Classical Nucleation Theory — Critical Droplet

CNT predicts the free energy barrier ΔG(r) = 4πr²γ − (4/3)πr³|Δμ|/v_m, where γ is surface tension and Δμ is the chemical potential difference. The critical radius r* = 2γv_m/|Δμ| is the unstable equilibrium — droplets above r* grow, below shrink.

Parameters

Surface tension γ 1.0 Supersaturation |Δμ| 0.5 Temperature kT 1.0 Mol. vol. v_m 1.0

Critical values

r*: —

ΔG*: —

Rate ∝ e^(−ΔG*/kT): —

Green curve = ΔG(r)
Dots = stochastic droplets
Below r*: shrink (metastable)
Above r*: grow (stable)