Brownian escape and force-driven transport through entropic barriers:Particle size effect

Brownian escape from a spherical cavity through small holes and force-driven transport through periodic spherical cavities for finite-size particles have been investigated by Brownian dynamic simulations and scaling analysis. The mean first passage time and force-driven mobility are obtained as a function of particle diameter a , hole radius R H , cavity radius R C , and external field strength. In the absence of external field, the escape rate is proportional to the exit effect, ( R H ∕ R C ) ( 1 − a ∕ 2 R H ) 3 ∕ 2 . In weak fields, Brownian diffusion is still dominant and the migration is controlled by the exit effect. Therefore, smaller particles migrate faster than larger ones. In this limit the relation between Brownian escape and force-driven transport can be established by the generalized Einstein-Smoluchowski relation. As the field strength is strong enough, the mobility becomes field dependent and grows with increasing field strength. As a result, the size selectivity diminishes.