Thermodynamics of Micellization of Ionized Surfactants: The Equivalence of Enthalpies of Micellization from Calorimetry and the Variation of Critical Micelle Points with Temperature as Exemplified for Aqueous Solutions of an Aliphatic Cationic Surfactant

There is considerable confusion on experimental and thermodynamic aspects of the formation of ionized surfactant micelles. Recent claims that the van't Hoff and calorimetric enthalpies of micellization of ionized surfactants represent different aspects of micellization are shown to be incorrect. New conductance and surface tension measurements on n-dodecyltrimethylammonium bromide (DTAB) in water and in cosolution with 0.1 M KBr over a range of temperatures are used to provide a set of critical micelle concentrations (cmc's). The molar enthalpies of micellization derived from these cmc's are compared with calorimetric enthalpies of micellization obtained from a critical survey of the literature and shown to be equivalent. This signifies that both enthalpies capture the contributions from all aspects of micellization of charged micelles. The apparent discrepancies arise from experimental problems, incorrect use of the van't Hoff equation, and failure to recognize the constraints of the Phase Rule and electroneutrality. Deficiencies in the application of the two major models of micellization, namely, the "mass-action"model and the "phase"model, are exposed. Neither model is generally valid. The van't Hoff enthalpies of micellization of DTAB in water are similar in the presence and absence of 0.1 M KBr, confirming a similar correspondence found with calorimetric enthalpies for DTAB in water and NaBr.