Dynamic Inhibition of Constrained Crystallization by Mesoscopic

© Copyright 2000 American Chemical Society

MARCH 21, 2000 VOLUME 16, NUMBER 6

Letters Dynamic Inhibition of Constrained Crystallization by Mesoscopic Morphology Modifiers A. J. Colussi,*,† M. R. Hoffmann,*,† and Y. Tang‡ W. M. Keck Laboratories, California Institute of Technology, Pasadena, California 91125, and Chevron Petroleum Technology Company, La Habra, California 90631 Received August 10, 1999. In Final Form: January 25, 2000 We investigate the mechanisms by which two chemically diverse polymer additives affect crystal separation from hexacosane/decane solutions under various conditions. The additives are dissimilarly effective for delaying the onset of crystallization in supercooled solutions, although none, of course, ultimately prevents their reaching equilibrium. Remarkably, one polymer significantly raises the dissolution temperature of the crystal aggregates grown in its presence, even at sub-parts-per-million additive levels. More interesting is the finding that sufficiently large concentrations of either additive are able to cap at a common minimum thickness the porous layers formed on a cold surface swept by undersaturated solutions. The thin layers formed in the presence of crystallization inhibitors are mesoscopically more compact (i.e., have pore sizes about 10-fold smaller) than those produced in their absence, although all meltswhen rid of solventsas neat hexacosane at 329.5 ( 0.5 K. We infer that inhibitors permanently limit the extent of crystal separation from undersaturated solutions subjected to fixed temperature constraints by blocking solute transfer across the boundary layer. This lasting action is mediated by the subtle modification of mesoscopic crystal morphology and is remotely related to the kinetics of isothermal crystal nucleation or the thermodynamics of phase separation.

Introduction 1

Crystallization is one of the oldest chemical operations. However, we cannot predict crystal structures from molecular information,2,3 avoid polymorphism under apparently identical conditions,4-7 or arrest crystallization indefinitely.8-11 The fact that some living organisms * To whom correspondence may be addressed. Telephone: (626) 395-3448. FAX: (626) 395-3170. E-mail: [email protected]. † California Institute of Technology. ‡ Chevron Petroleum Technology Company. (1) Tiller, W. A. The Science of Crystallization; Cambridge University Press: Cambridge, U.K., 1991. (2) Gavezzotti, A. Acc. Chem. Res. 1994, 27, 309. (3) Gdanitz, R. J. Curr. Opin. Solid State Mater. Sci. 1998, 3, 414. (4) Durbin, S. D.; Feher, G. Annu. Rev. Phys. Chem. 1996, 47, 171. (5) Caira, M. R. Top. Curr. Chem. 1998, 198, 163. (6) Dunitz, J. D.; Bernstein, J. Acc. Chem. Res. 1995, 28, 193. (7) Garcia, E.; Veesler, S.; Boistelle, R.; Hoff, C. J. Cryst. Growth 1999, 199, 1360. (8) Anwar, J.; Boateng, P. K. J. Am. Chem. Soc. 1998, 120, 9600.

survive subfreezing temperatures due to the presence of specific polypeptides in their internal media seems to suggest that it might be possible to halt crystallization by chemical means.12-16 This is the implicit, tantalizing premise on which important processes are currently engineered.17-20 It is fundamental to realize, however, that (9) Kern, R.; Dassonville, R. J. Cryst. Growth 1992, 116, 191. (10) Beiny, D. H. M.; Mullin, J. W.; Lewtas, K. J. Cryst. Growth 1990, 102, 801. (11) Land, T. A.; Martin, T. L.; Potapenko, S.; Palmore, G. T.; Yoreo, J. J. Nature 1999, 399, 442. (12) Haymet, A. D. J.; Ward, L. G.; Harding, M. H. J. Am. Chem. Soc. 1999, 121, 941. (13) Yeh, Y.; Feeney, R. E. Chem. Rev. 1996, 96, 601. (14) Worrall, D. Science 1998, 282, 115. (15) Williams-Seton, L.; Davey, R. J.; Lieberman, H. F. J. Am. Chem. Soc. 1999, 121, 4563 and references therein. (16) Weissbuch, I.; Popovitz-Biro, R.; Lahav, M.; Leiserowitz, L. Acta Crystallogr. 1995, B151, 115. (17) Lira-Galeana, C.; Firoozabadi, A.; Prausnitz, J. M. AIChE J. 1996, 42, 239.

