Thermal Behavior of Critical Micelle Concentration from the Standpoint of Flory-Huggins Model

Abstract

Temperature dependence of the critical micelle concentration (CMC), x CMC, in micellization can be described by ln x CMC = A + BT + C lnT + D/T, which has been derived statistical-mechanically. Here A, B, C, and D are fitting parameters. The equation fits the CMC data better than conventionally used polynomial equations of temperature. Moreover, it yields the unique(exponent) value of 2 when the CMC is expressed in a power-law form. This finding is quite significant, because it may point to the universality of the thermal behavior of CMC. Hence, in this article, the nature of the equation ln x CMC = A + BT + C lnT + D/T is examined from a lattice-theory point of view through the Flory-Huggins model. It is found that a linear behavior of heat capacity change of micellization is responsible for the CMC equation of temperature.