Space Correlations of Steric Origin in Plastic Crystals

Abstract

In plastic crystals, space correlations between molecular orientations can be of very different kinds. The most frequent ones are associated with steric hindrance and are more especially strong as molecules are less globular. X-rays studies have often shown them, for example in cyclohexane, succinonitrile, t-butyl chloride and bromide, camphene etc…. These correlations strongly influence both the static and dynamical behaviours of molecules. Here we care for the first case alone. The purpose of this paper is the theoretical study of entropy, X-ray scattering and dielectric constants, which have not been yet examined with accuracy. We present a systematic way of studying this kind of correlations, by use of a graphical series expansion of the thermodynamical functions. This method has been used successfully in the ice and dimer problem by Nagle^1,2. It is very convenient here because we are dealing with “all or nothing” correlations. So we can evaluate the partition function and the correlation lengths. A similar calculation, in presence of an applied electric field, gives the Kirkwood orientational correlation factor θ_k.