# Does the Topology of Polymer Brushes Determine Their (Vapor-)Solvation?

## TL;DR

This study investigates whether the structure of polymer brushes affects their swelling in vapor, using simulations to compare different brush topologies.

## Contribution

The study clarifies how topology influences swelling by showing that it depends on the grafting density definition.

## Key findings

- Equal or unequal swelling depends on how grafting density is defined.
- Suitably defined grafting density leads to topology-independent swelling.
- Flory–Huggins theory can describe swelling for all studied topologies.

## Abstract

When the topology of polymer brushes is changed from
linear to
cyclic or looped, many of the brush properties will be improved. Yet,
whether such a topology variation also affects the (vapor-)­solvation
and swelling of brushes has remained unclear. In fact, in a recent
publication, Vagias and co-workers (Macromolecular Rapid Communications
2023, 44 (9), 2300035) reported an
unequal swelling for linear and cyclic brushes and challenged theoreticians
to develop a new Flory–Huggins theory that includes topology
effects. In this letter, we address this challenge and employ molecular
dynamics simulations to study the vapor swelling of linear, looped,
and cyclic brushes. We find that the emergence of equal or unequal
swelling for different topologies depends on the definition of the
grafting density that is kept constant in the comparison. When suitably
defined, the degree of swelling is independent of the topology, and
the Flory–Huggins theory for brushes will describe brush swelling
for all topologies in the present study.