Formation of Liquid Inclusions in Adipic Acid Crystals during Recrystallization from Aqueous Solutions Geoff G. Z.
Zhang†
and David J. W. Grant*
Department of Pharmaceutics, College of Pharmacy, University of Minnesota, Weaver-Densford Hall, 308 Harvard Street S.E., Minneapolis, Minnesota 55455-0343 Received April 6, 2004;
CRYSTAL GROWTH & DESIGN 2005 VOL. 5, NO. 1 319-324
Revised Manuscript Received September 3, 2004
ABSTRACT: Liquid inclusions consist of pockets of saturated solution entrapped in host crystals during crystallization from solution. Inclusions are contaminants that exert deleterious effects on the properties of the host crystals. When adipic acid was crystallized from aqueous solutions by cooling, the amount of included water was found to be less at a higher initial temperature or after slower cooling. Changes in the degree of agitation in the practical range (150-350 rpm) did not influence the amount of included water. Addition of increasing concentration of seeds or sodium dodecylbenzenesulfonate to the crystallizing solution progressively decreased the amount of included water. Addition of trimethyldodecylammonium chloride to the crystallization solution exerted a complex effect, generally increasing the amount of included water. The inclusion of water in adipic acid crystals can be explained by the relatively high growth rates of the hydrophobic faces (010 and 110), and the relatively low growth rate of the hydrophilic face (001) of individual crystals, to extents that are determined by the experimental conditions. Introduction Liquid inclusions, a common type of three-dimensional defect, consist of pockets of saturated solution entrapped within the host crystals during crystallization from solution. The size of the inclusions may range from molecular dimensions to 10 µm, the former corresponding to a solid solution.1 Although they may be helpful in geological studies,2-6 inclusions exert several deleterious effects on the host crystals.7 Specifically, inclusions introduce impurities8 and influence mechanical properties9 (e.g., compactibility). Inclusions also facilitate or accelerate crystal growth (a phase transition), chemical reactions (corresponding to reduced stability and compatibility), and solidification (e.g., sintering or caking during processing). Adipic acid is used mainly in the manufacture of the polyamide, Nylon-6,6. The crystals often cake during storage or during transportation from the production site to the polymerization site. The liquid-filled inclusions are believed to migrate through the crystals when subject to temperature gradients and/or pressure gradients. When the included liquid emerges at the surface, solvent is released and may evaporate causing solid bridges to form between particles, corresponding to caking. Normal drying processes are usually inefficient in removing liquid inclusions.10,11 The causes of inclusion formation are still unclear, but the following mechanisms have been proposed and reviewed by Mullin:12 (a) Adsorption of impurities (or solvents) onto the growing faces leads to impeded growth and hence to inclusions;10 (b) inequalities of growth rates of different crystal faces;10,13 (c) cracking and resealing of formed crystals.10 Because most studies have focused on single crystals of inorganic compounds, rather than on organic compounds, thorough systematic * To whom correspondence should be addressed. † Present address: Pharmaceutics and New Technology Center, Global Pharmaceutical R&D, Abbott Laboratories, 100 Abbott Park Road, Abbott Park, IL 60064-6120.
studies of inclusions in organic crystals are desirable. Studies on polycrystalline powders crystallized under dynamic conditions should provide information that is relatively close to industrial crystallization and are of practical importance. The objectives of the present study on adipic acid crystals are (a) to investigate the influence of crystallization conditions on their inclusion contents, (b) to understand the mechanism of inclusion formation in the crystals, and (c) to develop means of reducing their inclusion content. Materials and Methods Materials. Adipic acid (Adi-pure, g 99.7 wt %) was kindly donated by E. I. du Pont de Nemours and Company (Wilminton, DE). Sodium dodecylbenzenesulfonate (SDBS) was provided by Rhoˆne-Poulenc (Cranbury, NJ). Trimethyldodecylammonium chloride (TMDAC) was purchased from TCI America (Portland, OR). Water was glass-distilled in-house. Methods. Crystallizer. Batch crystallization was performed in a 6-L cylindrical batch crystallizer, provided with an outer jacket connected to a programmable circulating water bath capable of heating or cooling the solution (of practical volume 1.5-5.0 L) at a predetermined linear rate (Figure 1). A stirrer with four sets of blades was directly rotated by a motor at a defined speed between 100 and 900 rpm. A temperature probe was inserted into the crystallizer via a port at the top. The temperature was measured at a point close to the center of the crystallizer and about one-fifth of the height above the bottom of the crystallizer. The tube for circulating the water from the crystallizer back to the water bath was submerged in a second water bath, so that the circulating water could be precooled, if necessary, before it was returned to the original water bath. Ice was added to this second water bath when the cooling capacity of the original water bath was insufficient to remove the heat released from the crystallizing solution (Figure 1). Crystallization Conditions. Adipic acid, in an amount equal to its aqueous solubility at the desired initial temperature,14 was weighed accurately and dissolved, at a temperature 5-10 °C above the desired initial temperature, in a defined volume of aqueous crystallization medium with or without additive. The solution was then filtered by suction through a Buchner funnel into a warm Buchner flask (each
10.1021/cg049868h CCC: $30.25 © 2005 American Chemical Society Published on Web 10/19/2004
320
Crystal Growth & Design, Vol. 5, No. 1, 2005
Zhang and Grant σ)
x( )
2
∂W ∂w0
σ ) 10000 ×
x
× σ02 +
( )
σ02
(100 - w0)
∂W ∂w1
+ 4
2
× σ12 σ12
(100 - w1)4
(2)
(3)
where σ0 and σ1 are the standard deviation of w0 and w1, respectively.
