The conclusion of classical Debye-Hückel theory that a phase separation may occur in highly unsymmetrical plasmas or electrolytes is shown to be false and to arise from a serious error in the treatment of the interaction of pairs of the most highly charged ions. After an approximate correction for this error, no phase separation is predicted. Specific application to iron in the solar plasmas is...

A theory of a confined two-dimensional electrolyte is presented. The positive and negative ions, interacting by a 1/r potential, are constrained to move on an interface separating two solvents with dielectric constants epsilon(1) and epsilon(2). It is shown that the Debye-Hückel type of theory predicts that this two-dimensional Coulomb fluid should undergo a phase separation into a coexisting l...

An extended Debye–Hückel theory with fourth order gradient term is developed for electrolyte solutions; namely, the electric potential φ(r) of bulk solution can be described by ∇2φ(r) = κ2φ(r) + LQ2∇4φ(r), where parameters κ and LQ are chosen to reproduce first two roots dielectric response function solution. Three boundary conditions solving problem proposed based upon continuity involving fun...

Recently we introduced a nonlinear partial differential equation (nPDE) of the third order for the first time. This new model equation allows the extension of the Debye-Hückel Theory (DHT) considering time dependence explicitly. This also leads to a new formulation in the meaning of the nonlinear Poisson-Boltzmann Equation (nPBE) and therefore we call it the modified PoissonBoltzmann Equation (...

We test the concepts of renormalized charge and potential saturation, introduced within the framework of highly asymmetric Coulomb mixtures, on exactly solvable Coulomb models. The object of study is the average electrostatic potential induced by a unique “guest” charge immersed in a classical electrolyte, the whole system being in thermal equilibrium at some inverse temperature β. The guest ch...

Large scale chemical reaction networks are a ubiquitous phenomenon, from the metabolism of living cells to processes in planetary atmospheres and chemical technology. At least some of these networks exhibit distinctive global features such as the "small world" behavior. The systematic study of such properties, however, suffers from substantial sampling biases in the few networks that are known ...

We study the counterion distribution around a spherical macroion and its osmotic pressure in the framework of the recently developed Debye-Hückel-hole-cavity (DHHC) theory. This is a local density functional approach which incorporates correlations into Poisson-Boltzmann theory by adding a free energy correction based on the one-component plasma. We compare the predictions for ion distribution ...