A theoretical justification for the application of the Arrhenius equation to kinetics of solid state reactions (mainly ionic crystals)

Abstract

Although the Arrhenius equation has been widely and successfully applied to innumerable solid state reactions, this use lacks a theoretical justification because the energy distribution amongst the immobilized constituents of a crystalline reactant is not represented by the Maxwell-Boltzmann equation. The present analysis focuses attention on the role of the reactant-product interface, the active zone within which chemical changes preferentially proceed in many solid state rate processes. We identify interface energy levels, that are the precursors to the bond redistribution step, as extensions to the band structure of the solid into the structurally less-regular reaction zone. These interface energy levels are analogous to impurity levels. Electron reorganization requires a locally high energy so that interface levels are appreciably above the Fermi level of the crystalline reactant (and product). Occupancy is determined by energy distribution functions based on Fermi-Dirac statistics for electrons and Bose-Einstein statistics for phonons. For the highest energies, necessary for reaction, both distributions approximate to the exponential energy term, thereby providing a theoretical justification for the application of the Arrhenius equation to reactions of solids. The treatment given here has been largely developed from the theory applicable to ionic solids and the conclusions are most directly relevant to reactions of this class of substance. It is intended, however, that the approach should be of value in extending theoretical understanding of all rate processes involving solids which require the preinvestment of energy in an electron reorganization step.