Exact mean-field theory of ionic solutions:: non-Debye screening

The main aim of this report is to analyze the equilibrium properties of primitive model (PM) ionic solutions in the formally exact mean-field formalism. Previously, we review the main theoretical and numerical results reported throughout the last century for homogeneous (electrolytes) and inhomogeneous (electric double layer, edl) ionic systems, starting with the classical mean-field theory of electrolytes due to Debye and Huckel (DH). In this formalism, the effective potential is derived from the Poisson-Boltzmann (PB) equation and its asymptotic behavior analyzed in the classical Debye theory of screening. The thermodynamic properties of electrolyte solutions are briefly reviewed in the DH formalism. The main analytical and numerical extensions of DH formalism are revised, ranging from the earliest extensions that overcome the linearization of the PB equation to the more sophisticated integral equation techniques introduced after the late 1960s. Some Monte Carlo and molecular dynamic simulations are also reviewed. The potential distributions in an inhomogeneous ionic system are studied in the classical PB framework, presenting the classical Gouy-Chapman (GC) theory of the electric double layer (edl) in a brief manner. The mean-field theory is adequately contextualized using field theoretic (FT) results and it is proven that the classical PB theory is recovered at the Gaussian or one-loop level of the exact FT, and a systematic way to obtain the corrections to the DH theory is derived. Particularly, it is proven following Kholodenko and Beyerlein that corrections to DH theory effectively lead to a renormalization of charges and Debye screening length. The main analytical and numerical results for this non-Debye screening length are reviewed, ranging from asymptotic expansions, self-consistent theory, nonlinear DH results and hypernetted chain (HNC) calculations. Finally, we study the exact mean-field theory of ionic solutions, the so-called dressed-ion theory (DIT). An analysis of its statistical foundations is reported together with a detailed study of its linear response function, (alpha) over cap (k), that generalizes the concept of screening length and contains all the information about the effective quantities. The relation of this quantity to the structure factor of the fluid is explicitly analyzed and the renormalized charges and screening length for a one component charged spheres (OCCS) system derived in the modified mean spherical approximation (MMSA), and a comparison of the DIT/MMSA predictions for the effective magnitudes to HNC results included. Besides,the predicted DIT/MMSA thermodynamic properties are studied for the RPM electrolyte and extensions, in this formalism to asymmetric electrolyte solutions presented. The main DIT results for the edl due to Ennu et al. are introduced and, finally, we analyze the main features of the application of the new equilibrium formalism to the calculation of transport coefficients, the so termed dressed ion transport theory (DITT). To this framework, the relaxation and electrophoretic corrections to the ionic mobility are interpreted in terms of the existence of new kinetic entities in the bulk solution: the effective or dressed particles. (C) 2003 Elsevier B.V. All rights reserved.