The conductivity of strong electrolytes from stochastic density functional theory

Abstract

Abstract. Stochastic density functional theory is applied to analyze the conductivity of strong two species electrolytes at arbitrary field strengths. The corresponding stochastic equations for the density of the electrolyte species are solved by linearizing them about the mean density of ionic species, yielding an effective Gaussian theory. The non-equilibrium density-density correlation functions are computed and the conductivity of the electrolyte is deduced. In the bulk, our results give a simple derivation of the results of Onsager and coworkers who used very different methods. The method developed here can also be used to study electrolytes confined in one and two dimensions and interacting via either the three dimensional Coulomb interaction or the Coulomb interaction corresponding to that dimension of space.

Fluctuating Hydrodynamics and Debye-Hückel-Onsager Theory for Electrolytes

“…Yet fluctuating hydrodynamics has many applications beyond this elegant and insightful formulation of classic results. One of the strengths of FHD is being able to model complex non-ideal multi-species mixtures including contributions due to mean fluid flow, temperature gradients, boundary conditions (e.g., see [12]), etc.…”

“…The present analysis was taken only to linear order but the extension to higher order is possible (e.g., corrections for strong fields are predicted for the relaxation term [12]). Using "one-loop" renormalization theory, in this work we were only able to compute the leading-order corrections ∼ √ I in the ionic strength I.…”

“…Numerical methods for solving the FHD equations are well-established and these are especially useful for including the effects of boundary conditions (e.g., conductivity corrections are predicted for the relaxation term in a confined binary mixture [12]) and nonlinearities. Care is needed, however, to avoid double-counting the contribution of the fluctuations to transport.…”

A Gaussian theory for fluctuations in simple liquids

“…It has been recently shown that linearizing the interaction term in Eq. (45) about the mean bulk density, while using the mean bulk density in the noise term, leads to an analytically soluble theory in the bulk which recovers the random phase approximation for the equal time correlation functions [66][67][68][69][70], notably this means that Debye-Hückel theory is obtained for Brownian electrolytes. The approach has been applied to a variety of driven and out of equilibrium systems.…”

The effect of driving on model C interfaces

“…where we have introduced the intrinsic velocity v 0 = √ α 2 λκ which depends on the microscopic dynamical quantity α associated with the model A dynamics of the field φ, as well as the microscopic static quantities κ (which generates the surface tension) and λ the coupling between the field ψ and φ. This appearance of dynamical and static quantities that are otherwise hidden in equal time correlation functions in equilibrium is already implicit in the works of Onsager [4] where it is used to compute the conductivity of Brownian electrolytes and the explicit expressions were derived using stochastic density functional theory in [12]. We also note that the universal thermal Casimir effect between model Brownian electrolyte systems driven by an electric field exhibits similar features, developing a dependency on both additional static and dynamical variables with respect to the equilibrium case [25] However for this small q expansion we see that the microscopic quantities D, the diffusion constant of the field φ, and the order parameter jump ∆ψ do not appear.…”