Critical Micelle Concentration Expressed in Molarity or Mole Fraction and Its Relation to Thermodynamic Potentials

몰농도 또는 몰분율로 표시되는 임계 미셀 농도와 열역학적 포텐셜과의 관계

The critical micelle concentration (CMC) at which micelles start to form from a surfactant solution is usually measured in terms of conventional concentration units. However, the thermodynamic potentials are expressed in terms of mole fraction $X_{CMC}$ and $X_{CMC}$ cannot be directly measured experimentally. The Gibbs free energy, ${\Delta}G^{\ast}_{mic}$, in particular is related to $X_{CMC}$ through ${\Delta}G^{\ast}_{mic}$ = $RTlnX_{CMC}$. When it comes to CMC, the molar CMC, $C_{CMC}$, differs only by the proportionality $C^{-1}_{w}$ with $C_{w}$ being the molarity of water. Hence, $C_{CMC}$ is found to be a proper representation of CMC. However, in calculation of ${\Delta}G^{\ast}_{mic}$ and other thermodynamic potentials from the CMC, $X_{CMC}$ or $C_{CMC}/C_{w}$ should be used.