Entropic, electrostatic, and interfacial regimes in concentrated disordered ionic emulsions

We develop a free energy model that describes two key thermodynamic properties, the osmotic pressureΠ and the linear elastic shear modulusG′p (i.e. plateau storage modulus), of concentratedmonodisperse emulsionswhichhave isotropic, disordered, droplet structures, and are stabilized using ionic surfactants. This model effectively incorporates the concept of random close packing or jamming of repulsive spheres into a free energy F that depends on droplet volume fraction φ and shear strainγbothbelowandabove the a critical jammingpoint φc≈0.646. This free energy has three terms: entropic, electrostatic, and interfacial (EEI). ByminimizingFwith respect to an averagedropletdeformationparameter that linksall three terms, we show that the entropic term is dominant forφwell belowφc, the electrostatic term is dominant for φ near but below φc, and the interfacial term dominates for larger φ. This EEI model describes measurements of G′p(φ) for charge-stabilized uniform emulsions having a wide range of droplet sizes, ranging from nanoscale to microscale, and it also is consistent with measurements ofΠ(φ). Moreover, it describesG′p(φ) for similar nanoemulsions after adding non-amphiphilic salt, when changes in the interfacial tension and the Debye screening length are properly taken into account. By unifying existing approaches, the EEI model predicts constitutive properties of concentrated ionic emulsions that have disordered, out-ofequilibrium structures through near-equilibrium free energy minimization, consistent with random driving Brownian excitations.