A thermodynamic analysis of the hydrogen ion titration of micelles

Abstract

A thermodynamic analysis of hydrogen ion titration is presented for association colloids with particular emphasis on surfactant micelles. When a particular type of the micellar Gibbs–Duhem relation (MGD), α M dμ I +(1−α M ) dμ N =0 [ α M: the degree of ionization of micelles; μ I, μ N: chemical potentials of ionized and nonionized species], holds, the free energy change accompanying the ionization of the micelle G ex can be evaluated from the titration data in the same manner as for covalently bonded colloids such as linear polyions. In the case where the regular solution approximation is valid for mixed micelles, the titration curve should be a straight line with a slope yielding the interaction parameter, and G ex is given as a function of α M 2. For dodecyldimethylamine oxide micelles for which the MGD relation has been shown to hold, values of the calculated electrostatic free energy G el were close to but significantly greater than experimental G ex values when the former were calculated on the basis of the Poisson–Boltzmann equation for either a sphere or a plate with smeared charges in a salt solution of infinite volume. When the critical micelle concentration (cmc) data are combined with the hydrogen ion titration data, we obtain a criterion to judge whether the above MGD relation holds or not. When the MGD relation holds, the monomer concentration C 1 can be evaluated from the hydrogen ion titration. For most cases examined, the C 1/ C 1( α M=0) from the titration agrees well with cmc/cmc( α M=0), suggesting cmc= C 1 above the cmc. For tetradecyldimethylamine oxide, the MGD relation does not hold in the range of low ionic strength and even at 0.1 M NaCl it has been found that C 1/ C 1( α M=0)<cmc/cmc( α M=0), due probably to enormous micelle growth.