10.1021/la991085o CCC: $19.00 © 2000 American Chemical Society Published on Web 02/17/2000

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crystallization inhibitors may delay nucleation and slow crystal growth but cannot ultimately prevent supersaturated solutions from reaching equilibrium, unless they thermodynamically destabilize the solid phase. In other words, mere kinetic control is obviously incompatible with the continuous operation of supercooled solutions. Here we show that inhibitors can, however, permanently limit crystallization from undersaturated solutions circulating over cold surfaces by effectively restricting heat and mass transfer via mesoscopic morphological modification of the solid layers that grow at the temperature discontinuity. More specifically, we find that stirred, isothermal, undersaturated n-C26H54/n-C10H22 solutions deposit porous hexacosane layers on refrigerated surfacessa case known in the literature as constrained crystallization1sthat grow indefinitely by letting the solute reach colder regions beneath the advancing crystal front.21,22 In contrast, the mesoscopically compact (at the micrometer scale) wax layers formed in the presence of chemical inhibitors reach finite thicknesses δ∞ (see Scheme 1), apparently because they create effective mass and thermal barriers. Actually, we find similar minimum δ∞ values for the chemically different poly(octadecyl methacrylate) (PODMA)san inhibitor that retards nucleation and growth but does not modify the temperature of crystal dissolutionsand for poly{N-[(2-hydroxymethyl)heptadecyl]allylmethyleneimine} (KJ-34), whuch performs efficiently at smaller concentrations although it raises crystal dissolution temperatures by up to 3 K. Since the pseudopolymorphs formed in the latter case reach their maximum dissolution temperatures at inhibitor concentrations about 10 times smaller than those required to produce the most compact layers, we infer that the molecular control of crystallization under nonisothermal conditions is actually mediated by mesoscopic morphological modification of the solids formed. Experimental Section We studied crystallization from stirred hexacosane (Aldrich, 99%) solutions (60 g, x26 ) 0.013) in n-decane (Aldrich, 99+%) maintained at TS ) 291.0 K, on a dipping, horizontal disk made of polished stainless steel (r ) 0.4 cm) in thermal contact with an otherwise insulated cooling device at TF < TS (Scheme 1). The stirrer was a rotating disk (r ) 0.8 cm) spun at Ω ) 5000 rpm (Pine Instruments) coplanar with the refrigerated disk above. Their (parallel) axes were 1.8 cm apart. The rotating disk forces the solution upward along its axis and then tangentially past (18) Coutinho, J. A. P.; RuffierMeray, V. Ind. Eng. Chem. Res. 1997, 36, 4977. (19) Chatterjee, A. K.; Phatak, S. D.; Murthy, P. S.; Joshi, G. C. J. Appl. Polym. Sci. 1994, 52, 887. (20) Claudy, P.; Le´toffe´, J. M.; Bonardi, B.; Despina, V.; Damin, B. Fuel 1993, 72, 821. (21) Nield, D. A.; Bejan, A. Convection in Porous Media, 2nd ed.; Springer: New York, 1999. (22) Wilcox, W. R. Prog. Cryst. Growth Charact. 1993, 26, 153.

Letters the cooled disk nearby at a Reynolds number Re ) 2.7 × 104.23 The temperature difference ∆T ) TS - TB between the solution bulk and the base of the cooled disk was monitored by a pair of low heat conductivity thermocouples. ∆T (g3 K) generally increases during experimentssbecause the growing wax deposits tend to thermally insulate the cold disk from the solutions providing an indirect measure of the layer depth δ as a function of time (see below). In separate experiments, the course of crystal homogeneous nucleation, growth, and dissolution was followed by light dispersion (at 480 nm) through magnetically stirred hexacosane/decane solutions contained in glass cuvettes. The temperature of the latter could be rapidly varied or set within (0.1 K by means of a thermoelectric-controlling device (HewlettPackard, model 89090A). Linear PODMA (degree of polymerization ≈ 10-11, Mw ≈ 4400, Polymer Source, Dorval, PQ, Canada), and KJ-34 (degree of polymerization ≈ 42, Mw ≈ 13 000, British Petroleum KJ-34) were dissolved as received in n-decane (KJ-34 dissolution required small toluene additions).

