Polymer Brush — Density Profile

End-grafted polymer chains stretch away from a surface. The Alexander-de Gennes and Milner-Witten-Cates parabolic profiles emerge from self-consistent field theory.

N (chain length): 100 sigma (grafting): 0.15 v (excluded vol): 1.0

L* = 0 | alpha = 0

Alexander (1977) / de Gennes (1980): brush height L ~ N*sigma^{1/3}*v^{1/3} (good solvent). Milner-Witten-Cates (1988) SCF: parabolic density profile phi(z) = phi_0*(1 - (z/L)^2). Real chains fluctuate around this mean-field profile.