Polymers grafted to porous membranes

TL;DR

This paper investigates how flexible polymers grafted to porous membranes behave in different solvent conditions, revealing distinct penetration and localization behaviors with specific scaling laws.

Contribution

It provides new insights into polymer-membrane interactions, especially the effects of solvent quality on polymer penetration and localization, with derived scaling laws for different solvent regimes.

Findings

Polymers in good solvent can penetrate the membrane with a finite average number of crossings.

In poor solvent, the polymer tends to stay on one side of the membrane for large N.

Scaling laws are established for good and theta solvents, based on random walk behavior.

Abstract

We study a single flexible chain molecule grafted to a membrane which has pores of size slightly larger than the monomer size. On both sides of the membrane there is the same solvent. When this solvent is good, i.e. when the polymer is described by a self avoiding walk, it can fairly easily penetrate the membrane, so that the average number of membrane crossings tends, for chain length $N\to\infty$, to a positive constant. The average numbers of monomers on either side of the membrane diverges in this limit, although their ratio becomes infinite. For a poor solvent, in contrast, the entire polymer is located, for large $N$, on one side of the membrane. For good and for theta solvents (ideal polymers) we find scaling laws, whose exponents can in the latter case be easily understood from the behaviour of random walks.