An Interpretation of Classical Transition State Theory for Kinetics in Materials Science

This paper introduces simple phenomenological rate theory from the perspective of molecular interconversions and then applies it, in the form of Transition State Theory, to processes such as atomic diffusion and thermally-activated crystal growth in condensed matter composed of very large numbers of atoms or molecules. It is shown that in classical Transition State Theory, the unimolecular rate constant is the “thermal frequency” kBT/h times a Boltzmann factor in the free energy of activation, provided the transition state is defined as a slice of 3N-dimensional configuration space of thickness equal to the thermal deBroglie wavelength, where N is the number of atoms in the system. Equivalently, the unimolecular rate constant is the product of a normal mode frequency and a Boltzmann factor in the free energy of activation, provided the free energy is evaluated for a 3N-1 dimensional hypersurface that is perpendicular to the direction of normal mode motion along the reaction coordinate. Various other expressions for the unimolecular rate constant are derived for various other definitions of the transition state. The apparent activation enthalpy and the pre-exponential factor in the Van’t Hoff-Arrhenius equation for the temperature-dependence of the unimolecular rate constant are interpreted in terms of 3N-dimensional thermodynamic properties of the system and the thermal frequency, as well as in terms of 3N-1 dimensional thermodynamic properties of the system and a normal mode frequency. The relationship between the back reaction and the forward reaction is developed, providing an expression for the net rate as a function of thermodynamic driving force. Examples are presented for which the ratio of net rate constant to the unbiased forward rate constant saturates or increases exponentially with increasing thermodynamic driving force. This approach was developed for teaching a graduate course in materials science called “Kinetics of Condensed Phase Processes” in the late 20th century.