Mechanism for entropy–enthalpy compensation in the fusion of organic molecules

Contrary to Waldenʹs Rule [P. Walden, Z. Elektrochem. 14 (1908) 713–728], the entropies of fusion of rigid organic molecules, ΔSf, are linearly related (entropy–enthalpy compensation) to the enthalpies of fusion, ΔHf, by an expression of the form ΔSf = a + bΔHf where a and b are constants [A.S. Gilbert, Thermochim. Acta 339 (1999) 131–142]. The compounds that show phase transitions in the solid state yield a value of the intercept a close to that expected (about 8 J K−1 mol−1) for the communal entropy of the liquid state. However, most compounds do not possess solid state transitions and for these the value of a is found to be much higher at around 30 J K−1 mol−1. A simple statistical mechanical treatment has been applied to the way the external vibrational modes (translational and librational) might change on fusion and gives some success in describing the features of the compensation observed, in particular the values of the intercepts. This involves consideration of the enthalpy of vapourisation of the liquids, ΔHv, as well as ΔHf. It appears that the ratio between these two parameters, ΔHf/ΔHv is a major determining factor so that compensation occurs more properly with this ratio than with ΔHf alone. The entropy and enthalpy changes for transitions in the solid state themselves also appear to be compensated in the same way as for fusion.