We investigate the structuring of charged spherical nanoparticles and micelles (i.e., "macroions") between two surfaces as a function of bulk macroion concentration. Structuring is deduced from measured force profiles between a silica particle and a silica plate in the presence of an aqueous macroion (Ludox silica nanoparticle or sodium dodecyl sulfate micelle) solution, obtained with an atomic force microscope. We observe oscillatory force profiles that decay with separation. We find that the wavelength of the force profiles scales with the bulk number density as rho(-)(1/3), rather than with the effective macroion size. Only at very high silica nanoparticle concentration (above 10 vol %) in a low ionic strength solution does the wavelength become smaller than that predicted by the simple rho(-)(1/3) scaling; however, the original scaling is recovered upon the addition of a small amount of electrolyte. A comparison between the measured wavelength and the predicted spacing between the macroions in the bulk shows that the two variables differ in both magnitude and bulk density scaling. This finding suggests that confined macroions are more ordered than those in the bulk and the nature of this ordering is maintained over a relatively wide range of bulk concentration.

This work investigates the synergistic effects of a neutral polymer and an anionic surfactant on depletion forces as a function of bulk polymer and bulk surfactant concentration. In this work, we measure the force between a silica particle and a silica plate in aqueous solutions of the polymer and the surfactant using atomic force microscopy. The polymer is the triblock copolymer poly(ethylene oxide-block-propylene oxide-block-ethylene oxide) (Pluronic F108), and the surfactant is sodium dodecyl sulfate (SDS). In F108-only solutions, the force between the silica particle and the silica plate is primarily repulsive for polymer concentrations ranging from 200 to 10 000 ppm. In SDS-only solutions, the net force between the silica surfaces is repulsive at all separations for concentrations below 16 mM SDS and is attractive with a structural force character above 16 mM SDS. When both F108 and SDS are present in the solution, a net attractive force is observed at SDS concentrations as low as 4 mM, a factor of 2 below the critical micelle concentration (cmc). We attribute this synergistic effect to the complexation of F108 with SDS in bulk solution at a critical aggregation concentration (cac) that is less than the cmc, producing a relatively large, charged complex that creates a significant depletion force between the particle and plate.

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