Brownian dynamics simulation study of self-diffusion of a charged particle in swollen counter-charged hydrogel modeled as cubic lattice

The tracer diffusion of a charged particle in an oppositely charged cubic lattice as a simplest model of charged hydrogel was studied by a Brownian dynamics simulation. The effect of the electrostatic attractive interaction between the tracer particle and the cubic lattice on the self-diffusion coefficient was mainly discussed, when the mesh size of the cubic lattice was sufficiently larger than the diameter of the particle. The charge density of the cubic lattice structure and the electrolyte concentration in the solvent were varied. The electrostatic force acting on the tracer particle was calculated using the potential screened by an electric double layer. The self-diffusion coefficient of the tracer particle significantly decreases as the charge density of the cubic lattice increases, while the increase in the electrolyte concentration in the solvent induces the disappearance of the effect of electrostatic attractive interaction on the self-diffusion coefficient, resulting into the asymptotical behavior to those observed in the non-charged cubic lattice. 2-Order reduction in the self-diffusion coefficient was obtained in this simulation and this shows the applicability of the control of diffusivity of ionic solutes in the swollen hydrogel by means of introducing ionic species covalently into the hydrogels. In the spatial distribution of the probability density of the charged tracer particle, the stochastic path along which the tracer particle tends to move was observed in the charged cubic lattice, which is caused by electrostatic potentials. The reduction of the self-diffusion coefficient in the charged cubic lattice is due to the transient entrapment at the point of local minimum of potential energy inside the stochastic paths.