Martensitic Phase Transition of Petroselinic Acid: Influence of Polytypic

Polytypism and solid-state phase transitions of petroselinic acid (cis-6-octadecenoic acid) have been investigated with microscopic observation and mi...
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J. Phys. Chem. B 1997, 101, 285-292

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Martensitic Phase Transition of Petroselinic Acid: Influence of Polytypic Structure Fumitoshi Kaneko* and Masamichi Kobayashi Department of Macromolecular Science, Graduate School of Science, Osaka UniVersity, Toyonaka, Osaka 560, Japan

Kiyotaka Sato Laboratory of Chemical Physics, Faculty of Applied Biological Science, Hiroshima UniVersity, Higashihiroshima, Hiroshima 724, Japan

Masao Suzuki Oleochemical Research Laboratory, NOF Corporation, Ohama, Amagasaki, Hyogo 660, Japan ReceiVed: August 21, 1996X

Polytypism and solid-state phase transitions of petroselinic acid (cis-6-octadecenoic acid) have been investigated with microscopic observation and micro-FT-IR spectroscopy. Polytypism was confirmed for the low-melting (LM) phase. In solution crystallization of the LM phase, polytypic transformation from a single-layered polytype to a double-layered one was observed. The LM phase performs a solid-state phase transition to the high-melting phase through two mechanisms. One mechanism involves the thermally induced nucleation and growth of the product phase, which is dominant upon a slow heating process. The other mechanism can be regarded as a martensitic transition, where rapid cooperative molecular displacements are initiated by a local stress. The martensitic transition occurs when a single crystal of the single-layered polytype suffers rapid heating or mechanical stress. However, no martensitic transition was observed for the double-layered polytype. The difference in transition behavior between the two polytypes was interpreted on the basis of crystal structures.

Introduction Polytypism has been found in some long-chain compounds, such as n-alkanes, n-alcohols and n-fatty acids.1-5 There are at least two polytypic structures for these compounds, singlelayered and double-layered structures. The former belongs to a monoclinic system and the latter to an orthorhombic system, so we call these polytypic structures “Mon” and “Orth II”, respectively (Figure 1). Concerning the inner structure of one layer, the Mon and Orth II types are identical. Only the stacking mode of molecular layers is different between them. However, it has been clarified by Kobayashi and his co-workers that thermodynamic and physical properties change systematically depending on the polytypic structure.6-9 For the B and E forms of stearic acid, the difference in lamellar stacking is reflected sensitively in the low-frequency region of vibrational spectra. We found that the density of state in Orth II is shifted to the low-frequency side compared with that in Mon. Thus, at an elevated temperature Orth II gets more vibrational entropy compared with Mon, which makes Orth II more stable than Mon. Elasticity is also different between Mon and Orth II. The C33 element of the stiffness tensor, which corresponds to the tensile modulus along the lamellar stacking direction, is nearly doubled in Mon. In the study on petroselinic acid (cis-6octadecenoic acid), we found also that the mechanism of solidstate phase transitions was controlled by polytypic structures. Petroselinic acid occupies a specific position in chemical structure among naturally occurring cis-monounsaturated fatty acids whose acyl hydrocarbon chain is divided into two segments by cis-CdC double bond; the methyl-terminal chain is about two times longer than the carboxyl-terminal one and contains an even-number of carbon atoms in contrast to the oddX

Abstract published in AdVance ACS Abstracts, December 1, 1996.

S1089-5647(96)02592-8 CCC: $14.00

Figure 1. Polytypic structures of fatty acids: single-layer structure, Mon, and double-layer structure, Orth II.

number of carbon atoms in most monounsaturated fatty acids. In previous study we found that this chemical structural feature has a large influence on physicochemical properties and polymorphism.10-14 (1) Petroselinic acid melts at appreciably higher temperatures (more than 10 °C) than oleic acid (cis-9octadecenoic acid) and asclepic acid (cis-11-octadecenoic acid), consisting of the same number of carbon atoms. (2) There is no reversible solid-state phase transition that has been found in many cis-monoenoic acids: oleic acid, erucic acid, palmitoleic acid, and so on. (3) Two polymorphic phases, high-melting (HM) and low-melting (LM) phases, form quite unique crystal structures. Concerning the packing of methyl terminals and the subcell structure, the LM phase is almost identical with the E and B forms of n-saturated fatty acids and forms the Orth II type structure.13 However, we could not confirm the polytypism of the LM phase. All crystal specimens we treated were Orth II. In comparison with the crystallization of n-saturated fatty acids, this experimental result seems strange. For the B and E forms of stearic acid, single crystals of Mon are easier to obtain than those of Orth II. Recently we found that on the crystallization of the E form single crystals start to grow as Mon, and then the overgrowth of Orth II took place on the flat (001) face of the © 1997 American Chemical Society

