# Lamplighter model of a random copolymer adsorption on a line

### L. I. Nazarov 1 S. K. Nechaev 2, 3 M. V. Tamm 4, 5

#### Condensed Matter Physics, Institute for Condensed Matter Physics, 2014, 17, pp.33002

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.

• 1. Institute of Mining, Siberian Branch
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. P. N. Lebedev Physical Institute
• 4. Physics Department
• 5. Department of Applied Mathematics