Quaternary mutual diffusion coefficients for aqueous solutions of a cationic–anionic mixed surfactant from moments analysis of Taylor dispersion profiles

Abstract

Taylor dispersion is used to measure mutual diffusion in aqueous solutions of dodecyltrimethylammonium bromide (DTAB) + sodium octanoate (NaOct), a cationic–anionic mixed surfactant. Diffusion of the four different constituent ions (DTA⁺, Br⁻, Na⁺, Oct⁻) constrained only by electroneutrality produces three independent solute fluxes. Mutual diffusion in these solutions is therefore a quaternary process described by nine D_ik coefficients. Injecting excess DTAB or NaOct into DTAB + NaOct carrier solutions produces remarkable refractive-index profiles with three maxima and two minima. Least-squares analysis of these profiles failed to converge, prompting the development of a procedure for the evaluation of quaternary D_ik coefficients from the heights, areas, first moments, and second moments of dispersion profiles. The reported D_ik coefficients describe the coupled diffusion of DTAB(1) + NaOct(2) + NaBr(3) components in solutions containing 40 mmol dm⁻³ total surfactant at 25 °C and four different DTAB:NaOct ratios. The results show that the unusual profile shapes are caused by strongly coupled diffusion, as indicated by large negative D₁₂, D₂₁ values and large positive D₃₂, D₃₁ values which exceed the magnitude of main-coefficients D₁₁ and D₂₂. Binary mutual diffusion coefficients for aqueous DTAB solutions and critical micelle concentration for DTAB + NaOct solutions are also reported.