observed in both. When a monochromatic (visible or ultraviolet) light beam is incident on a sample, it will be absorbed, transmitted, reflected, or scattered. The scattered light may be elastically scattered, having the same frequency as that of the incident beam (the Rayleigh scattering effect), or it may also be inelastically scattered, having frequencies different from that of the incident beam (the Raman effect). This shift in frequency is associated with the molecular vibrational and rotational energies of the molecules. The Rayleigh scattering intensity is only about 10~^ of that of the incident beam, while the Raman intensity is in the order of
10 of that of the incident beam.
The Raman study is considered to be well suited for the study of the crystallization processes in aqueous solutions for the following reasons: 25
1. The Raman spectra of water is very poor and generally does
not cause interferences.
2. The sample cell can be fabricated easily from pyrex or
quartz glasses.
3. The experiment can be conducted while the crystallization is
taking place.
Raman spectra of nitrates Raman spectroscopy has been used
extensively in many studies to evaluate the characteristics of
undersaturated ionic solutions, especially the aqueous metal nitrates
(Davis, 1967; Chang and Irish, 1973). One of the main reasons for these extensive studies is that the Raman spectrum of the nitrate ions is considered to be very sensitive to environmental changes.
The free nitrate ion has a symmetry and has three Raman-active fundamental vibrational frequencies (Irish, 1971):
yi(Ai') at 1050 cm"l,
^3(2') at 1380 cm~^, and
i'4(E') at 716 cm"!.
Figure 6 shows the Ramw and infrared spectra of the free nitrate ion and the corresponding fundamental vibrational frequencies.
Comprehensive reviews of the Raman studies of nitrate systems have been presented by Irish (1971), Irish and Brooker (1976), Verall (1973), and
Tobias (1973). 26 -A , -A
RAMAN INFRARED 1384 1050 825 719 cm'^ E' AÎ AJ E' °3h ^3 ^1 ^2 ^4 FIGURE 6. Raman and Infrared vibrational frequencies of free nitrate Ions 27 Frost and James (1982) have studied the yi(Ai') Raman band of various nitrate systems. Using band component analysis, they decomposed the band into as many as four component bands and assigned these bands to four ionic species of free solvated ions, solvent- separated ion pairs, contact-ion pairs, and ion aggregates. They observed that the relative intensities of these component bands depended on the solute concentration and on the cationic species. For the NaNOg and LiNOy systems, they assigned four component bands corresponding to the above ionic species, while for the KNO3 system, only three component bands were assigned. Frost and James (1982) suggested a combined band for the solvent-separated and contact-ion pairs. In further studies by Frost and James (1982), the effect of temperature on ionic species concentration in a 2M ITaNOg solution was evaluated. The results suggest that at higher temperatures relatively more solvated nitrate ions are present in the system. These investigations clearly suggest that various ionic species, including the ionic clusters or aggregates, exist even at relatively low concentrations, and well before saturation. In concentrated solutions, it is expected that more structured ordering occurs as suggested by Irish (1971) in a Raman study of LiNOy systems. The data obtained in this study were explained in terms of the quasilattice structure. The x-ray diffraction studies mentioned earlier support this observation. Raman studies of the characteristics of ion-ion and ion-solvent interactions in supersaturated solutions have been very limited. Two 28 of the most recent studies (Hussmann, 1984; McMahon, 1984) on the Investigation of supersaturated solutions will be described in the following section. Recent Studies There are basically two types of studies that will be examined: the Raman study and the column study. These studies are closely related to the work described in this report. Raman study Two recent Raman studies by Hussmann (1984) and McMahon (1984) investigated the characteristics of supersaturated solutions of NaXOg and KIIO3 systans, respectively. These studies were directed toward the understanding of the crystallization process. Following the procedure described by Frost and James (1982), the studies decomposed the band into four component bands in the case of the NaNOg system and into two component bands in the case of the KMO3 system. Figures 7 and 8 show the relative integrated intensity of the individual component band, as a function of concentration, for NaNOg and for KNO3 systems, respectively. The saturation concentrations were 8.1M for the NaNOg system and 3.7M for the KNO3 system. Some observations and conclusions of these studies are as follows: 1. A significant ordering of the solute occurs even before saturation. 29 2. There is no detectable increase of higher-ordered species as the saturation concentration is exceeded. 3. Undercooling a saturated solution does not affect the solution structures when measured by Raman spectroscopy. McMahon (1984) also evaluated the effect of impurity additions in the KNO3 system. A reduction in higher-ordered species was observed when 200 ppm of Cr^* ions were added to the solution. In a further study, Hussmann (1984) used micro Raman spectroscopy in order to investigated the solution structures at distances of 20 and 100 microns from the crystal-solution interface of a growing crystal. The results indicated that there was a depletion of higher-ordered species in the diffusion layer close to the growing crystal (Figure 9). Column experiment Other recent experimental studies that evaluated the characteristics of supersaturated solutions are those of Mullin and Leci (1969), who studied the citric acid solution system, and of Larson and Garside (1986a), who studied the NaNOg system. In this experiment, an isothermal column of about 40 cm high and 4-5 cm in diameter was filled with a solution that was subsequently brought to a supersaturated condition by lowering its temperature. The supersaturated solution was then left undisturbed from one to several days. A concentration gradient was developed between the top and the bottom of the column. The solution concentrations were determined by refractive index measurement (Mullin and Leci, 1969) and by density measurement (Larson and Garside, 1986a). 30 1.00 o AQUATED IONS A SOLVENT SEPARATED IONS O CONTACT ION PAIRS • AGGREGATES 0.80 - 0.60 < 0.40 - 0.20 0.00 0.00 4.00 6.00 CONCENTRATION mol dm-3 FIGURE 7. Integrated Intensities of component bands as functions of concentration for the NaNOg system (Hussmann et al., 1984) 31 1.00 RELATIVE INTENSiflES a - 1050.5 cm"^ b - 1049.0 cm'^ 0.80 co -jO.40 0.20 0.006 0.00 0.80 1.60 2.40 3.20 4.00 CONCENTRATION (M) FIGURE 8. Integrated Intensities of component bands as functions of concentration for the KNO3 system (McMeUion, 1984) 32 1.00 O AQUATED IONS A SOLVENT SEPARATED IONS 0.80 O CONTACT ION PAIRS • AGGREGATES sS 0.60 — 2 0.40 « 0.20 0.00 j. j. 0.0 20.0 40.0 60.0 80.0 100.0 i t DISTANCE FROM GROWING CRYSTAL pm FIGURE 9. Integrated intensities of component bands as functions of distance from a growing crystal—NaNO, system (Hussmann et al., 1984) 33 Larson and Garside (1986a) explained this concentration gradient in terms of excess molecular clusters. On the basis of the assumption of a quasl-equilibrium condition, they described the change In free energy (dGg) for a differential height in the column (dh) as follows: dGj, = OGg/ah) dh + OGg/aP) dP + OGc/aXj,) dXg, (16) where the terms on the right represent the effects of gravity, pressure (P), and mole fraction (Xg) changes, respectively, on the free energy (Gg) of the system. Using the thermodynamic relationships 8Gg/9h = -yMg, 3Gg/9P = yv, dP= pgh, and (17) aCg/aXg = (RT/Xg), one can obtain Equation (18) In (Xga/Xgj) = y[(M-pv)/RT]gH (18) where y = number of molecules in a cluster, M = molecular weight, g = gravitational acceleration, v = molal volume of the cluster, and subscripts B and T correspond to the bottom and top of column, respectively. Equation (18) suggests the relation between the concentrations of clusters at the top and the bottom of the column and the number of molecules in a cluster. If one further assumes that the concentration of the clusters can be represented by the difference between the solution concentration and the saturation concentration, then 34 ln(Xcg/XcT) a ln{(Xg-%g)/(xT-Xg)} (19) where Xg and Xq, are solute mole fractions at the bottom and top of the column, respectively, and x, is the solute mole fraction at saturation. Equation (19) relates the solution concentrations at the top and bottom levels of the column with the number of molecules in a cluster. Subsequently, the size of the cluster can also be determined. In a later study, Larson and Garside (1986b) explained the existence of these clusters by modifying the free energy equation of the classical nucleation theory to include the effect of cluster size on the interfacial tension. The resultant free energy curve (curve b in Figure 10) for the cluster system shows the presence of minimum free energy at a cluster size less than the critical size. The curve a shown in Figure 10 is for the classical nucleation theory. Figure 11 shows the cluster formation curves for different supersaturation levels; curve 2 is at a lower supersaturation level than curve 1, while curve 3 is at a higher supersaturation level than curve 1. It can be seen from Figure 11 that as the system becomes more supersaturated, the size of the critical nuclei decreases, while the relative size of the clusters increases with degree of supersaturation. 35 \ CLUSTER SIZE, r \ \ FIGURE 10. Free energy change for cluster and nuclei formation (Larson and Garside, 1986a) 36 • o < Cluster size.r |nm) I (5 -20 -30 -50 FIGURE 11. Effect of supersaturation on free energy curve (Larson and Garside, 1986b) 37 EXPERIMENTATION AND RESULTS Three different types of experimental studies were conducted for the present work: a laser Raman spectroscopic study, a vertical column experiment, and a microscopic observation of nucleatlon. The experimental apparatus, procedures, and results of each experiment are described in this section. Sodium nitrate (NaNOg) solution systems were used in all experiments. The saturated solutions were prepared by mixing the excess amount of solute materials required to reach saturation with deionlzed water at a given temperature. The slurries were agitated for at least 24 hours in order to ensure saturation. The crystals were prepared by slowly growing the seed crystals. Well-grown crystals were then selected and used. Laser Raman Spectroscopic Study Two types of experiments were carried out in the laser Raman spectroscopic study: a conventional Raman study and a microprobe Raman study. The conventional Raman experiment was performed in order to study the structures of the bulk solution, while the microprobe Raman experiment was carried out in order to study the solution structures at and near the crystal-solution interface of a growing crystal. 