Density-functional modeling of structure and forces in thin micellar liquid films

Abstract

Recent equilibrium force measurements on aqueous films of surfactant above the critical micelle concentration show oscillations for film thicknesses up to 50 nm. To model this phenomenon we express the micellar contribution to the disjoining pressure in terms of thickness-dependent inhomogeneous micelle number density distributions through the film. Density functional theory is used to calculate micelle density profiles, presuming the micelles to behave as charged spheres interacting with each other, and with the film interfaces, through screened-Coulomb potentials. The background electrolyte permits dilute micellar solutions to act as concentrated systems exhibiting pronounced layering in the film. For a 0.1 M sodium dodecylsulfate (SDS) film we find up to five micellar layers for a film thickness equal to ten micelle diameters (d), the layer separation scaling with the effective diameter (deff/d=1.86) which includes the micelle Debye atmosphere. The peaks are largest near the interfaces and decay toward the bulk density at the film midplane. The corresponding disjoining pressures show oscillations with the same distance scaling between the branches as in the density profiles; these values are consistent with experiment. With decreasing film thickness, the (meta-)stable disjoining pressure regions represent micellar layers in the film being forced closer together, raising the pressure until the interior layer is expelled, allowing more space between the remaining micellar layers at that thickness. Repulsive (positive) disjoining pressures result from layer separations less than the corresponding bulk value whereas attractive (negative) regions represent more distance between layers than that in the bulk. The 0.2 M SDS disjoining pressure isotherm exhibits one additional layer than the 0.1 M case for thicknesses up to 50 nm. The pressure magnitudes of the former case are about twice that of the latter. Addition of ionic salts greatly inhibits the long-range micellar structuring. For SDS foam films, predicted disjoining pressures are much higher than measured values. Comparison with cetyltrimethyl-ammonium bromide (CTAB) micellar films in the surface forces apparatus, however, shows near quantitative agreement. The nature of the confining interfaces thus plays a key role in supporting the internal micellar structuring.