Random sequential adsorption with two components: asymptotic analysis and finite size effects

Reeve, Louise; Wattis, Jonathan A.D.

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.

Citation

Reeve, L., & Wattis, J. A. (2015). Random sequential adsorption with two components: asymptotic analysis and finite size effects. Journal of Physics A: Mathematical and Theoretical, 48(23), Article 235001. https://doi.org/10.1088/1751-8113/48/23/235001

• Journal Article Type: Article
• Publication Date: May 21, 2015
• Deposit Date: Jul 3, 2015
• Publicly Available Date: Jul 3, 2015
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 48
• Issue: 23
• Article Number: 235001
• DOI: https://doi.org/10.1088/1751-8113/48/23/235001
• Keywords: Random sequential adsorption, asymptotic analysis, recurrence relations
• Public URL: https://nottingham-repository.worktribe.com/output/751787
• Publisher URL: http://iopscience.iop.org/1751-8121/48/23/235001
• Additional Information: This is an author-created, un-copyedited version of an article published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at doi: 10.1088/1751-8113/48/23/235001.; Reeve L and Wattis JAD 2015 Random sequential adsorption with two components: asymptotic analysis and finite size effects. Phys. A: Math. Theor. 48 235001