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.PACS numbers: 61.20. Qg,82.65.Dp,82.60.Lf The interaction between charged objects (interfaces, colloidal particles, membranes, etc) in solution is strongly affected by the presence of an electrolyte (salt) and is of great importance in biological systems and industrial applications [1,2]. The main effect is screening of the Coulomb interaction characterized by the so-called Debye-Hückel screening length [3], which depends on the ionic strength of the solution. The Deryaguin-LandauVerwey-Overbeek theory, based on the competition between screened Coulomb and attractive van der Waals interactions, has been very successful in explaining the stabilization of charged colloidal particles [4].One of the most widely used analytical method to describe electrolyte solutions is the Poisson-Boltzmann (PB) approach [5]. For low electrostatic potentials (less than 25 mV), the PB equation can be linearized and yields the Debye-Hückel theory [3]. The PB is a continuum mean-field like approach assuming point-like ions in thermodynamic equilibrium and neglecting statistical correlations. This theory has been successful in predicting ionic profiles close to planar and curved surfaces and the resulting forces. However, it is known to strongly overestimate ionic concentrations close to charged surfaces. In particular, this shortcoming of the PB theory is pronounced for highly charged surfaces and multivalent ions.Since the PB equation does not take into account the finite size of the adsorbing ions, the ionic concentration close to the surface can easily exceed the maximal allowed coverage by orders of magnitude. Several attempts have been proposed to include the steric repulsion in order to improve upon the PB approach [6,7]. One of the first attempts to incorporate steric effects is the Stern layer modification [6,8] of the PB approach. Steric effects are introduced by excluding the ions from the first molecular layer close to the surface. However, it seems difficult to improve on this method in a systematic way. More recent modifications [6,7,[9][10][11] rely either on Monte Carlo computer simulations or on numerical solutions of integral equations (the "hypernetted chain" equation [9]). These approaches involve elaborate numerical calculations and lack the simplicity of the original PB approach.In this Letter, we propose a simple way to include steric effects in the original PB approach. This modified PB equation clearly shows how ionic saturation takes place close to a charged surface. The equation is derived for 1:z asymmetric and z:z symmetric...

A wide variety of two- and three-dimensional physical-chemical systems display domain patterns in equilibrium. The phenomenology of these patterns, and of the shapes of their constituent domains, is reviewed here from a point of view that interprets these patterns as a manifestation of modulated phases. These phases are stabilized by competing interactions and are characterized by periodic spatial variations of the pertinent order parameter, the corresponding modulation period generally displaying a dependence on temperature and other external fields. This simple picture provides a unifying framework to account for striking and substantial similarities revealed in the prevalent "stripe" and "bubble" morphologies as well as in commonly observed, characteristic domain-shape instabilities. Several areas of particular current interest are discussed.

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.

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.PACS numbers: 61.20. Qg, 68.08.De, 82.60.Lf, 82.70.Dd Charged objects (ions, interfaces and particles) immersed in liquids play a central role in electrochemistry, colloidal science and biology ranging from electrolyte applications, stabilization of colloidal suspensions, protein folding and its biological activity, and even in protein aggregation [1,2,3,4,5,6,7].The most commonly used model -the PoissonBoltzmann model (PB) [1,3,4] -assumes point-like ions immersed in a continuum dielectric media and treats the system in a mean-field approximation. The medium is modeled by a homogeneous and isotropic dielectric constant. This model is simple, elegant and efficient. It is in good agreement with experiments for monovalent ions up to energies of order of k B T . However, careful measurements of the forces between two charged surfaces at nanometric scale show strong deviation from the simple PB picture [3]. In particular, the assumption that the continuum dielectric medium is homogeneous does not take into account the strong dielectric response of water molecules around charges. The discrete moments of water molecules will orient themselves close to charged ions and surfaces giving rise to hydration shells and to hydrophobic interactions, which can be measured at short distances, for example, between two charged plates (surface force balance apparatus). These hydration phenomena are very important in many biological processes such as protein folding, protein crystallization and interactions between charged biopolymers inside the cell.Most studies other than the PB rely on one of several theoretical techniques. Monte Carlo (MC) [8] or Molecular Dynamic (MD) [9] computer simulations take into account the discrete nature of the dipolar molecules. A second approach relies on liquid state theory, integral equation and other methods [10,11]. In simple planar geometry the latter gives good agreement with the MC and MD simulations. However, all these methods are rather cumbersome and involve heavy computation resources. In addition, they lack the simple physical picture provided by a Poisson-Boltzmann type of approach.In this Letter we propose another approach called the Dipolar Poisson-Boltzmann (DPB). Unlike the PB model where the solution is characterized by a homogeneous dielectric constant, in the DPB model we coarse grain the interaction of individual ions and dipoles interacting together. This makes the DPB an analytic extension of the PB formalism. Although it is done on a meanfield level, it includes some aspects of the discrete nature of the dipolar solvent mo...

The behavior of electrolyte solutions close to a charged surface is studied theoretically. A modified Poisson-Boltzmann equation which 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 the 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.

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.

No abstract

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.