Intermolecular forces and thermodynamical functions of orthorhombic polyethylene lattice

Abstract

Infrared and Raman data which are related to the intermolecular forces of the orthorhombic polyethylene lattice, the lattice mode frequencies, and the correlation field splittings of the methylene rocking and scissoring modes have been summarized through the temperature range of room to liquid heliumtemperature. The normal mode frequencies have been calculated for the three‐dimensional crystal lattice with the dimensions measured at various temperatures, two values of the setting angle, 48.8° and 42°, being adopted for the calculation. A pairwise intermolecular force field has been assumed and the Buckingham type potential functions V (r) =B exp(−C r)−A r −6 (r is the interatomic distance) have been taken into account for the atomic pairs of H–H and C–H with r<4.0 Å. The potential parameters for both kinds of atomic pair have been determined by the least‐squares method so as to reproduce the observed frequency data through the wide temperature range, and compared with the values reported previously. The errors involved in the intermolecular force constants thus determined and also in the calculated frequencies due to the uncertainty in the value of the setting angle assumed in the calculation have been estimated by the error‐transfer method. For the temperature dependence of the lattice mode frequencies an appreciable amount of discrepancy has still been recognized even after repetition of least‐squares fittings. This may be due to the approximation of the pairwise intermolecular potential and also to the anharmonic character of the lattice vibrations. The observed B 1u –B 2u correlation field splitting of the CH2 rocking, as well as the ν a –ν b splitting for the ν8 (the CH2 rocking–twisting) branch has been reproduced fairly well by the present calculation. Using the potential functions thus obtained, the thermodynamical functions, the internal energy, the entropy, the Helmholtz free energy, and the heat capacity of the orthorhombic polyethylene lattice have been calculated in the quasiharmonic approximation, giving a good agreement with the experimental results obtained by thermal measurements.