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Figure 2. Crystal structure of the HM and LM phases of petroselinic acid.

crystals, even though the Orth II region is predominant in the late stages.14-15 So we expected that single crystals of the LM phase would be Mon in the beginning of crystallization. We followed the crystallization of the LM phase by means of IR spectroscopy and confirmed the above expectation. Using single crystals of Mon and Orth II, we started to investigate the influences of polytypic structures on the LM f HM solid-state phase transition and found that the transition behavior depends significantly on the polytype of a starting LM crystal. Only a single crystal of Mon performs a martensitic solid-state transition accompanying a rapid cooperative molecular displacement under certain conditions, which is a new type of solid-state transition for fatty acids. In this paper we describe the crystallization process of the LM phase and the transition behavior of both the Mon and Orth II polytypes of the LM phase. We show that the polytypic structures of the LM phase have a significant influence on the molecular displacements during the LM f HM phase transitions. Experimental Section Sample. The sample (>99.9% purity) was supplied by NOF corporation. Acetonitrile (>99% purity, Nakarai Tesque) was used as solvent for growing single crystals.

Microscopic and Infrared Measurements. Crystal specimens were observed with a stereomicroscope (Olympus SZHILLK). Micropolarized infrared spectra were taken with a Jasco Janssen FT-IR spectrometer equipped with an MCT detector and a wire-grid polarizer. The resolution was set at 2 cm-1. Measuring temperature was controlled by thermostated water ((0.1 °C) and was monitored with a chromel-constantan thermocouple. Polymorphism of Petroselinic Acid Petroselinic acid crystallizes into two polymorphic phases, the high-melting phase (mp 30.5 °C) and the low-melting phase (mp 28.5 °C). Both solid phases can be obtained by solution and melt crystallization. The HM phase is more stable than the LM phase above 18.7 °C, and vice versa below 18.7 °C (the above data of the LM phase are of Orth II).10 These two solid phases show no reversible transition accompanying a conformational disordering that has been found in oleic acid, erucic acid, and so on. The crystal structures of the HM and LM (Orth II) phases are depicted in Figure 2.13,14 The cell parameters and other structural features are summarized in Table 1. The HM phase belongs to a triclinic system of space group P1h, where two crystallographically different molecules (A and

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TABLE 1: Crystal Data of the LM and HM Phases of Petroselinic Acid13,14 low-melting (Orth II) crystal system space group a (Å) b (Å) c (Å) R (°) β (°) γ (°) Z volume (Å3) dihedral angle of C-CdC-C (°) temperature (K)

orthorhombic Pbca 7.311(1) 5.565(1) 88.01(1)

8 3581.1(8) 157, 0, -160 263

high-melting triclinic P1h 5.359(1) 8.874(2) 41.391(5) 90.49(1) 89.12(2) 113.81(2) 4 1800.7(6) 91, 1, 130 for molecule A 137, 1, 119 for molecule B 263

