Thermodynamic Study of the Protonation of Dimethyldodecylamine N-Oxide Micelles in Aqueous Solution at 298 K. Establishment of a Theoretical Relationship Linking Critical Micelle Concentrations and pH Virginie Lair, † Sabbah Bouguerra, ‡ Mireille Turmine,* ,† and Pierre Letellier † Laboratoire d’Electrochimie et Chimie Analytique, UMR 7575, Energe ´ tique et Re ´ activite ´ aux Interfaces, Universite ´ Pierre et Marie Curie, case 39, 4 place Jussieu, 75252 Paris cedex 05, France, and Laboratoire Eau et Technologies membranaires, INRST, BP 95-2050 Hammam-lif, Tunis, Tunisie Received April 13, 2004. In Final Form: June 14, 2004 Dodecyldimethylamine N-oxide (DDAO) is a zwitterionic surfactant with acid-base properties. The proton dissociation constant of this surfactant was determined by a novel potentiometric method at “controlled chemical potential” of the proton using a classical pH-glass electrode. When the DDAO was in its monomeric form, the pKa was about 5, consistent with the value commonly reported in the literature. However, a unique proton dissociation constant specific to the micellar form of this surfactant could not be obtained. We found that the acid-base behavior of the DDAO micelles depended on their environment. Indeed, we were able to establish thermodynamic relations linking the critical micellar concentration to the degree of protonation of the micelles. The experimental values were in good accordance with this model. I. Introduction Dodecyldimethylamine N-oxide (DDAO) is a zwitteri- onic surfactant which forms neutral micelles at pH above 7 or cationic micelles at low pH. It also has the ability of being protonated in water, in an equilibrated way, to give the cationic species, DDAOH + . There have been numerous studies reported describing the acid-base properties of DDAO and its homologues which have alkyl chains of different lengths, both as monomers and aggregate forms and giving a variation of critical micelle concentration (cmc) according to the pH. 1-18 In all these works, it is assumed that the acid and basic monomers are linked in a classical proton exchange equilibrium characterized by a proton dissociation constant of the monomer, K a , equal to 4.95 in water at 298 K. 3 However, the properties of the aggregate forms are not always described in the same way. Maeda 14 analyzed the proto- nation curve of DDAO at concentrations above the cmc and concluded that the micellized DDAOH + behaves as weak monoacid in equilibrium with its neutral conjugate base, DDAO, also in an aggregated form, with a pK a of 5.95. In our opinion, there are several reasons why the notion of a pK a is not appropriate for this surfactant in its micellar form. The first is that the protonation of an aggregate of neutral surfactant leads to the continuous creation of mixed micelles of variable charge and of different stabilities according to the acidity of the medium. The values of standard chemical potentials of species constituting the aggregates, DDAO and DDAOH + , depend on the degree of ionization of the micelle and, therefore, on the acidity of the medium. Consequently, the acid- base equilibrium of aggregated species cannot be described by a single value of pK a independent of the pH of the medium. Rathman et al. 5 made this point and showed that there is no need to introduce an additional equilibrium constant for the protonation of the micellar surfactant because the surfactant in the micelle is in equilibrium with the amphiphilic monomer. The second reason is linked to the application of thermodynamic rules. Values of cmc of a surfactant susceptible to protonation depend directly on the degree of protonation of the micelle (see below). All published measurements of the cmc of DDAO aggregates 5,14,19 show a minimum for pH values close to 5. This phenomenon is not compatible with there being a single constant equi- * Email: turmine@ccr.jussieu.fr. † Laboratoire d’Electrochimie et Chimie Analytique, UMR 7575, Energe ´tique et Re ´activite ´ aux Interfaces, Universite ´ Pierre et Marie Curie. ‡ Laboratoire Eau et Technologies membranaires, INRST. (1) Kolp, D. G.; Laughlin, R. G.; Krause, F. P.; Zimmerer, R. E. J. Phys. Chem. 1963, 67, 51. (2) Herrmann, K. W. J. Phys. Chem. 1964, 68, 1540. (3) Tokiwa, F.; Ohki, K. J. Phys. Chem. 1966, 70, 3437. (4) Maeda, H.; Tsunoda, M.; Ikeda, S. J. Phys. Chem. 1974, 78, 1086. (5) Rathman, J. F.; Christian, S. D. Langmuir 1990, 6, 391. (6) Zhang, H.; Dubin, P. L.; Kaplan, J. I. Langmuir 1991, 7, 2103. 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(19) Peyre, V.; Baillet, S.; Letellier, P. Anal. Chem. 2000, 72, 2377. DDAOH + ) DDAO + H + 8490 Langmuir 2004, 20, 8490-8495 10.1021/la049067g CCC: $27.50 © 2004 American Chemical Society Published on Web 08/26/2004