38 Conventional Raman experiment In this experiment, the Raman spectra of NaNOg solutions were obtained and evaluated. The effects of concentration, supersaturation, and solvent systems were studied. The spectra obtained were compared with those of the melt and the solid phase. Experimentation Sample cell for solution The sample cell was similar to that used by Hussmann et al. (1984), except for certain modifications designed to improve the temperature control. The cell consisted of 1-cm square, water-jacketed quartz tubing of about 6 cm in length (Figure 12). It had two outlets of 6 mm in diameter and 1 cm in length. The cell was surrounded by circulating water inside the jacket, except at the two outlet ports. The cell used by Hussmann et al. (1984) had no water circulation at the two outlet ports nor at either end of the cell. The solution temperature was controlled by the temperature of the water circulating from a constant-temperature bath. The sample solution was filtered twice through a preheated syringe and a Millipore 0.22 micron filter (Type Millex-GV-025LS). After the solution was placed in the cell, the cell outlets were closed by rubber septa. Sample cell for melt The Raman cell used in obtaining the spectra of the NaXOg melt consisted of a piece of quartz tubing with a square section at the middle and round sections on each side (Figure 13). The NaNOg powder was placed inside the square tubing, and the 39 SOLUTION WATER INLET WATER OUTLET FIGURE 12. Schematic diagram of sample cell in Raman study of bulk solution 40 heat was provided by a heating tape wrapped around the tubing. The temperature of the melt sample was about 320*0. Raman spectrometer The Raman spectrometer used was a Spex model 1403 double monochromator equipped with a photomultiplier tube (Product For Research, Inc.) detector. The signals from the detector were sent to a Spex Digital Photometer. Both the Spex double monochromator and the Digital Photometer were interfaced with a Nicolet model 1180E computer in order to collect and accumulate data. The laser source was provided by a Spectra Physics model 2000 argon ion laser. In all test runs, a laser beam with a wavelength of 514.5 nm was used. The laser beam was directed through a Spex model 1460 Tunable Excitation Filter and then into a Spex model 1459 UVISIR Illuminator, which focused the beam at the sample and also focused the scattered radiation at the entrance slit of the double monochromator. The laser beam was passed once through the sample, and the scattered light was collected at a 90" angle from the incoming beam. The entrance slit of the monochromator was set at different widths, depending on the required resolution and signal intensity. Raman spectra acquisition In a typical Raman spectra acquisition run, the monochromator was calibrated with the carbon tetrachloride liquid capillary tube, the NaNOg powder, or both. The sample cell containing the solution was then placed in the sample chamber, and the optics were realigned for optimal signal collection. The typical spectra were taken with a laser power of about 0.2 Watts at 41 SQUARED TUBING INSULATOR HEATER ROUND TUBING sssssss FIGURE 13. Schematic diagram of sample cell used in Raman study of melt 42 the sample and with a scanning rate of about 0.5 an''Vsec. The spectra -1 were digitized at every 0.01 cm . The spectral resolution was about 0.5 cm"^. The Raman spectrum of a given spectral region was obtained by accumulating the signals obtained from multiple scans. In order to obtain spectra with relatively high signal-to-noise ratios, ten scans were usually accumulated for the solution spectra, while only a few scans were needed for the solid spectra. Results Figure 14 shows the spectrum of the NaNOg powder, which indicates the three vibrational frequencies of the nitrate ions. It can be seen that the relative intensity of the yi(Ai') vibrational frequency (at about 1068 cm~^) is much higher than those of the y^CE') —1 —1 and C4(E') located at 720 cm and 1380 cm , respectively. Unless otherwise stated, the spectra obtained and discussed in the present study refer to that of the yiC&i') vibrational frequency of the nitrate ions. The typical peak locations for these spectra are in the range of 1050 cm"^ to 1070 cm"^. The comparison of the spectra of the solution (saturated and measured at 30*C), the melt, and the solid phase (Figure 15) indicates a shift in the relative spectral positions towards higher wavenumber regions as one proceeds towards the more ordered structures (i.e., from the solution phase, to the melt phase, to the solid phase). There appears to be an overlap between the solution and the melt spectra, while the solid phase spectrum is somewhat separated from both the solution and the melt phases. Slight overlap is noted between the melt 1.0 NaNO* POWDER 0.9 0.8 < lU OL 0.7 g 0.6 0.5 lU oc 0.4 >- W t (0 z 0.3 0.2 0.1 0.0 I 500 600 700 800 900 1000 1100 1200 1300 1400 FIGURE 14. Raman spectrum of NaNOg powder ^^^^NUMBER 44 and the solid phases. It is expected that significant thermal broadening occurs in the spectra of the melt phase. In order to further evaluate the spectral differences of the solution, melt, and solid phases, the spectra of the low wavenumber region (below 250 cm"^) were obtained. For a crystalline phase, one or more peaks will occur at this low wavenumber region that will correspond to the lattice phonon of the crystalline phase. This lattice phonon is the characteristic of the lattice structure associated with the long-range molecular interactions in the crystalline phase. The results (Figure 16) indicate the presence of the lattice phonon peaks in the spectra of the solid phase. No lattice phonon was observed in the spectra of the saturated nor in the spectra of the supersaturated solution (up to 10*C undercooled). A weak and broad band is noted in the spectrum of the melt. These results further suggest that there seems to be no solid phase structure in the solution phase, even at a relatively high supersaturation level. The spectra of several NaNOg solutions at different levels of concentration are shown in Figure 17. The data were smoothed with the Savitsky-Golay smoothing routine, which is based on a nine-point averaging technique (Savitsky and Golay, 1964). Except for the saturated solution, the solutions were prepared by diluting saturated solutions with different amounts of deionized water. The results, as shown in Figure 17, show that as the solution concentration is increased, the spectrum shifts to a higher wavenumber region (i.e., towards the solid phase spectrum). 1.0 NaNO, SPECTRA 0.9 SOLUTION (SATURATED AT 30*C) 2 0.8 S 0.7 g g 0.6 CRYSTAL 0.5 lU flC 0.4 UI MELT AT @20»G Z 0.3 g 2 0.2 0.1 0.0 imWn di di l-i imm fVWwlhriLAWfl 1020 1030 1040 1050 1060 1070 1080 WAVENUMBER FIGURE 15. Raman spectra of NaNO^ crystal, melt, and solution. NaNO. SYSTEM ^CRYSTAL MELT (AT 320»C) SOLUTION (10*0 UNOERCOOLED AT 20*C) SOLUTION (SATURATED AT 30»G) 50 75 100 125 150 175 200 225 250 WAVENUMBER FIGURE 16. Raman spectra of solid, melt, and solutions at low wavenumber region 1. 0 NaNO. SOLUTIONS AT 30*0 0. 9 < 0. 8 lU Q. SATURATED SOLUTION O 0. 7 / NO DILUTION H U1 DILUTED 3:1 (HgO) > 0. 6 DILUTED 1:1 (H.O) H 0. 5 DILUTED 1:3 (H.O) UJ cc 0. 4 > H tn 0. 3 z lU H 0. 2 Z 0. 1 0. 0 1020 1030 1040 1050 1060 1070 1080 WAVENUMBER, CM'^ FIGURE 17. Comparison of spectra at different concentrations 48 In the present study, supersaturation was achieved by cooling the solution. Because the effect of supersaturation on Raman spectra could also be due to cooling, it was necessary to determine the effect of the temperature alone. Two spectra of a solution saturated at 30*C were obtained at 35"C and 70*C (Figure 18). There was some indication that the solution spectrum shifted slightly to the right (i.e., towards higher wavenumbers) as the solution was cooled. Irish and Davis (1968) also obtained similar results. The experimental study of the effect of supersaturation was carried out by subsequently cooling a solution of a given concentration from an undersaturated condition to a supersaturated condition. The spectra were taken at several predetermined undercoolings during the cooling process. Figure 19 shows the comparison between spectra at saturation and at 7"C undercooled, and Figure 20 shows the difference between the spectra at each level of undercooling with that at the saturation condition. The peaks at the lower wavenumber region indicate a shift towards the lower wavenumber region with respect to the spectrum at the saturation condition. This shift toward a lower wavenumber region indicates an increase in the intensity of the lower wavenumber region of the spectra and a slight decrease in the intensity of the higher region of the spectra. The data were further analyzed by decomposing the spectra into component bands. After the data were normalized and smoothed, a nonlinear curve-fitting analysis based on the Gauss-Newton technique 1.0 NaNO. SOLUTION 0.9 SATURATED AT 30»C T-aOOÇ (A) 0.8 T"7S«C (B) 0.7 g UJ 0.6 > 5 0.5 w 0.4 et DIFFERENCE (A - B) >- 0.3 t €0 z 0.2 lU 0.1 0.0 -0.1 1020 1030 1040 1050 1060 1070 1080 WAVENUMBER. CM'^ FIGURE 18. Ccxnparison of spectra of a solution at 35°C and at 70°C 1.0 NaNO, SOLUTION 0.9 SATURATED AT 30»0 ' 30*C (A) < 0.8 T-23«C (B) lU 0. 0.7 0.6 UJ > 0.5 lU 0.4 (C in > 0.3 o fc <0 z 0.2 DIFFERENCE (B - A) P! 0.1 0.0 -0.1 1020 1030 1040 1050 1060 1070 1080 WAVENUMBER. CM ^ FIGURE 19. Comparison of spectra of solution at saturation (30»C) and at 7"C undercooled NaNOa SOLUTION SATURATED AT 30»C DIFFERENCE SPECTRA T=20®C - T=30®C - T-30®C T=26®C - T=30®C T«35®C - T-30®C 1 1020 1030 1040 1050 1060 1070 1080 WAVENUMBER. FIGURE 20. Difference spectra between spectra at various undercoolings and the spectrum at saturation 52 (SAS Institute, Inc., 1985} was then performed with a summation model of a Cauchy function and a Gauss function, as described by Equation (20): I = Kg {B/(B^ + (y - + (Kg /S) {exp(-(y - fg) W)} (20) where Kg, B, and are parameters associated with the Cauchy distribution, and Kg, S, and Cg are parameters associated with the Gauss distribution. This summation model was found to be the best two- function model for the curve fitting purpose. Furthermore, the results seem to indicate that the Cauchy distribution represents more of the lower wavenumber region of the spectra, while the Gauss distribution represents more of the higher wavenumber region (Figure 21). Figure 22 shows the plots of the location of the peaks of the Cauchy and Gauss distributions versus degrees of undercooling. The solutions used in run series A and B were saturated at 30*>C. Additional results are given in Appendix. The data show that as the solution becomes supersaturated up to about 7*C undercooled, the peak locations of both distributions shift toward lower wavenumbers. At undercooling higher than 7*>C, a slightly reversed trend is noted. The relative intensities of each component distributions are determined by the relative areas of each distribution. Figure 23 shows the relative areas of the Cauchy and the Gauss distributions as a function of undercooling. It can be seen from this figure that the relative areas of the Gauss distribution 53 Increase with supersaturation, while the relative areas of Cauchy distribution decrease with supersaturation. The effect of solvent was studied so that the solvation characteristics of the solute clusters could be studied. In this study, several solvent systems were tested: methanol, dimethylsulfoxide (OMSO), dimethylformamide (DMF), and D2O. Except for the D2O system, there seem to be some problems associated with the use of these solvent systems. These problems include low solubility (methanol) and spectral interferences (DMSO and DMF). Thus, only the D2O system was used in the present study. Two levels of solute concentrations, 2M and 7M, of NaN0j-H20 and NaN03-D20 systems were evaluated. The results for the 2M concentration show no significant difference between the spectra of the two solution systems (Figure 24). kt the higher concentration of 7M, there was a significant difference in the location of the spectra. The spectrum for the NekH03-D20 system was located to the right of the spectrum for the NaN03-H20 system (Figure 25). The results suggest that there is a pronounced increase in the solute-solvent Interaction as the solute concentration is increased. Microprobe Raman experiment In the microprobe Raman experiment, the Raman spectra of NaNOg solutions at