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

Abstract

We develop a free energy model that describes two key thermodynamic properties, the osmotic pressure Π and the linear elastic shear modulus G′ p (i.e. plateau storage modulus), of concentrated monodisperse emulsions which have 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 strain γ both below and above the a critical jamming point ϕ c ≈ 0.646. This free energy has three terms: entropic, electrostatic, and interfacial (EEI). By minimizing F with respect to an average droplet deformation parameter that links all three terms, we show that the entropic term is dominant for ϕ well below ϕ c , the electrostatic term is dominant for ϕ near but below ϕ c , 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 of Π(ϕ). Moreover, it describes G′ 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.

Crossover between Athermal Jamming and the Thermal Glass Transition of Suspensions

“…The stress scale is found to be proportional to the thermal stress σ T ¼ αk B T=R 3 with α ¼ 35 000. The large prefactor α likely has to be attributed to the high entropic osmotic pressure that results from limited free volume for thermal motion [21,24,25]. A prefactor of order 10 4 can be calculated, e.g., from published MCT data for the thermal yield stress (ϕ ¼ 0.60, ϵ=k B T ¼ 10 5 − 10 7 ), while simulations in this case give α ∼ 10 3 [26].…”

An Emulsion Approach to Resolve the Paradox of 3D Printing of Very Soft Silicones

“…Another way to generate a yield stress fluid is to make emulsions. In that regard, an important work on the rheological behaviors of concentrated emulsion has been conducted by Mason et al [ 23–25 ] Their conclusions were that the interfacial structure of the droplets, responsible of the droplets size and their chemical interactions with the continuous phase, governs the behavior.…”

The liquid-glass-jamming transition in disordered ionic nanoemulsions

“…Recently, a near-equilibrium energy minimization approach has been introduced to model the entropic, electrostatic, and interfacial contributions to the free energy of a dense disordered system of droplets from the glassy regime just below jamming through and above the jamming point 35 . By taking appropriate derivatives of this free energy, this entropic-electrostatic-interfacial (EEI) model can then be used to predict the osmotic pressure and low-frequency shear elastic moduli of ionic colloidal emulsions and nanoemulsions 35 .…”

“…Recently, a near-equilibrium energy minimization approach has been introduced to model the entropic, electrostatic, and interfacial contributions to the free energy of a dense disordered system of droplets from the glassy regime just below jamming through and above the jamming point 35 . By taking appropriate derivatives of this free energy, this entropic-electrostatic-interfacial (EEI) model can then be used to predict the osmotic pressure and low-frequency shear elastic moduli of ionic colloidal emulsions and nanoemulsions 35 . This model accurately predicts the measured -dependent plateau elastic shear moduli, of colloidal droplets stabilized by Debye screened-charge repulsions over more than four orders of magnitude for droplet radii ranging from about 25 nm to about 1 micron 35 .…”

“…By taking appropriate derivatives of this free energy, this entropic-electrostatic-interfacial (EEI) model can then be used to predict the osmotic pressure and low-frequency shear elastic moduli of ionic colloidal emulsions and nanoemulsions 35 . This model accurately predicts the measured -dependent plateau elastic shear moduli, of colloidal droplets stabilized by Debye screened-charge repulsions over more than four orders of magnitude for droplet radii ranging from about 25 nm to about 1 micron 35 . Moreover, computer simulations and calculations 7 have treated jamming of soft colloidal objects and also show a less-abrupt transition in near .…”