A THEORY OF MELTING OF MOLECULAR-CRYSTALS .1. THEORY AND EVALUATION OF THE THERMODYNAMIC PROPERTIES OF MELTING

The Pople and Karasz theory of melting of molecular crystals, which is based on the theory of melting of inert gas crystals by Lennard-Jones and Devonshire, is extended using a third energy parameter, W ''. The extension is done as follows: the previous repulsive energy parameter W is divided into two parts. The first part is the interaction betwee n molecules which are on different sites with the same orientations, c alled again W. The second is the interaction between molecules on diff erent sites and also different orientations, namely W ''. W '' is comb ined with the previous W' and the new W energy parameters by the arith metic mean including an adjustable parameter. The thermodynamic proper ties are evaluated by the Bragg-Williams approximation. The theory is applied to plastic crystals and compared with the Pople and Karasz the ory. By introducing a physical realistic coupling between orientationa l and positional order, v, the theory gives a solid state rotational t ransition and melting transition. For values of v less than or equal t o 0.331 the two transitions are separate, while for values of v greate r than or equal to 0.331 they coalesce. The quantitative predictions o f the theory is compared with experimental results for plastic crystal s by plotting entropy and volume changes versus melting/boiling temper ature ratios. The agreement between our theory and the experimental da ta is better than the calculations of the Pople and Karasz theory, as result of the introduction of the parameter W '' in the present theory .