We present an extension to the Poisson-Boltzmann model where the dipolar features of solvent molecules are taken explicitly into account. The formulation is derived at mean-field level and can be extended to any order in a systematic expansion. It is applied to a two-plate system with oppositely charged surfaces. The ion distribution and profiles in the dipolar order parameter are calculated and can result in a large correction to the inter-plate pressure.
We present a soft-potential-enhanced Poisson-Boltzmann (SPB) theory to efficiently capture ion distributions and electrostatic potential around rodlike charged macromolecules. The SPB model is calibrated with a coarse-grained particle-based model for polyelectrolytes (PEs) in monovalent salt solutions as well as compared to a full atomistic molecular dynamics simulations with explicit solvent. We demonstrate that our modification enables the SPB theory to accurately predict monovalent ion distributions around a rodlike PE in a wide range of ion and charge distribution conditions in the weak-co…
In this paper we develop a simple theory to study the effects of ionic size on ionic distributions around a charged spherical particle. We include a correction to the regular Poisson-Boltzmann equation in order to take into account the size of ions in a mean-field regime. The results are compared with Monte Carlo simulations and a Density Functional Theory based on the Fundamental Measure approach and a second-order bulk expansion which accounts for electrostatic correlations. The agreement is very good even for multivalent ions. Our results show that the theory can be applied with very good a…
Poisson-Boltzmann theory is the cornerstone for soft matter electrostatics. We provide novel exact analytical solutions to this non-linear mean-field approach, for the diffuse layer of ions in the vicinity of a planar or a cylindrical macroion. While previously known solution are for homogeneously charged objects, the cases worked out exhibit a modulated surface charge --or equivalently surface potential-- on the macroion (wall) surface. In addition to asymptotic features at large distances from the wall, attention is paid to the fate of the contact theorem, relating the contact density of ion…
We present a method aimed at sampling charge density fluctuations in Coulomb systems. The derivation follows from a functional integral representation of the partition function in terms of charge density fluctuations. Starting from the mean-field solution given by the Poisson-Boltzmann equation, an original approach is proposed to numerically sample fluctuations around it, through the propagation of a Langevin like stochastic partial differential equation (SPDE). The diffusion tensor of the SPDE can be chosen so as to avoid the numerical complexity linked to long-range Coulomb interactions, ef…
Ionic solutions are often regarded as fully dissociated ions dispersed in a polar solvent. While this picture holds for dilute solutions, at higher ionic concentrations, oppositely charged ions can associate into dimers, referred to as Bjerrum pairs. We consider the formation of such pairs within the nonlinear Poisson-Boltzmann framework, and investigate their effects on bulk and interfacial properties of electrolytes. Our findings show that pairs can reduce the magnitude of the dielectric decrement of ionic solutions as the ionic concentration increases. We describe the effect of pairs on the…
Poisson-Boltzmann (PB) theory is the classic approach to soft matter electrostatics which has been applied to numerous problems of physical chemistry and biophysics. Its essential limitations are the neglect of correlation effects and of fluid structure. Recently, several theoretical insights have allowed the formulation of approaches that go beyond PB theory in a systematic way. In this topical review we provide an update on the developments achieved in self-consistent formulations of correlation-corrected Poisson-Boltzmann theory. We introduce the corresponding system of coupled nonlinear eq…
We propose a field-theoretical approach based on the thermodynamic perturbation theory and within it derive a grand thermodynamic potential of the inhomogeneous ionic fluid as a functional of electrostatic potential for an arbitrary reference fluid system. We obtain a modified Poisson-Boltzmann equation as the Euler-Lagrange equation for the obtained functional. Applying Noether's theorem to this functional, we derive a general mean-field expression for the stress tensor consistent with the respective modified Poisson-Boltzmann equation. We derive a general expression for the macroscopic force…
Dielectric permittivity of water confined in stacks of charged lipid layers: extracting profiles from molecular dynamics simulations using a modified Poisson-Boltzmann equation
Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière（里昂第一大学，法国国家科学研究中心，光物质研究所）；UPR 22/CNRS, Institut Charles Sadron, Université de Strasbourg（斯特拉斯堡大学，法国国家科学研究中心查尔斯·萨德龙研究所）
We extend our previous study of surface tension of ionic solutions and apply it to the case of acids (and salts) with strong ion-surface interactions. These ion-surface interactions yield a non-linear boundary condition with an effective surface charge due to adsorption of ions from the bulk onto the interface. The calculation is done using the loop-expansion technique, where the zero-loop (mean field) corresponds of the non-linear Poisson-Boltzmann equation. The surface tension is obtained analytically to one-loop order, where the mean-field contribution is a modification of the Poisson-Boltz…
We theoretically study electrostatic properties of electric double layer using a generalized Poisson-Boltzmann approach taking into account the orientational ordering of water dipoles and the excluded volume effect of water molecules as well as those of positive and negative ions with different sizes in electrolyte solution. Our approach enables one to predict that the number densities of water molecules, counterions and coions and the permittivity of electrolyte solution close to a charged surface, asymmetrically vary depending on both of sign and magnitude of the surface charge density and t…
We present a continuation of our theoretical research into the influence of co-solvent polarizability on a differential capacitance of the electric double layer [EPL 111, 28002 (2015)]. We formulate a modified Poisson-Boltzmann theory, using the formalism of density functional approach on the level of local density approximation taking into account the electrostatic interactions of ions and co-solvent molecules as well as their excluded volume. We derive the modified Poisson-Boltzmann equation, considering the three-component symmetric lattice gas model as a reference system and minimizing the…
The solution of the Poisson--Boltzmann equation for counterions confined between two charged plates is known analytically up to a constant, namely, the ion density in the middle of the channel. This quantity is relevant also because it gives access, through the contact theorem, to the osmotic pressure of the system. Here we compare the values of the ion density obtained by numerical and simulation approaches, and report a useful analytic approximation for the weak coupling regime in the absence of added salt, which predicts the value of the ion density in the worst case within 5%. The inclusio…
Hypothesis: Some ions can prevent bubbles from coalescing in water. The Gibbs-Marangoni pressure has been proposed as an explanation of this phenomenon. This repulsive pressure occurs during thin film drainage whenever surface enhanced or surface depleted solutes are present. However, bubble coalescence inhibition is known to depend on which particular combination of ions are present in a peculiar and unexplained way. This dependence may be explained by the electrostatic surface potential created by the distribution of ions at the interface, which will alters the natural surface propensity of …
The classical Poisson-Boltzmann equation (CPBE), which is a mean field theory by averaging the ion fluctuation, has been widely used to study ion distributions in charged fluids. In this study, we derive a modified Poisson-Boltzmann equation with a random field from the field theory and recover the ion fluctuation through a multiplicative noise added in the CPBE. The Poisson-Boltzmann equation with a random field (RFPBE) captures the effect of the ion fluctuation and gives different ion distributions in the charged fluids compared to the CPBE. To solve the RFPBE, we propose a Monte Carlo metho…
We study a classical system of identically charged counter-ions near a planar wall carrying a uniform surface charge density. The equilibrium statistical mechanics of the system depends on a single dimensionless coupling parameter. A new self-consistent theory of the correlation-hole type is proposed which leads to a modified Poisson-Boltzmann integral equation for the density profile, convenient for analytical progress and straightforward to solve numerically. The exact density profiles are recovered in the limits of weak and strong couplings. In contrast to previous theoretical attempts of t…
We propose a Poisson-Bikerman (PBik) formula for calculating the differential capacitance (DC) of electrical double layers (EDLs) in aqueous electrolytes or ionic liquids. The PBik theory is a generalization of the classical Poisson-Boltzmann theory to include different steric energies of different-sized ions and water similar to different electrical energies for different-charged ions. Water and ions with interstitial voids in this molecular mean field theory have their physical volumes as they do in molecular dynamics simulations. The PBik formula derived from Fermi distributions of ions and…
