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In many areas of research it is interesting how lattices can be filled withparticles that have no nearest neighbors, or they are in limited quantities.Examples may be found in statistical physics, chemistry, materials science,discrete mathematics, etc. Using Monte Carlo (MC) simulation we study thekinetics of filling of square lattice (2D). Two complementary rules are used tofill the lattice. We study their influence on the kinetics of the process aswell as on the properties of the obtained systems. According to the first rulethe occupied sites may not share edges (nearest neighbors occupations are notpermitted). Under this condition, the maximum possible concentration is 0.5,forming a checkerboard type structure. However, we found that if the depositionis done by random selection of sites the concentration of 0.5 is inaccessibleand the maximum concentration is Cmax(2D)=0.3638 (0.0003) for 2D lattice. Ifthe lattice is 3D we find that the maximal concentration is even lowerCmax(3D)=0.326 (0.001). The second rule establishes permission to break thefirst one with certain probability 0<=p<=1, thus the occupied sites can startto share edges when p>0. In this case higher then 0.3638 concentrations areaccessible, even up to C=1. Therefore the percolation threshold Pc can bereached. Its value depends on the value of the probability p. Our modeldescribes the kinetics of formation of thin films of particles attracted by thesubstrate but repulsing each other.

Maximal Density, Kinetics of Deposition and Percolation Threshold of Loose Packed Lattices