Activated barrier crossing dynamics in slow, viscous liquids

Abstract

Experimental studies of reaction rates in slow, viscous liquids have often led to results at variance with conventional theoretical approaches. Here we present a self-consistent microscopic calculation of the rate which uses for the first time, the mode coupling theory (MCT) to obtain the frequency dependent friction. When this microscopic expression for the friction is used to obtain the barrier crossing rate from the Grote-Hynes (G-H) formula, the following results are found. At intermediate viscosities, the calculated rate exhibits a fractional viscosity dependence with parameter values in agreement with the experimental results. For example, we find an exponent equal to 0.8 when the barrier frequency (ω_b) is equal to 2 × 10¹³ s^-1, whereas the earlier calculations obtained an unrealistic value (close to 0.1) for this value of the barrier frequency. At very high viscosities we find an inverse logarithmic dependence of the rate on viscosity. This prediction can be tested against experiments.