Thermally activated escape from a Lennard-Jones potential well

✍ Scribed by Richard S. Larson; Edwin J. Lightfoot

• Publisher: Elsevier Science
• Year: 1988
• Tongue: English
• Weight: 776 KB
• Volume: 149
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(88)90221-x

✦ Synopsis

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 p. The large-p result is seen to be consistent with that obtained from the Smoluchowski 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-p 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.