A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. For the Random Sequential Adsorption model, we introduce the 'availability' as a new variable corresponding to the number of available locations in which an adsorbate can be accommodated. We investigate the relation of the availability to the coverage of the adsorbent surface over time. Power law scaling between the two is obtained both through numerical simulations and analytical techniques for both one and two dimensional RSA, as well as in the case of competitive random sequential adsorption in one dimension.
Abstract. We consider the model of random sequential adsorption (RSA) in which two lengths of rod-like polymer compete for binding on a long straight rigid onedimensional substrate. We take all lengths to be discrete, assume that binding is irreversible, and short or long polymers are chosen at random with some probability. We consider both the cases where the polymers have similar lengths and when the lengths are vastly different. We use a combination of numerical simulations, computation and asymptotic analysis to study the adsorption process, specifically, analysing how competition between the two polymer lengths affects the final coverage, and how the coverage depends on the relative sizes of the two species and their relative binding rates. We find that the final coverage is always higher than in the one-species RSA, and that the highest coverage is achieved when the rate of binding of the longer polymer is higher. We find that for many binding rates and relative lengths of binding species, the coverage due to the shorter species decreases with increasing substrate length, although there is a small region of parameter space in which all coverages increase with substrate length.
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