Thermodynamics beyond dilute solution theory: Steric effects and electrowetting

Here, we address the impact that steric models, introducing finite ion size effects, have on the contact angle for charged surfaces. We review the two most common steric models, namely the excluded volume (commonly referred to as the Bikerman model) and the Carnahan-Starling (CS) models. We clarify the thermodynamics of the solid–liquid electrolyte interface and show that the common case of an electrolyte reservoir characterized by bulk ion concentrations corresponds to the thermodynamics of the grand potential with fixed ionic chemical potentials. The grand potential gives distinctly different interfacial energies compared to the free energy, which corresponds to a finite number of ions in an electrolyte solution (relevant in nanofluidics, for instance). Steric models may be applied to either thermodynamic scenario, and applications to electrowetting are shown under the grand potential (large droplets with a bulk reservoir in the center). When sufficiently large potentials are applied to conducting electrodes, the steric models, unlike the classical point charge model, introduce ion specificity into the electrowetting contact angle via finite ion sizes, which introduces an asymmetry in the contact angle at positive and negative potentials. For electrowetting on dielectrics (EWOD), the theoretical contact angles match experimental values well until electrode potentials of 240 V, with CS performing better than Bikerman. We hypothesize that contact angle saturation at 240 V may arise due to a switch in the thermodynamics of the solid–liquid interfacial energy from grand potential (bulk reservoir) to free energy (finite ion number) conditions, capping the formation of a counterion adsorption layer at the electrode surface.