Effect of an electric field on the stability of binary dielectric fluid mixtures

We consider the phase stability of binary fluid mixtures with constituents of contrasting dielectric properties in the presence of a static applied electric field, E₀. The dielectric fluid is modeled using a recently developed field-theoretic representation for the equilibrium behavior of a system of polarizable molecular species [J. M. Martin et al., J. Chem. Phys. 145, 154104 (2016)]. The dielectric displacement of the fluid, D, is obtained from a direct E₀ derivative of the fluid's free energy, illuminating coupled structural and electrostatic fluctuations that manifest in the dielectric properties of the fluid. Linearizing D with respect to E₀ yields an explicit, molecularly based expression for the dielectric constant of the fluid mixture, ϵ, through the relation D = ϵE₀. In the linear response regime, the composition dependence of ϵ completely specifies the applied field-dependent contribution to the fluid's miscibility, which we enumerate as a contribution χ_E to a Flory interaction parameter. Using a Gaussian approximation to the field theory, we obtain an expression for χ_E that relates structural and electrostatic contrast between dissimilar molecules to miscibility in the presence of an applied field. Specifically, contrast between wavevector-dependent, single-molecule correlation functions, Λ^_A/B(k), emerges as a necessary ingredient for electric field-induced mixing, corresponding to χ_E < 0. The character of χ_E is considered in three classes of binary systems: a binary simple fluid, a homopolymer blend, and a homopolymer solution. Within each system, the form for Λ^_A/B accounts for molecular architecture effects, such as chain connectivity. Our findings elucidate the conditions for which one should expect electric field induced mixing or demixing for each class of mixture.