Supplemental Information for ”understanding the Self-assembly of Chaged Nanoparticles at the Water/oil Interface”

This supplemental information describes a model which describes the adsorption of electrically charged, interfacially active nanocrystals at the water/heptane interface. Since dense systems of charged particles at the interface are inherently complex, this model is only intended as a first order approximation. First the chemical potential of particles in the bulk aqueous phase is calculated followed by the chemical potential of the particles at the interface. In the latter the particle surface coverage at the interface φs is required. Finally, using μbulk = μint the equilibrium density of particles φ eq s can be derived. 1. The chemical potential for charged nanocrystal in the aqueous phase We take the colloidal aqueous (bulk) phase to be sufficiently diluted so that interactions between the particles can be neglected. Also the particles are assumed to be monodisperse, equally charged and spherical, the latter condition results in translational degrees of freedom only. With these assumptions, there are two contributions to the bulk (Helmholtz) free energy. The first contribution is an ”ideal gas”-like term which was found to be: μideal kT = ln (