Monte Carlo simulations of random copolymers at a selective interface

TL;DR

This paper uses Monte Carlo simulations to study how random copolymers adsorb at solvent interfaces, revealing scaling laws for their size and density related to interfacial strength.

Contribution

It introduces numerical scaling relations for copolymer adsorption at interfaces, linking size and density to interfacial selectivity strength.

Findings

Radius of gyration scales with interfacial strength as $R_{gz}=N^{ u}f( ext{function of } ext{N} ext{ and } ext{chi})$

Monomer density at the interface scales as $ ext{chi}^{2 u}$ for small $ ext{chi}$

Numerical determination of monomer densities in solvents and their dependence on distance from the interface.

Abstract

We investigate numerically using the bond--fluctuation model the adsorption of a random AB--copolymer at the interface between two solvents. From our results we infer several scaling relations: the radius of gyration of the copolymer in the direction perpendicular to the interface ($R_{gz}$) scales with $\chi$, the interfacial selectivity strength, as $R_{gz}=N^{\nu}f(\sqrt{N}\chi)$ where $\nu$ is the usual Flory exponent and $N$ is the copolymer's length; furthermore the monomer density at the interface scales as $\chi^{2\nu}$ for small $\chi$. We also determine numerically the monomer densities in the two solvents and discuss their dependence on the distance from the interface.