Barrier properties of -mer packings

This work discusses numerical studies of the barrier properties of k -mer packings by the Monte Carlo method. The studied variants of regular and non-regular arrangements on a square lattice included models of random sequential adsorption (RSA) and random deposition (RD). The discrete problem of diffusion through the bonds of a square lattice was considered. The k -mers were perfectly oriented perpendicular to the diffusion direction and blocked certain fraction of bonds f b against diffusion. The barrier efficiency was estimated by calculation of the ratio D / D o where D is diffusion coefficient in direction perpendicular to the orientation of k -mers and D o is the same value for diffusion on the square lattice without blocked bonds, i.e., at f b = 0 . The value of k varied from 1 to 512 and different lattice sizes up to L = 8192 lattice units were used. For dense packings ( p = 1 ), the obtained D / D o versus f b dependences deviated from the theoretical prediction of effective medium (EM) theory and deviation was the most obvious for the regular non-staggered arrangement. For loose RSA and RD packings, the percolation like-behavior of D / D o with threshold at f b = p ∞ was observed and the data evidenced that their barrier properties at large values of k may be more effective than those of some dense packings. Such anomalous behavior can reflect the details of k -mer spatial organization (aggregation) and structure of pores in RD and RSA packings. The contradictions between simulation data and predictions of EM theory were also discussed.