Correlation effects,image charge effects and finite size in the macro-ion-electrolyte system: A field-theoretic approach

We consider a model of a macro-ion surrounded by small ions of an electrolyte solution. The finite size of ionic charge distributions of ions, and image charge effects are considered. From such a model it is possible to construct a statistical field theory with a single fluctuating field and derive physical interpretations for both the mean field and two-point correlation function. For point-like charges, at the level of a Gaussian (or saddle point) approximation, we recover the standard Poisson-Boltzmann equation. However, to include ionic correlation effects, as well as image charge effects of individual ions, we must go beyond this. From the field theory considered, it is possible to construct self-consistent approximations. We consider the simplest of these, namely the Hartree approximation. The Hartree equations take the form of two coupled equations. One is a modified Poisson-Boltzmann equation; the other describes both image charge effects on the individual ions, as well as correlations. Such equations are difficult to solve numerically, so we develop an (a WKB-like) approximation for obtaining approximate solutions. This, we apply to a uniformly charged rod in univalent electrolyte solution, for point like ions, as well as for extended spherically symmetric distributions of ionic charge on electrolyte ions. The solutions show how correlation effects and image charge effects modify the Poisson-Boltzmann result. Finite-size charge distributions of the ions reduce both the effects of correlations and image charge effects. For point charges, we test the WKB approximation by calculating a leading-order correction from the exact Hartree result, showing that the WKB-like approximation works reasonably well in describing the full solution to the Hartree equations. From these solutions, we also calculate an effective charge compensation parameter in an analytical formula for the interaction of two charged cylinders. Electronic supplementary material  Supplementary material in the form of a doc file available from the journal web page at and are accessible for authorised users.     

Debye-Hückel theory for slab geometries

The electrostatic interaction of charged particles through or at a low-dielectric slab, such as a lipid bilayer immersed in water or a self-assembled monolayer (SAM) on a metal substrate, is considered theoretically in the presence of salt within the Gaussian approximation using a generalized Green's formalism. A number of separate situations are discussed: i) The presence of a low-dielectric slab leads to pronounced interactions of a single charge with the slab via the formation of polarization surface charges. For SAMs on metal substrates, there is an intricate crossover from image-charge attraction to the metal substrate (for large distances) to image-charge repulsion from the SAM (for small distances) with a stable minimum at a distance of roughly 20 times the thickness of the hydrophobic film. For bilayers in water, the interaction of a single charge is always repulsive. ii) The surface potential of a SAM is calculated for the case when the hydrophobic layer contains dipole moments, which might explain the recently observed long-ranged repulsion of hydrophobic scanning tips from PEG-terminated SAMs on gold. iii) The interaction between charged particles through the bilayer is weakened. Oppositely charged particles still attract each other through the membrane. The free-energy minimum occurs as a result of the competition between self-repulsion from the slab and interparticle attraction and is located at a separation from the membrane surface which equals 15 times the membrane thickness. iv) Surface charges on the two surfaces of a bilayer attract each other through the bilayer unless the surface charge densities are the same, even if the signs are the same. v) All these effects are strongly influenced by the presence of salt. Received 25 January 2000     

Simulations of counterions at charged plates

Using Monte Carlo simulations, we study the counterion distribution close to planar charged walls in two geometries: i) when only one charged wall is present and the counterions are confined to one half-space, and ii) when the counterions are confined between two equally charged walls. In both cases the surface charge is smeared out and the dielectric constant is the same everywhere. We obtain the counterion density profile and compare it with both the Poisson-Boltzmann theory (asymptotically exact in the limit of weak coupling, i.e. low surface charge, high temperature and low counterion valence) and the strong-coupling theory (valid in the opposite limit of high surface charge, low temperature and high counterion valence) and with previously calculated correction terms to both theories for different values of the coupling parameter, thereby establishing the domain of validity of the asymptotic limits. Gaussian corrections to the leading Poisson-Boltzmann behavior (obtained via a systematic loop expansion) in general perform quite poorly: At coupling strengths low enough so that the Gaussian (or one-loop) correction does describe the numerical deviations from the Poisson-Boltzmann result correctly, the leading Poisson-Boltzmann term by itself matches the data within high accuracy. This reflects the slow convergence of the loop expansion. For a single charged plane, the counterion pair correlation function indicates a behavioral change from a three-dimensional, weakly correlated counterion distribution (at low coupling) to a two-dimensional, strongly correlated counterion distribution (at high coupling), which is paralleled by the specific-heat capacity which displays a rounded hump at intermediate coupling strengths. For the case of counterions confined between two equally charged walls, we analyze the inter-wall pressure and establish the complete phase diagram, featuring attraction between the walls for large enough coupling strength and at intermediate wall separation. Depending on the thermodynamic ensemble, the phase diagram exhibits a discontinuous transition where the inter-wall distance jumps to infinity (in the absence of a chemical potential coupling to the inter-wall distance, as for charged lamellae in excess solvent) or a critical point where two coexisting states with different inter-wall distance become indistinguishable (in the presence of a chemical potential, as for charged lamellae with a finite fixed solvent fraction). The attractive pressure decays with the inter-wall distance as an inverse cube, similar to analytic predictions, although the amplitude differs by an order of magnitude from previous theoretical results. Finally, we discuss in detail our simulation methods and compare the finite-size scaling behavior of different boundary conditions (periodic, minimal image and open). Received 6 November 2001     

Static polarizability effects on counterion distributions near charged dielectric surfaces: A coarse-grained Molecular Dynamics study employing the Drude model

Coarse-grained implicit solvent Molecular Dynamics (MD) simulations have been used to investigate the structure of the vicinal layer of polarizable counterions close to a charged interface. The classical Drude oscillator model was implemented to describe the static excess polarizability of the ions. The electrostatic layer correction with image charges (ELCIC) method was used to include the effects of the dielectric discontinuity between the aqueous solution and the bounding interfaces for the calculation of the electrostatic interactions. Cases with one or two charged bounding interfaces were investigated. The counterion density profile in the vicinity of the interfaces with different surface charge values was found to depend on the ionic polarizability. Ionic polarization effects are found to be relevant for ions with high excess polarizability near surfaces with high surface charge.     