and near the crystal-solution interface were evaluated. The spectra were compared with that of the bulk solution. CAUCHY + GAUSS < UJ Û. g UJ CAUCHY > ûl DATA s > GAUSS b CO z lU 0.0 1020 1030 1040 1050 1060 1070 1080 WAVENUMBER. CM ^ FIGURE 21. Deccm^sition of a spectrum into a summation of a Cauchy and a Gauss distribution functions. The data and the sum of the two functions are also shown 55 1052 QAUSS 1051 - o# RUN SERIES A § o • RUN SERIES B S 1050 - 5 CAUCHY a £ r % % % II III , 1 \ 1049 - J UNDER- SUPER SATURATED SATURATED 1048 1 -5 0 5 10 Undercooling, FIGURE 22. Locations of peaks of the Cauchy and the Gauss component bands at various undercoolings 56 1.0 o • RUN SERIES A 0.9 o m RUN SERIES B « 0.8 m 2 0.7 C « I 0.6 CAUCHY 0 e 1 — u P 1 • 1 t 1 1 « ( 1 t 1 S 0.4 t QAU88 1 0.3 - « 5Œ 0.2 _ 0.1 UNDER- SUPER SATURATED SATURATED 0.0 1 -5 0 5 10 Undercooling, FIGURE 23. Relative areas o£ the Cauchy and the Gauss component bands at various undercoolings NaNOg - 2.5M SOLUTIONS INH^O (A) < INDqO (B) tu Q. >lU U1 flC U1 -a > H (0 DIFFERENCE (B - A) z IS -0.1 1020 1030 1040 1050 1060 1070 1080 WAVENUMBER. CM'^ FIGURE 24. Con^arlson of spectra of 2M solution systems: NaM03-H20 and NaN03-D20 systems 1.0 NaNO, - 7M SOLUTIONS 0.9 (A) 0.8 < INDoO (B) g 0.7 0.6 UJ > 0.5 0.4 UJ flC 0.3 U1 >- a> fc 0.2 0) z lU 0.1 0.0 •0.1 DIFFERENCE (B - A) -0.2 ± 1020 1030 1040 1050 1060 1070 1080 WAVENUMBER. FIGURE 25. Comparison of spectra of 7M solution systems: MaN03-H20 and HaH03-D20 systems 59 Experimentation The microprobe used was a Spex 1482 Micramate Micro-sample Illuminator. It is a research-grade Zeiss microscope modified for Raman spectroscopic studies of microscopic scale. This microprobe system was grafted to the side entrance slit of the Spex model 1403 double monochromator previously described. A lOX, 0.22 numerical aperture objective lens was used in the microscope. After passing through the Spex model 1460 Tunable Excitation Filter, the laser beam was directed to the microscope and was focused on the sample. The size of the focused beam was about 20 microns in diameter. The laser power used was about lOmW at the sample. The spectral resolution was about 2 cm The microscope was equipped with a camera and a monitor for viewing the focused beam during alignment. Two types of experiments were carried out, one in which the crystal grew in a stagnant solution and the other in which the crystal grew in a flowing solution. In both experiments, the solutions were filtered once through No.4 Whatman filter paper. The experiment with the stagnant solution used a sample cell consisting of a thin, flat compartment of about 0.1 cm in thickness and 2 cm in diameter. It was made of a thin metal plate (2.5 cm x 7.5 cm x 0.1 cm) with a hole of about 2 cm in diameter. A thin cover glass was glued to the bottom of the hole. This sample cell was placed in a temperature-controlled holder that consisted of a cell holder and metal tubing in which the water flowed from a constant-temperature bath. Figure 26 is the schematic diagram of the sample cell and its holder. 60 METAL PLATE TOP VIEW COVER GLASS SIDE VIEW CRYSTAL AND SOLUTION COMPARTMENT (a) PLATE CELL PLATE CELL IS TO BE PLACED HERE BASE PLATE BRASS TUBING WATER OUT WATER IN (b) CELL HOLDER FIGURE 26. Schematic diagram of sample cell in micro Raman study of crystal-solution interface—stagnant solution system 61 In the test run, a small crystal of about 0.3cm X 0.3cm X 0.1cm were placed in the cover glass that had been preheated. A few drops of solution, saturated at a few degrees lower than that of the plate temperature, were carefully placed so that the crystal was within the solution. A thin cover glass was then placed on top of the crystal and solution. The temperature was then lowered slowly so that the solution was about 2*C undercooled. The spectrum of the solution at distances from 20 microns down to the interface was taken. Another spectra was also taken at a location eUwut 100 microns from the interface. In the experiment with the flowing solution, quartz glass tubing of about 1 cm in diameter and 10 cm in length was used. The middle section of this tubing was a 1-cm square quartz tube of about 4 cm in length. Figure 27 is the schematic diagram of the cell. In the test run, a single crystal was placed at the center of the square quartz tubing. The solution was then pumped from a reservoir through the cell and back to the reservoir. The linear velocity of the solution is about 0.3 cm s~^. A peristaltic pump was used to pump the solution. The temperature of the reservoir was adjusted so that the temperature at the square section was about 2<*C undercooled. The spectra were taken alternatively between the locations of 20 microns and less and of 100 microns from the interface. Results The comparison between the spectra of the solution phase at distances from 20 microns down to the interface and those at about 100 microns from the interface shows no significant difference 62 MICROSCOPE CRYSTAL OBJECTIVE LASER SOLUTION SQUARED FLOW BEAM TUBING BEAM SPOT ~ 100 MICRONS FROM CRYSTAL 'SOLUTION FLOW BEAM SPOT ~ 20 MICRONS FROM CRYSTAL 77777 GROWING / CRYSTAL/, FIGURE 27. Schematic diagram of sample cell in micro Raman study of crystal-solution interface—flowing solution system. 63 for the two cases tested in the present study. Figure 28 shows the spectral comparison for the case with the stagnant solution. As can be seen, the solid phase peak shows up in the spectra for the distances of less than 20 microns, which suggests that the beam spot touched the crystal-solution interface. Figure 29 shows the spectral comparison for the case with the flowing solution. Only the solution spectra were shown in this figure. These results show that with the 20 microns beam spot at and near the crystal-solution interface of a growing crystal, the present study could not detect the presence of significant solute clustering of much higher degree than that in the bulk solution. Column Experiment The purpose of this experiment was to study solute concentration gradients developed in a vertical, isothermal column. The effects of test duration, of degree of undercooling, and of column height are evaluated. Exper imentation The experimentation was basically similar to that performed by Larson and Garside (1986a) and by Mullin and Leci (1969). The apparatus consisted of a vertical, cylindrical glass column of about 4 cm in diameter that was equipped with a water jacket for constant temperature operation. Three different column heights were used: 40 cm, 80 cm, and 120 cm. Each column had five sampling ports equidistant between the top and bottom of the column. These sampling ports could 1.0 CRYSTAL - SOLUTION 0.9 INTERFACE <20 MICRON < 0.8 100 MICRON a.m 0.7 g UJ 0.6 0.5 tu fC 0.4 at > b CO 0.3 z IS 0.2 0.1 0.0 1020 1030 1040 1050 1060 1070 1080 WAVENUMBER, (:M ? FIGURE 28. Comparison of the spectra of solution at and near the crystal-solution interface- stagnant solution system 1.0 CRYSTAL - SOLUTION INTERFACE 0.9 <20 MICRON < 0.8 100 MICRON a! 0.7 S! 0.6 0.5 UJ 0.4 cc > 0.3 CO z 0.2 lU 0.1 0.0 -0.1 1020 1030 1040 1050 1060 1070 1080 WAVENUMBER, CM'^ FIGURE 29. Comparison of the spectra of solution at and near the crystal-solution interface- flowing solution systan 66 be closed with serum cap stoppers (rubber septa) so that solution samples could be removed with syringes. The stopper that covered the column also had a water jacket so that close control of temperature could be achieved. Figure 30 is the schematic diagram of the 40-cm column. In a typical test run, a clean, empty column was initially preheated by circulating water from a temperature-controlled bath through the column jacket. The temperature was usually about 5*C warmer than the saturation temperature of the solution to be tested. The saturated solution was transferred to the column by a peristaltic pump. The transfer tubing was equipped with heat exchanger tubing, which made the solution undersaturated during transfer, and with an on line filter, which filtered dust particles. Number 4 Whatman filter paper was used. After being filled with the solution, the column was maintained at the elevated temperature for about 30 minutes in order to dissolve any small crystals that might have formed during transfer. The column temperature was then lowered to the operating temperature, and the column was then allowed to stand for one to three days, depending on the objectives of the experiment. The solute concentrations of the sample solutions were determined by their densities. The density measurements were carried out with a Mettler/Paar DMA 55 Density Meter. This instrument is capable of measuring a density to within 2 x 10~^ g/ml. All density data were determined at 40.0<*C. 67 JACKETED STOPPER •WATER CIRCULATION 'OUTLET 40 cm SAMPLE PORTS (COVERED BY RUBBER SEPTA) = 0^ 0.7 cm OD WATER CIRCULATION INLET 4 cm M 6 cm FIGURE 30. Schematic diagram of the column used in the column experiment 68 Results Figure 31 shows the differences in the densities of the solution samples obtained from the top and bottom of the 40-cm column at various levels of supersaturation ratio S (defined as the ratio of the actual solution concentration to the saturation concentration at the operating temperature). The corresponding concentration differences are also shown in the figure. No significant density differences were observed when the solutions were saturated or undersaturated. As can be seen from the figure, no significant variations in concentration gradients were observed for the different levels of supersaturation tested. Also, there were no significant differences in concentration gradients for the test duration of one to three days. This suggests that the observed concentration gradients were established in about one day or less. The test results for the different column heights of 40 cm, 80 cm, and 120 cm also indicated no significant variations in concentration gradients with column height as shown in Figure 32. In most test runs, it was noted that the concentration profiles in the column indicated a sudden increase in concentration at the bottom of the column, as shown by the data in Figure 33. The above results were obtained from tests in which no crystals were formed in the solution. In some test runs, one or more crystals formed and grew at the bottom of the column. Solution samples were also taken for these runs, and the results show that there were also concentration gradients in which the concentration at the bottom of the 69 60 NmNO. - H.O tysUm (•aturat«d at 30*G) f 1 Day 50 X 2 Daya 6 3 Daya 40 X X 30 X + X + A & 20 + 10 1.000 1.005 1.010 1.015 Supersaturation ratio, S " c/c* FIGURE 31. Data for density differences between the bottom cund top of the 40-cm column 70 60 NaNOa - H.O _ at about 30*0) 6 Teat Duration Undargoollno 1 day 50 2*0 S O 3*0 ^ A 4 « CO 40 m - 4 E S a 0 O CO 30 3 9 o a a X m o 1 S 20 ^ 0 - 2 2 A • s X 10 0 1 < 1 1 1 40 80 120 160 Column height, cm FIGURE 32. Data £or density differences between the bottom and top of columns for different column heights - 71 1.3941 ° 40 çn^cojumn^ û 80 cm column o 120 cm column Cy 1.3940 // / 1.3939 I o» â >% g 1.3938 o- O <>• • o- 1.3937 1.3936 0.0 0.2 0.4 0.6 0.8 1.0 Column height, h/H — fraction of total height FIGURE 33. Density gradient data along the column height. The height ratio of one corresponds to the bottom of column 72 column (i.e., just above the growing crystals) was higher than the concentration at the top of the column as shown in Figure 34. The concentration ratios shown in Figure 34 indicate the supersaturation ratios before the crystals were formed during the tests. Thus, the results suggest that the concentration gradients were apparently maintained in the presence of growing crystals. Microscopic Observation of Nucleation Microscopic observation of nucleation was conducted so that the relative size of the nuclei initially produced under a very high level of supersaturation could be determined. Experimentation Sample cell In this experiment, a few drops of NaNOg solution (saturated at 33*C) were placed and sealed in a thin compartment cell of about 1.5 cm x 1.5 cm x 0.1 cm. The cell was prepared by initially glueing the edges of a thin cover glass to a microscope glass plate, allowing for a small opening necessary for the insertion of a needle. The cell was then filled completely with the solution through a heated syringe. The small opening was sealed with the glue, and the cell was placed and glued inside an open container. Figure 35 is the schematic diagram of the cell inside the container. Procedure Initially, the cell containing the solution was placed in an oven at about 50*C for about one hour in order to ensure the condition of undersaturation. The cell was then placed under a 73 60 NmNO. - H-O #y#tem ^ (••turat«d at about 30*G) - 6 Column h#laht# Duration 4.0 120 cm 50 - 1 day o # o 2 day# • • - 3 day# 6 a s z 09 CO «d 1 40 - 4 E o o X 0 (0 e o CO -TOP] • - 2 0 i o 1 a 20 2 2 < o • CD • X 10 1 < n 1 1 . 