Flory-Rehner Polymer Gel Swelling

Equilibrium swelling via osmotic pressure vs elastic restoring force

χ (Flory param): N (chain length): ν_e (crosslink density):

Flory-Rehner theory balances the osmotic free energy of mixing (Flory-Huggins) against the elastic free energy of network stretching. Equilibrium swelling ratio Q satisfies: μ_mix + μ_el = 0, giving ln(1-φ) + φ + χφ² + ν_eV₁(φ^1/3 - φ/2) = 0. Larger N or smaller χ increases swelling.