Isomerization dynamics in viscous liquids: microscopic investigation of the coupling and decoupling of the rate to and from solvent viscosity and dependence on the intermolecular potential

Abstract

A detailed investigation of viscosity dependence of the isomerization rate is carried out for continuous potentials by using a fully microscopic, self-consistent mode-coupling theory calculation of both the friction on the reactant and the viscosity of the medium. In this calculation we avoid approximating the short time response by the Enskog limit, which overestimates the friction at high frequencies. The isomerization rate is obtained by using the Grote-Hynes formula. The viscosity dependence of the rate has been investigated for a large number of thermodynamic state points. Since the activated barrier crossing dynamics probes the high-frequency frictional response of the liquid, the barrier crossing rate is found to be sensitive to the nature of the reactant-solvent interaction potential. When the solute-solvent interaction is modeled by a 6-12 Lennard-Jones potential, we find that over a large variation of viscosity (η), the rate (k) can indeed be fitted very well to a fractional viscosity dependence: (k ~ η^-α), with the exponent a in the range 1 ≥ α ≥ 0. The calculated values of the exponent appear to be in very good agreement with many experimental results. In particular, the theory, for the first time, explains the experimentally observed high value of a, even at the barrier frequency, ω_b ≈ 9 × 10¹²s^-1 for the isomerization reaction of 2-(2'-propenyl)anthracene in liquid n-alkanes. The present study can also explain the reason for the very low value of ω_b observed in another study for the isomerization reaction of trans-stilbene in liquid n-alkanes. For ω_b ≥ 2.0 × 10¹³s^-1, we obtain α ≈ 0, which implies that the barrier crossing rate becomes identical to the transition-state theory predictions. A careful analysis of isomerization reaction dynamics involving large amplitude motion suggests that the barrier crossing dynamics itself may become irrelevant in highly viscous liquids and the rate might again be coupled directly to the viscosity. This crossover is predicted to be strongly temperature dependent and could be studied by changing the solvent viscosity by the application of pressure.