Interfacial Tension of Electrolyte Solutions

A theory is presented to account for the increase in surface tension of water in the presence of electrolyte. Unlike the original ``grand-canonical'' calculation of Onsager and Samaras, which relied on the Gibbs adsorption isotherm and lead to a result which could only be expressed as an infinite series, our approach is ``canonical'' and produces an analytic formula for the excess surface tension. For small concentrations of electrolyte, our result reduces to the Onsager-Samaras limiting law.Comment: contains two figures. Journal of Chemical Physics, in pres

Non-linear charge reduction effect in strongly-coupled plasmas

The charge reduction effect, produced by the nonlinear Debye screening of high-Z charges occuring in strongly-coupled plasmas, is investigated. An analytic asymptotic expression is obtained for the charge reduction factor which determines the Debye-Hueckel potential generated by a charged test particle. Its relevant parametric dependencies are analyzed and shown to predict a strong charge reduction effect in strongly-coupled plasmas.Comment: 4 figure

Comparison of methods for estimating continuous distributions of relaxation times

The nonparametric estimation of the distribution of relaxation times approach is not as frequently used in the analysis of dispersed response of dielectric or conductive materials as are other immittance data analysis methods based on parametric curve fitting techniques. Nevertheless, such distributions can yield important information about the physical processes present in measured material. In this letter, we apply two quite different numerical inversion methods to estimate the distribution of relaxation times for glassy \lila\ dielectric frequency-response data at 225 \kelvin. Both methods yield unique distributions that agree very closely with the actual exact one accurately calculated from the corrected bulk-dispersion Kohlrausch model established independently by means of parametric data fit using the corrected modulus formalism method. The obtained distributions are also greatly superior to those estimated using approximate functions equations given in the literature.Comment: 4 pages and 4 figure

The Poisson-Boltzmann Theory for Two Parallel Uniformly Charged Plates

We solve the nonlinear Poisson-Boltzmann equation for two parallel and likely charged plates both inside a symmetric elecrolyte, and inside a 2 : 1 asymmetric electrolyte, in terms of Weierstrass elliptic functions. From these solutions we derive the functional relation between the surface charge density, the plate separation, and the pressure between plates. For the one plate problem, we obtain exact expressions for the electrostatic potential and for the renormalized surface charge density, both in symmetric and in asymmetric electrolytes. For the two plate problems, we obtain new exact asymptotic results in various regimes.Comment: 17 pages, 9 eps figure

Nonlinear screening of charged macromolecules

We present several aspects of the screening of charged macromolecules in an electrolyte. After a review of the basic mean field approach, based on the linear Debye-Huckel theory, we consider the case of highly charged macromolecules, where the linear approximation breaks down and the system is described by full nonlinear Poisson-Boltzmann equation. Some analytical results for this nonlinear equation give some interesting insight on physical phenomena like the charge renormalization and the Manning counterion condensation

Fractional Equations of Curie-von Schweidler and Gauss Laws

The dielectric susceptibility of most materials follows a fractional power-law frequency dependence that is called the "universal" response. We prove that in the time domain this dependence gives differential equations with derivatives and integrals of noninteger order. We obtain equations that describe "universal" Curie-von Schweidler and Gauss laws for such dielectric materials. These laws are presented by fractional differential equations such that the electromagnetic fields in the materials demonstrate "universal" fractional damping. The suggested fractional equations are common (universal) to a wide class of materials, regardless of the type of physical structure, chemical composition or of the nature of the polarization.Comment: 11 pages, LaTe

Lattice Models of Ionic Systems

A theoretical analysis of Coulomb systems on lattices in general dimensions is presented. The thermodynamics is developed using Debye-Huckel theory with ion-pairing and dipole-ion solvation, specific calculations being performed for 3D lattices. As for continuum electrolytes, low-density results for sc, bcc and fcc lattices indicate the existence of gas-liquid phase separation. The predicted critical densities have values comparable to those of continuum ionic systems, while the critical temperatures are 60-70% higher. However, when the possibility of sublattice ordering as well as Debye screening is taken into account systematically, order-disorder transitions and a tricritical point are found on sc and bcc lattices, and gas-liquid coexistence is suppressed. Our results agree with recent Monte Carlo simulations of lattice electrolytes.Comment: 25 pages, 3 figures, ReVTeX 4, Submitted to J. Chem. Phy

Electrostatic interactions mediated by polarizable counterions: weak and strong coupling limits

We investigate the statistical mechanics of an inhomogeneous Coulomb fluid composed of charged particles with static polarizability. We derive the weak- and the strong-coupling approximations and evaluate the partition function in a planar dielectric slab geometry with charged boundaries. We investigate the density profiles and the disjoining pressure for both approximations. Comparison to the case of non-polarizable counterions shows that polarizability brings important differences in the counterion density distribution as well as the counterion mediated electrostatic interactions between charged dielectric interfaces.Comment: 25 pages, 7 figure

Non-linear screening of spherical and cylindrical colloids: the case of 1:2 and 2:1 electrolytes

From a multiple scale analysis, we find an analytic solution of spherical and cylindrical Poisson-Boltzmann theory for both a 1:2 (monovalent co-ions, divalent counter-ions) and a 2:1 (reversed situation) electrolyte. Our approach consists in an expansion in powers of rescaled curvature $1/(\kappa a)$, where $a$ is the colloidal radius and $1/\kappa$ the Debye length of the electrolytic solution. A systematic comparison with the full numerical solution of the problem shows that for cylinders and spheres, our results are accurate as soon as $\kappa a>1$. We also report an unusual overshooting effect where the colloidal effective charge is larger than the bare one.Comment: 9 pages, 11 figure

Crossover Scales at the Critical Points of Fluids with Electrostatic Interactions

Criticality in a fluid of dielectric constant D that exhibits Ising-type behavior is studied as additional electrostatic (i.e., ionic) interactions are turned on. An exploratory perturbative calculation is performed for small ionicity as measured by the ratio of the electrostatic energy to the strength of the short-range nonionic (i.e., van der Waals) interactions in the uncharged fluid. With the aid of distinct transformations for the short-range and for the Coulombic interactions, an effective Hamiltonian with coefficients depending on the ionicity is derived at the Debye-Hueckel limiting-law level for a fully symmetric model. The crossover between classical (mean-field) and Ising behavior is then estimated using a Ginzburg criterion. This indicates that the reduced crossover temperature depends only weakly on the ionicity (and on the range of the nonionic potentials); however, the trends do correlate with the, much stronger, dependence observed experimentally.Comment: 25 pages, 4 figure; submitted to J. Chem. Phy