Solvent effects on kinetics of solution-mediated transition of stearic acid polymorphs

Journal of Crystal Growth 72 (1985) 699—704 North-Holland, Amsterdam

699

SOLVENT EFFECTS ON KINETICS OF SOLUTION-MEDIATED TRANSITION OF STEARIC ACID POLYMORPHS K. SATO

*,

K. SUZUKI and M. OKADA

Faculty ofApplied Biological Science, Hiroshima University. 720 Fukuyama, Japan

and N. GARTI Casali Institute of Applied Chemistry, Hebrew University of Jerusalem. 91904 Jerusalem, Israel Received 5 February 1985; manuscript received in final form 9 May 1985

The effects of solvent on the transition kinetics of polymorphic modifications of stearic acid have been examined in polar and nonpolar solutions. Two typical polymorphs, B (low-temperature stable) and C (high-temperature stable), and the solvents (butanone, methanol, n-hexane and decane) were studied. In all solutions the transitions from B to C and from C to B took place at temperatures above and below 32°C,at which the free energies of B and C have the same value, respectively. The rates of the C —~ B transition were significantly dependent both on temperature and solvent. First, the transition rate was fastest between 22 and 26°C.This was due to two conflicting factors: the free energy difference between B and C which decreases as the temperature approaches 32°C,and the rates of dissolution of C and growth of B which increase with temperature. Secondly, the solvent exclusively influenced the C —~ B transition; polar solvents, especially methanol, caused a significantly more rapid transition than nonpolar solvents, the rates being relatively higher than those predicted by the solubility values. It was inferred that the different growth units (monomers in the polar solvents and dimers in the nonpolar ones) and the twisted lateral interface structures of the B polymorph would be responsible for the present solvent effect.

I. Introduction Stearic acid has four polymorphic modifications: A, B, C and E [1—3].All of them, except E, can crystallize from solution around room temperature. Recently several papers have dealt with the crystallization of stearic acid polymorphs in relation to crystallization conditions such as temperature, supersaturation and solvent. Efforts have mainly been directed to two aspects: thermodynamics and kinetics. These can be summarized as: (1) Thermodynamics (a) stability of polymorphs [4—6], (b) solubility [6,7], (c) solute—solvent interaction [8,9], (d) surface energy, step energy and equilibrium crystal shape [10], *

To whom all correspondence should be addressed,

(e) solid-state transition Eli]. (2) Kinetics (a) occurrence of polymorphs [4,5,12—14], (b) growth kinetics [15,16]. These studies have clarified the following points: (a) B and C are the most stable polymorphs at temperatures below and above 32°C,respectively; A is always metastable. (b) The occurrence of B prevails at lower temperatures and lower supersaturations, while A and C preferably occur at higher temperatures and supersaturations. (c) Stearic acid molecules form dimers in nonpolar solvents, whereas only monomers exist in polar solvents. (d) The effect of solvent on the crystallization process is likely to be related to the solute—solvent interaction. To elucidate the solvent effect, this paper is aimed at measuring the rate of solution-mediated transition between the polymorphs in a variety of

0022-0248/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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K. Sato et al.

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Solvent effects on polymorphic transition kinetics

solvents. These transitions result from the differences in free energies of the three polymorphs. The most stable form can grow at the expense of the less stable ones. It is expected that the effect of solvent would be revealed in the rates of this solution-mediated transitions. Here only B and C were taken into account because many important data are lacking on the A form.

ter). The (003) reflection was chosen as a reference. The concentrations were determined at intervals ranging from 3 to 10 mm, depending on the temperature.

2. Results 2.1. n-Hexane and decane solutions

2. Materials and methods Stearic acid was purchased from Ishizu Seiyaku. Its purity was guaranteed to be more than 99%. No further purification was done. The following solvents were utilized: nonpolar aprotic n-hexane (Yoneyama Pharmacy with a purity of 98%), polar protic methanol (Yoneyama Pharmacy, 99.6%) and polar aprotic butanone (Nakarai Chem. Inc., 99%). In addition, nonpolar aprotic decane (Tokyo Kasei Inc., 99%) was sometimes used. The transition rate was defined as the rate of change in fractional concentrations of C and B powder crystals suspended in the solution. A large amount of B and C crystals were separately ground for several hours prior to the experiment. The size of the powders was measured by an optical microscope in the suspended solution of n-hexane at 10°C. As the solubility of stearic acid at this temperature is very low (0.1 g per 100 g solvent), no appreciable dissolution occurred during the examination of the particle sizes which was done within about 20 mm. Thus the average particle size was found to be about 30 ~m for both poiymorphs. The same samples were utilized throughout the experiments. A mixture of B and C powders was put into the solution, which had been saturated with respect to the more stable form at a given temperature. The amounts of solution and powder were always 15 and 1.5 g. The suspension was stirred with a magnetic stirrer (about 300 rpm). The temperature of the suspension was held at 14 to 38°Cwithin ±0.1°Cvia the thermostated water surrounding the growth cell. The samples of 1.5 cm3 were withdrawn, filtered, and dried as quickly as possible. The ratio of the B and C concentrations was measured as a function of time from X-ray spectra (Rigaku diffractome-

