This work discusses numerical studies of the barrier properties of k-mer packings by 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 quadratic 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.
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