Kinetics of copolymer localization at a selective liquid-liquid interface

TL;DR

This paper develops a scaling theory for the kinetics of block-copolymer localization at a liquid-liquid interface, predicting different relaxation times for Rouse and Zimm dynamics, and validates these predictions with simulations.

Contribution

It introduces a simple analytic scaling model for copolymer localization kinetics at interfaces, distinguishing Rouse and Zimm dynamics, and compares predictions with Monte Carlo simulations.

Findings

Rouse dynamics predicts faster perpendicular flattening than parallel.

Scaling laws for relaxation times depend on block size and chain length.

Simulation results agree with the theoretical scaling predictions.

Abstract

The localization kinetics of a regular block-copolymer of total length $N$ and block size $M$ at a selective liquid-liquid interface is studied in the limit of strong segregation between hydrophobic and polar segments in the chain. We propose a simple analytic theory based on scaling arguments which describes the relaxation of the initial coil into a flat-shaped layer for the cases of both Rouse and Zimm dynamics. For Rouse dynamics the characteristic times for attaining equilibrium values of the gyration radius components perpendicular and parallel to the interface are predicted to scale with block length $M$ and chain length $N$ 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 characteristic coil flattening time is predicted to scale with block size as $\propto M$. Since typically $N\gg M$ for multiblock copolymers, our results suggest that the flattening dynamics proceeds faster perpendicular rather than parallel to the interface, in contrast to the case of Zimm dynamics where the two components relax with comparable rate, and proceed considerably slower than in the Rouse case. We also demonstrate that, in the case of Rouse dynamics, these scaling predictions agree well with the results of Monte Carlo simulations of the localization dynamics. A comparison to the localization dynamics of {\em random} copolymers is also carried out.