A Theory of Melting of Molecular Crystals: the Complete Picture of Transition Temperatures

Abstract

The theory of melting of molecular crystals with orientational degrees of freedom developed by Pople and Karasz (P and K) [1,2] is extended using a third energy parameter W'', in our previous papers [3-5]. The extention is done as follows: the previous repulsive energy parameter W is devided into two parts. The first part is the interaction between molecules which are on different sites with the same orientations, called again W. The second is the interaction between molecules on different sites and also different orientations, namely W''. W'' is combined with previous W' and the new W energy parameters by the arithmetic mean including an adjustable parameter. The present model is applied to study the thermodynamic properties of melting [3], solid-solid transitions and the complete phase diagrams for transitions under pressure [4], as well as the thermodynamics of solid-nematic and nematic-isotropic liquid transitions [5]. The quantitative predictions of the present model is compared with experimental results for plastic crystals by plotting the entropy of melting as a function of the ratio of melting and the ratio of solid temperatures , the entropy of melting as a function of volume changes and also the melting entropy versus the solid transition entropy. It is found that the agreement between the present theory and experimental data is better than the calculation of P and K theory. In this work, we give the complete pictures of transition temperatures and compare with the P and K theory as well as it volume dependence modification which was done by Chandrasekhar, Shashidar and Tara (CST) [6-7]. In order to study the complete pictures of transition temperatures, first we plot the reduced transition temperatures of solid-solid (S-S), solid-liquid (S-L), solid-nematic (S-N) and nematic-isotropic liquid (N-I) transitions as a function of \nu which is a measure of the relative energy barriers for the rotation of a molecule and for its diffusion to an interstitial site, together with the values given by the P and K and CST theories. Then, entropy and volume changes of S-S, S-L, S-N and N-I transitions as a function of \nu are calculated and plotted along the P and K and CST theories.