An Examination of the Nucleation Kinetics of n-Alkanes in the

Nov 13, 1996 - Differential thermal analysis is used to examine the kinetics of nucleation associated with the melt phase crystallization of n-alkanes...
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An Examination of the Nucleation Kinetics of n-Alkanes in the Homologous Series C13H28 to C32H66, and Their Relationship to Structural Type, Associated with Crystallization from Stagnant Melts A. M. Taggart and F. Voogt† Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow, U.K.

G. Clydesdale and K. J. Roberts*,‡ Centre for Molecular and Interface Engineering, Department of Mechanical and Chemical Engineering, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, U.K. Received January 24, 1996. In Final Form: June 17, 1996X Differential thermal analysis is used to examine the kinetics of nucleation associated with the melt phase crystallization of n-alkanes in the homologous series C13H28 to C32H66. Crystallization studies from stagnant melt samples reveal a direct correlation between structural type and nucleation behavior, notably demonstrating an alternating behavior between the even and odd carbon number homologues which decreases in extent as a function of increasing chain length. This effect is mirrored in calculations of the lattice energies based on the crystallographic structures with greater lattice stability being found for the even carbon number n-alkanes which crystallize in the triclinic crystal structure. The data are consistent with a heterogeneous nucleation mechanism associated with preferential nucleation at the free surface of the sample associated with surface freezing.

1. Introduction Crystallization, an important purification and separation technique for the chemical, food, and personal products industrial sectors, involves the formation of a regular three-dimensional solid phase in melt, solution or vapor phases, and/or polymorphic transformations in solid phases. Supersaturation provides the thermodynamic driving force for this process which is subdivided into nucleation and growth stages: initially 3D nucleation occurs from which 2D crystal growth proceeds. In the nucleation stage, supersaturation causes the formation and agglomeration of molecular solute clusters. These clusters are maintained in a dynamic equilibrium which is dictated by the balance between the volume and surface contributions to their excess free energy.1,2 A wide range of cluster sizes are formed, and at sufficient cluster size the bulk volume term dominates over the surface term and a viable stable particle (critical nucleus) is formed. Growth is delayed until the critical nucleus is achieved and continues until the supersaturation is relieved. Nucleation occurs within a metastable zone, which is the region between equilibrium saturation and the point of bulk nucleation and spontaneous growth.3 Within the metastable zone the nucleation process is kinetically driven.4 Primary nucleation phenomena can be subdivided into those occurring via two mechanistic actions: homogeneous and heterogeneous. In the former, nuclei molecular * To whom correspondence may be addressed. † Visiting researcher from the Katholieke Universiteit Nijmegen, Nijmegan, The Netherlands. ‡ And also at CCLRC Daresbury Laboratory, Warrington WA4 4AD, U.K. X Abstract published in Advance ACS Abstracts, October 15, 1996. (1) Walton, A. G. In Nucleation; Zettlemoyer, A. C., Ed.; Marcel Dekker Inc.: New York, 1969; p 225. (2) Larson, M. A.; Garside J. J. Cryst. Growth, 1986, 76, 88. (3) Mullin, J. W. In Crystallization, 3rd ed.; Butterworth-Heinemann: London, 1993. (4) Myerson, A. S. In Handbook of Industrial Crystallization; Butterworth-Heinemann: London, 1993.

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clusters are presumed to form homogeneously throughout a crystallizing medium devoid of any inhomgeneities such as would result from any temperature and/or concentration gradients. A detailed examination of the idealized homogeneous case yields a number of important fundamental parameters such as the interfacial tension and critical nuclei size (see, e.g., ref 3). However, in practical terms, most crystallization reactions can be expected to be dominated by a heterogeneous nucleation mechanism associated with the localized formation of critical nuclei clusters on heterogeneous particulate matter within the bulk phase, the interface between the mother phase and the crystallizer vessel, and the surface of the mother phase itself if not totally contained. In such cases the availability of preferred heteronucleation sites has the effect of lowering the interfacial tension between the mother and crystallizing phases, thus reducing the free energy barrier to nucleation. In practical terms a change from a homogeneous to a heterogeneous nucleation mechanism can be observed via a reduction in the metastable zone width (MSZW). The crystallization of long chain hydrocarbons is generically important in a wide range of industrial processes such as the processing of oils, fats, and surfactants.5-15 Within this perspective n-alkanes provide (5) Turnbull, D.; Cormia, R. L. J. Chem. Phys. 1961, 34, 820. (6) Smyth, C. P. Trans. Faraday. Soc. 1946, 42A, 175. (7) Turnbull, D.; Cohen, M. H. In Modern Aspects of the Vitreous State; MacKenzie, J. C., Ed.; Butterworth-Heinemann: London, 1960. (8) Stewart, A. C., PhD thesis. The nucleation of eicosane from solution in the presence of close homologues; University of Strathclyde, Glasgow, U.K., 1986. (9) Beiny, D. H. M., PhD thesis. The influence of habit modifying polymers on the crystallization of higher normal alkanes in hydrocarbon solvents; University College, London, U.K., 1987. (10) Gerson, A. PhD thesis. Structural and kinetic studies associated with the crystallization of n-alkanes, homologous mixtures and real waxes; University of Strathclyde, Glasgow, U.K., 1990. (11) Mazee, W. M. Anal. Chem. Acta 1957, 17, 97. (12) Bonsoor, D. H.; Bloor, D. J. Mater. Sci. 1977, 12, 1559. (13) Turner, W. R. Ind. Eng. Chem. Prod. Res. Dev 1971, 10, 238. (14) Denis, J. Fr. Pet. Inst. Rev 1987, 42, 1.

