Relating multicomponent mutual diffusion and intradiffusion for associating solutes. Application to coupled diffusion in water-in-oil microemulsions

The binary mutual diffusion coefficient (D) for a dilute solution of a self-associating solute and the solute intradiffusion coefficient (D*) are related by D = D* + (dD*/dC), where C is the total solute concentration. This relation is extended to multicomponent systems. For solutions of two associating solutes, the ternary mutual diffusion coefficients D11, D12, D21, D22 and the solute intradiffusion coefficients D*1, D*2 are found to be related by D11 = D1* + C1∂D*1/∂C1, D12 = C1∂D*1/∂C2, D21 = C2∂D*2/∂C1, and D22 = D2* + C2∂D*2/∂C2. These results are used to interpret coupled diffusion in water + AOT (sodium bis(2-ethylhexyl)sulfosuccinate) + n-heptane (water-in-oil) microemulsions. Although the water(1) and AOT(2) components associate and intradiffuse together through the heptane–continuous solvent as AOT-coated water droplets, and hence D*1 ≈ D*2, the mutual diffusion of AOT is more rapid than that of water (D22 > D11), and there are counter-current coupled flows of AOT (D21 < 0) and large co-current coupled flows of water (D12 > 0). This behavior can be understood by noting that added water reduces the Brownian motion of the droplets by swelling the water cores (∂D*i/∂C1 < 0), whereas added AOT reduces the droplet size (∂D*i/∂C2 > 0) by providing more surfactant to coat the water. The predicted water and AOT intradiffusion coefficients are the eigenvalues of the mutual diffusion coefficient matrix.