B) locate at an asymmetric unit. The conformation of C-CdC-C portion can be recognized as skew, cis, skew type for both molecules A and B. The methyl-terminal polymethylene chains form a M// type subcell, and the carboxyl-terminal chains form an O⊥ like subcell. The Orth II type of the LM phase belongs to an orthorhombic system of space group Pbca. The dihedral angles of the cisolefin group are 157, 0, -160°, which rather deviate from the skew, cis, skew′ conformation. The polymethylene chains form an O⊥ type subcell in both methyl- and carboxyl-terminal sides, and incline toward the bs axis of the O⊥ subcell by 27° (the setting of subcell axes is made according to orthorhombic polyethylene15), which is the so-called (011) inclination. There are two bimolecular layers in a repeating period, which are related to each other by 2-fold screw axis along the c axis. The LM phase forms lozenge-shaped plate crystals whose acute and obtuse bisectrices are parallel to the a and b axes of the unit cell. Results 1. Crystallization Process of the LM Phase. The infrared band due to the methyl symmetric deformation is sensitive to the difference in lamellar stacking. As we reported previously, the band of the bs component appears at 1374 cm-1 in Mon and 1382 cm-1 in Orth II.4,16,17 The crystallization process of the LM phase has been followed using this IR band. Figure 3 shows polarized IR spectral changes of a single crystal that were generated from an acetonitrile solution by cooling. Only the 1374 cm-1 band due to Mon appeared just after the occurrence of the crystal. However, the 1382 cm-1 band due to Orth II was observed clearly 2 h after the occurrence, and the 1374 cm-1 band disappeared 3 h after. So we conclude that the LM phase occurs as the Mon type at the first stage of crystallization, and then Orth II is generated on the grown Mon crystals. The Orth II region grows through solution-mediated phase transition from Mon to Orth II. This process has been observed already for the B and E forms of n-saturated fatty acids,17 but the transformation from Mon to Orth II proceeds sooner in petroselinic acid than in n-fatty acids; in the case of n-saturated fatty acids, most single crystals generated by a cooling method remained the Mon type even after 1 day from their occurrence. In previous study about the LM phase,13,18 single crystals were grown under moderate conditions and were kept in solution at least half a day after their occurrence. Therefore, all crystals may have transformed to the Orth II type before crystal specimens were collected from the solution. 2. Solid-State Transitions from the LM Phase to the HM Phase. A. Transition Induced by Mechanical Stress. We found a solid-state phase transition from the LM(Mon) phase to the

Figure 3. Infrared spectral changes of a single crystal of the LM phase kept in a solution: solid line, the electric vector parallel to the acute bisectrix of the lozenge-shaped crystal; broken line, parallel to the obtuse bisectrix.

HM phase induced by a mechanical stress onto a single crystal. For example, when a local stress is added onto a crystal (e.g., a press with the end of a needle), a part of the crystal transforms to the HM phase. This process proceeds so quickly that we cannot follow it with the naked eye. The transition can be confirmed easily with microscopic observation. When a single crystal specimen is set at an extinction angle and a stimulation is given to the specimen, a part of crystal bursts into a bright transformed region (Figure 4a). The bright band near the center of the crystal is the transformed region. The transformed region showed also clear extinction in a different arrangement. The micro-IR spectra of this region show clear dichroism as well as the unchanged region, as shown in Figure 4b. In the LM phase the 720 cm-1 rb(CH2) band and the 730 cm-1 ra(CH2) band due to the O⊥ subcell appear with polarization parallel to the acute and obtuse bisectrices. The doublet bands due to the CH2 scissoring show the same polarization. In the transformed HM region, the 723 cm-1 band shows clear polarization parallel to the acute bisectrix. The band is ascribed to the CH2 rocking mode of the M// type subcell and the dC-H out-of-plane deformation mode, and the polarization indicates that the b axis of the HM phase is nearly parallel to the acute bisectrix. The above results indicate that the transformed HM region keeps a fairly good orientation. Transformed regions often present complex zigzag patterns, as shown in Figure 5. In some crystals the whole transformed region of a zigzag pattern exhibits the extinction under cross-Nicol at the same time. However in many cases a zigzag pattern is composed of several kinds of domains that show the clear extinction at their inherent extinction angles respectively. The latter case can be recognized

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Figure 4. (a) HM region transformed by mechanical stress in a single crystal of the LM phase and (b) the infrared spectra of the HM (bottom) and LM (top) regions.

as twinning under the effect of stresses arising out of the phase transition. Figure 5a shows a characteristic pattern of a transformed region: domains of different orientation fringe the zigzag region. The transition induced by a mechanical stress takes place only in single crystals of Mon. In case of crystals of Orth II, such transitions could not be observed even with a stress large enough to crack single crystals. B. Transition Induced by Rapid Heating. We found that upon a rapid heating process the LM(Mon) phase transforms to the HM phase with a mechanism similar to the transition induced by a mechanical stress. When a specimen is heated

rapidly (more than 10 °C/min) to a temperature above 28.5 °C (the melting point of the LM phase), the crystal transforms to the HM phase in an instant. This transformation happens in the whole region of a single-crystal specimen. Although a transformed crystal usually consists of several domains of different orientation (in Figure 6a, there are four different orientations), in certain crystals a large domain covers almost the whole region. In this case the crystal morphology changes also in an instant; the acute angle alters from 75 to 68° as shown in Figure 6b. For single crystals of Orth II, such a clear momentary phase transition has not be observed. Rapid heating makes the greater