© 1996 American Chemical Society

Nucleation of n-Alkanes

a well-defined and representative system for studies of some of the generic aspects of long chain materials as well as being important commercially in their own right (e.g., waxing in fuel lines). Structural studies on normal alkanes were first performed by Muller16-18 with detailed lattice parameters measured for C18H38,19 C20H42,20 C23H48,21 and C25H52.22 Full structures have been determined for triclinic C18H38,23 monoclinic C36H74,24 and orthorhombic C23H48.25 Nyburg and Potworowski26 predicted the lattice parameters of the n-alkanes in the range n ) C6-C40 while Luth et al.27 proposed an overall scheme for the expected crystal structures. These predictions have recently been verified experimentally.28 Single n-alkanes crystallize in one of three crystal systems according to the value and parity of n thus: triclinic,12 e n(even) e 26, P-1 (Z ) 1); monoclinic, 28 < n(even) < 36, P21/a (Z ) 2); orthorhombic, 36 < n(even) < 60, Pbca (Z ) 4); n(odd), Pbcm (Z ) 4). All of these, apart from the triclinic structure, exhibit similar subcell intermolecular packing motifs. n-Alkanes can also crystallize into pseudohexagonal crystal structures: 13 e n e 31 with space group Cmcm29 and 18 e n e 32 with space group P63/mmc.30 These structures or rotator phases are associated with a transitional phase between the fully crystalline phase and the melting point of the n-alkane. This phase is characterized by a rotational disorder along the long molecular axis of the n-alkane molecule.31 Luth27 and Retief32 performed structural studies on binary mixtures of n-alkane melts. In both cases continuous solid solutions were found which crystallized in orthorhombic crystal lattices. Recent structural analysis of binary mixtures of n-alkanes melts verified binary mixtures to crystallize in orthorhombic crystal lattices with space group symmetry Fmmm (Z ) 4).33 The varied molecular packing observed in the even number n-alkane crystal structures makes this homologous series an attractive model system to investigate whether crystal chemistry and the kinetics of nucleation are inter-related and, if so, in what manner. In this paper we examine this perspective through a study of the nucleation behavior of pure n-alkane melts and binary mixtures in the range C13H28 to C32H66 when crystallized under stagnant conditions. In this we use differential thermal analysis (DTA) to detect nuclei formation and dissolution (melting), to kinetically measure the MSZW (15) Holder, G. A.; Winkler, G. A. J. Inst. Petr. 1965, 51, 228. (16) Muller, A. Proc. R. Soc. London, Ser. A 1928, 120, 437. (17) Muller, A. Proc. R. Soc. London, Ser. A 1930, 127, 417. (18) Muller, A. Proc. R. Soc. London, Ser. A 1932, 138, 514. (19) Muller, A.; Lonsdale, K. Acta Crystallogr. 1948, 1, 129. (20) Crissman, J. M.; Passaglia, E.; Eby, R. K.; Colson, J. P. J. Appl. Crystallogr. 1970, 3, 194. (21) Retief, J. J.; Engel, D. W.; Boonstra, E. G. J. Appl. Crystallogr. 1985, 18, 150. (22) Retief, J. J.; Engel, D. W.; Boonstra, E. G. J. Appl. Crystallogr. 1985, 18, 156. (23) Nyburg, S. C.; Luth, H. Acta Crystallogr. 1972, B28, 2992. (24) Schearer, H. M; Vand, V. Acta. Crystallogr. 1956, 9, 379. (25) Smith, A. E. J. Chem. Phys. 1953, 22, 2229. (26) Nyburg, S. C.; Potworowski, J. A. Acta. Crystallogr. 1973, B29, 347. (27) Luth, H.; Nyburg, S. C.; Robinson, P. M.; Scott, H. G. Mol. Cryst. Liq. Cryst. 1972, 27, 337. (28) Craig, S. C.; Hastie, G. P.; Roberts, K. J.; Sherwood, J. N. J. Mater. Chem. 1994, 4, 977. (29) Doucet, J.; Denicolo, I.; Craievich, A. F. J. Chem. Phys. 1981, 75, 1523. (30) Denicolo, I.; Craievich, A. F. J. Chem. Phys. 1983, 78, 1465. (31) McClure, D. W. J. Chem. Phys. 1968, 49, 1830. (32) Retief, J. J.; Engel, D. W.; Boonstra, E. G. J. Appl. Crystallogr. 1985, 18 150. (33) Gerson, A. R.; Roberts, K. J.; Sherwood, J. N. In Particle design via crystallization; Ramanarayanan, R., Kern, W., Larson, M., Sikdar, S., Eds.; AIChemE series 284; American Institute of Chemical Engineers: Vol. 27, p 104.

