When polymers are densely grafted to a surface, they stretch away (brush regime) due to
excluded-volume repulsion between chains. The brush height scales as:
H ~ N·σ^(1/3)·b^(5/3)·v^(1/3)
where N = degree of polymerization, σ = grafting density, v = excluded volume.
The parabolic density profile predicted by self-consistent field theory (SCF):
φ(z) = φ₀[1 − (z/H)²]
(Milner–Witten–Cates 1988). Poor solvent (χ > 0) causes collapse; good solvent (χ < 0) swells chains.
Each chain performs a MC random walk with excluded-volume repulsion.