Thermally Activated Escape from a Lennard-Jones Potential Well

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Abstract

The Kramers theory of chemical kinetics is modified in order to describe the escape of particles from a potential well of the Lennard-Jones type, for which there is no well-defined barrier position or curvature. Approximate analytical methods are used to derive from the Fokker-Planck equation two distinct formulas for the escape rate, each valid in a different regime of the friction constant β. The large-β result is seen to be consistent with that obtained from the Smoluchoeski equation, and it shows that the resistance to escape is dominated by a purely diffusive component that causes nonequilibrium effects to be felt well down into the reactant region. On the other hand, the small-β result describes a situation in which diffusional resistance is of minor importance, and the escape rate is determined largely by the characteristics of the well itself. The approximate formulas give a reasonably good picture of the transition between the two kinds of limiting behavior.