Polymer Chain Adsorption on a Solid Surface: Scaling Arguments and Computer Simulations

TL;DR

This study combines scaling arguments and computer simulations to analyze polymer adsorption phase transitions and kinetics on solid surfaces, focusing on copolymer structures and their critical behavior.

Contribution

It introduces a comprehensive approach using scaling theory and numerical simulations to predict polymer adsorption behavior and kinetics, including analytic expressions for structural statistics.

Findings

Phase diagrams for adsorption thresholds derived from scaling.

Analytic expressions for adsorbed segments and structural distributions.

Good agreement between theory, simulations, and Monte Carlo results.

Abstract

We examine the phase transition of polymer adsorption as well as the underlying kinetics of polymer binding from dilute solutions on a structureless solid surface. The emphasis is put on the properties of regular multiblock copolymers, characterized by block size M and total length N as well as on random copolymers with quenched composition p of sticky and neutral segments. The macromolecules are modeled as coarse-grained bead-spring chains subject to a short-ranged surface adhesive potential. Phase diagrams, showing the variation of the critical threshold for single chain adsorption in terms of M and p are derived from scaling considerations in agreement with results from computer experiment. Using both scaling analysis and numerical data from solving a system of coupled Master equations, we demonstrate that the phase behavior at criticality, and the adsorption kinetics may be adequately predicted and understood, in agreement with the results of extensive Monte Carlo simulations. Derived analytic expressions for the mean fraction of adsorbed segments as well as for Probability Distribution Functions of the various structural building blocks (i.e., trains, loops, tails) at time t during the chain attachment process are in good agreement with our numeric experiments and provide insight into the mechanism of polymer adsorption.