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 In x(CMC) = A + BT + C InT + 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 oft 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 In x(CMC) = A + BT + C InT + 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.