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

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).