Martensitic Phase Transition of Petroselinic Acid

J. Phys. Chem. B, Vol. 101, No. 2, 1997 289 transitions. The poly(methylene) chains incline toward the bs axis in the LM (Orth II) phase, and the inclination direction is inverted alternately at every stacking of the bimolecular layer. Therefore the LM phase of Orth II shows no remarkable intensity changes with the rotation of crystal about the φ axis (the acute bisectrix). However, after the transition, marked intensity changes were observed. We conclude that the LM(Orth II) phase transformed to the HM phase of the single-layer structure. Discussion

Figure 5. Typical zigzag patterns of the HM phase transformed by mechanical stress.

part of a single crystal fuse. In this case a few infusible domains grow as the HM phase in the melt. C. Transition Induced by Slow Heating. Upon slow heating both the Mon and Orth types of the LM phase change to the HM phase. There are no large differences in transition behavior due to polytypic structures by slow heating (e.g. 1 °C/min). Contrary to the case of rapid heating, the phase transition by slow heating can be followed by microscopic observation. The transition starts one or several points in a crystal, and transformed areas spread over the crystal. The morphology of a single crystal does not change definitely. Although the transformed crystal shows clear polarized infrared spectra, the extinction under the cross-Nicol is not as clear as that of the crystals transformed by a mechanical stress or by rapid heating. It seems that the transformed crystal is an agglomerate composed of small HM crystals whose crystal axes are relatively well aligned. A similar state of the resultant crystals was observed in the E f C transition of stearic acid.19,20 We have confirmed with oblique IR transmission method20 that the LM(Orth II) phase transforms to the HM phase of the single-layered structure. The obtuse bisectrix (//bs) of a singlecrystal specimen was set parallel to the electric vector of the incident radiation, and the crystal was rotated around the acute bisectrix (//as). Figure 7 shows the spectral changes on the

1. Factors for Polytypism. As described above, we confirmed the polytypism in the LM phase. The double layered polytype, Orth II, has been found in n-alkanes, n-saturated fatty acids, and cis-unsaturated fatty acids. The common feature in the polymorphs forming the Orth II structure is that the (011) plane of the O⊥ subcell is parallel to the methyl terminal plane of bimolecular layers. With this arrangement of the methyl terminals, the cohesive energy of hydrocarbon chains at the lamellar interface is almost the same between Mon and Orth II.6 We infer that polytypism will be found widely in crystalline states of long-chain compounds satisfying the above condition. The Mon type of the LM phase is recognized as a transient state to the stable state Orth II. 2. Martensitic Transition. The first-order solid-state phase transition is divided into two stages, nucleation and growth, and the growth mechanism of product phase can be classified into two types, molecular jumps and cooperative displacements. The latter is called martensitic transition and has been found in metal alloys, chemical compounds, and macromolecules.21-23 In the former mechanism, the rearrangement of molecules at the growing face of the product phase takes place through thermally activated molecular jumps. On the other hand, a martensitic transition accompanies cooperative displacements of numerous molecules at the growing face. The growth of the product phase on the martensitic transition is significantly faster than that in the transitions of thermally activated jumps. As described in the previous section, the LM(Mon) phase shows two types of transition behaviors depending on the conditions. It seems that the two transition behaviors correspond the two growth mechanisms of the product phase. The transition caused by mechanical stress or by rapid heating has several features of a martensitic transition; (1) the transition proceeds significantly rapidly, (2) the transformed regions are highly oriented, (3) there is a certain relationship in the direction of the crystallographic axes between the mother and product phases, and (4) sometimes the transformed region forms a characteristic zigzag pattern. This may be the first case of martensitic transition in fatty acids and other lipid-related compounds, as far as we know. According to our experimental results, the LM(Mon) phase is the most unstable among LM(Mon), LM(Orth II), and HM, but nevertheless the martensitic transition does not start spontaneously. We consider that the shear stress component of a local stress is a trigger for the martensitic transition. In the case of a rapid heating, lack of uniformity of temperature may cause a local stress in specimens. Shear stress would induce the nucleation of the HM phase, and the occurrence of the nucleus would generate also a stress in the surrounding mother phase. With this stress the neighboring molecules in the mother phase change their positions cooperatively, and the displacement proceeds like a wave front. The displacement can be recognized as a plastic wave: a kind of stress wave whose strain exceeds the limit of elastic deformation. We infer that the characteristic zigzag patterns are produced by the reflection

