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 one-dimensional 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.
Highlights
Random Sequential Adsorption (RSA) is a model that has been of interest since the 1939 paper by Flory [11] and 1958 paper by Renyi [24]
Due to its many applications, random sequential adsorption (RSA) is of wide interest in many fields of science, including physics [5, 7, 16], biology [8], pharmacy [20, 23] chemistry [1, 17] and computer science [21]
The one-polymer formulation of RSA was first proposed by Renyi [24]; in this model, the substrate is continuous and the expected density of cars parked on a street of infinite length is 74.75979%
Summary
Random Sequential Adsorption (RSA) is a model that has been of interest since the 1939 paper by Flory [11] and 1958 paper by Renyi [24]. After deriving the pdes for the evolution of the gap length distribution, they present numerical results showing the total coverage against the probability of the shorter polymer binding. This is paper is the closest in spirit to the work we present below in Sections 2 and 3. By considering exclusion circles around each adsorbed disc, they deriving odes for the coverage due to each size of disc These yield the approximate behaviour of the system in the jamming limit, and in the case of the small discs becoming vanishingly small, the results are highly accurate.
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