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Field theory of structured liquid dielectrics

We develop of a field-theoretic approach for the treatment of both the non-local and the non-linear response of structured liquid dielectrics. Our systems of interest are composed of dipolar solvent molecules and simple salt cations and anions. We describe them by two independent order parameters, the polarization field for the solvent and the charge density field for the ions, including and treating the non-electrostatic part of the interactions explicitly and consistently. We show how to derive functionals for the polarization and the electrostatic field of increasingly finer scales and solve the resulting mean-field saddle-point equations in the linear regime. We derive criteria for the character of their solutions that depend on the structural lengths and the polarity of the solvent. Our approach provides a systematic way to derive generalized polarization theories.