Structure and Crystallization Behavior of the β Phase of Oleic Acid, страница 9

(3) The intense reflections in the region of 18 < 2θ < 30°, which are due to the subcell structure, appear at almost the same position with similar relative intensity ratios.

It might be concluded that the β₂ phase also forms the interdigitated structure whose lamellar thickness is about the same as that of β₁ and that polymethylene chains are accommodated in the T subcell.

In this measurement, the peak width of the β₂ phase became sharper during a gradual transformation to the β₁ phase at 15.5 °C. It seems that some disorders have been incorporated into the β₂ specimen during the crystallization at a large supercooling of about 5 °C.

3. Possibility of Order−Disorder Transitions. Although there is a reversible order−disorder transition accompanying conformational disordering at the methyl side chains between the α and γ phases, the β phase does not show such a reversible transition. This characteristic can be easily understood with the crystal structure; a methyl terminal group is surrounded by carboxyl groups forming dimers with hydrogen bonds. Therefore, the conformational disordering at the methyl terminals needs a much larger activation energy in β than in the other polymorphs, leading to little possibility of transition.

4. Factors Affecting the Formation of Interdigitated Structures. We interpret the fact that the β phase has so far been found only in oleic acid as follows. Oleic acid only has the same number of carbon atoms between methyl and carboxyl side chains of natural cis-monounsaturated fatty acids. If there is a difference in chain length, the interdigitated structure should produce a void at the methyl terminal or carboxyl terminal. For example, the virtual β phase of palmitoleic acid (cis-9-hexadecenoic acid) has a void at the methyl terminals, which decreases the cohesive energy of the lattice. In the case of shorter carboxyl side chains, there is a void at the carboxyl terminals and hydrogen bonds cannot be formed. This is clearly an unfavorable structure. Therefore, the coincidence in the number of carbon atoms between methyl side and carboxyl side chains is a very important factor for the interdigitated structure.

5. Crystal Growth. As described in the Introduction, the rate of crystal growth of the β phase is unusually lower than that of the other polymorphic phases of long-chain compounds. Furthermore, the occurrence of the β phase is rare compared with the α and γ phases. In other words, the nucleation rate is also quite low.

On the basis of the crystal structure of the β phase, we infer that the following factors are the causes for the rareness of crystal occurrence and the low growth rate. One factor is the conformation of cis-olefin groups. As stated above, the conformation of this portion can be recognized as trans−cis−trans type. According to the molecular mechanics calculation, this conformation is less stable at least by 1.5 kcal/mol than the minimum energy.¹² To build a single crystal of β, a cluster should be formed where molecules take this unstable conformation. That is clearly a high-energy state. Therefore, the nucleation of β is energetically unfavorable. A similar discussion can be made for the process of crystal growth. A molecule that has attached to a crystal face should take the trans−cis−trans conformation in order to coalesce into the crystal face; this process may be energetically unfavorable and could be a bottleneck of the crystal growth.

The detailed information about the structure of the (001) face has not been obtained. However, from the crystal structure, the (001) face of β is unique; the density of molecular chains at the (001) face is one-half that of the interior of single crystals. In case of usual polymorphs of long-chain compounds, the average distance between nonbonded atoms is largest at the lamellar interface. The intermolecular interactions along the lamellar stacking direction are weak compared with those in the lateral direction. Therefore, the surface energy, i.e., energy necessary for forming a crystal face per unit area, takes a minimum value at the (001) face. In the case of the β phase where a molecule of a dimer penetrates into the next layer, the intermolecular interaction at the interface becomes much stronger, which may result in a large surface energy of the (001) face. The estimation of the surface energy is difficult at present, since it needs detailed information about the surface structure. However, it is reasonable to attribute one reason for the low nucleation and growth rates to the high surface energy of the crystal faces. It is well-known that the surface energy of the lamellar folding of polymer crystals is significantly larger than that of lateral faces, and therefore, the melt−crystallization of macromolecules needs a large supercooling.³⁶ For the melt crystallization of β, however, a large supercooling is not available because the nucleation and crystal growth of the α phase surpass those of the β phase.