Entropic, Electrostatic, and Interfacial Model for Osmotic Pressure and Shear Moduli of Concentrated Disordered Charged Droplets

We present a free energy model describing the osmotic pressure Π and the linear plateau shear moduli G'_p of disordered charge-stabilized uniform emulsions for droplet volume fractions φ below, near, and above the jamming point. The three principle contributing free energy terms arise from entropy, screened-charge electrostatic interactions, and interfacial droplet deformations (EEI). We numerically evaluate Π(φ) and G'_p(φ) by minimizing the total free energy with respect to a common average deformation parameter which links all three terms and taking the appropriate thermodynamic derivative. We demonstrate that this EEI model fits measurements of Π(φ) and G'_p(φ) for quenched disordered nano- and micro-scale monodisperse charge-stabilized emulsions, including those having added concentrations of NaCl. In addition, trends in optical measurements of long-time plateau mean square displacements of monodisperse charge-stabilized emulsions having varying φ and concentrations of NaCl can match the trends in low-frequency G'_p(φ) predicted by this EEI model. This EEI model may serve as a good starting point for understanding other disordered systems of charge-stabilized uniform spherical soft colloidal objects.