Effect of temperature on the salt-induced sphere–rod transition of micelles of dodecyltrimethylammonium bromide in aqueous NaBr solutions

Abstract

The density of aqueous NaBr solutions of dodecyltrimethylammonium bromide (C₁₂TAB) and ultrasound velocity in them have been measured as a function of surfactant concentration at NaBr concentrations 0–5.00 mol kg^–1 and at temperatures 15–50 °C. Their adiabatic compressibility has been calculated by means of the Laplace equation. Based on a phenomenological treatment giving the density and the adiabatic compressibility of aqueous solutions of surfactant as a function of surfactant concentration, the apparent adiabatic compressibility of the surfactant in the form of spherical and rod-like micelles has been derived at different NaBr concentrations and at different temperatures.

The apparent molar volume of the surfactant in the rod-like micelle is slightly larger than that in the spherical micelle at each temperature. The apparent adiabatic compressibility of the surfactant in the spherical micelle initially decreases upon addition of a small amount of NaBr, and then it remains constant or slightly increases with further addition of NaBr. The apparent adiabatic compressibility of the surfactant in the rod-like micelle increases with increasing NaBr concentration at each temperature, with an abrupt change at the threshold.

The threshold NaBr concentration for the sphere–rod transition of the surfactant can be determined from variation of the apparent adiabatic compressibility of the surfactant in the micellar forms with NaBr concentration. It increases with rising temperature and changes from 1.64 mol kg^–1 at 20 °C to 2.86 mol kg^–1 at 45 °C.

The initiation of the sphere–rod transition of micelles is attributed to a change in the hydration state of the surfactant with the NaBr concentration, and the threshold NaBr concentration is defined by the chemical potential of water in solution, with which hydration water on spherical and rod–like micelles are in equilibrium and where the hydration water has an equal escaping tendency on both micelles.