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 -Delta S similar to (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].