Entropy of Polymer Brushes in Good Solvents: A Monte Carlo Study

Entropy of polymer brushes composed of monodisperse flexible polymer chains regularly grafted on a flat substrate plane with an equal “ spacing ” is numerically studied in the good solvent limit. We consider systems of not only a free polymer brush but also a compressed polymer brush and two polymer brushes facing each other at a “ distance ”. The total number of configurations, entropy, and force are calculated for various chain lengths and graft densities by means of Monte Carlo simulations using an efficient enrichment algorithm on a simple cubic lattice. We demonstrate that the effect of excluded volume plays an essential role. We find that the entropy of a free polymer brush falls as −Δ S ∼ ( spacing ) -2.4±0.1, while the entropy of a compressed polymer brush and two polymer brushes agrees very well with the analytical SCF theory by Milner, Witten, and Cates [ Macromolecules 1988, 22, 2610−2619]. The resulting interlayer force agrees also excellently well with the recent experiments by Yamamoto et al. [ Macromolecules 2000, 33, 5602−5607].