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

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 (<i>Macromolecular Rapid Communications</i> <b>2023</b>, <i>44</i> (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.