Aspects of the stabilisation of emulsions by solid particles: Effects of line tension and monolayer curvature energy

It is well-documented that solid particles can be effective stabilisers of emulsions, and that the type of the emulsion formed is related, inter alia, to the particle wettability. In general it is to be expected that the free energy change accompanying the formation of a solid-stabilised emulsion will be positive and that emulsion stability will therefore be kinetic in nature. Recently work has appeared showing that very small solid particles, with radius around say 15 nm, can be excellent stabilisers of emulsions. This raises the possibility that line tension acting in the three-phase contact lines around adsorbed particles could have an effect on particle adsorption and hence on their effectiveness as emulsion stabilisers. We explore the effects of both positive and negative line tension on the free energy of adsorption of spherical particles at spherically curved liquid interfaces and on the free energy of drop formation. For small particles it is shown that physically realistic values of positive line tension can lead to exclusion of particles from drop interfaces, either by rendering the adsorption free energy positive or by creating energy barriers to adsorption. We also consider the effects of lateral interactions between adsorbed particles on particle adsorption, particularly strong Coulombic repulsion mediated through the oil phase. It is known that the preferred type of emulsions stabilised by surfactants can be accounted for by the existence of a curvature energy possessed by close-packed surfactant monolayers. We show here that close-packed monolayers of spherical particles at a liquid surface also possess curvature energies, and we calculate bending elastic moduli (κ) as a function of particle size, oil/water interfacial tension, line tension and contact angle. For a monolayer of (hypothetical) particles with radius 0.5 nm (similar to that of a low molar mass surfactant), the value of κ is expected to be of the order of kT, just as for surfactant monolayers. It has been assumed in our work that equal spherical particles are hexagonally close-packed around spherical drops. It is well known however that such packing is not possible, but we show in an Appendix that the assumption of hexagonal packing leads to only small errors (in the context) in calculated free energies of emulsion formation and in the calculated bending elastic moduli of particle monolayers.