Mutual diffusion with equal eigenvalues in solutions of strongly associated surfactants. A new kind of multicomponent diffusion

Taylor dispersion is used in this study to measure ternary mutual diffusion coefficients (Dik) for aqueous solutions of Triton X-100 + Brij 35 mixed nonionic surfactants. The dispersion profiles appeared to be measured precisely, but they could not be analyzed by using established techniques. Least-squares procedures, for example, failed to converge. These difficulties appeared to be caused by nearly identical eigenvalues of the Dik matrix and the resulting numerical ill conditioning of the fitting equations. Yet Brij 35 diffuses significantly more slowly than Triton X-100, as indicated by the broader profiles generated by Brij 35 concentration gradients. The puzzling diffusion behavior is investigated by using theory to estimate Dik coefficients for solutions of mixed nonionic surfactants. At compositions well above the critical micelle concentration, where the diffusion of free surfactant monomers is negligible, the predicted eigenvalues approach the mixed-micelle diffusion coefficient and become identical within the precision of the Taylor measurements (about ±2%). Techniques for measuring multicomponent mutual diffusion have relied on the assumption of distinct eigenvalues of the Dik matrix. Prompted by the evidence that common surfactants provide exceptions to this longstanding rule, equations derived for equal-eigenvalue dispersion profiles are used to evaluate Dik coefficients for aqueous Triton X-100 + Brij 35 solutions. Results are also reported for aqueous tetradecylsulfobetaine + hexadecylsulfobetaine solutions. The physical significance of mutual diffusion with equal eigenvalues is discussed in terms of the loss of a degree of freedom when associating solute components A and B diffuse together AnBm complexes.