David Andelman

STERIC EFFECTS IN ELECTROLYTES : A MODIFIED POISSON-BOLTZMANN EQUATION

The adsorption of large ions from solution to a charged surface is investigated theoretically. A generalized Poisson-Boltzmann equation which takes into account the finite size of the ions is presented. We obtain analytical expressions for the electrostatic potential and ion concentrations at the surface, leading to a modified Grahame equation. At high surface charge densities the ionic concentration saturates to its maximum value. Our results are in agreement with recent experiments.

Neutral and charged polymers at interfaces

Abstract Chain-like macromolecules (polymers) show characteristic adsorption properties due to their flexibility and internal degrees of freedom, when attracted to surfaces and interfaces. In this review we discuss concepts and features that are relevant to the adsorption of neutral and charged polymers at equilibrium, including the type of polymer/surface interaction, the solvent quality, the characteristics of the surface, and the polymer structure. We pay special attention to the case of charged polymers (polyelectrolytes) that have a special importance due to their water solubility. We present a summary of recent progress in this rapidly evolving field. Because many experimental studies are performed with rather stiff biopolymers, we discuss in detail the case of semi-flexible polymers in addition to flexible ones. We first review the behavior of neutral and charged chains in solution. Then, the adsorption of a single polymer chain is considered. Next, the adsorption and depletion processes in the many-chain case are reviewed. Profiles, changes in the surface tension and polymer surface excess are presented. Mean-field and corrections due to fluctuations and lateral correlations are discussed. The force of interaction between two adsorbed layers, which is important in understanding colloidal stability, is characterized. The behavior of grafted polymers is also reviewed, both for neutral and charged polymer brushes.

Phase transitions in Langmuir monolayers of polar molecules

Insoluble Langmuir monolayers are investigated in the presence of dipolar forces which can have two origins: permanent dipoles in neutral monolayers and induced dipoles in charged monolayers. The main effect of the additional long‐range repulsive interactions is to stabilize undulating phases at thermodynamic equilibrium. Phase diagrams are obtained in two limits: close to the liquid–gas critical point via a Ginzburg–Landau expansion of the free energy (mainly within a mean‐field approximation), and at low temperatures by free energy minimization. Possible applications of this theory to experiments at the liquid–gas, liquid expanded–liquid condensed, and solid–liquid transitions are discussed.

Theory of Spontaneous Vesicle Formation in Surfactant Mixtures

The curvature elastic energy of bilayer vesicles formed by a mixture of two surfactants, which individually form either micelles or lamellar bilayer phases is described theoretically. In the limit of large bending elastic modulus K being much greater than the temperature T, the free energy is minimized by vesicles with different concentrations of the two surfactants in each monolayer of the bilayer. Vesicles are more stable than lameliar structures only when interactions or complexing of the two surfactants is taken into account.

Adsorption of large ions from an electrolyte solution: a modified Poisson–Boltzmann equation

Abstract The behavior of electrolyte solutions close to a charged surface is studied theoretically. A modified Poisson–Boltzmann equation that takes into account the volume excluded by the ions in addition to the electrostatic interactions is presented. In a formal lattice gas formalism the modified Poisson–Boltzmann equation can be obtained from a mean-field approximation of the partition function. In an alternative phenomenological approach, the same equation can be derived by including the entropy of the solvent molecules in the free energy. In order to visualize the effect of steric repulsion, a simple case of a single, highly charged, flat surface is discussed. This situation resembles recent adsorption experiments of large ions onto a charged monolayer. A simple criterion for the importance of the steric effects is expressed in terms of the surface charge density and the size of the ions. It is shown that when these effects are important a saturated layer is formed near the surface. A modified Grahame equation relating the ion concentration at the surface to the surface charge density is obtained.

Structure and phase equilibria of microemulsions

We present a simple phenomenological model to describe the phase equilibria and structural properties of microemulsions. Space is divided into cells of side ξ; each cell is filled with either pure water or oil. Surfactant molecules are presumed to form an incompressible fluid monolayer at the oil–water interface. The monolayer is characterized by a size‐dependent bending constant K(ξ), which is small for ξ≥ξK, the de Gennes–Taupin persistence length. The model predicts a middle‐phase microemulsion of structural length scale ξ≊ξK which coexists with dilute phases of surfactant in oil and surfactant in water. (These phases have ξ≊a, a being a molecular length.) On the same ternary phase diagram, we find also two regions of two‐phase equilibrium involving upper‐ and lower‐phase microemulsions that coexist with either almost pure water or oil. At low temperatures and/or high values of the bare bending constant, K0≡K(a), the middle‐phase microemulsion may be entirely precluded by separation to a lamellar phase...

Dipolar Poisson-Boltzmann Equation: Ions and Dipoles Close to Charge Interfaces

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 interplate pressure.

Dielectric constant of ionic solutions: a field-theory approach.

We study the variation of the dielectric response of a dielectric liquid (e.g. water) when a salt is added to the solution. Employing field-theoretical methods, we expand the Gibbs free energy to first order in a loop expansion and calculate self-consistently the dielectric constant. We predict analytically the dielectric decrement which depends on the ionic strength in a complex way. Furthermore, a qualitative description of the hydration shell is found and is characterized by a single length scale. Our prediction fits rather well a large range of concentrations for different salts using only one fit parameter related to the size of ions and dipoles.

Water, electricity, and between… On electrowetting and its applications

Imagine a drop of water lying on a surface, pulled into a ball by surface tension. With electricity it is possible to change the shape of the drop and cause it to flatten out. This is electrowetting, a physical phenomenon which has aroused great interest in recent years as it has found new applications. Here we will describe the phenomenon and two of its applications: variable-focus liquid lenses and paper-thin, video-rate, reflective color displays.

Random Surface Model for the L3-Phase of Dilute Surfactant Solutions

We present a simple model for the anomalous (flow-birefringent) isotropic phase, known as L3, that is seen in certain surfactant solutions at volume fractions of a few percent. The proposed structure consists of locally sheetlike sections of semi-flexible surfactant bilayer, connected up at larger distances into a multiply connected random surface, having a preferred structural length scale of order the persistence length of the bilayer. A first-order transition between this isotropic sheetlike phase and the nearby swollen lamellar phase is described.