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and hence derive nucleation rate data. The results are rationalized with thermodynamic data and previously published nuceation studies and are discussed in terms of n-alkane chain length and crystal structure type with reference to the crystal lattice stability of the known phases. 2. Metastable Zone Width: Background Theory The MSZW measures the maximum allowable undercooling (∆Tmax) in a system prior to bulk nucleation and growth.

MSZW ) Tsat - Tcryst(b ) 0°C/min)

(1)

The MSZW or ∆Tmax provides information on the degree of temperature below the saturation temperature the samples can be cooled before bulk crystallization commences. From measurements of the dependence of the MSZW on the rate of solution cooling, b, nucleation kinetic parameters can be found.34-39 At the first instant when crystals appear, that is, once a certain degree of supersaturation, ∆Cmax, has been achieved, corresponding to the metastable zone limit (i.e., MSZW ) ∆Tmax), the following mass nucleation rate equation can be applied to describe the kinetics of the nucleation process:

Jn ) kn∆Cmaxm

(2)

where Jn, kn, and m are the mass nucleation rate, nucleation rate constant, and nucleation order, respectively, and ∆Cmax is equal to

∆Cmax ) (dC*/dT)∆Tmax

(3)

where dC*/dT is the rate of change of concentration with temperature. This equation applies to a linear range of solubility or ideal solution behavior; however, with reference to n-alkane melts the concentration does not vary as a function of temperature, and therefore the degree of supersaturation is controlled entirely by ∆Tmax. Thus

∆Cmax = ∆Tmax

(4)

The nucleation rate can also be expressed as

Jn ) (/[1 - C( - 1)])((dC*/dT)(dT/dt))

(5)

where T is the temperature, t is the time, and  is the ratio of molecular weights of hydrated salt to anhydrous salt. In the case of n-alkane crystallization from the melt where no hydration occurs and the change in concentration as a function of temperature is a constant the first two terms in eq 5 are equal to 1. Equating eqs 2 and 5 for Jn gives

(dT/dt) ) kn ∆Cmaxm

(6)

where dT/dt is the rate of change of temperature with respect to time which is equivalent to the cooling rate, b. Substituting for the cooling rate and supersaturation, ∆Cmax (in terms of eq 4) gives (34) Gerson, A. R.; Roberts, K. J; Sherwood, J. N. Powder Technol. 1991, 65, 243. (35) Mullin, J. W.; Jancic, S. J. Trans Inst. Chem. Eng. 1979, 57, 188. (36) MacKenzie, R. C. In Differential Thermal Analysis; Academic Press: London, 1970; Vol. 1. (37) Nyvlt, J. J. Cryst. Growth 1968, 3, 4, 377. (38) Nyvlt, J.; Rychly, R.; Gottfried, J.; Wurzelova, J. J. Cryst. Growth 1970, 6, 151. (39) Roberts, K. J.; Sherwood, J. N.; Stewart, A. J. Cryst. Growth 1990, 102, 419.

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b ) kn[ ∆Tmax]m

Taggart et al.