Fig. I shows the transition rates in the n-hexane solutions. The rate is expressed by f( I), which is the fraction of C present in the powder at the exposure time of t~ Three aspects are worthy of examination: the direction of the transition, its rate and its temperature dependence. First, the direction of the transition is from B to C (B C hereafter) above 32°Cand from C to B (C B) below 32°C.This corresponds to the free energies of B and C, which have the same value at 32°C.In all solutions, the same result for the direction of the transition was obtained. With increasing temperature, the transition rate for C B first increased and then decreased. The maximum rate appeared around 22°C. This was due to the opposing effects of thermodynamic and kinetic factors, as discussed later. Above 32°C,the B C transition rate increased monotonically with temperature. The transitions both for C B and B C in —‘

—*

-+

—~

—

‘f

7

~ / Ip6

—~

at ‘°

I

c

I

j381/5

nJ~ane

°C

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•

0

0.

32 ~

.

•

/“\ 22’~ A 26°C

-

-

3O’~ 28~C

~

4°C

\\ \ \~°

\

~

at B

minI Fig. 1. Transition between B and C polymorphs of stearic acid in n-hexane solution.

K Sato et at

I

I

I

/ Solvent effects on polymorphic for C

I

thanol f(t)

~ ~c

me

//

B differs from that in n-hexane, revealing

a somewhat sigmoid shape. The transition in methanol seems to be of second order, whereas it was of first order in n-hexane. In the C B transition region, the C crystals disappeared much more rapidly in both methanol and butanone than in n-hexane. The opposite was true for B —s C, demonstrating a clear-cut solvent effect on the transition rate. Even between methanol and butanone, a significant difference was observed: the C B transition occurred more rapidly in methanol than in butanone and vice versa for B —s C.

~

—

—‘

701

transition kinetics

36 ~

—~

~_—“

o.~~

~.

\~ \N~

—,

4~

O.C

0

30

60(minl

Fig. 2. Transition between B and C polymorphs of stearic acid in methanol solution.

3. Discussion 31. Thermodynamic and kinetic factors

decane solutions showed quite the same time dependence as those in n-hexane at every temperature examined. The only difference was that the rates of transitions were always lower in decane than in n-hexane. Two typical data in the decane solution will be shown later. 2.2. Methanol and butanone solutions Figs. 2 and 3 show the transitions in methanol and butanone solutions. The C B transition has its maximum rate around 26°C(methanol) and 22°C(butanone). In methanol, the change of f(t) —~

I

7 /

L

I

r/36.C

~

fw ~

~

-

In the present transition the essential processes are the growth of the more stable polymorph and the dissolution of the less stable one. Spontaneous nucleation probably does not occur because of the very low supersaturation achieved. Therefore, two dominant factors are involved: the driving force for the transition due to the difference in the free energies of B and C, and the kinetics of growth and dissolution. These two factors are discussed here in terms of recent studies on solubility [6], and on the growth as well as dissOlution rates [15—17]of stearic acid. Solubility is of most importance. The larger the solubility, the faster should be the growth and dissolution of crystals [18]. According to a recent experiment [6], the solubility for each polymorph of stearic acid can be expressed as

::r~~e:a!n:!anone

and as

lnX=_~+~+(k.~_~) 22C~\~I 4.C

\

~

I8

C

30

(minI

Fig. 3. Transition between B and C polymorphs of stearic acid in butanone solution.

(1)

(2)

for methanol. In eqs. (1) and (2), i~Hdand ~Sd are respectively the enthalpy and entropy of dissolution, k is a correction term for methanol solution and R is molar gas constant. The driving force for a transition can also be

K. Sato et al.

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Solvent effects on polymorphic transition kinetics

Table I Supersaturation (a) due to solubility difference of B and C, calculated from eq. (3) using i~ H~ B — ~ HdC = 4.5 kJ/mol and 4.8 J/mol.K ~SdB~ ~Sdc=l Temperature (°C) ~ (%) 14 18 22 26 28 30

11.1 8.3 5.6 3.1 1.8 0.6

34 36 38

1.7 2.9 4.0

+

R

1

2 —1. j

The values of a for B

~±

crystals at the transition time of t divided by its initial amount. The‘parameter k’ is the growth rate of B, being dependent both on supersaturation and on temperature [18]: i (B) — ~

k’

=

b exp[

RT

(5)

]~2.