1 1.000 1.005 1.010 1.015 ^ 1.020 Supersaturation ratio, S - c/c (prior to crystallization) FIGURE 34. Data for density differences between the bottom and top of the column in the presence of one or more growing crystals at the bottom of column 74 KD ^ I*® SIDE VIEW GLUE © MICROSCOPE OBJECTIVE © COVER GLASS (0.1 cm ABOVE GLASS PLATE) ^ GLASS PLATE ® PLASTIC CONTAINER (1) © TOP VIEW FIGURE 35. Schematic diagram oC cell used in microscopic observation of nucleation 75 microscope, and the container was filled with water at about 35°C. The solution was scanned by use of the microscope in order to check if crystals were present. The microscope was connected to a camera and a video cassette recorder (VCR). After it was ascertained that no crystals were present, the warm water was withdrawn from the container via the syringe and the iced water was placed in the container. At that moment, the timer was started, and the solution was then scanned for a crystal. After one was located, the growing crystal was monitored for several minutes. Results Figure 36 shows the plot of crystal size versus time for two crystals obtained in two similar runs. The crystals obtained had the typical habit of a well-grown NaNOg crystal and had no indications of overgrown or needle-type structures. The crystal size was determined by measuring its length. The data show that the growth rates of the crystals were relatively constant, at about 1 micron/sec after the initial observation of the nuclei. Extrapolation of the data to zero time suggests that the nuclei either formed directly at relatively large sizes of about 20 to 40 microns or initially grew at a significantly higher rate. In any case, the results appear to support the model of a relatively large cluster being formed under a condition of very high supersaturation, just before the nucleation process. 76 160 NmNOg Solution Saturitod at 33*G Quonehod to 0"G 120 S IE 80 \ \ \ I \ /X 40 y 1 1 ' 1 10 20 30 40 50 Time, toe FIGURE 36. Crystal size versus time data for the microscopic observation experiment 77 It Should be noted here that in some runs, the nuclei were not observed until after one minute. The data of these runs are not shown in Figure 36. In all tests, however, the sizes of the first nuclei observed were comparable to those given here. 78 DISCUSSION The shape of the Ramaui spectra of the solution obtained in the present study, especially those at higher concentrations, indicates that the spectra are generally asynmetrical. The comparison of the spectra at different solute concentrations (Figure 17} shows asymmetrical changes between the lower wavenumber region and the higher wavenumber region of the spectra. The present study attributes this spectral asymmetry to the presence of more than one type of ionic species in the solution system. Recent studies (Hussmann et al., 1984; Frost and James, 1982) suggested as many as four types of ionic species may be present in NaNOg solution systems. The results of the vertical column experiment show that a concentration gradient exists when a supersaturated solution is placed in a vertical column. The relatively higher solute concentration at the bottom of the column is likely due- to the presence of more of the higher-ordered ionic species (i.e., those having higher solute concentrations) at the bottom of the column than at the top of the column. The microscopic observation of the nucleation process in a highly supersaturated solution suggests the formation of relatively large solute clusters prior to nucleation. All of the aforementioned results suggest that solute clustering takes place in NaNOg, in which stable solute clusters exist. These solute clusters presumably have a higher solute concentration than does the lower-ordered species. 79 The spectra of the solution systems with different concentration levels indicate no significant change in the general shape of the spectra (i.e., no new shoulder or peak developed) as the the solution concentration is increased. Also, the curve-fitting analysis of the spectra indicates that the spectra can be satisfactorily represented by a relatively simple model of the sum of two distribution functions, a Gauss and a Cauchy function. Considering these observations, the present study considers the solute clustering in NaNOg solution systems in terms of two groups of ions associations, the lower-ordered species and the higher-ordered species. The higher-ordered species will also be referred to as solute clusters or simply as clusters. In the following discussion, the results of the experimental studies will be discussed in relation to the nature and characteristics of the solute clusters and to the effect of supersaturation. The shift toweurds higher wavenumber regions with increasing concentration suggests that the higher wavenumber regions represent the higher-ordered ionic species. A previous study with aqueous MgSO* solution system (Davis and Oliver, 1973) attributed the higher- frequency shoulder of the sulfate spectra to the formation of a contact-ion-pair species. Hayes et al. (1984) arrived at a similar conclusion in their Raman study of the (NH*)2S04 solution system. They also suggested that the higher-ordered region of the spectra shows more Gaussian-like distribution than the lower-ordered region. The spectral analysis used in the present study seems to be consistent with this 80 conclusion: the lower-ordered species are represented by the lower wavenufflber regions with a Cauchy-like spectral distribution and the higher-ordered species are represented by the higher wavenumber region with a Gaussian-like distribution. The results of the effects of concentration also indicate that the relative amount and degree of solute clustering of both the lower- ordered species and the cluster phase increase with concentration. Thus, at different levels of concentration, the solution systems will establish different distributions between the higher-ordered species and the lower-ordered species. Furthermore, the degrees of clustering of the lower-ordered species and the higher-ordered species will be different at different solute concentrations (for example, the higher- ordered species at 8M solution will have a higher degree of solute clustering than those at 2M solution). Thus, the terms lower-ordered species and higher-ordered species used in the present study are relative terms depending on solute concentration. The laser Raman spectroscopic study of the solution system shows that no crystalline phase structure exists in NaNOg solution systems tested in the present study, even in systems with a relatively high level of supersaturation. The solution systems tested had solute concentrations ranging from 2M to about 8M. These results are in disagreement with those of Hussmann et al. (1984), who suggested that the cluster (aggregate) phase had a solid-like structure. In their curve-fitting analysis, in which the solution spectra were decomposed 81 into four component bands, Hussmann et al. (1984) suggested that the presence of the solid-phase component band gave better curve-fitting results. The present study finds that the decomposition of the solution spectra into two nonsolid phase bands gives satisfactory curve-fitting results. Furthermore, considering the relatively large peak separation between the solution and the solid-phase spectra and considering the absence of lattice phonon in the low wavenumber region, the present study suggests that there are no crystalline or solid-phase structures in the solution systems tested. The method of spectral analysis presented in this study is somewhat different than that of Hussmann et al. (1984). In this study, the spectra of the solution phase were decomposed into a sum of two distribution functions, the Cauchy and the Gauss functions, while in the study carried out by Hussmann et al. (1984), the spectra of the solution phase were decomposed into four Lorentzian-Gaussian product functions. Note that the Cauchy distribution is similar to the Lorentzian distribution. Also, the present study allows the peak of each component band to vary, while in Hussmann's study the peak of each component band is fixed at a given wavenumber. The results of solvent effects indicate that at a relatively high solute concentration, both the lower-ordered species and the clusters are affected by the change in the solvent system. The present study interprets these results in terms of the solvated structure of the cluster phase. The clusters apparently consist of solute and solvent 82 molecules. As the relative amount of cluster increases in the solution system, the solute-solvent interactions within the solvated solute clusters will become more pronounced. For a given solute concentration, as the solution becomes supersaturated, there are some indications that both the lower wavenumber and the higher wavenumber regions of the spectra shift towards the lower wavenumbers (i.e., the spectra apparently shift towards lower wavenumber region). This is confirmed by the shifts towards the lower wavenumbers of the peak locations of both the Cauchy and the Gauss component bands (Figure 22). However, the results also show that the Gauss characteristics of the spectral distribution apparently increases with supersaturation (Figure 23). Because the increase in the Gauss characteristics of the spectra indicates an increase in the ion-ion interactions, some of the clusters apparently become more ordered with increasing supersaturation. Thus, the results suggest that as the solution becomes supersaturated, some of the clusters become less ordered as indicated by the shift towards lower wavenumbers, while other clusters become more ordered as indicated by the increase in Gauss characteristic of the spectra. Furthermore, the shift toward the lower wavenumber region of the spectra suggests that some of the lower-ordered species become less ordered with the increase in supersaturation. The present study interprets these results in terms of the coalescence and/or growth of some of the clusters, the breakup of other clusters, and the dilution of some of the lower- 83 ordered species. As the solution becomes supersaturated, some of the clusters coalesce and/or grow to form larger clusters that may also have a higher internal solute concentration. Because these larger clusters have lower specific surface areas and have higher solute concentration than before coalescence and/or growth, some of the solvent molecules that have been associated with the clusters prior to coalescence are freed to the surroundings and consequently dilute other clusters and the lower-ordered species. It is noted that at supersaturation levels of higher than 7*0 undercooling, there is a slightly reversed trend in which the spectra shift towards a higher wavenumber region. The Gauss characteristic of the spectra apparently continues to increase with supersaturation. This may indicate that some of the coalesced clusters undergo significant increase in the degree of clustering at relatively high supersaturation levels. The shift of the spectra towards the lower wavenumber region, as the solution becomes supersaturated, was also observed by Hussmann et al. (1984). On the basis of an analysis of the Raman spectra of several NaNO^ solutions of different concentrations, they observed that the spectra of the supersaturated solution (2°C undercooled) showed higher intensity signals at lower wavenumber regions than the spectra obtained from saturation concentration. This observation, however, was not explained in their study. 