Calculation of the elastic constants and the lattice energy of the polyethylene crystal

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Abstract
To calculate the elastic constants, (Cij), of the polyethylene (PE), Born's dynamical theory of long wave method has been used for a model of interatomic interactions representing inter‐ and intramolecular force fields. Among various types of interaction potentials between nonbonded atoms, two sets of H‐H, C‐H, and C‐C interaction potentials have been adopted which give the best results in reasonable agreement with the data of the lattice parameters and the angle between plane of the zigzag chain and crystallographic axis in the PE lattice. It has been also verified that the lattice energy of PE can be calculated successfully by using the present, potentials. In order to calculate the elastic constant, H‐H and C‐H interactions with close distances have been taken into account for the intermolocular force fields. On the other hand the Urey‐Bradley force field has been used for intramolecular interactions. An expression is obtained which relates Horn's force constants to the macroscopic elastic constants in the orthorhombic system. The calculation has been also made on Cij in a rigid model of molecular chain, but it is found that the increments of elastic constants due to the rigid model are at most a few per cent. The elastic moduli along the a, b, and r, axes and also the normal of the (110) plane have been derived from Cij and compared with values experimentally determined by x‐ray diffractometry. Furthermore, the space averages for compressional, shear, and Young's moduli of PE polycrystals oriented in all directions, and the T3 low‐temperature dependence of heat capacity are discussed.

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