First exit time of termites and random super-normal conductor networks

Numerical study of diffusion on a random-mixed-bond lattice

Diffusion on lattices with random mixed bonds in two and three dimensions is reconsidered using a random walk (RW) algorithm, which is equivalent to the master equation. In this numerical study the main focus is on the simple case of two different transition rates W(1),W(2) along bonds between sites. Although analysis of diffusion and transport on this type of disordered medium, especially for the case of one-bond pure percolation (i.e., W(1)=0 ), comprises a sizable subliterature, we exhibit additional basic results for the two-bond case: When the probability p of W(2) replacing W(1) in a lattice of W(1) bonds is below the percolation threshold p(c) , the mean square displacement r(2) is a nonlinear function of time t . A best fit to the lnr[(2) vs ln t plot is a straight line with the value of the slope varying with p,Delta,d , where Delta identical with W(2)/W(1) and d is the dimension, i.e., r(2) proportional, variant t(1+eta(p,Delta,d)) with eta>0 for Delta>1 . In other terms, all the diffusion (D identical with(r)(2)/2t proportional, variant t(eta)) is anomalous superdiffusion for p<p(c) and Delta>1 for d=2,3 . Previous work in the literature for d=2 with a different RW algorithm established an effective diffusion constant D(eff) , which was shown to scale as (p(c)-p)(1/2) . However, the anomalous nature (time dependence) of D(t) becomes manifest with an expanded regime of t , increased range of Delta , and the use of our algorithm. The nature of the superdiffusion is related to the percolation cluster geometry and Lévy walks.

Percolative Transport and Cluster Diffusion Near and Below the Percolation Threshold of a Porous Polymeric Matrix

PURPOSE

The purpose of this research was to develop a quantitative mass transport model to describe the release of a drug from a porous inert matrix dosage form near and below the percolation threshold for the system.

METHODS

Cumulative release profiles were generated for a series of tablets composed of a binary mixture of varying amounts of non-conducting (poly(vinyl stearate)) and conducting (benzoic acid) components. The porous microstructure was analyzed using re-constructed three-dimensional images of leached microtomed tablet sections. Poly(vinyl stearate) was characterized for transport properties, molecular weight and thermal properties.

RESULTS

Based on percolation theory, the binary matrix was determined to have a percolation threshold of 0.09 +/- 0.02. Transport, which could not be explained by "classical" percolation theory or surface diffusion alone, was observed below the percolation threshold for the system.

CONCLUSIONS

A model describing transport near and below the percolation threshold in matrices composed of two phases, polymer and drug, was developed. The percolation model developed accounts for diffusion within the porous structure and through the inert, insoluble polymeric amorphous regions of the matrix. The low percolation threshold and subsequently high coordination was concluded to be due to the biphasic classical porous and nonclassical polymeric diffusional transport mechanisms associated with the system studied.