Evaluation of the rate constant and deposition velocity for the escape of Brownian particles over potential barriers

TL;DR

This paper derives a formula for the deposition velocity of Brownian particles over potential barriers, connecting different regimes of particle response times using the Fokker-Planck equation.

Contribution

It introduces a unified approach to calculate particle deposition velocity across various response time regimes based on the Fokker-Planck framework.

Findings

Deposition velocity reduces to Smoluchowski's solution for small response times.

Deposition velocity aligns with transition state theory for large response times.

Provides a continuous formula bridging different particle response regimes.

Abstract

We analyze the escape of Brownian particles over potential barriers using the Fokker-Planck equation in a similar way to that of Chandrasekhar (Rev. Modern Phys., 1943), deriving a formula for the particle deposition velocity to a surface as a function of the particle response time. For very small particle response times, the particle deposition velocity reduces to that obtained using a quasi-steady solution of Smoluchowski's equation and for very large particle response times, the deposition velocity corresponds to that based on the transition state method (E. Wigner, Trans. Faraday Soc., 1938).