A model for the evaluation of thermodynamic properties for the solid-solid and melting transitions of molecular crystals

The theory of fusion of molecular crystals with orientational degrees of freedom developed by Pople and Karasz [1] is extended by taking into account the existence of more than two possible positions of minimum orientational energy in the crystal. Now the model has two parameters: D, the number of these possible positions; and as before, v, a measure of the relative energy barriers for the rotation of a molecule and for its diffusion to an interstitial site. The main features derived from the model, when D > 2, are (1) solid-solid and melting transitions are always of first order; (2) the values of v at which solid-solid transition and fusion temperatures (T_t and T_m) coalesce increase when D increases; (3) solid-solid transition entropies increase with D and for each D, with v; (4) at constant v there is a decrease of T_t and of T_m when D increases; (5) relative volume changes on melting become smaller than the relative volume changes at the solid-solid transition when v > 0.26, this change becomes as small as 4 per cent for D = 60 and v = 0.5. The quantitative predictions of the model are compared with experimental results for plastic crystals. There is good agreement between theory and experiment. For solid-solid transitions the agreement is much better than with the calculations of Pople and Karasz, as would be expected from the fact that in the present theory D is a parameter.