Results
Figure 1. Schematic drawing of the batch crystallizer used for the crystallization of adipic acid from aqueous solutions with linear cooling rates. at a temperature 5-10 °C above the desired initial temperature). Immediately after filtration, the clear solution was transferred to the 6-L cylindrical crystallizer previously equilibrated at the desired initial temperature. The stirrer was then turned on and the stirring rate was adjusted to the designated rpm. In the cooling program, the temperature was reduced at a linear rate to 25 °C, and was maintained at 25 °C for an additional 2 h for complete crystallization. This cooling program was started once the temperature of the solution had reached the desired initial temperature (( 0.2 °C). After crystallization, the suspension was quickly filtered by suction on a Buchner funnel. The crystals were then washed with distilled water (3 times, 50 mL each; or, for crystallization in the presence of surfactants, 3 × 50 mL for 0.1 mg/mL of surfactant, 6 × 50 mL for 1.0 mg/mL of surfactant, or 12 × 50 mL for 10 mg/mL of surfactant). The adipic acid crystals were kept on the Buchner funnels for at least 1 h for initial drying. The crystals were then spread onto a Petri dish, air-dried overnight, further dried over phosphorus pentoxide in a vacuum oven at ambient temperatures for three more days, and then characterized further, as described below. In the seeding experiments, the adipic acid seeds were prepared by manual grinding the original powder. The seeds were suspended in a saturated aqueous solution of adipic acid at ambient temperatures at a ratio of 10 mL of solution per gram of seeds, 10 to 30 min before use. After the solution had equilibrated at the desired initial temperature, the seed suspension was added to the solution and the cooling program was initiated. The transfer efficiency of the seeds was visually estimated to exceed 90%. Determination of the Amount of Included Water. The water content of each sample of crystals (w, % w/w), both intact and shattered, was measured by Karl Fischer titrimetry (KFT) using a Moisture meter (Model CA-05, Mitsubishi Chemical Industries Ltd., Tokyo, Japan) and was expressed as the mean of six measurements. The crystals were shattered by manual grinding in a mortar with a pestle for 5 min. The shattered crystals were dried over phosphorus pentoxide in a vacuum oven to a constant weight before the water content was determined. The amount of included water (W, mg of water per g of adipic acid) was determined quantitatively by subtracting the water content of the shattered and dried crystals (subscript 1) from that of the intact crystals (subscript 0), thus:
W)
(
)
w1 w0 × 1000 100 - w0 100 - w1
(1)
The corresponding standard deviation, σ, of the amount of included water was calculated according to eq 3, derived from eq 2:15
Crystallization Conditions that Determine the Amount of Included Water. The dependence of included water in the adipic acid crystals on the following crystallization conditions was examined in turn: initial temperature; cooling rate; stirring rate. Each of these variables is an important intensity factor in determining the properties of the resulting crystals. Table 1 summarizes the detailed crystallization conditions. In addition, the effects of the concentration of added surfactant or of added seeds (seeding density) were studied. Effect of Initial Temperature. Figure 2A shows that, upon increasing the initial temperature or supersaturation, the included water content decreases from 10.4 mg/g at 30 °C to 3.0 mg/g at 70 °C. Although the shape of the adipic acid crystals is essentially the same, the particle size of the crystals increases with increasing initial temperature of crystallization. Effect of Cooling Rate. Figure 2B plots the included water content of the crystals at cooling rates of 1.0, 0.33, 0.10, and 0.033 °C/min. The content of included water, despite its large variation, tends to increase with increasing cooling rate, which enforces an increasing rate of desupersaturation. Presumably, the higher crystallization rate that results from a higher cooling rate causes the crystals to develop a higher concentration of defects, such as inclusions of the solution. Effect of Stirring Rate. Figure 2C shows the influence of the degree of agitation (i.e., stirring rate) on the content of included water. The stirring rates employed ranged from 150 ( 10 rpm to 350 ( 10 rpm. Over this range of stirring rates, the