Origin of the sub-diffusive behavior and crossover from sub-diffusive to super-diffusive dynamics near a biological surface
Abstract
Diffusion of a tagged particle near a constraining biological surface is examined numerically by modeling the surface-water interaction by an effective potential. The effective potential is assumed to be given by an asymmetric double well constrained by a repulsive surface towards r
→ 0 and unbound at large distances. The time and space dependent probability distribution P(r,t) of the underlying Smoluchowski equation is solved by using the Crank–Nicholson method. The mean square displacement shows a transition from sub-diffusive (exponent α
≈ 0.46) to a super-diffusive (exponent α
≈ 1.75) behavior with time and ultimately to diffusive dynamics. The decay of self intermediate scattering function (Fs(k,t)) is non-exponential in general and shows a power law behavior at the intermediate time. Such features have been observed in several recent computer simulation studies on the dynamics of water in