(7)

Taking the logarithms, eq 7 can be transformed into

log(b)) log kn + m log(∆Tmax)

(8)

From eq 8 it follows that the dependence of the maximum undercooling achievable in n-alkane melt systems, prior to bulk nucleation, on the cooling rate b should be linear on a logarithmic scale with the slope and intercept equal to the nucleation reaction order, m, and nucleation rate constant, kn, respectively. This equation assumes any changes in supersaturation are caused by the nucleation and not the crystal growth process. This relationship should be sufficient when dealing with systems which crystallize as rapidly as n-alkanes. Mullin and Jancic35 cast some doubt on the reliability of the assumption that the assessed ∆Tmax corresponds to the width of the metastable zone. They note that the size of the detected particle may be substantially greater than that of the newly formed nucleus. Thus ∆Tmax may be substantially and variably greater than the true measured MSZW. Thus both ∆Tmax and growth rate of the crystal are dependent on b. They comment that the slope of the plot from eq 8 should therefore always be steeper than that expected for nucleation alone by a factor dependent on the sensitivity of the device used to detect crystallites. It can also to be expected that practical measurements in bulk samples, where a heterogeneous nucleation can be expected, are likely to exhibit narrower MSZW than for the same samples measured under homogeneous nucleation conditions. 3. Materials and Methods 3.1. Sample Preparation. A series of pure n-alkane melts were investigated within the homologous series, C13H28 to C32H66. All, with the exception of C27H56, C29H60, and C31H64, were purchased from Aldrich. The latter were synthesized40 using the Wittig reaction in which an alkane was formed from the appropriate tri-phenylphosphonium bromide and aldehyde followed by hydrogenation using hydrogen and a palladium catalyst. Gas chromatograms showed all samples to have purities greater than 98%. All materials were recrystallized twice from the melt before filtration in an attempt to remove residual heterogeneous particulate contaminants. Binary melts from these starting materials in mole ratios of 1:3, 1:1, and 3:1 were also prepared. 3.2. Differential Thermal Analysis. DTA records the difference between the sample temperature and an inert but representative standard (in this case ethane-1,2-diol) as a function of heating and cooling. This method provides an alternative analysis technique to differential scanning calorimetry (DSC) which was not employed for the nucleation experiments due to a combination of its small sample size (∼µg) and the fact that the temperature (heat flow) is measured through the sample holder thus providing a significant “wall” effect in terms of providing a nucleation surface. In contrast in our DTA measurements we used two cylindrical tube glass sample cells (size ca. 10 cm × 0.5 cm diameter) containing approximately 2g of each of the sample and reference materials, respectively. Temperature measurement platinum resistance thermometers (sensitivity ca. 0.05 °C) were suspended within the liquid phase with the measurement cells being typically 80% full of sample. The sample and reference cells were immersed in a Haake F3C recirculating bath, filled with a water-ethylene glycol mixture. The measured temperatures were logged by a PC controller which also controlled the temperature of the recirculating bath. A fiberoptic turbidity probe could also be used34 to detect the onset of nucleation, although this necessitated the use of larger sample volumes which for the measurements on stagnant melts presented here led to an increased sensitivity of the technique to (40) Gerson, A. R.; Roberts, K. J; Sherwood, J. N.; Taggart, A. M. J. Cryst. Growth 1993, 128, 1176.

Figure 1. Experimental data from cooling/heating cycle (0.75 °C/min) showing DTA temperature difference and light transmittance changes (%/100) associated with (a) crystallite formation and (b) crystallite dissolution of octacosane, C18H38, from the melt. temperature variations within measurement cell. The data acquisition strategy had the following features: temperature of sample and reference material recorded with the specimens subjected to identical temperature environments; cooling and heating rates of 0.75, 0.50, 0.25, and 0.10 °C/min were used; three repeat cycles for each of these rates were used to eliminate statistical variation with spurious data being eliminated by cycle reruns; samples held 10 °C above the melting temperature for ca. 30 min between each cooling and heating cycle to ensure all crystal embryos have been dissolved. The onset of nucleation (Tcryst) is defined when the gradient of the differential temperature (Tsam - Tref) as a function of time deviates from the baseline, dT/dt > 0 during the cooling cycle. Dissolution temperature (Tdiss) is defined when the differential temperature is at its maximum, dT/dt ) max during the heating cycle. These parameters were defined with the aid of our existing turbidimetric instrument.34 All transformations involving energy changes in the samples are reflected in the DTA temperature profile. Measured crystallization and dissolution temperatures found with DTA were superior in quality to those measured using turbidometry (Figure 1). Equilibrium crystallization (Tcryst) and dissolution (Tdiss) temperatures were determined by extrapolating plots of the onset temperatures for nucleation/dissolution against their respective cooling/heating rates to obtain temperatures commensurate with a zero rate. From this the equilibrium MSZW was also determined. 3.3. Differential Scanning Calorimetry. The enthalpies of crystallization for all the samples were measured41 using a conventional DSC (Mettler-Toledo TA8000) using a sample size of 10µg and a heating rate of 5 °C/min. 3.4 Lattice Energy Calculations. To assess the reactive stabilities for the various n-alkanes solid-state structures, lattice energies were calculated. For this it was first necessary to build molecular models of each n-alkane. Molecular models were built using the molecular graphics package CERIUS42 by ethane polymerization. The built molecular structures were then minimized using MOPAC43 with the resultant structures being fitted to known and representative crystal structures (e.g., C18H38, C23H48, and C36H74 for triclinic, monoclinic and orthorhombic (41) Blazek, R. P. A. In Thermal Analysis; Van Nostrand Reinhold Co.: New York, 1973. (42) CERIUS version-3.2, a product of Molecular Simulations Ltd, Cambridge, U.K. (43) MOPAC, A general Molecular Orbital Package. Stewart, J. J. P. Air Force Systems Command USAF.

