Adsorption Kinetics of a Single Polymer on a Solid Plane

TL;DR

This paper develops a theoretical and simulation-based model for the adsorption kinetics of a single polymer on a flat surface, revealing power-law growth of adsorbed segments and exponential train length distribution, applicable to various copolymer types.

Contribution

It introduces a unified theoretical framework combining Fokker-Planck equations and Monte Carlo simulations for polymer adsorption kinetics, including copolymer variations.

Findings

Mean adsorbed fraction grows as t^{1/(1+ u)}

Train lengths follow an exponential distribution

Model accurately predicts adsorption dynamics for different copolymer types

Abstract

We study analytically and by means of an off-lattice bead-spring dynamic Monte Carlo simulation model the adsorption kinetics of a single macromolecule on a structureless flat substrate in the regime of strong physisorption. The underlying notion of a ``stem-flower'' polymer conformation, and the related mechanism of ``zipping'' during the adsorption process are shown to lead to a Fokker-Planck equation with reflecting boundary conditions for the time-dependent probability distribution function (PDF) of the number of adsorbed monomers. The theoretical treatment predicts that the mean fraction of adsorbed segments grows with time as a power law with a power of $(1+\nu)^{-1}$ where $\nu\approx 3/5$ is the Flory exponent. The instantaneous distribution of train lengths is predicted to follow an exponential relationship. The corresponding PDFs for loops and tails are also derived. The complete solution for the time-dependent PDF of the number of adsorbed monomers is obtained numerically from the set of discrete coupled differential equations and shown to be in perfect agreement with the Monte Carlo simulation results. In addition to homopolymer adsorption, we study also regular multiblock copolymers and random copolymers, and demonstrate that their adsorption kinetics may be considered within the same theoretical model.