Dynamic percolation in microemulsions

Abstract

We study a model for dynamic percolation relevant to the electrical conductivity of water in oil microemulsions. The charge carriers reside on percolation cluster sites and can propagate by hopping between nearest-neighbor sites. The cluster sites also undergo diffusion, so that the clusters continuously rearrange themselves. The conductivity below the percolation threshold $p_c$ is finite and, as p→$p_c$, increases as ‖$p_c$-p${\Vert }^{\mathrm{-}s̃}$ where s̃ differs from the static exponent s. In the neighborhood of $p_c$, the conductivity depends as a power law on the rate of cluster rearrangement.