Gabriel Téllez

Onsager-Manning-Oosawa condensation phenomenon and the effect of salt.

Making use of results pertaining to Painlevé III type equations, we revisit the celebrated Onsager-Manning-Oosawa condensation phenomenon for charged stiff linear polymers, in the mean-field approximation with salt. We obtain analytically the associated critical line charge density and show that it is severely affected by finite salt effects, whereas previous results focused on the no salt limit. In addition, we obtain explicit expressions for the condensate thickness and the electric potential. The case of asymmetric electrolytes is also briefly addressed.

TWO-DIMENSIONAL COULOMB SYSTEMS ON A SURFACE OF CONSTANT NEGATIVE CURVATURE

We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential created by one point charge exists and goes to zero at infinity. The pressure can be expanded as a series in integer powers of the density (the virial expansion). The correlation functions have a thermodynamic limit, and remarkably that limit is the same one for the Coulomb interaction and some other interaction law. However, special care is needed for defining a thermodynamic limit of the free energy density. There are sum rules expressing the property of perfect screening. These generic properties can be checked on the Debye–Hückel approximation, and on two exactly solvable models, the one-component plasma and the two-component plasma, at some special temperature.

Nonlinear 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 coions, divalent counterions) and a 2:1 (reversed situation) electrolyte. Our approach consists of an expansion in powers of rescaled curvature 1/ (kappaa), 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 kappaa>1. We also report an unusual overshooting effect where the colloidal effective charge is larger than the bare one.

The polydisperse cell model: Nonlinear screening and charge renormalization in colloidal mixtures

We propose a model for the calculation of renormalized charges and osmotic properties of mixtures of highly charged colloidal particles. The model is a generalization of the cell model and the notion of charge renormalization as introduced by Alexander et al. [J. Chem. Phys. 80, 5776 (1984)]. The total solution is partitioned into as many different cells as components in the mixture. The radii of these cells are determined self-consistently for a given set of parameters from the solution of the nonlinear Poisson-Boltzmann equation with appropriate boundary conditions. This generalizes Alexanderss model where the (unique) Wigner-Seitz cell radius is solely fixed by the colloid packing fraction. We illustrate the technique by considering a binary mixture of the colloids with the same sign of charge. The present model can be used to calculate thermodynamic properties of highly charged colloidal mixtures at the level of linear theories, while taking the effect of nonlinear screening into account.

Singular behavior at the edge of Laughlin states

A distinguishing feature of fractional quantum Hall (FQH) states is a singular behavior of equilibrium densities at boundaries. In contrast to states at integer filling fraction, such quantum liquids posses an additional dipole moment localized near edges. It enters observable quantities such as universal dispersion of edge states and Lorentz shear stress. For a Laughlin state, this behavior is seen as a peak, or overshoot, in the single particle density near the edge, reflecting a general tendency of electrons in FQH states to cluster near edges. We compute the singular edge behavior of the one particle density by a perturbative expansion carried out around a completely filled Landau level. This correction is shown to fully capture the dipole moment and the major features of the overshoot observed numerically. Furthermore, it exhibits the Stokes phenomenon with the Stokes line at the boundary of the droplet, decaying like a Gaussian inside and outside the liquid with different decay lengths. In the limit of vanishing magnetic length the shape the overshoot is a singular double layer with a capacity that is a universal function of the filling fraction. Finally, we derive the edge dipole moment of Pfaffian FQH states. The result suggests an explicit connection between the magnitude of the dipole moment and the bulk odd viscosity.

Exact asymptotic expansions for the cylindrical Poisson–Boltzmann equation

The mathematical theory of integrable Painleve/Toda type systems sheds new light on the behaviour of solutions to the Poisson–Boltzmann equation for the potential due to a long rod-like macroion. We investigate here the case of symmetric electrolytes together with that of 1:2 and 2:1 salts. Small and large scale features are analysed, with particular emphasis on the low salinity regime. Analytical expansions are derived for several quantities relevant for polyelectrolyte theory, such as the Manning radius. In addition, accurate and practical expressions are worked out for the electrostatic potential, which improve upon previous work and cover the full range of radial distances.

Screening of charged spheroidal colloidal particles

We study the effective screened electrostatic potential created by a spheroidal colloidal particle immersed in an electrolyte, within the mean field approximation, using Poisson-Boltzmann equation in its linear and nonlinear forms, and also beyond the mean field by means of Monte Carlo computer simulation. The anisotropic shape of the particle has a strong effect on the screened potential, even at large distances (compared to the Debye length) from it. To quantify this anisotropy effect, we focus our study on the dependence of the potential on the position of the observation point with respect with the orientation of the spheroidal particle. For several different boundary conditions (constant potential, or constant surface charge) we find that, at large distance, the potential is higher in the direction of the large axis of the spheroidal particle.

Density functional theory study of electric potential saturation: planar geometry.

We investigate the possibility of electrostatic potential saturation, which may lead to the phenomenon of effective charge saturation. The system under study is a uniformly charged infinite plane immersed in an arbitrary electrolyte made up of several microspecies. To describe the electric double layer, we use a generic local density functional theory in which the local microionic density profiles are arbitrary functions of the local electrostatic potential. A general necessary and sufficient condition is obtained for saturation, whereby the electrostatic potential created by the plane becomes independent of its bare charge, provided the latter is large enough. As a consequence, for most situations, the following simple and practical sufficient condition follows: if, as the electric potential psi--> infinity, the local theory predicts that the highest valency counterions density diverges as psi(nu) with some nu>1 or faster, then the electrostatic potential will saturate. Otherwise, if the counterion density diverges as psi or slower, or does not diverge as psi--> infinity, the electric potential will not saturate. Using this condition, we investigate the possibility of the saturation phenomenon within the framework of recent theories proposed in the literature to describe electrical double layer beyond the Poisson-Boltzmann description.

On the bulk modulus of the cell model of charged macromolecules suspensions

We study theoretically the bulk modulus (inverse of the compressibility) of a suspension of charged objects (macroions), making use of a cell model to account for the finite density of macroions. The diffuse layer of charged microspecies around a macroion is described by a generic local density functional theory. Within this general framework, we obtain the condition for a positive bulk modulus, which is fulfilled by several proposals made in the literature and rules out the possibility of a critical point. We show that a sufficient condition for a positive compressibility also ensures that the same theory produces repulsive effective pair potentials.

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–Hückel theory, we consider the case of highly charged macromolecules, where the linear approximation breaks down and the system is described by the 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.