Solvent and nonlinear effects on the charge renormalization of nanoparticles within a molecular electrolyte model

A general analysis of the effect of the molecular structure of a polar solvent on the effective interactions among suspended charged nanoparticles (macroions up to 30 nm in size) is performed using a simple molecular model for the solvent in the supporting electrolyte. The solvent molecules are modeled as small rods with end point charges of opposite sign and equal magnitude, whereas the small ions are assumed to be point-like. We compare the renormalized charges of the effective pair potentials (EPPs) among the spherical nanoparticles, obtained after contracting the supporting electrolyte, with those obtained from a similar model, which does not include the solvent molecules. The parameters of both models have been adjusted to give the same screening length. The comparison shows that the renormalized charges are overestimated when the molecular structure of the solvent is neglected. This is in agreement with the image charge effect induced by the different permittivities inside and outside the nanoparticles for the model with explicit solvent molecules; an effect that is missing in the model without solvent molecules. A new numerical method allows us to explore macroion diameters much larger than the solvent molecular size.     

On the absence of charge symmetry in electrostatic interaction between charged drops and hard particles

It is shown that the analytical expressions for the energy and force of electrostatic interaction between charged conducting particles (drops), a point charge, and a finite-size particle, as well as between a particle (a drop or a point charge) and a conducting plane, are asymmetric with respect to the sign of one of the charges. This is because the polarization interaction is always attractive irrespective of the signs of interacting particles. The absence of this symmetry leads to the self-constriction of charged aerodispersed systems containing a condensed phase, for example, plasma or liquid-droplet systems.     

Electrostatic image effects for counterions between charged planar walls

We study the effect of dielectric inhomogeneities on the interaction between two planparallel charged surfaces with oppositely charged mobile charges in between. The dielectric constant between the surfaces is assumed to be different from the dielectric constant of the two semiinfinite regions bounded by the surfaces, giving rise to electrostatic image interactions. We show that on the weak-coupling level the image charge effects are generally small, making their mark only in the second-order fluctuation term. However, in the strong-coupling limit, the image effects are large and fundamental. They modify the interactions between the two surfaces in an essential way. Our calculations are particularly useful in the regime of parameters where computer simulations would be difficult and extremely time consuming due to the complicated nature of the long-range image potentials.     

Dynamical properties of Ag-Cu binary alloy from molecular dynamics simulation

Molecular dynamics simulations (MD) of dynamical properties of molten binary Ag-Cu alloy is presented at various temperature above the eutetic temperature. Atoms in the system have been modelled through an interatomic Lennard-Jones potential interaction. The structure, through the effective pair distribution function allows to determine the Enksog collision frequency as well as the coordination of atoms in the first shell. The surface traction, which is the force per unit area between the species shows a long separation oscillation about the value zero, while the collision frequency of pairs of atoms increase with increasing temperature. The adhesion energy between components found to be 3.4178 J/m². In agreement with theory, we found a decrease in surface tension of Ag-Cu alloy as temperature increases. Separation of atoms pairs in the first shell might be responsible for a non linear relationship found between temperature and coordination number in present calculations.     

Water contact angles on charged surfaces in aerosols

Interactions between water and solid substrates are of fundamental importance to various processes in nature and industry. Electric control is widely used to modify interfacial water, where the influence of surface charges is inevitable. Here we obtain positively and negatively charged surfaces using LiTaO₃ crystals and observe that a large net surface charge up to 0.1 C/m² can nominally change the contact angles of pure water droplets comparing to the same uncharged surface. However, even a small amount of surface charge can efficiently increase the water contact angle in the presence of aerosols. Our results indicate that such surface charges can hardly affect the structure of interfacial water molecular layers and the morphology of the macroscopic droplet, while adsorption of a small amount of organic contaminants from aerosols with the help of Coulomb attraction can notably decrease the wettability of solid surface. Our results not only provide a fundamental understanding of the interactions between charged surfaces and water, but also help to develop new techniques on electric control of wettability and microfluidics in real aerosol environments.     

Beyond Poisson-Boltzmann: Fluctuation effects and correlation functions

We formulate the exact non-linear field theory for a fluctuating counter-ion distribution in the presence of a fixed, arbitrary charge distribution. The Poisson-Boltzmann equation is obtained as the saddle-point of the field-theoretic action, and the effects of counter-ion fluctuations are included by a loop-wise expansion around this saddle point. The Poisson equation is obeyed at each order in this loop expansion. We explicitly give the expansion of the Gibbs potential up to two loops. We then apply our field-theoretic formalism to the case of a single impenetrable wall with counter ions only (in the absence of salt ions). We obtain the fluctuation corrections to the electrostatic potential and the counter-ion density to one-loop order without further approximations. The relative importance of fluctuation corrections is controlled by a single parameter, which is proportional to the cube of the counter-ion valency and to the surface charge density. The effective interactions and correlation functions between charged particles close to the charged wall are obtained on the one-loop level. Received 8 February 1999 and Received in final form 15 May 1999