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Table 1. Experimental Data from a Sequential Series of Slow Cooling/Heating Cycles for C18H38 Crystallized from the Melt Using DTA Showing the Run by Run Repeatability rate/°C min-1

Tcryst/°C

Tdiss/°C

MSZW/°C

0.75

26.19 26.21 26.16 26.45 26.33 26.37 26.41 26.53 26.58 26.51 26.52 26.57

28.11 28.13 28.08 27.98 28.01 28.04 27.84 27.89 27.91 27.76 27.78 27.84

1.56 1.54 1.59 1.31 1.42 1.38 1.34 1.22 1.17 1.24 1.23 1.18

0.50 0.25 0.10

crystal structures, respectively) using the molecular modeling package INTERCHEM44 in order to arrange the molecules in their correct molecular packing motif. Fractional crystal unit cell coordinates for each structure were generated using the cell parameters measured by Craig et al.28 The lattice energies for the resulting model structures were calculated by the program HABIT45 using a combined Buckingham46 and coulombic type interatomic potential energy (U) function of the form

U ) A/r-6 + B/r12 + q1q2/r

Figure 2. Experimental data from slow cooling/heating cycle showing Tcryst, Tdiss, and MSZW associated with crystallite dissolution and precipitation from C18H38 melt. The measured saturation temperature (Tdiss at b ) 0 °C/min) was 27.75 °C.

(9)

where r is the inter-atomic distance and the atom-atom parameters A and B are taken from Williams.47 The partial atomic charges q1 and q2 were calculated by semi-empirical quantum chemistry calculations using MOPAC42 assuming no overall charge on the n-alkane molecule.

4. Results 4.1. Nucleation Studies. Crystallization and dissolution temperatures and MSZWs measured for C18H38 melt at various cooling/heating rates are given in Table 1 and in Figure 2. Experimentally it was found the faster the cooling rate, the greater the degree of undercooling achieved in the system prior to bulk nucleation. It was noted the closeness of Tcryst and Tdiss is improved by the slower cooling and heating rates employed in the measurement technique.34 MSZW measurements (Figure 3) were found to reflect alkane structure and chain length dependence. Large MSZW were found for even n-alkanes of triclinic lattice structure for 14 e n e 26, although these values decrease exponentially as chain length increased. Small MSZW were found for even (n > 26) and odd (13 e n e 31) alkanes and for all binary n-alkane mixtures. A linear dependence was found between the measured MSZW and the rate of solution cooling for all systems studied. Correlation coefficients were found to be greater than 0.9 for all systems. These results conform to that predicted using eq 8. Nucleation reaction orders and nucleation rate constants were calculated from the slope and intercept of a plot of log(b) versus log(MSZW). Figure 4 illustrates the variation in slope and intercepts found for the different polymorphic forms (triclinic/monoclinic/ orthorhombic) present within the n-alkane homologous series. Steeper slopes and larger intercepts were generally found with triclinic crystal systems compared with monoclinic and orthorhombic crystal systems. Nucleation (44) Bladon, P.; Brekenridge, R. University of Strathclyde, U.K., 1989. (45) Clydesdale, G.; Docherty, R.; Roberts, K. J. Computer. Phys. Commun. 1991, 64, 311. (46) Buckingham, R.; Corner, J. Proc. R. Soc. London 1947, 189, 118. (47) Williams, D. E. J. Chem. Phys. 1966, 45, 3370.

Figure 3. Equilibrium metastable zone widths as a function of carbon chain length for single homologues and binary mixtures in the range C13H28 to C32H66.

Figure 4. Plot of log(cooling rate) versus log(maximum undercooling), eq 8, as calculated from DTA measurements for selected n-alkane melts in the range C13H28 to C32H66.

reaction orders and rate constant calculated as a function of carbon chain length are given in Figure 5. Higher nucleation reaction orders were found for triclinic crystal systems compared with monoclinic and orthorhombic systems, with values decreasing as a function of increasing carbon chain length. In contrast, higher nucleation rate constants were found for orthorhombic crystal systems compared to triclinic systems, although triclinic rate

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Taggart et al.

