Computer simulation studies of anomalous diffusion in gels: Structural properties and probe-size dependence

Abstract

We have carried out simulations of particle diffusion through polyacrylamide gel networks. The model structures were built on a diamond lattice, in a simulation box with periodic boundary conditions. The method of structure generation consists of a random distribution of knots on the lattice and interconnection between randomly chosen pairs of knots. The structures generated by this procedure approximate the topology of real polymer gels. Parameters that control the distance between knots and the degree of stretching of the chain permit us to simulate a polyacrylamide system in which the concentration of species as well as the degree of crosslinking can be compared to realistic gels as prepared by the available experimental procedures. These structures were geometrically characterized by the analysis of the pore size distribution and excluded volume. The structures thus generated are used as model networks for Monte Carlo studies of the diffusion of hard spheres in the restricted geometry. Modeling the deviations from the normal diffusion behavior as a purely geometrical phenomenon, these simulations can give us insights into the factors which lead to anomalous diffusion in gel-like systems. In these simulations a sphere of variable radius is allowed to perform an off-lattice random walk through the space between the generated structures, which are assumed to be rigid. It will be shown that the study of the influence of tracer size on diffusion is complementary to the study of the influence of obstacle concentration on the diffusion of monodispersed particles. While the latter method can give us information about the fractal nature of the internetwork space the former method provides information about the fractal nature of the network and the connectivity of the internetwork space.

Brownian Dynamics Simulation of Self-Diffusion of Ionic Large Solute Molecule in Modeled Polyelectrolyte Gel

“…This indicates that as far as the self-diffusion in the short time scale is concerned, the effect of the interaction between the tracer particle and the model polymer network is insignificant. In the intermediate time scale, the slopes of the curves deviate from unity, which is often referred to as "anomalous diffusion" [5,6]. In the long time scale, all the slopes shown in Fig.…”

“…The algorithm to move the tracer particle interacting with the polymer network through the hardcore potential can be found in Ref. [4], which is a modification of the method employed by Netz et al [5,6].…”

New insights into diffusion in 3D crowded media by Monte Carlo simulations: effect of size, mobility and spatial distribution of obstacles

“…For example, Netz and Dorfmuller 42 performed a Monte Carlo study of the diffusion of hard spheres in a restricted geometry, which give us insights into the factors that lead to anomalous diffusion, showing that the influence of tracer size is complementary to the influence of obstacle concentration on the diffusion processes.…”

Computer Simulations of the Dynamic Properties of Methane in a Model Silica Gel

“…The time dependence of the MSD is different at different periods of time. Three different time regimes have been distinguished by analyzing the movement of the tracer from the time dependence of the correlation function of the scattered-light intensity [18,19]: (i) the diffusion process is normal at short times, (ii) becomes anomalous at moderate times and (iii) returns to normal for large delay times. Normal diffusion assumes here that time dependence of the fluid molecule dynamics is subject to the law of deterministic motion (Newtonian dynamics) on the initial ballistic phase and satisfies the Fick's second law and isotropy (Euclidean dynamics) on a long time scale.…”