On the thermodynamics of particle-stabilized emulsions: curvature effects and catastrophic phase inversion.

The flexural properties of a particle adsorption monolayer are investigated theoretically. If the particles are not densely packed, the interfacial bending moment and the spontaneous curvature (due to the particles) are equal to zero. The situation changes if the particles are closely packed. Then the particle adsorption monolayer possesses a significant bending moment, and the interfacial energies of bending and dilatation become comparable. In this case, the bending energy can either stabilize or destabilize the Pickering emulsion, depending on whether the particle contact angle is smaller or greater than 90 degrees . Theoretical expressions are derived for the bending moment, for the curvature elastic modulus, and for the work of interfacial deformation and emulsification. The latter is dominated by the work for creation of a new oil-water interface and by the work for particle adsorption. The curvature effects give a contribution of second order, which is significant only for emulsification at 50:50 water/oil volume fractions. A thermodynamic criterion for the type of the formed emulsion is proposed. It predicts the existence of a catastrophic phase inversion in particle-stabilized emulsions, in agreement with the experimental observations. The derived theoretical expressions could find application for interpretation of experimental data on production and stability of Pickering emulsions.