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Figure 6. Crystals transformed by rapid heating: (a) four different extinction arrangements of a transformed crystal and (b) changes of crystal habit.

of the stress wave; when the wave meets a large defect hard to pass and the energy of the wave is not dissipated at the defect, the wave is reflected and the martensitic transition proceeds in the direction of the reflection. If the local stress is not enough to produce the nucleus of the HM phase, the nucleation should take place by thermal agitation and the product phase grows by thermally activated jumps. We consider that the LM f HM phase transition by slow heating and most irreversible transitions of long-chain compounds occur in this way. 3. Factors for Martensitic Transition. Usually a martensitic transition does not accompany large displacements of atoms or molecules.17,18 It seems that relatively small displacements are necessary for the rapid growth of a product phase. Although the difference in structure between the LM and HM phases is not small, there are several structural advantages for the occurrence of the martensitic transition. Since the carboxyl groups of fatty acids are dimerized in solid states, the carboxyl terminals are difficult to displace, compared

with methyl terminals. So we consider that the similarity in the packing of the carboxyl terminal chains is an important factor for the martensitic transition. As depicted in Figure 8, in the HM phase carboxyl terminal chains form a structure similar to the O⊥ subcell in the LM phase. Therefore, large displacements of carboxyl terminals are not necessary for the transformation from LM(Mon) to HM. The flexibility of cis-C(5)-C(6)dC(7)-C(8) group seems to be another important factor. The dihedral angles should change from 157, 0, -160 to 91, 1, 130° (molecule A) or to 127, 1, 119° (molecule B), but the large potential barriers for this conformation change is not so large.24 Owing to this flexibility of the cis-olefin group, the structural change of subcell from O⊥ to M// in the methyl-terminal chain does not need large displacements of the carboxyl-terminal chains. Now we compare the LM f HM transition with the E f C transition of stearic acid (n-C18 acid) that exhibits no martensitic transition. Features of the two transitions are summarized in Table 2. Both the E and C phases form the O⊥ subcell, and

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Figure 9. Cis and trans-tautomerism of dimerized carboxyl groups.

Figure 7. Infrared spectral change on the LM(Orth II) f Mon transition measured by the oblique transmission method.

Figure 8. Arrangement of carboxyl-terminal chains in the HM phase.

TABLE 2: Comparisons between the LM f HM and E f C Transitions13-14,26,27 LM f HM transition a (Å) b (Å) ab sin γ (Å2) V (Å3) d001 (Å2) inclination of chain (°) a

LM

HM

5.567 7.311 40.7 1791 44.0 26a

5.359 8.874 43.5 1801 41.4 31a

E f C transition

change

E

C

change

2.8 10 -2.6 5a

5.603 7.360 41.2 1825 43.9 27

9.36 4.95 46.3 1845 30.0 35

5.1 20 -3.9 8

The inclination of the methyl-terminal chains.

the polyethylene chains incline toward the a axis by 27° in E and by 35° in C. However, the relationship between subcell and main lattice is different; the unique b axis is parallel to the as axis in E and to the bs axis in C. If the transition takes place without a change of the inclination direction, the length of the a and b axes should change largely. In practice the E f C transition is initiated with thermally induced nucleation and accompanies large precessional displacements of acyl chains (about by 70-80° or 160-180°). Changes in lamellar thickness, cross-sectional area (ab sin γ), chain inclination, and cell volume are also larger on the E f C transition than on the LM f HM transition (Table 2).