Figure 7. Enthalpies of crystallization of n-alkane melts and binary mixtures in the range C13H28 to C32H66 from DSC measurements.

Figure 5. (a) Nucleation reaction orders and (b) nucleation rate constants as calculated from the slope of log(b) versus log(∆Tmax), eq 8, for n-alkane melts of C13H28 to C32H66.

Figure 8. Lattice energies of n-alkanes in the range C13H28 to C32H66 as calculated from intermolecular force calculations.

Figure 6. DSC data C18H38 melt, rotator phase transformation (A) melting transition (B).

constants increased as carbon chain length increased. Nucleation reaction orders and rate constants were found to alternate between the even and odd n-alkane crystal melts with both patterns converging as a function of increasing molecular chain length. 4.2. Enthalpies of Crystallization. Only DSC peak areas associated with crystallization were assessed. Rotator phase transitions observed in odd (13 e n e 31) and even (n e 18) pure n-alkane melts and binary mixtures were not taken into account. However, it is important to note that the alternating even/odd pattern is independent on the absence and presence of rotator phase transitions. Figure 6 illustrates the enthalpy of crystallization and the rotator phase transition associated with cooling C18H38 melt from the liquid state to the solid crystalline state. Variation of enthalpies of crystallization as a function of n-alkane chain length are shown in Figure 7.

Enthalpies of crystallization measured were found to reflect alkane chain length dependence. Large amounts of energy were liberated from the liquid-solid phase transition of triclinic even n-alkane melts. These values decreased as carbon chain length increased. Relatively constant values were found for even (n > 26) and odd (13 e n e 31) alkane melts and for all binary mixtures. Enthalpies of crystallization were found to converge as carbon chain length increased. 4.3. Lattice Energies. Lattice energies of the nalkane homologues are summarized in Figure 8. There is a clear pattern in the lattice energies of the single n-alkanes. The even n-alkanes have consistently higher negative lattice energies than would be expected from an interpolation of lattice energies between the odd n-alkanes within this range. Even n-alkane lattice energies decrease as carbon chain length increases while odd n-alkanes remain constant; this illustrates the converging nature of even and odd n-alkanes as chain length increases. Results suggest even n-alkanes are more stable than odd nalkanes, the difference diminishing as a function of increasing molecular weight. 5. Discussion 5.1. Structure/Kinetic Inter-relationships. Triclinic crystal systems are found to be more dependent on concentration or, alternatively, demand higher degrees of supersaturation/undercooling compared to monoclinic and orthorhombic crystal systems before bulk nucleation and crystal growth commences. This is verified by large MSZW measurements and calculated nucleation reaction orders. This implies triclinic even n-alkanes have greater difficulty in nucleating and agglomerating to achieve the

Nucleation of n-Alkanes

critical nucleus, which may be to a certain extent a function of the molecular arrangement of the molecules of the crystallizing substance.38 Triclinic crystal systems have unimolecular unit cells whereas monoclinic and orthorhombic crystal systems have bimolecular and tetramolecular unit cells, respectively. Triclinic systems have therefore greater packing efficiency and thus stability compared with monoclinic and orthorhombic systems. This difficulty of triclinic crystal systems to nucleate is coupled with slow nucleation rate constants. Molecular volumes of the different polymorphs48 illustrate triclinic crystal systems have higher density, greater packing efficiency, and, therefore, stability compared to monoclinic and orthorhombic crystal systems; therefore more energy would be expected for its nucleation and growth. Density measurements found for n-alkanes show even n-alkanes in the solid state have greater density than their neighboring odd n-alkane homologues.49 nAlkane solubility measurements from previous studies40,50 also illustrate the triclinic is the most stable and least soluble solid-state structure. This complements our n-alkane nucleation kinetic behavior. Enthalpies of crystallization reflect the amount of energy associated with the liquid to solid phase transition. Triclinic crystal systems liberate the greatest transition enthalpy compared to monoclinic and orthorhombic polymorphs, because of its greater packing efficiency and crystal structure stability. This is in agreement with molecular modeling calculations of the crystal lattice energies based on intermolecular force calculations on these materials. Even n-alkanes have consistently higher negative lattice energies than would be expected from an interpolation of lattice energies between the odd n-alkanes within this range. The lowest energy conformation for the crystal packing of even and odd n-alkanes is the alternating trans zigzag arrangement where molecules are stacked parallel to each other. Strong methylene-methylene (CH2) intermolecular interactions exist between molecules packed sideways compared with weak methyl-methyl (CH3) end chain interactions. Parallel packing is energetically more favorable compared with end-to-end methyl-methyl (CH3) packing. The longer the molecular chain the stronger the overall CH2-CH2 interactions, therefore the greater the attractive intermolecular energy available to pull the homologues out of solution and therefore the easier the precipitation process. Faster nucleation kinetics (nucleation rate constants) are expected as carbon chain length increases. All studies illustrated an alternating pattern between the even and odd n-alkane structures which converge as a function of increasing carbon chain length. To explain this pattern, differences between the even and odd length n-alkane homologues were considered. Differences between n-alkane crystal structures arise due to the different packing arrangements of the molecules within their bonding networks. Studies have shown the CH2 side chain packing is essentially the same between the triclinic (even) and orthorhombic (odd) structures;10 therefore the crystal packing differences must be attributed to the packing of the terminal CH3 groups. For odd n-alkanes the terminal CH3 groups pack in the same direction, whereas for the even n-alkanes they protrude in opposite directions. For the shorter length even n-alkanes, the terminal CH3CH3 interactions dominate the solid-solid packing making the formation of an orthogonal unit cell very difficult, (48) Broadhurst, M. G. J. Res Natl. Bur. Stand. 1970, 66a, 241. (49) Seyer, W. F.; Patterson, R. F.; Keays, J. L. J. Res. Natl. 66, 179. (50) Roberts, K. J.; Sherwood, J. N.; Taggart, A. M. Proceedings from 12th Symposium on Industrial Crystallization, Warsaw 1993, 3, 63.

