Nucleation & Growth

Physics: Classical nucleation theory (Gibbs 1876): ΔG(r) = 4πr²γ − (4π/3)r³·ΔG_v; surface term competes with bulk driving force ΔG_v = (k_BT/v_m)·ln(S). Maximum at critical radius r* = 2γ/ΔG_v; barrier ΔG* = 16πγ³/(3ΔG_v²) = (4/3)πr*²γ. Nucleation rate J = A·exp(−ΔG*/k_BT) — highly sensitive to supersaturation. Heterogeneous nucleation on substrates reduces barrier by factor f(θ) = (2+cosθ)(1−cosθ)²/4 where θ is contact angle. Wilson cloud chamber detects ionizing particles by triggering nucleation. Spinodal decomposition: no barrier, spontaneous phase separation when ∂²G/∂c² < 0.