Lamplighter model of a random copolymer adsorption on a line

TL;DR

This paper introduces a lamplighter model for a random copolymer adsorbing on a line, revealing self-organization and a nontrivial energy scaling behavior through a novel mapping to a lamplighter random walk.

Contribution

It presents a new model of copolymer self-packaging with quenched interactions, mapped onto a lamplighter random walk, showing unique energy scaling laws.

Findings

Energy scales as $E o N^{3/4}$ for large N.

Model demonstrates self-organization behavior.

Mapping to lamplighter random walk elucidates the process.

Abstract

We present a model of an AB-diblock random copolymer sequential self-packaging with local quenched interactions on a one-dimensional infinite sticky substrate. It is assumed that the A-A and B-B contacts are favorable, while A-B are not. The position of a newly added monomer is selected in view of the local contact energy minimization. The model demonstrates a self-organization behavior with the nontrivial dependence of the total energy, $E$ (the number of unfavorable contacts), on the number of chain monomers, $N$: $E\sim N^{3/4}$ for quenched random equally probable distribution of A- and B-monomers along the chain. The model is treated by mapping it onto the "lamplighter" random walk and the diffusion-controlled chemical reaction of $X+X\to 0$ type with the subdiffusive motion of reagents.