aqueous solution of adipic acid exhibits laminar flow and the content of included water remains constant. Summarizing the effects of the crystallization conditions, the initial temperature and cooling rate significantly affect the amount of included water in the adipic acid crystals, while the stirring rate in the range studied has no impact. Therefore, the following crystallization conditions were used in all subsequent crystallization studies: cooling from 40 to 25 °C; cooling rate 0.33 °C/ min; stirring rate 250 rpm. Influence of Surfactants on the Amount of Included Water. The presence of surfactants in the crystallization medium is known to change the growth rates of the faces and, as a result, modifies the habit of the adipic acid crystal.16-20 A defined concentration either of an anionic surfactant, sodium dodecylbenzenesulfonate (SDBS), or of a cationic surfactant, trimethyldodecylammonium chloride (TMDAC), was added to the aqueous solution during crystallization. The concentration added was either 0.1, 1.0, or 10.0 mg/mL. Crystallization in the presence of these additives greatly diminished the size of the crystals. The morphology of
Liquid Inclusions in Adipic Acid Crystals
Crystal Growth & Design, Vol. 5, No. 1, 2005 321
Figure 3. Influence of the concentration of a surfactant in the aqueous crystallization solution on the amount of included water in adipic acid crystals: sodium dodecylbenzenesulfonate (SDBS); trimethyldodecylammonium chloride (TMDAC). The error bars represent standard deviations of three replicates of crystallization. Included water in the absence of surfactant, mean + and - standard deviation (- - - ).
Figure 2. Influence of the following crystallization conditions on the amount of included water in adipic acid crystals upon recrystallization from aqueous solutions: (A) initial temperature; (B) cooling rate; (C) stirring rate. The error bars represent standard deviations of three replicates of crystallization. Table 1. Summary of the Crystallization Conditions Employed for the Aqueous Crystallization of Adipic Acid by Cooling controlled variable
initial temp (°C)
initial temp
30, 35, 40, 50, 60, 70 40
cooling rate
stirring rate 40
final cooling stirring temp (°C) rate (°C/min) rate (rpm) 25
0.33
250
25
0.033, 0.10, 0.33, 1.0 0.33
250
25
150, 250, 350
the adipic acid crystals obtained was not significantly changed by 0.1 mg/mL of SDBS or by all three concentrations of TMDAC in the crystallization media. However, SDBS at 1.0 or 10.0 mg/mL led to needle-shaped crystals. Figure 3 shows that increasing concentrations of SDBS in the crystallization solution reduced the amount of included water progressively. SDBS at 10.0 mg/mL caused the amount of included water to decrease to about 22% of that in its absence. When TMDAC was
Figure 4. Influence of the mass concentration of added seeds to the aqueous crystallization solution on the amount of included water in adipic acid crystals upon crystallization. The y error bars represent standard deviations of the included water in the crystals of a single replicate of crystallization. The x error bars represent higher than 90% efficiency in the seed transfer.
present in the crystallization media at 0.1 mg/mL, the amount of included water in the adipic acid crystals doubled, whereas at 1.0 mg/mL it decreased to about 94% of that in its absence, while at 10.0 mg/mL it increased by about 25%. Influence of Seeds on the Amount of Included Water. As a result of seeds added early in the cooling process, Figure 4 shows that the amount of included water in the final crystals decreased appreciably at low seeding densities and leveled off at higher seeding densities. The least amount of included water is only about 14% of that in the absence of seeds. Discussion Crystallization Process upon Cooling a Saturated Solution at a Linear Rate. Upon cooling, a saturated solution may become supersaturated. Despite the existence of this driving force, crystallization may not occur and the solution may remain supersaturated within the metastable zone. However, once the system
322
Crystal Growth & Design, Vol. 5, No. 1, 2005
Figure 5. Schematic representation of the following processes in solution crystallization upon cooling a saturated solution: nucleation (N); initial crystal growth (ICG); steady crystal growth (SCG) under the following conditions: (A) high initial temperature without seeds; (B) low initial temperature without seeds; (C) low initial temperature with seeds.
