We analyze theoretically the electrostatic interaction of surface-charged colloids at water interfaces with special attention to the experimentally relevant case of large charge densities on the colloidwater interface. Whereas linear theory predicts an effective dipole potential the strength of which is proportional to the square of the product of charge density and screening length, nonlinear charge renormalization effects change this dependence to a weakly logarithmic one. These results appear to be particularly relevant for structure formation at air-water interfaces with arbitrarily shaped colloids.PACS numbers: 82.70.DdThe effective interactions of colloids trapped at fluid interfaces reveal qualitatively new features when compared to the ones in colloidal bulk solutions. First, there is the possibility of long-ranged capillary attractions mediated by deformations of the interface [1,2]. Second, many colloids carry a significant amount of charge (e.g. charge-stabilized polymeric colloids, mineralic disks, proteins) and the exponentially screened electrostatic interactions in ionic bulk solvents become longer-ranged at interfaces between water and a nonpolar medium (typically air or oil). At such interfaces the colloids exhibit effective dipole-like repulsions which lead to the stabilization of two-dimensional crystals even at low surface coverages [3]. These effective dipoles originate from colloidal surface charges on the water side and a cloud of screening ions in the water phase which is asymmetric with respect to the interface plane. Within a simple model (the only analytically tractable one) the colloids are approximated as equal point charges q located in the interface plane and the water phase is treated as a linearly screening medium. To leading order the interaction between two charges q in the interface plane at separation d is given by [4]Here, ǫ 1 and ǫ 2 are the permittivities of the nonpolar medium and water, respectively, and ǫ 0 is the dielectric constant of vacuum. According to this linear model the repulsion depends quadratically on the Debye screening length κ −1 = (ǫ 2 ǫ 0 /(2βc 0 e 2 )) 1/2 where c 0 is the concentration of monovalent ions in bulk water, e is the elementary charge, and β −1 = k B T . On this basis one would expect the repulsion U ∝ c 2 ) invalidate the naive use of the linearized Debye-Hückel (DH) model with bare charges. Strong charge renormalization will occur due to the nonlinear contributions of the governing Poisson-Boltzmann equation (PB) in the water phase. The renormalization procedure (based on the separation of length scales) consists of the identification of the appropriate corresponding linear solution of the PB problem at distances > κ −1 from the charges. There the electrostatic potential Φ is small and linear DH electrostatics holds: ∇ 2 Φ ≃ κ 2 Φ. For a uniformly charged wall or sphere, this solution has the same functional form as if the entire problem is solved within the linear theory and the nonlinear effects alter only the prefactor. This prefactor ...

We incorporate ion polarizabilities into the Poisson-Boltzmann equation by modifying the effective dielectric constant and the Boltzmann distribution of ions. The extent of the polarizability effects is controlled by two parameters, γ(1) and γ(2); γ(1) determines the polarization effects in a dilute system and γ(2) regulates the dependence of the polarizability effects on the concentration of ions. For a polarizable ion in an aqueous solution γ(1) ≈ 0.01 and the polarizability effects are negligible. The conditions where γ(1) and/or γ(2) are large and the polarizability is relevant involve the low dielectric constant media, high surface charge, and/or large ionic concentrations.

Colloidal spheres driven through water along a circular path by an optical ring trap display unexpected dynamical correlations. We use Stokesian dynamics simulations and a simple analytical model to demonstrate that the path's curvature breaks the symmetry of the two-body hydrodynamic interaction, resulting in particle pairing. The influence of this effective nonequilibrium attraction diminishes as either the temperature or the stiffness of the radial confinement increases. We find a well-defined set of dynamically paired states whose stability relies on hydrodynamic coupling in curving trajectories.