In eq. (5), b (time~)is a kinetic factor and ~Eg is the activation energy for the growth of B. Use of 2 assumes that the growth of B is by a spiral a growth mechanism. This was experimentally confirmed in n-hexane [15]. Using eqs. (3)—(5), we

=exp~—(~Hd1 RT —~Hd,) i~Sd

—~

dfdBk,B (4) dt where B is the relative value of the amount of B

1

—

C B the rate determining step is the growth of B crystals, with the solution concentration being near to the solubility of C. Thus the transition rate df/dt can be written as

~‘~J

expressed as the diffference in the solubilities, which correspond to the free energies, of two forms, X 1 and X2, in terms of a supersaturation:

xt

crystal. This was confirmed in decane solution for the growth of B and the dissolution of C at different temperatures as the measured in the system [17]. This leads to conclusion thatflow for

(3)

C are given in table 1.

3.2. Temperature dependence The most significant temperature dependence appeared in the C —s B transition region. The present discussion is therefore limited to this transition. As described before, the transition rates showed the maximum values around 22°C (nhexane and butanone) and 26°C(methanol). This can be explained in terms of thermodynamic driving force which decreases with increasing temperature as shown in table 1, and of the growth and dissolution rates which increase with increasing temperature. One therefore expects that, due to these two conflicting factors, the C B transition rate should show a maximum versus T. A numerical examination of the n-hexane solution may be a better example because of its first order reaction. The rate of dissolution is expected to be much larger than that of the growth of —

carried out a computer simulation by varying the values of b and i~E5.The best fitted curves with those displayed in fig. 1 were obtained with the values of b = 4 x 1027 and z~E5(B)= 150 kJ/mol. These two values are of reasonable magnitudes as are those experimentally obtained for the growth of B in decane solution: b (in decane) = 4 x 10~~ and L~Eg (in decane) = 120 kJ/mol [17]. In methanol and butanone suspensions, a simulation was not made because second order, or at least the more than first order, reactions apparently occurred. However, whatever the order of reaction, the temperature dependence must qualitatively be explained in terms of two conflicting factors in the same manner as that in n-hexane. 3.3. Solvent effect To better demonstrate the solvent effect, fig. 4 shows typical data examined at 28 and 36°Cincluding results for decane. For C —s B at 28°C,the transition rates increase in the following sequence: decane

<

n-hexane ~z butanone

<

methanol,

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Solvent effects on polymorphic transition kinetics

703

peratures: decane < methanol ____________

28°C(C~B)I 0

30

time

60

(mini

<

n-hexane < butanone,

except for methanol versus n-hexane at 28°Cwhere X(methanol) is larger by 25% than X(n-hexane). The order of the magnitude of solubility is only consistent with that for the transition rate in nhexane and decane, which are homologous short chain alkanes. The discrepancy between the transition rates and solubilities is manifest in the other solvents. For C B at 28°C the transition rate in methanol is twice as high as in butanone and 6 times higher than in n-hexane. The solubility, however, in methanol is about 2.5 times lower than in —

Fig. 4. Transition between B and C polymorphs of stearic acid in (1) methanol, (2) butanone, (3) n-hexane and (4) decane solutions at 28 and 36°C.

whereas for B methanol

<

—

C at 36°C:

decane ~z butanone

<

n-hexane.

From this, one can conclude that the polar solvents favour C —~ B, whereas B C prevails in the nonpolar solvents. Even in polar solvents, protic methanol accelerates C —s B more than aprotic butanone. Here, we discuss this clear-cut solvent effect. The solvent acts in three ways [18]. The first one is due to the solubility as mentioned above: a higher solubility causes a higher transition rate [19]. The second is due to the viscous property of the solvent. The third is the steric effect between solute and solvent in the bulk solution as well as at the solid—liquid interface. These three aspects are sometimes conflicting, First we examine the effect of the solubility. Table 2 shows the solubilities of C at 28 and 36°C in the four solvents employed. The solubility X increases in the following sequence at both tern—~

Table 2 Solubilities (X) of stearic acid of C polymorph in butanone, n-hexane, methanol and decane, as expressed in the number of solute molecules per unit volume of solution

