Computer simulation studies of diffusion in gels: Model structures

Abstract

We have investigated particle diffusion through different obstacle geometries by computer simulations. The model structures used in this work — randomly placed point obstacles and cage-like structures — were chosen with the aim of represent a broad range of geometrical structures similar to gels and in order to be compared with our previous simulations of particle diffusion through polyacrylamide gels. The diffusion behavior was studied as a function of tracer size and obstacle concentration. The isomorphism between the diffusion of finite-sized tracers and the diffusion of point tracers in the presence of expanded obstacles was applied. Only hard-sphere interactions of the tracer with the immobile obstacles were considered and the theoretical description was made in terms of theory of the obstruction effect. In the case of randomly placed point obstacles an analytical expression for the dependence of the diffusion coefficient on tracer radius and obstacle concentration, applying the model of spherical cells, could be deduced. The same description was applied numerically to the other model systems. Up to moderatly high fractions of excluded volume this description was found to be successful. For very high fractions of excluded volume — higher concentrations or larger tracers — the validity of Fick’s second equation for describing diffusion breaks down and anomalous diffusion was found. The anomalous diffusion exponent diverges as the tracer size becomes comparable to the size of the pores. Analysis of the trajectory of tracers in the cases where an anomalous diffusion takes place shows a Levy-flight-like characteristic.