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The adsorption of surfactants from dilute oil solutions on to solid surfaces is studied as a function of surface curvature and surface coverage. Coarse-grained molecular models, computer simulations, and umbrella sampling are used to compute the dependence of the free energy of adsorption on to a spherical colloid surface with radius R. It is shown that for fixed surface coverage, and with all other things being equal, the free energy of adsorption decreases with decreasing R. For fixed surface curvature, the free energy of adsorption increases with increasing surface coverage. These trends arise from the excluded-volume interactions between the surfactant tails. The dependence on surface curvature is due to the geometrical effect of there being more free volume for the surfactant tails with a smaller colloid radius. The consequences of these effects on equilibrium partitioning are examined. It is shown that for surfactants adsorbed on small-colloid and large-colloid surfaces in mutual equilibrium with a dilute solution, the surface coverage of the small particles is significantly greater. The implications for industrial applications are discussed and could be significant.

The effects of surface curvature on the adsorption of surfactants at the solid–liquid interface