84 According to the results of the Raman study, the clusters apparently exist In supersaturated and saturated, as well as in undersaturated, solutions as indicated by the solution spectra at various concentration levels (Figure 17) and by the spectra of solutions at 5"C above the saturation temperature (Figure 22). The results of the column experiment, however, indicate that no significant concentration gradient is observed when the solution is saturated or undersaturated. The present study suggests that solute clustering occurs in undersaturated, saturated, and supersaturated solutions, as indicated by the results of the Raman study. The degree of clustering, however, will likely be different among these solutions. Thus, for a given solution concentration, the degree of clustering is expected to be higher at supersaturation than at saturation, which in turn would be higher than at undersaturation. The results of the present study further indicate that apparently only some of the clusters undergo increases in degree of clustering, which occurs at the expense of other clusters and at the dilution of the lower-ordered species. Thus, at saturated and at undersaturated conditions, the relative difference between the concentrations of the lower-ordered species and the cluster phase will be much smaller than at supersaturated conditions. The column experiment apparently could not detect the concentration differences under these conditions. The estimated number of molecules in a cluster, y, as calculated from equation (18) gives results ranging from 1.0 x 10 to 3.6 x 10 85 molecules. On the basis of the assumption that the clusters have a solid phase density, the equivalent diameters of the clusters are calculated and the results are shown in Figure 37. This figure indicates a decreasing trend in cluster size with supersaturation. These results are not in agreement with the coalescence process described in the above discussion of the Raman spectra because of the assumption used in deriving equation (18) that the solute concentration in excess of the saturation concentration exists as clusters. This assumption does not consider the coalescence process. Note that the tests described here used the same solute concentration (i.e., saturated at about 30*C), and the supersaturations were established by cooling the solutions to different degrees of undercooling. Another procedure would be to carry out the experiment under the same operating temperature, with varying levels of solute concentrations. The results of the microprobe Raman study suggest that with an observation field of about 20 microns, there is no significant difference between the solution structure at ëuid near the crystal- solution interface of a growing crystal and that in the bulk solution. It is expected, however, that at the crystal-solution interfaces of a growing crystal, the solute molecules are continuously integrated into the surface and the solvent molecules are continuously dislodged from the surface. Thus, there must be a region just above the surface of the crystal in which the solute diffusion process occurs because of solute depletion due to crystal growth. This region presumably 86 8.0 ClutUr 81%## NaNO« - H.O Syst#fn (Sttur8t#d at 30"C) 7.0 E e + + I 6.0 E + « + + Q + t 6.0 + + 9 5 4.0 3.0 1.000 1.005 1.010 1.015 Supersaturation ratio, S » c/c" FIGURE 37. Estimated cluster sizes as calculated from equation (18) 87 consists of a subreglon that has a relatively higher solute concentration and is located just next to the crystal surface and of another subreglon that has a lower solute concentration (Figure 38). Clontz (1970) has described a similar model. Under the experimental conditions tested in the microprobe Raman study, this region (i.e., the thickness d in Figure 38) is apparently very small compared to the 20-micron laser spot used. It is likely that the thickness of this region is of the same order as the cluster size. Furthermore, it is expected that the thickness of this region will increase with super saturation. The results for the column experiment with growing crystals at the bottom of the column show that the concentration gradient is apparently maintained during crystal growth. These results indicate that the solution near the crystal-solution interface maintains the establishment of solute clustering even as the solute molecules are being depleted. The results also appear to be consistent with the suggestion that the diffusion layer is relatively thin. 88 SOLID CONCENTRATION •INTERFACE DURING CRYSTAL GROWTH BULK CONCENTRATION t—1 H I- DISTANCE FROM CRYSTAL SURFACE CRYSTAL SURFACE FIGURE 38. Concentration profile at and near crystal-solution interface of a growing crystal 89 PROPOSED MECHANISMS OF CRYSTALLIZATION FROM SOLUTION Based on the results and observations of the present study, this chapter discusses the proposed models of solute clustering and the mechanisms governing crystallization from solution. The discussion consists of three sections: the phenomenon of solute clustering in solution, the mechanism of nucleation, and the mechanism of crystal growth. It should be noted that although the models and the mechanisms proposed here are based on the results of the present study with a highly soluble solution system, it is likely that they can also be applied to other systems, such as lower solubility and precipitating systems. Solute Clustering in Solution The results of the present study seem to be consistent with the model that there are solute clusters in a concentrated NaNOg solution system. Some of the solute molecules are associated with higher- ordered structures (i.e., those having a higher solute concentration), while others are associated with lower-ordered species (i.e., smaller clusters, ion pairs, and solvated ions). In the present discussion, the higher-ordered structures will be referred to as solute clusters, in that they are considered to have structures more closely resembling solid/crystalline phase structures than those of the lower-ordered species. 90 The solute clusters are apparently solvated clusters consisting of the solute and the solvent molecules, and they do not possess crystalline phase structures. These solute clusters are present in supersaturated and saturated, as well as in undersaturated, solutions. The relative number of clusters and the degree of clustering increase with solution concentration. Effect of supersaturation For a given concentration, as the solution becomes supersaturated, a dynamic rearrangement apparently occurs between the lower-ordered species and the cluster phase. This rearrangement is explained in terms of the coalescence and/or growth of some of the clusters accompanied by the breakup of other clusters and by the dilution of some of the lower-ordered species as the solution becomes more supersaturated. The larger clusters that are formed apparently have a higher degree of solute clustering (i.e., become a higher-ordered species) than before coalescence and/or growth. Because of the relatively lower specific surface area and the relatively higher solute concentration within the coalesced clusters, some of the solvent molecules, which are associated with the clusters before the coalescence and/or growth, are freed to surroundings and solvate some other clusters and lower-ordered species. Thus, in the process of coalescence, some clusters become larger at the expense of other clusters and the dilution of lower-ordered species. 91 Thermodynamic considerations of solute clustering In the following discussion, the thermodynamic considerations of solute clustering in solution systems will be described and discussed. If one considers a nonideal solution system, the free energy (G) versus the solute mole fraction (x) curve can be represented by the following relation: G = H - T S (21) where H is enthalpy and S is entropy. Depending on the system under consideration, the enthalpy term may be negative (exothermic) or positive (endothermic). At relatively high temperatures (i.e., those far above the saturation temperature), the T S term will be dominant, and the curve will show continuous upward curvature for all solute mole fractions. At relatively lower temperatures, the enthalpy term may be significant or dominant, as compared with the T S term. Equation (21) suggests that the change in free energy with temperature can be determined by 3G/3T S (22) Thus, as the temperature is lowered, each point on the curve rises according to its molar entropy, S. Because the molar entropy of a mixture is generally higher than that of its components, the middle portion of the curve will rise faster than do its sides. Thus, at a relatively lower temperature and depending on whether the H term is 92 negative or positive, it is possible to obtain two typés of energy curves, as shown in Figure 39a and 39b, respectively. For a negative H term, the free energy curve will be concave upward for all solute mole fractions (Figure 39a); while for a positive H term, the free energy curve may develop a smooth hump in the middle portion of the curve (Figure 39b). Figure 39a illustrates a solution system that consists of a relatively uniform single-phase system. Figure 39b illustrates a solution system that may have developed a miscibility gap, suggesting the possible presence of two phases having different solute compositions as represented by the two minima. The present study explains the coexistence of the lower-ordered species and the cluster phase in NaNOg solution systems in terms of the miscibility gap as described by the minima in the free energy curve such as described in Figure 39b. Note that these phases are solution phases, not solid phases. In this system, one phase can be formed from another phase by continuous change in the solute concentration within the phase. In terms of the present study, these two phases are the lower-ordered species and the cluster phases. Hill (1963) discussed the free energy of small (microscopic) systems and suggested additional terms to be added to Equation (21) in order to account additional energy terms (such as rotational, vibrational, and surface energies) that may be important in small systems. Thus, in small systems, such as solute clusters, it is possible that the minima in the free energy curve are because of these additional energy terms. 