Viscosity theory frequency-dependent friction

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. 

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 ... 

For a large particle in a fluid at liquid densities, there are collective hydro-dynamic contributions to the solvent viscosity r, such that the Stokes-Einstein friction at zero frequency is In Section III.E the model is extended to yield the frequency-dependent friction. At high bath densities the model gives the results in terms of the force power spectrum of two and three center interactions and the frequency-dependent flux across the transition state, and at low bath densities the binary collisional friction discussed in Section III C and D is recovered. However, at sufficiently high frequencies, the binary collisional friction term is recovered. In Section III G the mass dependence of diffusion is studied, and the encounter theory at high density exhibits the weak mass dependence. 

As an example of the influence of these relaxation times, the frequency dependence of the viscosity of the n-alkanes deduced by Sceats and Dawes is show in Figure 13. This dependence can be used to model the hydrodynamic contribution to the friction of a particle using Zwanzig-Bixon generalized hydrodynamic theory. 

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