To explore charge regulation (CR) in physicochemical and biophysical systems, we present a model of colloidal particles with sticky adsorption sites which account for the formation of covalent bonds between the hydronium ions and the surface functional groups. Using this model and Monte Carlo simulations, we find that the standard Ninham and Parsegian (NP) theory of CR leads to results which deviate significantly from computer simulations. The problem of NP approach is traced back to the use of bulk equilibrium constant to account for surface chemical reactions. To resolve this difficulty we present a new theory of CR. The fundamental ingredient of the new approach is the sticky length, which is non-trivially related with the bulk equilibrium constant. The theory is found to be in excellent agreement with computer simulations, without any adjustable parameters. As an application of the theory we calculate the effective charge of colloidal particles containing carboxyl groups, as a function of pH and salt concentration.Electrostatic interactions play a fundamental role in physics, chemistry, and biology. The long-range nature of the Coulomb force, however, makes it very difficult to study theoretically 1 . In aqueous systems ions are usually hydrated by water molecules. On the other hand, acids lose proton, which associates with the water molecule forming a hydronium ion 2 . There are many reactions that are controlled by pH, and the acid-base equilibrium directly influences the functionality of biomolecules. Although pH can be easily tuned in experiments, it is much more difficult to account for the chemical equilibrium in theoretical and simulation studies 3 .Colloidal particles often have organic functional groups on their surfaces. In aqueous systems these groups dissociate, loosing a proton, resulting in a colloidal surface charge 4-7 . The amount of surface charge strongly depends on the pH of the environment 8,9 and is controlled by the chemical equilibrium between hydronium ions and the functional groups. This process is known as charge regulation (CR) 10-16 . The concept of charge regulation was first described by Linderstrøm-Lang 17-19 and studied theoretically by Ninham and Parsegian. 20 . CR is of fundamental importance in colloidal science 10,21-32 and biophysics 33-39 . It has been applied to explore the stability of electrical double layers 9,40-45 and is of great technological importance in fields as diverse as mineral preparation, agriculture, ceramics, and surface coating 46 .Consider a weak acid HA in equilibrium with bulk water, HA+H 2 O ⇄ H 3 O + +A -. For dilute solutions the concentration of all species is controlled by the law of mass action, K eq = c HA /c A -c H +,where K eq is the equilibrium constant and c indicates the concentration of each specie. Ninham and Parsegian (NP) supposed that the same equilibrium relation will hold for the reactive (acidic) sites on the colloidal surface with the local concentration of hydronium determined by the Boltzmann distribution, c surfq is the proto...

This review explores the number of mean-field constructions for ions whose structure goes beyond the point-charge description, a representation used in the standard Poisson-Boltzmann equation. The exploration is motivated by a body of experimental work which indicates that ion-specific effects play a significant role, where ions of the same valence charge but different size, polarizability, or shape yield quite different, and sometimes surprising results. Furthermore, there are many large ions encountered in soft-matter and biophysics that do not fit into a point-charge description, and their extension in space and shape must be taken into account of any reasonable representation.

Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, h_{λ}(r,r^{'}), in which interactions λu(r,r^{'}) are gradually switched on as λ changes from 0 to 1. The function h_{λ}(r,r^{'}) is then obtained from the inhomogeneous Ornstein-Zernike equation and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. The two equations do not yet constitute a closed set. In the present work we use the closure c_{λ}(r,r^{'})≈-λβu(r,r^{'}), known as the random-phase approximation (RPA). We demonstrate that the RPA is identical with the variational Gaussian approximation derived within the field-theoretical framework, originally derived and used for charged particles. We apply our generalized RPA approximation to the Gaussian core model and Coulomb charges.

Electrostatic interactions between charged, distant colloids in a bulk electrolyte solution do not depend on the inherent structure of ions and a solvent forming a double layer. For charged colloids trapped at an interface between an electrolyte and air this no longer holds; as the electrostatic interactions are mediated via air and the field lines determining the interactions originate at the charged surface, these details come into prominence. Using the Langevin-Poisson-Boltzmann equation we investigate how steric effects and the polarization saturation of a solvent effect the contact potential at the colloid surface and, in consequence, the long range interactions between colloids trapped at an interface. For a surface charge 0.4 C m(-2) the combination of these effects can increase the interactions by up to ∼40 times when compared to Poisson-Boltzmann calculations. The validity of these enhancement mechanisms is supported by recent experimental data (K. Masschaele et al., Phys. Rev. Lett., 2010, 105, 048303).

We study charge regulation of colloidal particles inside aqueous electrolyte solutions. To stabilize colloidal suspension against precipitation, colloidal particles are synthesized with either acidic or basic groups on their surface....