93 ° X, SOLUTE MOLE FRACTION ^ (a) H IS NEGATIVE X, SOLUTE MOLE FRACTION (b) H IS POSITIVE FIGURE 39. Free energy versus solute mole fraction diagram for systems with (a) negative H and (b) positive H 94 The presence of the lower-ordered species and the cluster phase In an undersaturated solution suggests that the two minima can develop at conditions of uzidersaturation with respect to the solid phase. Unless otherwise stated, the term saturation In this discussion will refer to saturation with respect to the solid phase. Figure 40a illustrates the free energy of an undersaturated solution system, In which both solution phases (lower-ordered species and cluster phase) are below the solid-phase curve. Note that the solid-phase curve is represented by a steep free energy curve with a minimum at the mole fraction x=l. This will correspond to a system that crystallizes as a pure compound and has no stable hydrated form, such as the NaNO^ system. As the temperature is lowered further, the solution curve will rise faster than that of the solid phase. At the saturation temperature, it is possible to draw a straight-line tangent to the two solution phases and also to the solid phase (Figure 40b). Further decreases in tanperature will make the solution supersaturated. The middle section of the free energy curve will continue to rise at a faster rate tlian do the sides. Thus, it is possible that as the solution becomes supersaturated, the minimum corresponding to the lower-ordered species may shift towards a lower concentration, while the minimum corresponding to the cluster phase may shift towards a higher concentration (points A' and B' in Figure 40c, respectively). Furthermore, for a given solution concentration, the relative amount of the lower-ordered species and the cluster phase can be estimated from 95 SOLID PHASE G FREE ENERGY (c) SUPERSATURATED SOLID PHASE (b) SATURATED SOLUTION PHASE (a) UNDERSATURATED j I LOWER-ORDERED CLUSTER PURE PHASE PHASE SOLID X. SOLUTE MOLE FRACTION FIGURE 40. Free energy versus mole fraction diagram for solution phases with solute clustering. The relative position of the solid phase is also shown 96 the lever-rule principle. Thus, depending on the changes in the relative position of these minima, rearrangement in terms of the degree of clustering and the relative amount between the lower-ordered species and the clusters will occur when the solution becomes supersaturated. When the condition of a given solution is changed, the transformation and rearrangement of the lower-ordered species and the cluster phase may occur by means of different mechanisms, depending on the degree of the change. In the case of the transformation of the cluster phase into lower-ordered species, the cluster is simply broken into lower-ordered species by means of a dilution process. In the transformation/rearrangement of the lower-ordered species into the cluster phase, two conditions may occur: one in which the change is relatively small and the other in which the change is significantly large. When the change is relatively small—for example, a slight change in the degree of supersaturation—the free energy of the lower-ordered species is likely below the splnodal point of the new equilibrium condition (Figure 41). Under this condition, the transformation from the lower-ordered species into the cluster phase may occur by way of either of the following two mechanisms: 1. Cluster growth. Because the new equilibrium condition may favor a higher solute concentration within clusters, the cluster may release some solvent molecules Into their surroundings, creating a relatively lower concentration 97 region around the cluster. Some of the lower-ordered species and/or other clusters may diffuse into this lower concentration region and subsequently become integrated into the cluster. 2. Cluster coalescence. Some of the clusters may coalesce to form larger clusters. Because of the lower specific surface area and the more concentrated structure of the coalesced clusters, some of the solvent molecules are released into the surroundings and dilute other clusters and lower-ordered species. Thus, the coalescence process produces larger and possibly more concentrated clusters at the expense of other clusters and the dilution of the lower-ordered species. When the change in condition is significantly large—for example, during quenching—some of the lowered-ordered species may become highly unstable amd have free energies corresponding to the condition beyond the spinodal point (Figure 42). Slight fluctuations in the system will cause some of the lower-ordered species to decompose into the cluster phase and into lower structures through a spinodal-type decomposition (uphill diffusion process). A review on the concept of spinodal decomposition has been given by Cahn (1968). More discussion on spinodal decomposition will be given later in the discussion of nucleation mechanisms. 98 SPINODAL POINT FREE ENERGY FREE ENERGY H h *0 2 *2 LOWER-ORDERED CLUSTER PHASE PHASE X. SOLUTE MOLE FRACTION FIGURE 41. Free energy diagram of solute cluster system with a relatively small degree of change 99 SPINODAL ^ / POINT X. / G FREE ENERGY ' 1 1 ! i i G FREE ENERGY Xj Xj Xg Xg LOWER-ORDERED CLUSTER PHASE PHASE X, SOLUTE MOLE FRACTION FIGURE 42. Free energy diagram of solute cluster system with a relatively large degree of change 100 Cluster Interface The presence of the clusters and of the lower-ordered species In the solution system suggests that there are some mlcroreglons that have a higher solute concentration (i.e., clusters) and there are other mlcroreglons that have a lower solute concentration (i.e., lower- ordered species). The coexistence of these mlcroreglons of different concentrations at quasi-equilibrium suggests the presence of an interface structure between the clusters and the lower-ordered species. At this quasi-equilibrium condition, the chemical potentials of the lower-ordered species and the clusters are the same and are represented by the common tangent at points corresponding to their solute concentrations. The concentration (composition) profile of the interface between two coexisting phases in a nonuniform solution system with a free energy curve similar to Figure 43 has been discussed and proposed by Cahn and Milliard (1958). Their analysis suggests that in order for the interfacial surface energy to be minimal, the following equation should be valid: dx/da = (Af(x)/k)l/2 (23) where x is the solute mole fraction, a is distance, and Af(x) is the excess free energy of the system with respect to the quasi-equilibrium free energy of the mixture. By examining the function Af(x) between the two solution phases (Figure 43), one can see that the composition 101 profile Is sigmoid in shape, as shown in Figure 44. Cahn and Milliard (1958) also show that the interface thickness increases with temperature and approaches infinity at temperatures just below the critical temperature. The present study suggests that the interface profile of the clusters can be represented by this model. Solute concentration within the cluster In order to estimate the concentration profile within a cluster, one needs to evaluate the change in molar free energy within the cluster system. If one considers that the cluster is in a condition of quasi-equilibrium and assumes that the free energy is a function of only temperature (T), pressure (P), and composition (x), then dG= (3G/3T)dT + OG/3P)dP + (3G/3x)dx = 0 (24) Furthermore, the pressure is expected to be constant within the cluster and (3G/3x) is nonzero. Thus, for an isothermal system, one has dx = 0, or X = constant This analysis shows that under a condition of quasi-equilibrium, the solute concentration within the cluster is uniform. Nucleation from Solution In the following discussion, the proposed mechanisms of nucleation from solution that is based on the solute clustering model will be presented. The discussion covers only the qualitative description of 102 G FREE ENERGY LOWER-ORDERED CLUSTERS SPECIES X, MOLE FRACTION FIGURE 43. Free energy diagram of a cluster system 103 # DISTANCE FIGURE 44. Concentration profile of the interface between the lower- ordered species and the cluster phase 104 the mechanismsf based on the thermodynamic consideration of the solution system. In a solution system with solute clustering, the lower-ordered species and the clusters coexist in the solution. The proposed nucleation mechanisms for this system consider the solvated solute clusters described in the previous section as the precursor to the formation of new nuclei. Gibbs's classical nucleation theory suggests that the formation of a new nucleus from solution requires the clustering of solute molecules in quantities sufficient in number to provide the energy needed to form an interface structure during transformation. The present study indicates that solvated solute clusters apparently do not show significant change towards solid phase structure, even as the solution becomes highly supersaturated. The liquid-to-solid transformation during the nucleation process, therefore, appears to occur suddenly rather than gradually. Thus, the mechanisms of nucleation from solution to be proposed here are largely related to how some of the solvated solute clusters can form solute-only clusters that are large enough in number to subsequently transform into the solid phase. The relative positions of the free energy curves of the cluster and the solid phases can indicate one of the following: 1. A stable condition. This refers to a condition in which the solid phase is unstable with respect to the cluster phase (i.e., the solid-phase curve is above the solution-phase 105 curve), as illustrated by Figure 45a. Under this condition the crystallization process will not occur. 2. A metastable condition. This refers to a condition in which the cluster phase can be in coexistence with the solid phase through a connnon tangent, as shown in Figure 45b. 3. An unstable condition. This refers to a condition in which the cluster phase is unstable with respect to the solid phase, as given by Figure 45c. Two basic mechanisms for the formation of a new nucleus from a solution are proposed, depending on the environment to which the clusters are subjected. In one case, the clusters are in a metastable environment, while in the other case the clusters are in an unstable environment. In the present treatment, the system being considered is the solvated clusters rather than the whole solution system. Nucleation under metastable condition In the nucleation mechanism under metastable condition, the clusters are in a metastable condition with respect to the solid phase (Figure 46). Nucleation occurs when the clusters encounter significant disturbances or fluctuations, which allow them to form a collection of solute-only molecules that is sufficiently large to overcome the interfacial surface energy upon the transformation process. In other words, the collection of solute molecules must be larger than that of the critical-size nucleus described by classical nucleation theory. It should be noted here that when the disturbances and/or the fluctuations 106 SOLID UNSTABLE PHASE SOLUTION G, FREE PHASE ENERGY METASTABLE SOLUTION PHASE STABLE SOLUTION PHASE X, SOLUTE MOLE FRACTION FIGURE 45. Free energy diagram of the solution phases of a solute clustering system 107 are relatively small, concentration fluctuation occurs momentarily and subsequently diminishes and the nucleation process will not occur. If one considers a cluster that has a solute mole fraction represented by point C in Figure 46, the nucleation process can occur when there are fluctuations within the cluster system that cause a formation of a region within the cluster that has a relatively higher solute mole fraction, for example, that of point A of Figure 46. The solution phase of the solute molecules within this region is unstable with respect to the solid phase. If the number of molecules within this unstable region is large enough to overcome the interfacial energy requirement, then phase transformation occurs and a stable nucleus is formed. If, on the other hand, the number of solute molecules is not large enough to overcome the required interfacial energy, the phase transformation will not occur. Because the solution system is metastable with respect to the solid phase, it is presumably possible to have a condition in which the nucleation process does not occur because the disturbance and/or fluctuations in the system are relatively small. This explains the situation in which a supersaturated solution, in the absence of a solid phase, can exist without nucleation until it is disturbed, for example, by agitation. 