4. Effects of Polytype Structure. As described above, only the Mon polytype of the LM phase is able to perform the martensitic transition to the HM phase. In case of the transition of LM(Orth II) by slow heating, the double-layered structure changes to the single-layered structure. This suggests that the double-layered structure of the HM phase is energetically remarkably higher than the single-layered structure. The unstability of the double-layered structure of the HM phase is assigned to the intermolecular interaction at the lamellar interface. Similar polymorph-polytype composite phase transitions have been observed in the E f C and B f C transitions also. In this case, the molecules should perform large displacements in at least every second bimolecular layer. Under this condition a martensitic transition accompanying cooperative displacements of numerous molecules seems significantly difficult. Probably the energy barrier for the nucleation is remarkably high. Only the transition mechanism of the thermally induced nucleation and growth by thermally activated molecular jumps is possible for single crystals of the LM(Orth II) phase. In case of the solid-state phase transition of this type, a single crystal cannot transform to the product phase so quickly. Therefore, a large portion of a single crystal of Orth II melts by rapid heating. 5. Driving Force for the LM f HM Transition. The unit cell volume increases on the E f C transition and similarly by about 5 Å3 per dimer on the LM f HM transition (Table 2). The increment of cell volume indicates that the cohesive energy owing to van der Waals’ interaction cannot be assigned to the driving force for these transitions. In the case of the E f C transition, the dynamic property of dimerized carboxyl groups in the C form is considered as the cause of the transition.6 As described in Figure 9, there are two potential minima for the hydrogen atom of carboxyl groups in the C form, and therefore the C(3)-C(2)-C(1)dO group may take cis or trans-conformation about the C(2)-C(1) bond. There is dynamic equilibrium between the two stable conformations through simultaneous transfer of two hydrogen atoms in a pair of dimerized carboxyl groups, and the ratio of cis-conformers to trans-conformers depends on temperature. In the B and E forms of n-saturated fatty acids, such as cis-trans-tautomerism does not occur and all molecules take the cis-conformation. So in the highest temperature range, the C form is thermodynamically stable due to the large configurational entropy about the carboxyl terminals. Carboxyl terminals in the LM phase take almost the same arrangement as those in the E form13,25 and show similar characteristics. The dynamic property of carboxyl groups is reflected in IR spectra. In particular the IR band due to O-H out-of-plane σ(O-H) mode reflects sensitively.27 The frequency of this band

292 J. Phys. Chem. B, Vol. 101, No. 2, 1997 increases as the proton transfer is activated. An intense band appears at 944 cm-1 in the C form and at 893 cm-1 in the E form. In the case of the LM phase, the band appears at 892 cm-1, while two intense components appear at 925 and 910 cm-1 in the HM phase. Judging from the frequency of the σ(O-H) mode, the dynamic equilibrium of carboxyl hydrogen atom can be expected only for the HM phase. The results of crystal structure analysis are consistent with the IR data. It is considered that the distance between the hydrogen-bonded oxygen atoms is related to the occurrence of tunneling exchange of the H atom.28 The probability of the tunneling motion is quite small for O‚‚‚O distances greater than 2.64 Å. In the E form and the LM phase, the O‚‚‚O length is 2.67 and 2.68 Å and the C-O and CdO bonds take standard bond lengths. On the other hand, the O‚‚‚O length is 2.62 Å in the C form and in the HM phase is 2.66 Å for molecule A and 2.63 Å for molecule B. From the above data, we infer that the dynamic cis-transtautomerism occurs only in the HM phase and the stabilization owing to configurational entropy is the driving force for the LM f HM transition. Conclusion The mechanism for the solid-state phase transition from the LM phase to the HM phase in petroselinic acid has been studied. We obtained the following results. (1) The LM phase has two polytypic structures, single-layered structure (Mon) and double-layered one (Orth II). (2) There are two types of mechanisms for the LM f HM phase transition; one is a usual thermally induced nucleation and growth, and the other is a martensitic transition. (3) Only the LM(Mon) phase exhibits a martensitic phase transition if a single-crystal specimen suffers a mechanical stress or rapid heating. (4) The LM(Orth II) f HM transition is a polymorph polytype composite phase transition. On the basis of the experimental results, we also draw the following inferences. (1) When a local stress exceeds a certain threshold, the martensitic transition to the HM phase takes place. (2) The possibility of the martensitic transition depends on the extent of rearrangement necessary for the occurrence of the HM phase.

