We present a microfield approach for studying the dependence of the orientational polarization of the water in aqueous electrolyte solutions upon the salt concentration and temperature. The model takes into account the orientation of the solvent dipoles due to the electric field created by ions, and the effect of thermal fluctuations. The model predicts a dielectric functional dependence of the form ɛ(c)=ɛ_{w}-βL(3αc/β),β=ɛ_{w}-ɛ_{ms}, where L is the Langevin function, c is the salt concentration, ɛ_{w} is the dielectric of pure water, ɛ_{ms} is the dielectric of the electrolyte solution at the molten salt limit, and α is the total excess polarization of the ions. The functional form gives a remarkably accurate description of the dielectric constant for a variety of salts and a wide range of concentrations.

The increasing number of experimental observations on highly concentrated electrolytes and ionic liquids show qualitative features that are distinct from dilute or moderately concentrated electrolytes, such as self-assembly, multiple-time relaxation, and under-screening, which all impact the emergence of fluid/solid interfaces, and transport in these systems. Since these phenomena are not captured by existing mean field models of electrolytes, there is a paramount need for a continuum framework for highly concentrated electrolytes and ionic liquids. In this work, we present a self-consistent spatiotemporal framework for a ternary composition that comprises ions and solvent employing free energy that consists of short and long range interactions, together with a dissipation mechanism via Onsagers' relations. We show that the model can describe multiple bulk and interfacial morphologies at steady-state. Thus, the dynamic processes in the emergence of distinct morphologies become equally as important as 1

Room temperature ionic liquids are attractive to numerous applications and particularly, to renewable energy devices. As solvent free electrolytes, they demonstrate a paramount connection between the material morphology and Coulombic interactions: the electrode/RTIL interface is believed to be a product of both polarization and spatiotemporal bulk properties. Yet, theoretical studies have dealt almost exclusively with independent models of morphology and electrokinetics. Introduction of a distinct Cahn-Hilliard-Poisson type mean-field framework for pure molten salts (i.e., in the absence of any neutral component), allows a systematic coupling between morphological evolution and the electrokinetic phenomena, such as transient currents. Specifically, linear analysis shows that spatially periodic patterns form via a finite wavenumber instability and numerical simulations demonstrate that while labyrinthine type patterns develop in the bulk, lamellar structures are favored near charged surfaces. The results demonstrate a qualitative phenomenology that is observed empirically and thus, provide a physically consistent methodology to incorporate phase separation properties into an electrochemical framework.

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We investigate the self-focusing dynamics of super-Gaussian optical beams in a Kerr medium. We find that up to several times the critical power for self-focusing, super-Gaussian beams evolve towards a Townes profile. At higher powers the super-Gaussian beams form rings which break into filaments as a result of noise. Our results are consistent with the observed self-focusing dynamics of femtosecond laser pulses in air [1] in which filaments are formed along a ring about the axis of the initial beam where the initial beam did not form a ring.

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