A transport model for the adsorption of surfactant from micelle solutions onto a clean air/water interface in the limit of rapid aggregate disassembly relative to diffusion and supporting dynamic tension experiments

A transport theory and supporting experiments are detailed for the adsorption of surfactant from micelle solutions onto a clean air/water interface. The study focuses on adsorption from very dilute solutions consisting of globular aggregates. In the usual mechanism conceived for the adsorption process, when a clean interface is created in the solution of monomer and globular aggregates, monomer initially kinetically adsorbs from the sublayer onto the surface, depleting the sublayer concentration of monomer. This depletion, as it perturbs the micelle/monomer equilibrium, is followed by the disassembly of aggregates in the sublayer (to replenish monomer). Co-currently, aggregates and monomer diffuse from the bulk to the depleted sublayer. Thus in this classical picture, while the micelles provide a reservoir for monomer adsorption by their disassembly – and thereby enhance the adsorption rate – they provide no direct route for adsorption. 14 15 16 17 18 19 20 Using this picture as a starting point, in this study an asymptotic transport theory is constructed for the case in which the time scale for the diffusion of the monomer is much slower than the time scale for the kinetic breakdown of the aggregates. With this separation of time scales, disassembly of micelles takes place only along a boundary separating regions without micelles (micelle-free zones) from regions containing micelles. In the regions containing micelles, the larger rate of disassembly relative to the rate of diffusion of monomer maintains the monomer concentration at the critical aggregate concentration (CCAC). Two regimes arise: in the first, at low aggregate concentrations, micelle diffusion cannot keep up with the kinetic surface adsorption of monomer, and a micelle-free zone emerges from the surface and moves into the bulk. Micelles diffuse from the bulk to the boundary of the zone, break-up and monomer diffuses through the micelle-free zone and kinetically adsorbs onto the surface. In the second regime, at higher aggregate concentrations, the micelle diffusive flux is commensurate with the kinetic rate of monomer surface adsorption, and a micelle-free zone does not form. Micelles diffuse directly to the surface, and break-up in the sublayer; monomer then kinetically adsorbs onto the surface. The adsorption rate is limited only by the kinetics of monomer adsorption since the monomer sublayer concentration is equal to the CCAC, and represents the fastest rate that surfactant can adsorb onto the surface in the absence of diffusion barriers. Numerical solutions are obtained for a polyethoxylated surfactant C14E6 whose micelle disassembly time scale satisfies the requirement that it be faster than the diffusion time scale of the monomer. For C14E6 the monomer adsorption parameters and diffusion coefficient of monomer are obtained from separate dynamic tension measurements below the CCAC; the micelle diffusion coefficient is estimated from the literature. A critical total surfactant concentration of 4.25CCAC is computed, below which a micelle-free zone forms and above which the zone does not form, and surface concentrations and tension reductions as a function of time are simulated for both regimes. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37