Kaneko et al. (3) The HM phase is stabilized by dynamic proton transfer. References and Notes (1) Amelinckx, S. Acta Crystallogr. 1955, 8, 530; Ibid, 1956, 9, 16; Ibid. 1956, 9, 217. (2) Boistelle, R.; Simon, B.; Pepe, G. Acta Crystallogr. 1976, B32, 1240. (3) Kobayashi, M.; Kobayashi, T.; Itoh, Y.; Chatani, Y.; Tadokoro, H. J. Chem. Phys. 1980, 72, 2024. (4) Kobayashi, M.; Sakagami, K.; Tadokoro, H. J. Chem. Phys. 1983, 78, 6391. (5) Kobayashi, M.; Kobayashi, T.; Itoh, Y.; Sato, K. J. Chem. Phys. 1984, 80, 2897. (6) Kobayashi, M.; Kobayashi, T.; Cho, Y.; Kaneko, F. Makromol. Chem., Macromol. Symp. 1986, 5, 1. (7) Itoh, Y.; Kobayashi, M. J. Phys. Chem. 1991, 95, 1794. (8) Sato, K.; Kobayashi, M. Crystals 1991, 13, 65. (9) Sato, K.; Kobayashi, M.; Morishita, H. J. Cryst. Growth 1988, 87, 236. (10) Sato, K.; Yoshimoto, N.; Suzuki, M.; Kobayashi, M.; Kaneko, F. J. Phys. Chem. 1990, 94, 3180. (11) Simpson, T. D. In Fatty Acids; Pryde, E. H., Ed.; The American Oil Chemicsts’ Society: Champaign, IL, 1985; Chapter 8. (12) Sato, K. In AdVance in Applied Lipid Research; Padley, F., Ed.; JAI Press: New York, 1996; Vol. 2. (13) Kaneko, F.; Kobayashi, M.; Kitagawa, Y.; Matsuura, Y.; Sato, K.; Suzuki, M. Acta Crystallogr. 1992, C48, 1054. (14) Kaneko, F.; Kobayashi, M.; Kitagawa, Y.; Matsuura, Y.; Sato, K.; Suzuki, M. Acta Crystallogr. 1992, C48, 1057. (15) Bunn, C. W. Trans. Faraday Soc. 1939, 35, 482. (16) Kaneko, F.; Simofuku, T.; Miyamoto, Y.; Kobayashi, M.; Suzuki, M. J. Phys. Chem. 1992, 96, 10554. (17) Kaneko, F.; Sakashita, H.; Kobayashi, M.; Suzuki, M. J. Phys. Chem. 1994, 98, 3081. (18) Kaneko, F. Doctoral Thesis, Faculty of Science, Osaka University, 1989. (19) Kaneko, F.; Kobayashi, M.; Kitagawa, Y.; Matsuura, Y. J. Phys. Chem. 1992, 96, 7104. (20) Kaneko, F.; Shirai, O.; Miyamoto, H.; Kobayashi, M.; Suzuki, M. J. Phys. Chem. 1994, 98, 2185. (21) Urusovskaya, A. A. Modern Crystallography. IV. Physical Properties of Crystals; Shavslov, L. A., Ed.; Springer Verlag: Berlin, 1988. (22) Raghavan, V.; Morris Cohen Treatise on Solid State Chemistry. 5. Change of State; Plenum: New York, 1975. (23) Kiho, H.; Peterlin, A.; Geil, P. H. J. Appl. Phys. 1964, 35, 1599. (24) Kaneko, F.; Yamazaki, K.; Kobayashi, M.; Kitagawa, K.; Matsuura, Y.; Sato, K.; Suzuki, M. J. Phys. Chem. 1996, 100, 9138. (25) Kaneko, F.; Kobayashi, M.; Kitagawa, Y.; Matsuura, Y. Acta Crystallogr. 1990, C46, 1490. (26) Malta, V.; Celloti, G.; Zannetti, R.; Martelli, A. J. Chem. Soc. B. 1971, 548. (27) Zerbi, G.; Dellepiane, G. J. Raman Spectrosc. 1982, 12, 165. (28) Matsushita, E.; Matsubara, T. Prog. Theor. Phys. 1982, 6, 1.