Thermal expansion and Grüneisen functions of polymer crystal models: 1. Central forces

Abstract

With typical pair potentials, a bond is stretched by vibrations along the bond directions, while contraction is caused by the tension set up by vibrations normal to the bond direction. The rôle of these two effects is studied in calculations for parallel linear-chain and zigzag-chain models. For linear chains and rigid zigzag chains, expansion is positive in the plane normal to the chain direction, although it may be strongly anisotropic in this plane. Expansion along the chain direction is negative, and typically an order of magnitude less than that normal to the chain. For a flexible zigzag chain with bond angle 90°, expansion is positive in all directions; the Grüneisen tensor is approximately isotropic, but elastic anisotropy leads to smaller expansion coefficients in the molecular planes. The Reuss-averaged Grüneisen function derived from (6–12) pair potentials is about 3.5 for most of the models; this is higher than observed experimentally in polycrystalline polyethylene, indicating the need for more realistic models of organic polymers.