Results and Discussion Figure 1 shows ∆T vs time traces in wax deposition experiments with inhibited and uninhibited solutions. As expected, the induction periods preceding the onset of nucleation and growth depend on the solution history, are not quite reproducible, and, therefore, do not provide useful information or technical possibilities for reliable control.1,9,24,25 It was found that pristine solutions usually take much longer to crystallize than those reused. In contrast, the limiting ∆T∞ values reached at longer times are fairly reproducible. It is apparent that (1) in the absence of inhibitors, the crystal layer continues to grow, albeit more slowly, even after the cold disk is completely covered at the end of the sigmoidal stage,26 (2) a plateau is reached instead in the presence of inhibitors at parts per million levels (by weight relative to the solvent), (3) the ∆T∞ vs [inhibitor] dependence exhibits saturation behavior, i.e., the inhibitors have a limiting effect on ∆T∞, and hence on δ∞, (4) the ∆T∞ ) 4.3 ( 0.05 K values at saturation are very similar for both inhibitors, and (5) KJ-34 is as efficient as PODMA, but at concentrations about 10 times smaller. The crystal layers formed in the absence of inhibitors are thick (a few millimeters), very porous, and anisotropic, displaying feathery structures normal to the cold disk (Figure 2A). We found that the pores occlude solvent comprising ca. 70% of the net crystal weight. The compact and more regular morphology of the thinner inhibited films (δ∞ ≈ 100 µm, as determined by optical microscopy) is markedly different (Figure 2B). To check whether inhibitors also affect the thermodynamics of phase separation, we determined (1) the melting points TM of the dry crystals (after removing the occluded solvent under vacuum at room temperature) collected from the cold disk in the presence and absence of inhibitors and (2) the dissolution temperatures TD of the suspended crystals formed in rapidly cooled hexacosane solutions. We found that the TM’s of the neat and inhibited hexacosane crystals are identical within experimental (23) Littell, H. S.; Eaton, J. K. J. Fluid. Mech. 1994, 266, 175. The Reynolds number Re ) (2πΩ/60)r2/ν ) 2.7 × 104 (Ω ) 5000 rpm is the disk rotation frequency, r ) 0.8 cm is the rotating disk radius, and ν ) 1.26 cSt is the kinematic viscosity of n-decane at 20 °C) is about an order of magnitude smaller than the threshold of turbulence and is equivalent to pumping 36 000 barrels of oil/day through a 20 in. diameter pipe. (24) Burton, W. K.; Cabrera, N.; Frank, F. C. Philos. Trans. R. Soc. London 1951, A243, 300. (25) Cabrera, N.; Vermilyea, D. A. The growth of crystals from solution. Growth and Perfection of Crystals; Doremus, R. H., Roberts, B. W., Turnbull, D., Eds.; Wiley: New York, 1958; p 393. (26) Cahn, J. W. Thermodynamics and Kinetics of Phase Transformations. In Materials Research Society Symposiums Proceedings; Im, J. S., Park, B., Greer, A. L., Stephenson, G. B., Eds.; Elsevier: New York, 1996; Vol. 398, pp 425-437 and references therein.

Letters

Figure 1. (A) Growth of hydrocarbon films on a cooled disk from a stirred n-C26H54 (x26 ) 0.013) solution in n-decane maintained at 291.0 K. The temperature difference ∆T between the solution bulk and the disk is a measure of film thickness. The use of symbols is as follows: 0, neat solution; O, ], 4, and 3, in the presence of 10, 30, 50, and 118 ppm of poly{N-[(2hydroxymethyl)heptadecyl]allylmethyleneimine} as crystallization inhibitor, respectively. Notice (1) the longer delay for the onset of crystal growth at larger inhibitor concentrations, (2) the ongoing growth of the uninhibited film, (3) the plateau ∆T∞ values reached in the inhibited solutions, and (4) the saturation value ∆T∞ ) 4.25 ( 0.05 above 30 ppm inhibitor. (B) As in Figure 1A, but using poly(octadecyl methacrylate) as inhibitor. Symbols O and 0 represent the presence of 100 and 200 ppm of inhibitor, respectively.

error and coincide with the melting point of n-C26H54 (TM ) 329-330 K) for both PODMA and KJ-34 as inhibitors. Dissolution temperatures TD are operationally defined as the minimum temperatures at which the absorbance of the preformed cloudy hexacosane suspensions eventually decays to zero (see Figure 3). We found that TD does not change perceptibly by adding up to 200 ppm PODMA to hexacosane/decane solutions. In contrast, KJ-34 has a marked positive effect on TD. Actually, TD increases by 2 K upon addition of only 0.3 ppm KJ-34 and then up to 3.5 ( 0.5 K at g4 ppm KJ-34 (Figure 3). Since the time constants for the disappearance of inhibited and uninhibited crystals following positive temperature step increases are nearly identical (τ ) 94 ( 5 s), the higher TD’s actually reflect the enhanced thermodynamic stability of the solvated pseudopolymorphs generated in the presence of KJ-34, rather than the development of kinetic barriers to dissolution.

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Figure 2. (A) Optical micrograph of the hexacosane deposits (light features) formed on the cold disk in the absence of inhibitors. The longitudinal structures are normal to the disk surface, i.e., parallel to the temperature gradient. (B) Optical micrograph of the hexacosane deposits (light features) formed on the cold disk in the presence of 200 ppm poly{N-[(2hydroxymethyl)heptadecyl]allylmethyleneimine}.

