Voltage-dependent capacitance of metallic nanoparticles at a liquid/liquid interface

A theoretical model is described for the voltage-dependent capacitance across the interface between two immiscible electrolytic solutions that is partially or completely covered with nanoparticles. The model is based on the description of competitive contributions of electrical double layers at the free interface and around nanoparticles. The effect of different system parameters is rationalised, and theoretical predictions are shown to be in agreement with available experimental data. The model provides a route for the characterisation of nanoparticle layers at liquid/liquid interfaces using capacitance measurements.