is beyond the metastable zone and within the labile region, nuclei are formed spontaneously and grow into macroscopic crystals. Figure 5 represents such a system. During the entire crystallization process, the supersaturation (σ ) concentration/solubility - 1) may vary greatly at different temperatures, as shown schematically in Figure 6. In both Figures 5 and 6, the crystal growth process is divided into two segments, namely, initial crystal growth (ICG) and steady crystal growth (SCG). During ICG, σ is high and crystal growth proceeds rapidly at a rate that decreases greatly as the solution is depleted. Eventually, the continuous decrease in temperature causes the system to reach a steady state, corresponding to SCG. When otherwise identical solutions are cooled from different initial temperatures, the maximum supersaturation (σmax) may or may not be substantially different, depending on the widths of the metastable zone of the
Zhang and Grant
Figure 6. Schematic representation of desupersaturation (solid curve proceeding from right to left) during the following processes in solution crystallization process upon cooling a saturated solution: nucleation (N); initial crystal growth (ICG); steady crystal growth (SCG) under the following conditions: (A) high initial temperature without seeds; (B) low initial temperature without seeds; (C) low initial temperature with seeds.
system at various temperatures, although Figure 6 shows a significant difference. However, the contribution from SCG is greater when a solution is cooled from a higher initial temperature. Different cooling rates can strongly influence the width of the metastable zone, which increases with increasing cooling rate.12 Consequently, σmax increases and the contribution from SCG decreases. The stirring rate may also affect the width of the metastable zone, but appears not to exert a significant influence in the case of adipic acid crystallization. When seeds of the crystallizing phase are present, the crystallization process is affected profoundly. Primary nucleation is largely avoided. The value of σmax is
Liquid Inclusions in Adipic Acid Crystals
drastically reduced and the contribution from SCG is significantly increased. The decrease of σmax is believed to be a function of the seeding density. A higher seeding density leads to faster overall crystal growth rate and, therefore, to a lower value of σmax. An additive in the crystallization medium may change the solubility curve and increase the width of the metastable zone.12,21 This increase of metastable zone width is a function of the concentration of the additive. For some additives at certain concentrations, the width of the metastable zone is increased so much that no nucleation is observed. However, this effect was not observed with adipic acid, whereas nucleation still occurred at all additive concentrations employed. When nucleation is still possible, it usually occurs at a higher σmax. Meanwhile, considerably more nuclei are formed. However, the influence on crystal growth is complicated,12 especially when the differences between the properties of the individual crystallographic faces and competition between adsorption of solute molecules and solvent molecules are considered. During crystallization, a small difference between the initial and final temperature produces small crystals. After nucleation and ICG, the solution is depleted and the temperature is already close to the final temperature, so crystal growth is less steady and the crystals are small. On the other hand, a higher initial temperature results in larger crystals. After nucleation and ICG, further SCG affords crystals of larger size, because the temperature of the solution is still much higher than the final temperature. Influences of Crystallization Conditions on the Amount of Included Water. The amount of included water decreases with increasing initial temperature (Figure 2A), indicating that the formation of water inclusions is more significant at the initial stage of crystallization, i.e., during nucleation (N) and initial crystal growth (ICG), when the supersaturation is relatively high. The nuclei, of course, represent a very small weight fraction of the crystals. Therefore, most of the included water is probably incorporated during the ICG period. The lack of dependence of the amount of included water on the stirring rate (Figure 2C) indicates that the degree of agitation does not change the profile of σ vs T. In fact, the visual onset temperature of crystallization remains the same, within experimental error, at these stirring rates. A lower cooling rate results in a narrower metastable zone width and, therefore, a lower σmax and a higher contribution from SCG. The result is a smaller amount of included water in the adipic acid crystals (Figure 2B). To summarize, the dependence of the amount of included water on initial temperature, cooling rate, and stirring speed indicates that the included water is mainly incorporated during ICG and is a function of the supersaturation. Influence of Seeds and Additives on the Amount of Included Water. The addition of seeds results in a significant decrease in the amount of included water. As discussed above, the presence of seeds largely eliminates nucleation, and therefore greatly reduces σmax, shortens ICG, and prolongs SCG. When an additive is introduced into the crystallization media, σmax and the contribution from ICG are
