Surfactant Self-Assembly & Micelle Formation
Critical micelle concentration, size distribution, and phase behavior
CMC: — | Aggregation number: —
Above the critical micelle concentration (CMC), amphiphilic molecules aggregate into micelles.
Free energy: ΔG_mic = kT ln(CMC). Shorter tails → higher CMC. Each additional CH₂ group reduces CMC ~3×.
The Nagarajan-Ruckenstein model gives optimal aggregation number N_agg ∝ n².
Packing parameter p = v/(a₀·l): p<1/3 → spherical, 1/3–1/2 → cylindrical, ~1/2 → bilayer.