Dual percolation threshold in two-dimensional microporous media

We have constructed a lattice model to probe the two-dimensional (2D) microporosity of intercalated layered systems of the type ${\mathit{A}}_{1\mathrm{-}\mathit{x}}$${\mathit{B}}_{\mathit{x}}$L, where A and B are two types of intercalants sandwiched between host layers L. Percolation of a probe particle in this 2D microporous medium has been studied analytically and by Monte Carlo simulation. Depending on the transverse layer rigidity, which is characterized by a healing length λ, we find two ‘‘normal’’ percolation thresholds that coalesce for a particular value of λ=${\lambda }_1$. However, percolation at this point belongs to a different universality class compared with the site percolation in 2D system even though the correlations are of short range. In fact, for λ=${\lambda }_1$, the percolation is hull percolation which has been studied earlier by Saleur and Duplantier. Anomalous diffusion on these systems has also been investigated for λ=${\lambda }_1$ using analytic and simulation methods.