A comparison of diffusion coefficients for ternary mixed micelle solutions measured by macroscopic gradient and dynamic light scattering techniques

Abstract

Taylor dispersion is used to measure ternary mutual diffusion coefficients (D_ik) for aqueous solutions of decylsulfobetaine (SB10) (1) + dodecylsulfobetaine (SB12) (2), SB10 (1) + SB14 (2), and SB12 (1) + SB14 (2) mixed zwitterionic micelles. Cross-coefficient D₂₁ for the coupled flow of surfactant 1 produced by a concentration gradient in surfactant 2 is relatively small for these solutions, but D₁₂ reaches values as large as the main D_ii coefficients. The results are interpreted by using the equation D_ik = ∂(C_iD_i*)/∂C_k to relate the ternary mutual diffusion coefficients to the concentration-weighted average diffusion coefficients D_i* of the micellar and free-monomer forms of the surfactants. The macroscopic-gradient Taylor measurements are compared with diffusion coefficients measured by dynamic light scattering (DLS), which monitors microscopic concentration fluctuations. At most compositions, the intensity autocorrelation function G(τ) is a single exponential decay in D⁽²⁾, the smaller eigenvalue of the mutual diffusion coefficient matrix. A contribution from D⁽¹⁾ is identified at high solute fractions of surfactant 1. The DLS results are consistent with contributions to G(τ) from uncoupled fluctuations in the concentrations of eigencomponents defined as the linear combinations of surfactants 1 and 2 that diagonalize the D_ik matrix. A procedure for the rapid and convenient DLS measurement of ternary mutual diffusion coefficients, including the cross-coefficients for coupled diffusion, is suggested, using the Onsager reciprocal relation together with the eigenvalues and pre-exponential factors from G(τ).