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Polymer brushes can grow on almost any solid surface, and by design, exhibitdiverse properties and functionalities, thus they have been widely used in manyemerging applications in engineering, energy, and medicine. In particular, someapplications such as actuation, molecule release, and friction switch requirethe polymer brushes to change their heights between dry and wet states, andmaximizing such height change is critical for the optimal performance of theseapplications. While scaling laws have long been proposed to qualitativelydetermine brush heights, a theory that can quantitatively predict brush heightsand conditions for maximizing brush height change is still lacking yet isvaluable for the practical design of polymer brushes. Here, we take athermodynamic approach to formulate a polymer brush theory to calculate brushheights at various conditions of graft area, degree of polymerization (DP), andsolvent qualities. Our model consists of two parts-the freely-jointed chainmodel to describe the elasticity of brushes and the Flory-Rehner model todescribe the mixing of brushes and solvents. The calculated brush heights atboth dry and wet states fairly agree with the experimental data from theliterature. The calculated brush heights are further used to determine theconditions for the maximum brush height change. Our theory can guide the designof polymer brushes for optimal functional performance in various applicationsand also can couple with other models to describe more complex behaviors ofpolymer brushes.

A polymer brush theory for quantitative prediction of maximum height change between dry and wet states