Viscosity Grote-Hynes theory

In the limit of very large viscosity, such as the one observed near the glass transition temperature, it is expected that rate of isomerization will ultimately go to zero. It is shown here that in this limit the barrier crossing dynamics itself becomes irrelevant and the Grote-Hynes theory continues to give a rate close to the transition theory result. However, there is no paradox or difficulty here. The existing theories already predict an interpolation scheme that can explain the crossover to inverse viscosity dependence of the rate... 

The isomerization rate is calculated using the Grote-Hynes formula, given by Eqs. (320) and (322). The frequency-dependent friction ( (z)) and viscosity (rj) has been obtained from the mode coupling theory presented in Section IX. For convenience the rate is expressed in terms of the dimensionless quantity k in the following form ... 

An elegant explanation for the unusual viscosity dependence was provided by the non-Markovian rate theory (NMRT) of Grote and Hynes [149] which incorporates the idea of frequency dependence of the friction. According to this theory the friction experienced by the reactive motion is not the zero frequency macroscopic friction (related to viscosity) but the friction at a finite frequency which itself depends on the barrier curvature. The rate is obtained by a self-consistent calculation involving the frequency-dependent friction. 

Recently much attention has been aroused on solution reactions whose rates decrease as the viscosity Tj of solvents increases. These reactions cannot be rationalized in the framework of the transition state theory. To describe them, two currents of theories have been developed by extending the Kramers theory. One was initiated by Grote and Hynes, while the other by Sumi and Marcus. Recent data on thermal Z/E isomerization of substituted azobenzenes and A/ -benzyU-deneanilines confirms the applicability of the latter for 77 variation over 10 times under pressure. 

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