(34c) Diffusion and Percolation in Systems Exhibiting Dynamic Disorder: Simulation and Scaling Results

The analysis of diffusion through disordered structures is a problem of widespread interest to many areas of science and engineering, and many of the most successful theories in this area have used percolation concepts. In our presentation we will discuss a novel approach for analyzing the problem of diffusion through heterogeneous network structures exhibiting dynamical disorder. Potential areas of application of this work include a variety of problems including analyzing ionic conduction in polymers, electron-hole recombination in amorphous semiconductors, polymer gelation, turbulent diffusion, the efficacy of corrosion-resistant metal-organic coatings, and ionic conductance through supercritical microemulsion mixtures.

We describe how we use the Ising model paradigm, in conjunction with kinetic Monte Carlo simulations, for generating dynamical network configurations that are consistent with Kawasaki lattice dynamics (i.e. constant conducting-site density). At any point during the simulations conducting-site pathways (with density) are taken to be given by the network of up spins, using the Ising terminology, with the non-conducting-sites represented by the network of down spins.

In addition to the simulation results we provide a theoretical analysis of the problem by firstly providing a rationale as to why we partition the net displacement of the RWs throughout the network into two terms representing: (1) the contribution to transport by ?hopping' through nearest neighbor conducting sites (the so-called ?percolation' mechanism) and (2) the self-diffusion of the site itself on which the RW finds itself at any given point in time, respectively. The ?percolation- diffusion' component exhibits non-trivial scaling behavior, with a new scaling exponent that describes the cage trapping time of the RWs in conducting site clusters. We show how the value of this exponent can be found from computer simulation results and compare our results to conductance measurements in supercritical microemulsions and recently published diffusion data taken in dense colloidal suspensions.