J. Phys. Chem. 1995, 99, 12896-12901
12896
Size Distribution Model for Chemical Interdiffusion in Water/AOT/Heptane Water-in-Oil Microemulsions Derek G. Leaist” and Ling Hao Department of Chemistry, University of Westem Ontario, London, Ontario, Canada N6A 5B7 Received: February 13, 1995; In Final Form: June 5, 1995@
The Taylor dispersion method has been used to measure ternary interdiffusion coefficients for water-in-oil microemulsions prepared from water AOT (sodium bis(2-ethylhexyl) sulfosuccinate) heptane. In this system the water and AOT components diffuse together through the heptane-continuous medium as surfactantcoated water droplets. Yet the diffusion coefficient of AOT is up to 3 times larger than the diffusion coefficient of water. Although concentration gradients in AOT produce cocurrent coupled flows of water, gradients in water produce counterflows of AOT. This unexpected behavior is attributed to changes in the average droplet size along the diffusion path. Whereas an increase in the concentration of AOT produces a larger number of smaller, more rapidly diffusing droplets, an increase in the concentration of water has the opposite effect. The analysis confirms the experimental result that the diffusion of water and surfactant in a microemulsion produces two distinct diffusional relaxation times, even in cases of negligible droplet polydispersity.
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Introduction Oils are almost insoluble in water. Nevertheless, large amounts of oil can be dispersed in water by using surfactants to coat and stabilize nanometer-sized droplets of microemulsified oil. Water-in-oil microemulsions are prepared by stabilizing nanodroplets of water in an oil-continuous phase. The microstructure of these systems leads to a number of interesting properties’*2as well as important practical application^^^^ related to petroleum recovery, cleaning processes, digestion, and the formulation of lubricants, paints, and food products. The work reported here is a study of chemical interdiffusion (mutual diffusion) in water-in-oil microemulsions. If the water and surfactant components migrate together through the oil as surfactant-coated water droplets, it seems reasonable to use Fick’s binary diffusion e q ~ a t i o n ~ , ~ J = -DVC
(1)
to relate the droplet flux J to the gradient in the gradient VC in droplet concentration. D is a “pseudobinary” microemulsion diffusion coefficient. Measured values of D have been used to estimate the sizes of microemulsion droplet^.^ Both theory and experiment show, however, that accurate treatments of chemical interdiffusion based on eq 1 are limited to two-component mixtures.6 In three-component mixtures, for example, chemical interdiffusion generally produces two independent diffusional flows. These considerations suggest that a more complete description of interdiffusion in water( l)/surfactant(2)/oil(O) systems might be offered by the temary Fick equations6q7
J , = - D l l V C I - D12VCz J2 = - D 2 , V C , - Dz2VC2
(3)
which relate the independent molar fluxes of water(1) and surfactant(2) to the gradients in concentration of these components. Interdiffusion coefficients* D11 and 0 2 2 give the fluxes of the components down their own concentration gradients. Cross-coefficients Dl2 and D21 are included to allow for the @
Abstract published in Advance ACS Abstracts, July 15, 1995.
coupled flux of water caused by the gradient in surfactant, and vice versa. The concentrations CI and CZin eqs 2 and 3 are well-defined stoichiometric concentrations of total water and total surfactant components. Equations 2 and 3 provide an unambiguous description of microemulsion diffusion because assumptions about the size, composition, or polydispersity of the microemulsion droplets are not required. Why would it be necessary to describe microemulsion diffusion with ternary Fick equations (instead of the simpler binary equation) if it is accepted that water and surfactant migrate together as surfactant-coated water droplets? Microemulsion droplets are dynamic entities. They collide and exchange both surfactant and water molecules on a microsecond time scale, which is very rapid compared to diffusion. Suppose the concentration of total surfactant is fixed, but one region of the system contains a higher concentration of water. In this case water molecules can move down their concentration gradient by hopping from one droplet to another during dropletdroplet collisions. This will allow water to diffuse through the system without a corresponding flow of surfactant. Similarly, rapid exchange of surfactant between droplets will allow surfactant to diffuse down its gradient, independently of water. These considerations prompted us to test the pseudobinary treatment of microemulsion diffusion (eq 1) by measuring temary interdiffusion coefficients (eqs 2 and 3) for water(l)/ AOT(2)/heptane(O) microemulsions. The “effective” diffusion coefficient4 D (eq 1) is related to the Dik coefficients. Also, coupled diffusion is measured for a microemulsion. The transport of water as surfactant-coated water droplets ‘‘carries along” surfactant and vice versa. We wanted to see if this behavior produces unusually large cocurrent coupled flows. The present results show that AOT diffuses several times more rapidly than water in water/AOT/heptane microemulsions. Although AOT does indeed cotransport water, diffusing water is found to produce countercurrent coupled flows of AOT. A simple model for microemulsion diffusion is developed to help understand the results. Water/AOT/oil microemulsions have been extensively studied. In addition to diffusion coefficients,4-6,8-‘2 phase equilibria? densities,I3refractive indexes,l4compre~sibilities,‘~ vapor pressures,2 light scattering,”.’2 neutron scattering,I6 and viscositiesI5 have been measured. The properties of these microemul-
0022-3654/95/2099-12896$09.00/0 0 1995 American Chemical Society
Chemical Interdiffusion in Microemulsions
J. Phys. Chem., Vol. 99, No. 34, 1995 12897
sions are simplified because cosurfactants, such as alcohols, are not required.2
Materials. Water was purified by distillation and ion exchange. Reagent grade AOT (Fisher) was dried in a vacuum oven at 80 OC. The residual water content (