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resulting in a unimolecular triclinic crystal lattice being preferred. As the chain length increases (n > 26) the interchain interactions begin to become more important51,52 over the end chain forces within the overall packing energetics of the unit cell. Thus the unit cell incrementally adopts a more orthogonal lattice by transforming to a bimolecular, monoclinic unit cell. For odd n-alkanes the mirror symmetry of the molecule tends to preclude optimal close packing and the unit cell is therefore found to be a tetramolecular orthorhombic crystal lattice over the entire homologous range. Studies have shown the packing of monoclinic and orthorhombic lattice structures are very similar since both have the same orthorhombic subcell packing.28 If this assumption was correct, it would be expected that any solid state measurements would reflect this alternating even/odd pattern which converges as the carbon chain length increases or as the ratios of the CH3 terminal end groups to CH2 side groups diminish. On observation of experimental n-alkane phase behavior and theoretical lattice energy calculations, this assumption appears to be the case. 5.2. Nucleation Mechanism. Previous nucleation studies on n-alkanes have been carried out on surfactantstabilized dispersions of the alkanes in an aqueous mother phase53-56 with nucleation detected via optical birefringence,53-54 dilitometry,55 and differential scanning calorimetry.56 In this setup nucleation is confined to a homogeneous mechanistic process as confirmed via careful kinetic measurements made as a function of droplet size.57 While, for example, Ulmann et al.55 have shown odd/even behavior in the measured MSZWs for the homologous series C5H12 to C16H34, their values differ typically by an order of magnitude from those measured here. Similar orders of magnitude were also observed in the other droplet measurements;53,54,56 see comparison of data given in Table 2, thus confirming a heterogeneous mechanism for the work presented here. (Note: the data given in refs 5356 have been measured via a number of techniques using different cooling rates, thus producing kinetic-dependent data. In contrast our data are measured as a function of several cooling rates and extrapolated back to zero rate, thus producing an equilibrium value.) Recently in studies by our group58,59 and others60-63 it has been shown that n-alkane liquids undergo surface freezing during cooling prior to full crystallization in the bulk phase. These studies thus provide experimental evidence for the occurrence of preferential surface nucleation on exposed n-alkane liquid surfaces, which would be indicative of a surface-mediated heterogeneous nucle(51) Clydesdale, G. PhD thesis. The Development of predictive approaches for modeling the polymorphic stability and crystal habit of normal alkanes and other molecular crystals, University of Strathclyde, Glasgow, U.K, 1991. (52) Clydesdale, G.; Roberts, K. J. In Particle Design via Crystallization; Ramanarayanan, R., Kern, W., Larson, M., Sikdar, S., Eds.; AIChemE symposium series 284; American Instituted of Chemical Engineers: New York, 1991; Vol. 87, p 130. (53) Turnbull, D.; Cormia, R. L. J. Chem. Phys. 1961, 34, 820. (54) Phipps, L. W. Trans. Faraday Soc. 1964, 60, 343. (55) Uhlmann, D. R.; Kritchevsky, G.; Straff, R; Scherer, G. J. Chem. Phys. 1975, 62, 4896. (56) Oliver, M. J.; Calvert, P. D. J. Cryst. Growth 1975, 30, 343. (57) Calvert, P. D. J. Polm. Sci. Polym. Phys. Ed. 1976, 14, 2211. (58) Earnshaw, J. C.; Hughes, C. J. Phys. Rev. 1992, A46, 4494. (59) Hastie, G. P.; Johnstone, J.; Roberts, K. J.; Fischer, D. Faraday Trans 1996, 92, 783. (60) Hastie, G. P.; Johnstone, J.; Roberts, K. J; Fischer, D. J. Cryst. Growth, in press. (61) Wu, X. Z.; Ocko, B. M.; Sirota, E. B.; Sinha, S. K.; Deutsch M. Physica A 1993, 200, 751. (62) Wu, X. Z.; Sirota, E. B.; Sinha, S. K.; Deutsch M.; Ocko, B. M. Phys. Rev. Lett. 1993, 70, 958. (63) Wu, X. Z.; Ocko, B. M.; Sirota, E. B.; Sinha, S. K.; Deutsch M.; Cao, B. H.; Kim, M. W. Science 1993, 261, 1019.