108 G, FREE ENERGY METASTABLE SOLUTION PHASE STABLE SOLUTION PHASE X. SOLUTE MOLE FRACTION FIGURE 46. Free energy diagram of a metastable solution system 109 Wucleatlon under unstable condition In the nucleation mechanism under unstable condition, nucleation occurs when the solution is suddenly brought into a very high supersaturation level in which the solute cluster phase is unstable with respect to the solid phase. The free energy diagram for this condition is illustrated in Figure 47. Once the system is brought to this condition, a slight perturbation in the system can cause a spinodal-type decomposition through uphill diffusion. Such a decomposition causes the lower-ordered species to diffuse into the cluster phase to continuously build up the concentration within the clusters and to eventually become nuclei. When a solution system is suddenly brought into a highly supersaturated condition, at which the new cluster phase to be established (point B in Figure 47} is unstable with respect to the solid phase, there is a rearrangement between the lower-ordered species and the cluster phase. Such a rearrangement is described in the discussion of solute clustering in which some of the lower-ordered species undergo spinodal-type decomposition or diffuse into the clusters. The clusters that are formed may continue to build up their concentration and size and subsequently transform into the solid phase. Because the spinodal decomposition can be relatively large in spatial extent, it is expected that the nuclei that are formed under this condition may be significantly larger than the critical-size nuclei or the nuclei that are formed under the metastable condition 110 \ UNSTABLE SOLUTION PHASE G, FREE ENERGY STABLE SOLUTION PHASE X, SOLUTE MOLE FRACTION FIGURE 47. Free energy diagram of an unstable solution system Ill described in the previous section. The nuclei in the microscopic observation experiment may be formed through this spinodal-type mechanism. Under the relatively high supersaturation condition described above, it is likely that in addition to the spinodal-type mechanism the nucleation mechanism described under the metastable condition will also occur because of the reduction in supersaturation as the nucleation occurs and because of the fluctuations in the solution system. Metastable versus unstable nucleation mechanisms The metastable and the unstable nucleation mechanisms described above are basically similar to the classical nucleation and the spinodal decomposition mechanisms, respectively, that have been studied extensively in the field of metallurgy. In the following discussion, the differences between the two mechanisms will be described briefly. In this discussion, metastable nucleation is also referred to as classical nucleation (or simply, nucleation) and unstable nucleation is also referred to as spinodal decomposition. The free energy curve of a system with two coexisting phases, in which one phase can be transformed into the other by continuous change in solute concentration, is given in Figure 48. The spinodal point in the curve is defined as the limit of metastability, beyond which a homogeneous phase will be unstable (i.e., no longer metastable). At point A in Figure 48, the solution system is beyond the spinodal point and therefore, unstable. A slight fluctuation in the 112 CO SPINODAL POINTv g LOWER-ORDERED CLUSTER PHASE PHASE X, SOLUTE MOLE FRACTION FIGURE 48. Free energy curve showing the nucleatlon and the splnodal decomposition 113 system will cause a splitting (decomposition) of some solute molecules into a lower concentration phase and a higher concentration phase, as shown by line a. This decomposition is thermodynamically favorable because it lowers the free energy of the system as indicated by the small arrow below point A. The system will continue to decompose until it reaches the common tangent between the lower-ordered species and the cluster phase. Note that the decomposition process requires an uphill diffusion of solute molecules towards a higher concentration region (i.e., up the concentration gradient). At point B in Figure 48, the solution system is metastable (i.e., below the spinodal point). A slight fluctuation in the system will not cause decomposition, because there will be an increase in the free energy of the system. The free energy of the system will be lower only if there are large fluctuations in the system, as indicated by line b. Figure 49 further illustrates the difference between nucleation (metastable nucleation) and spinodal decomposition (unstable nucleation). In metastable nucleation, a small nucleus is initially formed and subsequently grows by solute diffusion down the concentration gradient. In unstable nucleation (spinodal decomposition), a slight fluctuation causes the buildup of solute concentration through an uphill diffusion process (i.e., up the concentration gradient). This concentration buildup will continue until solid concentration is reached. Under this condition, the nucleus formed may be relatively large. 114 NUCLEATION \ t "S 2 "à EARLY LATER FINAL i DISTANCE SPINODAL MECHANISM EARLY LATER FINAL FIGURE 49. Comparison between metastable and unstable nucleation mechanisms 115 Crystal Growth from Solution This section presents the proposed model of solution structures as related to crystal growth from solution. The model emphasizes the solution structure at and near the crystal-solution interface of a growing crystal. As in the discussion of the nucleation process, the model presented here deals mainly with the solution systems in which solute clustering occurs. Consider the free energy of a saturated or undersaturated solution system of concentration xq at temperature Tl, as shown in Figure 50. As discussed in the previous section, there is a distribution of the relative amount of the lower-ordered species and the cluster phase that can be estimated from the lever-rule principle. The concentrations of these phases are represented by the relative positions of the points at the common tangent line (Figure 50). As the temperature of the solution is lowered and the solution becomes supersaturated, the lower- ordered species and the cluster phase will undergo rearrangement or transformation through coalescence, or growth, or both, in order to establish a new distribution of lower-ordered species and the cluster phase. The solute concentrations of the clusters and the lower-ordered species may also be different under the new equilibrium condition, as shown by curve b in Figure 50. Thus, as described in the previous discussion of the effect of supersaturation, some of the clusters become larger and more concentrated at the expense of other clusters and the dilution of lower-ordered species. If this solution system at 116 temperature T2 is in contact with a crystal, the crystal will grow that will result in continuous depletion of solute molecules in the solution system. As the solution concentration decreases, Xq will shift towards a more dilute concentration, as shown by arrow p in Figure 50, and dynamic rearrangement/transformation between the lower-ordered species and the clusters occurs in order to adjust for the continuous changes in the system. Because of this dilution process in which xq moves towards a more dilute region, the lever rule requires that there will be a depletion of the relative number of clusters. This process will continue until xq reaches saturation concentration. As postulated before, some of the solute molecules in the region next to the crystal-solution interface of a growing crystal have higher degrees of solute clustering (i.e., higher solute concentration) than that in the bulk solution (see Figure 38). The solute concentration in this region is represented by a point beyond point A in Figure 50 (for example, point C). These molecules are unstable with respect to the solid phase. Next to this region is the region in which the solute concentration is relatively less than that in the bulk solution (Figure 38). In this latter region, the solute concentration is represented by a point to the left of bulk solution concentration and the relative amount of solute clustering is less than that in bulk solution. This suggests that the solute clusters are likely the diffusing species during the crystal growth process. 117 SOLID PHASE SPINODAL POINT FREE ENERGY FREE ENERGY X, X X, X X LOWER-ORDERED CLUSTER PHASE PHASE X, SOLUTE MOLE FRACTION FIGURE 50. Free energy diagram of solution and solid phases during crystal growth process 118 CONCLUSIONS 1. The results of the experimental studies, consisting of a laser Raman spectroscopy study, an isothermal column experiment, and a microscopic observation of nucleation, show some evidence of solute clustering in the NaNO^ solution systems tested. The solutions ranged in concentration from 2M to 8M. This solute clustering can be categorized into two groups of solvent-solute associations, the higher- ordered species or clusters, and the lower-ordered species. The clusters are considered to have structures closer to the solid/crystalline structures than those of the lower-ordered species. 2. The solute clusters appear to be solvated solute clusters consisting of solute and solvent molecules. These clusters do not have crystalline phase structures. 3. The solute clusters may exist in saturated and supersaturated, as well as in undersaturated, solutions. 4. For a given solution concentration and as the solution becomes supersaturated, a dynamic rearrangement occurs between lower-ordered ionic species and clusters. The present study explains this rearrangement process in terms of the coalescence of some of the clusters at the expense of other clusters and the dilution of the lower-ordered species. 119 5. The results of the isothermal column experiment show that when a supersaturated solution is placed in a vertical column, a concentration gradient is developed between the top and bottom of column with the concentration at the bottom is higher than that at the top. No significant gradient is observed when the solution is saturated or undersaturated. There are no significant variations in concentration gradients with different test durations of 1 to 3 days, with different degrees of undercooling of 1*C to 3*C, and with different column heights of 40 cm to 120 cm. 6. The microscopic observation of the nucleation process shows that when an NaNOg solution saturated at 33*C is suddenly cooled to about 0*C (i.e., a condition of very high supersaturation), the initial size of the nucleus formed can be on the order of 20 to 30 microns. These results suggest a process of size and concentration buildup of solute clusters prior to nucleation. 7. The thermodynamic analysis of solute clustering appears to be consistent with the concept of a miscibility gap in nonideal solution systems. The free energy versus solute mole fraction curve consists of two minima, one at a lower solute mole fraction that corresponds to the lower-ordered species and the other at a higher solute mole fraction that corresponds to the cluster phase. The relative amount and concentration of these stable phases change with temperature and hence with degree of supersaturation. 120 8. The microprobe Raman study, which used a laser spot of 20 microns, did not show a significant difference between structures at < near the crystal-solution interface of a growing crystal and those in the bulk solution. These results suggest that no significant solute clustering structure exists at the crystal-solution interface of a growing crystal. 