Crystal Growth & Design, Vol. 5, No. 1, 2005 323
Figure 7. The morphology, faces, and orientation of the molecules with respect to the faces of adipic acid crystals according to Michaels and Colville.18
increased and the contribution from SCG is reduced. Intuitively, it may seem that the amount of included water should increase. However, the presence of additives often decreases the crystal growth rate, which may disfavor the water inclusion. The growth rate of individual crystals will decrease to a greater extent because of the increased number of nuclei created when additives are present. The influence of an additive on water inclusion therefore reflects all these considerations and may be quite complex. Figure 7 shows the morphology, faces, and orientation of the molecules with respect to the faces of adipic acid crystals. The assignment of the faces in Figure 7 follows that of Michaels and Colville.18 However, various reports on the crystal growth of adipic acid have subsequently appeared, such as Davey et al.22 In their early work, Michaels and Colville18 demonstrated that the cationic surfactant, TMDAC, is chemisorbed most strongly onto the (001) face (C), which has the highest density of hydroxyl groups among the expressed faces of adipic acid. As a result of this adsorption, the growth rate of the C face decreases to the greatest extent. On the other hand, the anionic surfactant, SDBS, is physically adsorbed onto the (010) face (A) and onto the (110) face (B) more strongly than onto the (001) face (C). In this case, the retardation of the growth rates of the A and B faces is greater than that of the more weakly adsorbing C face. When SDBS is present in the crystallization medium, the amount of included water decreases, probably because the crystal growth rate is sufficiently reduced, especially of the A and B faces. From the data presented by Michaels and Colville,18 the growth rate ratio (rateA+B/rateC) decreases from about 1.5 in the absence of surfactant to 0.9 with 0.1 mg/mL of SDBS and to about 0.7 with 1.0 mg/mL of SDBS. The retardation effects of surfactants on growth rate levels off at high surfactant concentrations.18 Although these workers did not employ the highest surfactant concentration, 10.0 mg/mL, used in this study, the growth rate ratio is expected to remain constant at this higher concentration. The decrease in the growth rate of individual crystals is probably solely responsible for the further decrease in the amount of included water. At 0.1 and 1.0 mg/mL TMDAC, the growth rate ratio increases to 2.2 and 3.0, respectively. Therefore, the amount of included water is expected to increase monotonically, provided that the growth rate ratio is the only control-
324
Crystal Growth & Design, Vol. 5, No. 1, 2005
ling factor. However, the experimentally observed trend is different, indicating a complex interplay between the increase of growth rate ratio, the increase of σmax, and the decrease of the growth rate of individual crystals. At low TMDAC concentration, the width of the metastable zone is not significantly affected, suggesting that σmax and the growth rate of individual crystals remain relatively constant. The growth rate ratio, however, increases substantially causing the initial increase of water inclusion. At medium TMDAC concentration, the width of the metastable zone is significantly altered. Therefore, all three factors are working simultaneously. The overall result is a slight decrease in the water inclusion. As mentioned above, the growth rate ratio will be similar at 10.0 and 1.0 mg/mL of TMDAC. A slight increase in the amount of included water is a result of the increase in σmax and the decrease in the growth rate of each individual crystal. Mechanism of the Formation of Water Inclusions. Several mechanisms of inclusion formation have been proposed.10,13 Each mechanism may be responsible for certain systems and types of liquid inclusions. However, when adipic acid is crystallized from aqueous solutions via cooling, none of them can accommodate all the experimental results. Cracking and resealing of formed crystals cannot explain the difference between the amount of included water in the presence of the cationic and anionic surfactants. Neither can it explain the lack of dependence on the stirring rate. Inequality of growth rates cannot account for the smaller amount of included water in the needle-shaped crystals than in the more symmetrical crystals, nor the