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Taggart et al.

Table 2. Comparison of Experimentally Derived MSZWs as Part of This Study with Those Previously Cited53-56 for Single Normal Alkanesa metastable zone widths (MSZW)/°C n-alkane C5H12 C6H14 C7H16 C8H18 C10H22 C11H24 C12H26 C13H28 C14H30 C15H32 C16H34 C17H36 C18H38 C19H40 C20H42 C21H44 C22H46 C23H48 C24H50 C25H52 C26H54 C27H56 C28H58 C29H60 C30H62 C31H64 C32H66 C34H70 C36H74

this work

0.30 2.94 0.31 2.20 0.13 1.22 0.18 0.94 0.19 0.68 0.24 0.55 0.14 0.37 0.30 0.29 0.31 0.32 0.25 0.21

ref 53

ca. 12 ca. 12.3 ca. 12.9

ref 54

ref 55

ref 56

29.0 33.5 19.0 24.0 24.0 17.9 22.0 15.3

29.86 28.98

13.5 15.2 16.7

21.88 16.07 17.02 14.56 13.57 13.86 13.42

9.4 13.63 ca. 13 14.90 9.8 14.05 14.0 ca. 15

16.11 23.6 14.44

a

The data given on refs 53-56 have been measured by a number of techniques using different cooling rates, thus producing kineticdependent data. In contrast, our data are measured as a function of several cooling rates and extrapolated back to zero rate, thus producing an equilibrium value.

ation mechanism for the bulk crystallization of these materials. This supposition is also confirmed, to a degree, by the measured increase34 in the MSZW of a wax sample following the addition of surfactant in measurements carried out in a similar manner and with the same apparatus as that used in this study.

6. Conclusions Experimental n-alkane phase behavior and theoretical lattice energy calculations reflect the different types of crystallographic form present within the n-alkane homologous series. Nucleation kinetic and structural studies illustrate an alternating pattern of even- and oddnumbered n-alkane homologues which converge as a function of increasing molecular weight. Greater crystal lattice stabilities are found for those n-alkanes which have an even carbon number and which crystallize in the triclinic crystal structure. Convergence of the even and odd n-alkanes as a function of carbon chain length results from the abatement of the ratio of the terminal CH3 groups to the side chain CH2 groups. Solid state phase behavior of n-alkanes is found to vary depending on the number and parity of n. Correlation of these data with previously published data is consistent with a heterogeneous nucleation mechanism associated with preferential crystallization associated with surface freezing on the free liquid surface providing much lower MSZWs than would be expected for a pure homogeneously nucleating system. Acknowledgment. We are grateful to Exxon Chemical for the support of this research and for the financial support to A.M.T.64 and to Dr. Graham Jackson who synthesized the odd numbered n-alkanes which were not commercially available, EPSRC for the provision of computer modeling facilities (research grant GR/H/40891) and for the financial support of a research fellowship (G.C.) and senior fellowship (K.J.R.); C. Kerr for help with the data acquisition software, Professor A. Jones (University College London) and G. P. Hastie for helpful discussions, and Professor P. Bennema (University of Nijmegen) for his interest in the work as well as facilitating the visit of (F.V.) to Strathclyde University. We are also grateful to one of the reviewers for drawing our attention to some of the literature on the nucleation of long chain hydrocarbons. LA9600816 (64) Taggart, A. M. PhD thesis. Nucleation, Growth and Habit Modification of n-alkanes and Homologous Mixtures in the Absense and Presence of Flow Improving Additives; University of Strathclyde, Glasgow, U.K, 1995.