Figure 3. Absorbance vs time of n-C26H54 (x26 ) 0.013) solutions in n-decane: O, neat; 0, plus 5 ppm KJ-34, after thermalization at 283.0 (1), 288.0 (2), 289.0 (3), 290.0 (4), and 291.0 K (5). All decays are exponential with τ ) 94 ( 5 s.

In other words, both inhibitors can limit crystal growth to nearly the same extent under nonequilibrium conditions (see Figure 1), although KJ-34 induces the formation of a solid that is thermodynamically more stable than the pseudopolymorphs generated by cooling undoped solutions. If a thermodynamic effect were at work, KJ-34should have performed as a crystallization promoter rather than as an inhibitor because its solutions become supersatu-

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rated at higher temperatures. The fact that TD is significantly affected at trace levels and displays a saturation dependence on [KJ34] excludes colligative effects and suggests the efficient seeding of a pseudopolymorph.5-7 Moreover, since the concentration range in which TD’s change is an order of magnitude smaller that the one associated with the effects shown in Figure 1, the two phenomena may have a common physical basis, but are not correlated. The observation of stationary, increasingly compact crystal layers of finite thickness under a temperature gradient in the presence of crystallization inhibitorss regardless of the kinetic or thermodynamic factors associated with nucleation and growthsis a novel finding. It is at variance with the conventional notion that chemical inhibitors directly halt crystallization in supersaturated solutions by a molecular mechanism. Upon cooling an undersaturated solution, crystal growth at the thermal boundary will cease when the wax/solution interface reaches the temperature TE at which the solid is in equilibrium with the solute at the given concentration. This condition can be realized, however, if conduction were the exclusive mechanism of heat transfer through the crystals, for convection or diffusion through porous layers would negate the existence of a single temperature interface.1,22,27 Scheme 1 illustrates the growth of a compact crystal film from an unsaturated solution maintained at TS forced past a cold surface at TB(t). If heat flows by convection across the stirred solution/crystal interface at TI and by conduction through the crystal layer, at steady state27

Q˙ ) h(TS - TI) ) k(TI - TB)/δ

(1)

where h is the convective heat transfer coefficient in this setup, k is the thermal conductivity of the film, and δ is its thickness. If TS is kept constant, the limiting δ∞ value follows from eq 1 and the condition TI ) TE: (27) Incropera, F. P.; DeWitt, D. P. Fundamentals of Heat and Mass Transfer, 2nd ed.; Wiley: New York, 1985.

δ∞ )

(

)

k TE - TB h TS - TE

(2)

In other words, there exists an inverse, unique relationship between δ∞ and the stationary TB values for purely conductive wax films. From eq 2 we estimate δ∞ ≈ 55 µm for a compact paraffin film with k ) 2.4 mW cm-1 K-1,27 h ) 2600 mW cm-2 K-1 (at Ω ) 5000 rpm),28 TS ) 291 K, TB ) 286 K, and TE ) 289 K, which is entirely compatible with the typical thickness of inhibited films. Notice that δ∞ is an inverse function of convective forcing, since TB < TS is always an increasing function of Ω. The fact that the hexacosane deposits continue to grow at ∆T > ∆T∞ in the absence of inhibitors reveals that the thicker layers may provide better overall thermal insulation, but they do not prevent the solute from slowly reaching into the colder core. Clearly, eqs 1 and 2 do not apply to these porous deposits. In this context, compactness is defined by the average pore size below which net solute transport normal to the cold surface becomes negligible within the crystal layer.1,22,29 We conclude that chemical inhibitors can indefinitely cap crystallization in open systems under nonequilibrium conditions by promoting mesoscopic morphology modifications that link crystal layer thickness to solution thermodynamics. The optimal inhibitor is the one that produces a compact layer at the minimal dose. Further work is underway. LA991085O (28) We determined that in our setup h(mW cm-2 K-1) ) 304 + 0.84Ω0.93, between 200 e Ω/rpm e 8000. (29) Skelland, A. H. P. Diffusional Mass Transfer; Wiley: New York, 1974. Mass transfer may result from temperature as well as from concentration gradients. The ongoing crystallization itself generates convective motion that must be taken into account. These phenomena depend on solute and solvent properties. We estimate that convection contributes less than 5% to the thermal conductance of a slab of (10 µm × 10 µm × 1 mm) cells filled with liquid hydrocarbon separated by 10 µm wax walls under a longitudinal 10 K drop. Convective conductance, being proportional to the cells cross section, is enhanced in larger pore structures (see, e.g., ref 27, p 684).