Theoretical investigation on the conformation of polymer brushes in mixtures of binary solvents

Polymer brushes are extensively used in various applications, such as antifouling coatings and biomedical sensors. Mixed solvents entail versatile regulations on the conformation of polymer brushes. The understanding of the conformation of polymer brushes in mixtures of two solvents, however, is far from mature. In this work, we develop a self-consistent field (SCF) theory and an Alexander-de Gennes (A-dG) theory to examine the chain conformation of polymer brushes in mixtures of two miscible solvents. We systematically investigate how the Flory-Huggins interaction parameters among the three components, the composition of the mixed solvent, the grafting density, and the chain length, influence the brush height and the density profiles of various species. Our calculations exhibit many non-trivial phenomena, such as the collapse of brushes in mixtures of two good solvents and the worsening of solvent quality when adding a good solvent to a poor solvent. The physical mechanisms of these intriguing phenomena are rationalized via the interplay among the chain conformation entropy, the mixing entropy of the two solvents, and the competition in the interactions among the three species. Quantitative comparison between the SCF and the A-dG theories demonstrates that the latter theory can qualitatively capture the variation trends of the brush height and the average concentrations of different species, while the former theory can provide more detailed descriptions on the density profiles of various species in the brush. Our results here not only exhibit the richness and complexity of polymer brushes in mixed solvents but also provide valuable principles for the rational design of stimuli-responsive brushes.