Barrier properties of k-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 fb against diffusion. The barrier efficiency was estimated by calculation of the ratio D/Do where D is diffusion coefficient in direction perpendicular to the orientation of k-mers and Do is the same value for diffusion on the square lattice without blocked bonds, i.e., at fb=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/Do versus fb 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/Do with threshold at fb=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.