difference between the effects of the cationic and ionic surfactants. Adsorption of impurities (or solvents) onto the growing faces can explain some results for adipic acid but not the influence of cooling rate, seeds, and the amount of included water at high levels of additive concentration. From the results described above, the inclusion of water in adipic acid crystals can be best explained by the faster growth of both the (010) face (A) and (110) face (B), and by the slower growth of the (001) face (C) for each individual crystal. Factors that can affect any one of these rates may play a role. The factors observed in this study are initial temperature, cooling rate, seeds, and additives. All of these four factors, in one way or another, determine the relative contribution of ICG and SCG, the overall growth rate of individual crystals, and the growth rate ratio (rateA+B/rateC). These three factors then determine the absolute growth rates of the three predominant crystallographic faces, A, B, and C. These facial growth rates ultimately determine the amount of included water or crystallization solvent upon crystallization of the crystals from solution at a linear cooling rate. Methods for Reducing the Amount of Included Water in Adipic Acid Crystals. The above results show that the included water in the adipic acid crystals is reduced significantly by cooling from a higher initial temperature, by cooling at a slower rate, and by crystallizing in the presence of SDBD or seeds. A combination of the above approaches may sometimes exert a synergistic effect and further reduce the amount of included water. These synergistic effects of the crystallization
Zhang and Grant
factors can be unveiled most effectively, by detailed statistical design of the experiments. Conclusions Upon crystallization of adipic acid by cooling its aqueous solution, the amount of included water decreases with increasing initial temperature and slower cooling. Changes in the degree of agitation from 150 to 350 rpm did not influence the amount of included water. Added seeds or increasing concentrations of SDBS in the crystallizing solution decreases the amount of included water. The addition of TMDAC to the crystallization solution exerted a complex effect, generally increasing the amount of included water. The relatively high growth rates of the hydrophobic faces (010 and 110), and the relatively low growth rate of the hydrophilic face (001) of individual crystals explain the amount of included water, which in turn is influenced by the above experimental conditions. Acknowledgment. We thank Dr. Reginald Davis, Dr. Daniel A. Green, and Dr. Paul Meenan of E.I. du Pont de Nemours and Company, Experimental Station, Wilmington, DE, for encouragement and support, and for the gift of adipic acid. We also thank the Du Pont Educational Program for partial financial support and the Graduate School of the University of Minnesota for a Doctoral Dissertation Fellowship for one of us (G.G.Z.Z.). References (1) Buckley, H. E. Crystal Growth; John Wiley and Sons: New York, 1951. (2) Shepherd, T. Chem. Br. 1997, April, 28. (3) Samson, I. M.; Liu, W.; Williams-Jones, A. E. Geochim. Cosmochim. Acta 1995, 59, 1963. (4) Satish Kumar, M.; Santosh, M. J. Geol. Soc. India 1994, 43, 659. (5) Van Den Kerkhof, A. M.; Touret, J. L. R.; Kreulen, R. J. Metamorph. Geol. 1994, 12, 301. (6) Le´cuyer, C.; O’Neil, J. R. Bull. Soc. Ge´ ol. Fr. 1994, 165, 573. (7) Huettenrauch, R. Acta Pharm. Technol. 1978, Suppl. 6, 55. (8) Halasz, S.; Bodor, B. J. Cryst. Growth 1993, 128, 1212. (9) Law, D. Influence of Composition of the Crystallization Medium on the Physical Properties and Mechanical Behavior of Adipic Acid Crystals, Ph.D. Thesis, University of Minnesota, Minneapolis, USA, 1994. (10) Denbigh, K. G.; White, E. T. Chem. Eng. Sci. 1966, 21, 739. (11) Wilcox, W. R. Ind. Eng. Chem. 1968, 60, 13. (12) Mullin, J. W. Crystallization, 3rd ed.; Butterworth-Heinemann: Oxford, UK, 1993. (13) Rosmalen, R. J.-V.; Bennema, P. J. Cryst. Growth 1977, 42, 224. (14) Grant, D. J. W.; Mehdizadeh, M.; Chow, A. H.-L.; Fairbrother, J. E. Int. J. Pharm. 1984, 18, 25. (15) Topping, J. Errors of Observation and Their Treatment, 3rd ed.; Chapman and Hall: London, UK, 1962. (16) Canselier, J. P. J. Disp. Sci. Technol. 1993, 14, 625. (17) Fairbrother, J. E. Effect of Trace Additives on the Crystal Growth Rate and Habit of a Pharmaceutical Excipient, Adipic Acid, Ph.D. Thesis, University of Nottingham, Nottingham, UK, 1981. (18) Michaels, A. S.; Colville, A. R. J. J. Phys. Chem. 1960, 64, 13. (19) Michaels, A. S.; Tausch, F. W. J. J. Phys. Chem. 1961, 65, 1730. (20) Moilliet, J. L.; Collie, B. Surface Activity, 2nd ed., D. Van Nostrand Company: Princeton, NJ, 1961. (21) Myerson, A. S.; Jang, S. M. J. Cryst. Growth 1995, 156, 459. (22) Davey, R. J.; Black, S. N.; Logan, D.; Maginn, S. J.; Fairbrother, J. E.; Grant, D. J. W. J. Chem. Soc., Faraday Trans. 1992, 88, 3461.
CG049868H
