Abstract
The recombination of nearest neighbors in a condensed matrix of free radicals was modeled by Jackson and Montroll as irreversible, sequential, random dimer filling of nearest-neighbor sites on an infinite, three-dimensional lattice. Here we analyze the master equations for random dimer filling recast as an infinite hierarchy of rate equations for subconfiguration probabilities using techniques involving truncation, formal density expansions (coupled with resummation), and spectral theory. A detailed analysis for the cubic lattice case produces, e.g., estimates for the fraction of isolated empty sites (i.e., free radicals) at saturation. We also consider the effect of a stochastically specified distribution of nonadsorptive sites (i.e., inert dilutents).
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Evans, J.W., Nord, R.S. Random dimer filling of lattices: Three-dimensional application to free radical recombination kinetics. J Stat Phys 38, 681–705 (1985). https://doi.org/10.1007/BF01010485
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DOI: https://doi.org/10.1007/BF01010485