121 RECOMMENDATIONS FOR FUTURE WORKS The following recommendations are proposed for future study. 1. A systematic study that utilizes different experimental methods Is needed In order to evaluate further the structures and characteristics of solute clusters and their relation to crystallization from solution. Two experimental methods are recommended: diffraction and spectroscopic methods. The diffraction methods may Include x-ray, neutron, and electron diffraction. In addition to Raman spectroscopy, other spectroscopic techniques may include Infrared, UV-vlslble, and nuclear magnetic resonance. The selection and preliminary study of systems and the feasibility of the proposed experimental techniques should be carried out before detailed experimental studies are undertaken. 2. A study should be conducted that will test the validity of the model postulated in the present study. This model suggests that the solution systems with positive H (endothermlc systems) may produce a solubility gap and give rise to stable clustering, while the systems with negative H (exothermic systems) will not produce stable solute clusters. One such study, for example, could utilize an isothermal column experiment in which various exothermic and endothermlc solution systems could be tested. 3. Further study should be undertaken that uses direct microscopic observations of the nucleation process with special experimental or 122 monitoring techniques, such as high-speed, computer-controlled scanning; high-speed cameras; and image analyzers. 4. An expansion of the thermodynamic analysis of the solvated solute cluster model should be developed that will incorporate various physical and thermodynamic properties, such as the solute-solvent interaction within a cluster, the miscibility gap in a nonideal solution system, the determination of critical size clusters, the effect of supersaturation, the relationship of free energy to cluster size, and the effect of temperature. 5. Computer simulation studies of solute-clustering phenomena with such simulation techniques as the Monte Carlo and the Molecular Dynamic should be carried out. These simulation studies should include the solvated solute clusters model described in this study. 6. Further experimental investigation into the possible sources of secondary nuclei is needed. The results of the present study suggest that there is no significant "semi-ordered" layer at the interface of a growing crystal. Thus, two possible sources for secondary nucleation are likely to be the solute clusters in the bulk solution and the crystal breakage. Experimental confirmation of the bulk solution sources is needed. 123 BIBLIOGRAPHY Benema, P. 1976. Theory and experiment for crystal growth from solution: Implication for industrial crystallization. Pages 91-112 in J. W. Mullin, ed. Industrial Crystallization. Plenum Press, New York. Berglund, K. A. 1981. Formation and growth of contact nuclei. Ph. D. Dissertation. Iowa State University, Ames, Iowa. Bockris, J. 0. 1949. Ionic Solvation. Quarterly Review 3: 173-180. Bockris, J. 0. and A. K. Reddy. 1970. Modern Electrochemistry. Plenum Press, New York. Botsaris, G. D. 1976. Secondary Nucleation—A review. Pages 3-22 in J. W. Mullin, ed. Industrial Crystallization. Plenum Press, New York. Buckingham, A. D. 1957. A theory of ion-solvent interaction. Disc. Faraday Soc. 24: 151-157. Buckley, H. E. 1951. Crystal Growth. John Wiley and Sons, Inc., New York. Burton, W. K., N. Cabrera and F. C. Frank. 1951. The growth of crystal and equilibrium structure of their surfaces. Phil. Trans. Roy. Soc. London 243: 299. Cahn, J. W. 1968. Spinodal decomposition. Trans. Met. Soc. AIME. 242: 166-180 Cahn, J. W. and J. E. Milliard. 1958. Free energy of a nonuniform system. I. Interfacial Free Energy. J. Chem. Phys. 28, No. 2: 258-267. Caminiti, R., G. Licheri, G. Poschina, G. Piccaluga and G. Pinna. 1980. Interactions and structure in aqueous NaNOg solutions. J. Chem. Phys. 72: 4522-4528. Chang, T. G. and D. E. Irish. 1973. Raman and Infrared spectral study of magnesium nitrate-water systems. J. Phys. Chem. 77: 52-57. Clontz, N. A. 1970. The effects of a solute seed crystal and crystal- solid contacts on nucleation in a flowing supersaturated magnesium sulfate heptahydrate. PhD Dissertation. North Carolina State University, Raleigh, North Carolina. 124 Clontz, N. A. and W. L. McCabe. 1971. Contact nucleation of magnesium heptahydrate. Chem. Eng. Prog. Sym. Ser. 67: 6-17. Davis, A. R. 1967. Vibrational spectral studies of aqueous metal nitrate systems. Ph.D. Thesis. University of Waterloo, Waterloo, Canada. Davis, A. R. and B. G. Oliver. 1973. Raman spectroscopic evidence for contact-ion pairing in aqueous solutions. J. Phys. Chem. 77: 1315-1316. Ebrahim Khan, M. K. 1981. Generation and growth of contact nuclei in the ammonium dihydrogen phosphate-water system. M.Ph. Thesis. University College, London. Estrin, J. 1976. Secondary nucleation. Pages 1-42 in W. R. Wilcox, ed. Preparation and properties of solid state materials. Vol. 2. Marcel Dekker, Inc., New York. Frank, H. S. and w. Y. Wen. 1957. Structural aspects of ion-solvent interactions in aqueous solutions: A suggested picture of water structure. Disc. Faraday Soc. 24: 133-141. Frost, R. L. and D. W. James. 1982. Ion-ion interactions in solution. Chem. Soc., Faraday Trans. 78: 3223-3279. Garside, J., I. T. Rusli and M. A. Larson. 1979. Origin and size distribution of secondary nuclei. AZChE J. 25: 57. Garside, J. and R. J. Davey. 1980. Secondary contact nucleation: Kinetics, growth and scale-up. Chem. Eng. Commun. 4: 393-424. Ghosh, J. C. 1918. The abnormality of strong electrolytes. J. Chem. Soc. 113: 229-558. Gibbs, J. W. 1928. Collected works. Vol. 1. Longmans Green and Co., Mew York. Hayes, C. A., P. Kruus, and W. A. Adams. 1984. Raman spectroscopic study of aqueous («#4)250* and ZnSO* solutions. J. Sol. Chem. 13, No. 1: 61-75. Hill, T. L. 1963. Thermodynamics of small systems. Benjamin, New York. Howe, R. A., W. S. Howells and J. E. Enderby. 1974. Ion distribution and long-range order in concentrated electrolyte solutions. J. Phys. C: Solid State Physics 7: Llll. 125 Hussmann, G. A. 1984. The characterization of solution near a growing NaNOg crystal. M.S. Thesis. Iowa State University, Ames, Iowa. Hussmann, G. A., M. A. Larson, and K. A. Berglund. 1984. Characterization of solution structure near the surface. Page 21 In S. J. Janclc and E. J. de Jong, eds. Industrial Crystallization 84. Elsevier, Amsterdam. Irish, D. E. 1971. Vibrational spectral studies of electrolyte solutions and fused salts. Pages 187-258 in S. Petruccl, ed. Ionic Interactions: From dilute solution to fused salts. Vol. 2. Academic Press, New York. Irish, D. E. and M. H. Brooker. 1976. Raman and Infrared spectral studies of electrolytes. Pages 212-307 in R. J. H. Clark and R. E. Hester, eds. Advances in Raman and infrared spectroscopy. Heydon, London. Irish, 0. E. and A. R. Davis. 1968. Interactions in aqueous metal nitrate solutions. Can. J. Chem. 46: 943-951. Jackson, K. A. 1958. Mechanisms of growth. Page 174 in Liquid Metals and Solidification. American Society for Metals, Cleveland. Johnson, R. T., R. W. Rousseau and W. L. McCabe. 1972. Factors affecting contact nucleatlon. AIChE Sym. Ser. 68 (121): 31-41. Kato, T. and J. Umemura and T. Takenaka. 1978. Raman spectral studies of ionic motion and ionic interaction in aqueous nitrate solutions. Mol. Phys. 36: 621-639. Kaufman, E. L. 1980. Photographic observation of secondary nucleatlon. M.S. Thesis. Iowa State University, Ames, Iowa. Kossel, W. 1927. Zur Theorie des Kristallwachstums. Nachr. Ges. Wiss. Gottinge. Larson, M. A. 1981. Secondary nucleatlon: An analysis. Chem. Eng. Commun. 12:161-169. Larson, M. A. and J. Garside. 1986a. Solute clustering in supersaturated solutions. Chem. Eng. Sci. 41, No. 5: 1285-1289. Larson, M. A. and J. Garside. 1986b. Solute clustering and interfacial tension. J. Crystal Growth 76: 88-92. McMahon, P. M. 1984. A Raman spectroscopic study of the structure of supersaturated potassium nitrate solutions. M.S. Thesis. Iowa State University, Ames, Iowa. 126 Mullln, J. W. 1972. Crystallization. Butterworth, London. Mullin, J. W. and C. L. Leci. 1969. Evidence of molecular cluster formation in supersaturated solution. Phil. Mag. 19: 1075-1077. Ohara, M. and R. C. Reid. 1973. Modeling crystal growth rates from solution. Prentice Hall, Inc., Englewood Cliffs, New Jersey. Ostwald, W. 1897. Studien uber die Blldung und Umwandlung fester Korper. Z. Physik. Chem. 22: 289. Pitha, J. and R. N. Jones. 1967. An evaluation of mathematical functions to fit Infrared band envelopes. Can. J. Chem. 45: 2347-2351. Randolph A. D. and M. A. Larson. 1971. Theory of particulate processes. Academic Press, New York. Samoilov, 0. Y. 1965. Structure of aqueous electrolyte solutions and the hydration of ions. Consultants Bureau, New York. SAS Institute, Inc. 1985. SAS User's Guide: Statistics. SAS Institute, Inc., Gary, North Carolina. Savitzky, A. and M. J. E. Golay. 1964. Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36, No. 8: 1627-1639. Strickland-Constable, R. F. and R. E. A. Mason. 1966. Breedings of crystal nuclei. Trans. Faraday Soc. No. 518, 62:455. Sung, C. Y., J. Estrin and 6. R. Youngquist. 1973. Secondary nucleatlon of magnesium sulfate by fluid shear. AIChE J. 19, No. 5: 957-962. Tobias, S. R. 1973. Applications to inorganic chemistry. Pages 406-512 in A. Anderson, ed. The Raman effect. Marcel Dekker, Inc., New York. Verall, R. E. 1973. Infrared spectroscopy of aqueous electrolyte solutions. Pages 211-264 in F. Franks, ed. Water, a comprehensive treatise. Plenum Press, New York. 127 ACKNOWLEDQIENTS The author wishes to express deep appreciation to Dr. M. A. Larson, author's major professor and chairman of author's Advisory Committee, for the guidance, suggestions, and encouragement throughout this study. The author thanks Dr. G. L. Schrader, author's co-major professor, for the guidance, suggestions, and discussions in the areas of Raman spectroscopy. The author also wishes to thank other members of author's Advisory Committee, Dr. R. S. Hansen, Dr. G. R. Youngqulst, Dr. H. T. David, and Dr. R. K. Trlvedl. A gratitude is also expressed to Dr. H. T. David and Mr. R. K. Guo for the discussions and assistance in statistical analysis as part of Engineering Research Institute Statistical Assistance Program. The author is thankful to the National Science Foundation (NSF) for the financial support through Grant No. CBT8419428, and also to the Chemical Engineering Department of Iowa State University for the computer support. Also, the author would like to thank the faculty, staff, and fellow graduate students at the Chemical Engineering of Iowa State University. APPENDIX! RESULTS OF CURVE-FITTING ANALYSIS TABLE A.l. Results Of curve-fltting analysis Run Tonperature Cauchy Gauss code CO Pc Kg B Vg Kg S Run series A (saturation temperature: 30.0«C) NN0095 35.0 1049.72 2.70 4.39 1051.75 2.76 6.83 NN0096 30.0 1049.66 2.61 4.48 1051.74 2.94 6.85 NN0097 25.0 1049.31 2.56 4.51 1051.61 3.02 6.82 NN0098 23.0 1049.01 2.42 4.52 1051.10 3.43 6.82 NN0099 20.0 1049.15 2.47 4.48 1051.26 3.19 7.00 Run series B (saturation temperature: 30.0*C) NN0193 35.0 1049.87 2.75 4.57 1051.79 2.89 6.82 NN0199 27.0 1049.91 2.64 4.54 1051.76 3.02 6.96 NN0202 25.0 1048.98 2.64 4.48 1051.00 3.01 7.06 NN0205 22.0 1049.09 2.47 4.49 1050.78 3.24 7.13 NN0210 20.0 1048.87 2.47 4.60 1051.04 3.37 6.91 Run series C (saturation temperature: 30.0°C) NN0116 30.0 1050.43 2.72 4.56 1052.44 2.76 6.72 NN0117 30.0 1050.30 2.70 4.46 1052.20 2.79 6.87 NN0118 30.0 1050.26 2.73 4.45 1052.27 2.84 6.85 NN0119 30.0 1050.39 2.68 4.42 1052.55 2.94 6.82 NN0120 30.0 1050.50 2.76 4.49 1052.44 2.80 6.72