Multi-excitation entropy: its role in thermodynamics and kinetics

Abstract

This review concerns the concept of multi-excitation entropy (MEE) and its consequences. When a fluctuation involving a large number of excitations occurs, for example, when a large activation barrier is overcome, there must be a large entropy associated with this fluctuation. First, the concepts of free energy and entropy, of activated processes and the Arrhenius and Eyring equations are reviewed. The tendency to neglect entropy, whose value is difficult to determine, in modelling kinetic processes, is briefly discussed. We then present a review of the experimental observations of the phenomenon which is variously known as the Compensation Law, the Isokinetic Rule and the Meyer–Neldel Rule (MNR). These observations include examples from chemistry, condensed matter physics, biology and geology. Arguments are then presented for the importance of entropy and particularly of MEE in both kinetics and thermodynamics, when activation energies are large. After a discussion of non-entropic models of compensation, we present results which support the MEE model as an explanation of MNR. The behaviour of systems with low activation energies, or at high temperatures, to which the MEE model does not apply, is then discussed. Several consequences of MEE, including applications to the interpretation of experimental data, particularly the unification of models of dc and ac electrical properties of materials are considered. The high temperature behaviour of systems which obey the MNR at low temperature is then explained, and the idea of a total entropy, of which the MEE is a part, is introduced, as is the correlation between the two empirical parameters encountered in MNR. Finally, these ideas lead to verified predictions of reasonable values of attempt frequencies and cross sections in kinetic processes, which initially appear unreasonable.