Copolymer adsorption kinetics at a selective liquid-liquid interface: Scaling theory and computer experiment

TL;DR

This paper develops a scaling theory and confirms via simulations how block-copolymer chains adsorb and flatten at a liquid-liquid interface, revealing different timescales for perpendicular and parallel relaxation.

Contribution

The study introduces a simple analytic scaling theory for copolymer adsorption kinetics and validates it with extensive Monte Carlo simulations.

Findings

Perpendicular relaxation time scales as M^{1+2 u}

Parallel relaxation time scales as N^2

Flattening occurs faster perpendicular to the interface

Abstract

We consider the adsorption kinetics of a regular block-copolymer of total length $N$ and block size $M$ at a selective liquid-liquid interface in the limit of strong localization. We propose a simple analytic theory based on scaling considerations which describes the relaxation of the initial coil into a flat-shaped layer. The characteristic times for attaining equilibrium values of the gyration radius components perpendicular and parallel to the interface are predicted to scale with chain length $N$ and block length $M$ as $\tau_{\perp} \propto M^{1+2\nu}$ (here $\nu\approx 0.6$ is the Flory exponent) and as $\tau_{\parallel} \propto N^2$, although initially the rate of coil flattening is expected to decrease with block size as $\propto M^{-1}$. Since typically $N\gg M$ for multiblock copolymers, our results suggest that the flattening dynamics proceeds faster perpendicular rather than parallel to the interface. We also demonstrate that these scaling predictions agree well with the results of extensive Monte Carlo simulations of the localization dynamics.