Solvent

X _______________________

28°C

36°C

Butanone n-Hexane Methanol

1.05 x 1020 9 3.07 x i0~ 3.83x1019

Decane

9.61x10’8

2.26 X 1020 1.11 X 1020 9.1OX1O’9 3.61x10’9

_____________________________________________

butanone. The same result arises betweenmethanol and n-hexane as well as decane. For B —* C at 36°C, the transition in n-hexañe occurs more rapidly. It appears clear when we compare nhexane with butanone: the transition rates are of the same order, while the solubility in n-hexane is twice lower than in butanone. In addition, the order of the magnitude of the viscosities we evaluated was also found to be contradictory to the transition rates. The diffusion constants of stearic acid in solutions were calcu-lated by using Wilke and Chang’s equation [20], having the following sequence in the orders of magnitude: decane < methanol < n-hexane < butanone, both at 28 and 36°C. From this one can conclude that the solvent effects on the B and C transitions cannot be explained by the solubility nor by the viscosity effect. Therefore, we reached some stearic effects due to solvent—solute interaction via both different growth units of stearic acid and different interface structures of B and C. First, monomers are favoured in polar solvents, whereas dimers in nonpolar solvents especially in short chain alkanes [6,7,9,21]. Secondly, the distinctive difference between B and C appears in the lateral (110) interfaces, which play a dominant role in the growth. This is illustrated in fig. 5. An all trans conformation resulted in the straight chain packing for C, whereas a partially twisted structure results for B due to a gauche conformation at

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K Sato et al.

/

Solvent effects on polymorphic transition kinetics

enabling him to join this study. K. Sato is also _~~kink-1-

indebted to Dr. R. Boistelle and Dr. W. Beckmann for useful discussions.

B—form

References

_________

______

C—form Fig. 5. Molecular structures of the lateral (110) interfaces of B and C polymorphs of stearic acid. Solid and open circles mean carbon and oxygen atoms.

C1—C3 carbons [22]. Therefore, the latter conformation resulted in the twisted lamellae interface on the {110} planes for B [23].By combining these two aspects one can speculate that the adsorption onto the B faces is dependent on the solvent via different’ growth units. The monomer species can be adsorbed more easily at the terraces between the twisted portion around COOH groups and the CH3 end groups. The solute—solvent interaction, for example via strong hydrogen bonding in methanol, may decrease the activation energy for adsorption. Meanwhile, the dimers in the nonpolar solvents may encounter some difficulty in the adsorption due to geometrical resistance at the twisted portions for B. To verify this speculation, spectroscopic experiments as well as a theoretical evaluation of the solvent-dependent interface kinetics are needed.

Acknowledgements One of the authors (N.G.) expresses his thanks to the Japanese Society for Promotion of Science for its help in visiting Hiroshima University and

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Boistelle, J. Colloid Interface Sci. 94 (1983) Boistelle, J. Crystal Growth 66 (1984) 441. R. Boistelle and K. Sato, J. Chem. Eng. 215. F. Rouquerol and H. Beckmann, Thermo-

chim. Acta 66 (1983) 295. [8] G. Zerbi, G. Minoni and A.P. Julloch, J. Chem. Phys. 78 (1983) 5853. [9] W. N. Garti and K.and Sato,R.toBoistelle, be published. [10] Beckmann J. Crystal Growth 67 (1984) 271. [11] K.S. Kunihisa, Thermochim. Acta 31(1979)1. [121 N. Garti, E. Wellner and S. Sang, Thermochim. Acta 37 (1980) 131. [13] N. Garti, E. Wellner and S. Sang, Kristall Tech. 15 (1980) 1303. [141E. Wellner, N. Garti and S. Sang, Crystal Res. Technol. 16 (1981) 1283. [15] Y. Maeyashiki, M. Okada and K. Sato, Japan. J. AppI. Phys. 21(1982) L781. [16] K. W. Sato Beckmann R. Boistelle, to be published. [17] and R.and Boistelle, to be published. [18] R. Boistelle, Crystal Growth in Nonaqueous Solutions, in: Interfacial Aspects of Phase Transformation, Ed. B. Mutaftschiev (Reidel, Dordrecht, 1982). [19] R.J. Davey in: Abstracts 7th Intern. Conf. on Crystal Growth, Stuttgart, 1983. [20] C.R. Wilke and P. Chang, AIChE J. 1(1955) 264. [21] Y. Murata, K. Motomura and R. Matsuura, Mem. Fac. Sci. Kyushu Univ., Ser. C, 11(1978) 29. [22] M. Goto and E. Asada, Bull. Chem. Soc. Japan 51(178) 2456.

-

[23] M. Goto, private communication.