Polymer Brush — Alexander-de Gennes Theory

Chain length N: 50 Grafting density σ: 0.30 Compression D/L: 1.00 Animate Compression

Alexander-de Gennes brush: L ~ N·σ^{1/3} (brush height). Density profile c(z) ~ (1−z/L)^{3/4}. Compression by surface at D < L costs osmotic free energy F/A ~ kT/b³ · σ^{5/4} · [(L/D)^{5/4} + (D/L)^{7/4}] — the basis of steric colloidal stabilization.