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 Crank-Nicholson
method. The mean square displacement shows a transition from sub-diffusive
(exponent α∼ 0.43) to a super-diffusive (exponent α∼
1.75) behavior with time and ultimately to a 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 dynamics of
water in protein and micellar hydration shell. The present analysis provides a
simple microscopic explanation for the transition from the sub-diffusivity and
super-diffusivity. {\em The super-diffusive behavior is due to escape from the
well near the surface and the sub-diffusive behavior is due to return of
quasi-free molecules to form the bound state again, after the initial escape}Comment: 5 pages including 5 figures and 1 table. Submitted to PhysChemCom
