J.P. Badiali

A microscopic model for the liquid metal-ionic solution interface

Abstract A microscopic model for the metal-solution interface is presented, which, for the first time, includes both a non-ideal treatment of the metal and a molecular model for the solution side. The metal is described by a jellium model including electron-ion pseudo-potential. The solution is treated as a mixture of hard spheres with point dipoles (solvent molecules) or point charges (ions). The statistical mechanics is solved using mean spherical approximation. No a priori separation is introduced between compact and diffuse layers. A simplified version of the model is applied to the case of Hg-DMSO systems.

Effect of solvent on properties of the liquid metal surface

We calculate the difference in the surface potentials between the free surface of a liquid metal and the same metal in an ideally polarizable interface at the point of zero charge. This difference, δχm, is due to the deformation of the electronic cloud of the metal by the solvent molecules. The simple model used for the free (metal-metal vapor) surface yields qualitatively correct work functions for a number of metals (Hg, Cd, In, Zn, Pb, Ga, Al). Two simple ways to model the metal-solvent interaction are proposed and calculations of δχm made for each. One, the dielectric film model, considers only an electrostatic interaction between metal electrons and solvent, while the other, the repulsive core model, considers only the exchange repulsion between metal electrons and the cores of solvent molecules. For Zn, Cd and Hg the dielectric film model, with parameters chosen according to conventional electrochemical wisdom, gives values for δχm which are close to those estimated in the literature. For Ga and Al, the effect of the solvent is much greater because of the larger electron density and smaller ion size. The repulsive core model can give similar results, but there is an arbitrariness in the choice of the barrier strength parameter. Again, Ga is more sensitive to the presence of solvent. The effect of changing certain parameters in both models, and of combining the two, is considered.

Contribution of the metal to the differential capacity of an ideally polarisable electrode

Abstract We consider the response of the metal in the ideally polarisable electrode to charging of the electrode, using a model for the metal surface in contact with the solvent of the electrolyte phase previously presented by us in this journal. We show that the effect of the solvent on the electrons of the metal cannot be considered to be simply that of a repulsive barrier. When the electrode charge varies qM(dip), the metal contribution to the double layer, is modified, implying a contribution which varies along the electrocapillary curve. By considering an electrostatic interaction between metal and solvent, we find an acceptable value for the contribution of the metal to the double-layer capacity. Furthermore, the introduction of appropriate parameters for the metals shows that one should expect CGa>CHg at the potential of zero charge, in accord with experimental observations. The influence of the choice of parameters, particularly those which express the interpenetration of metal and solvent in our model, is discussed as well as other possible models. The different contributions of electrons of different metals probably need to be considered in evaluating models for the inner-layer contribution to the capacity.

The metal in the polarisable interface coupling with the solvent phase

Abstract A quantum mechanical treatment of the conduction electrons of a metal in a polarisable interface shows that they can make an appreciable contribution to the electrical capacitance. Results for six metals are given, showing how differences in metal properties account qualitatively for experimentally observed differences in interfacial capacities, when the solvent is replaced by a dielectric film. To justify the neglect of solvent structure when metal properties are treated, the coupling between metal and solvent is discussed for orientable point solvent dipoles, and for a representation of the solvent polarisation by a pair of charged planes. The electron profile affects the polarisation of the solvent near the point of zero charge, but the solvent structure has an almost negligible effect on the metal contribution to the capacity. One parameter in our model, the distance from metal ions to the first solvent layer, can be expected to vary as the interface is charged, due to changed bonding. Coupling by such an effect can be quite important, and severely decreases the variation of metal capacity with charge.

Contribution of the metal to the differential capacitance of the ideally polarizable electrode

Abstract We have examined the direct contribution of the metal to the differential capacitance of an ideally polarizable electrode in the absence of ionic specific adsorption. Before the recent explicit calculations using the methods of surface physicists, the real importance of the metal was not realized. The basic ingredients which enter in the different models are analysed. The discussion is focused on two simple metals (Hg and Ga), and some peculiarities relative to the noble metals are emphasized.

Contact conditions for the charge in the theory of the electrical double layer

In this paper, from the Born-Green-Yvon equations of the liquid-state theory, we derive a general expression for the charge-density contact value at charged interfaces. This relation is discussed, in particular, for symmetrical electrolytes. We emphasize an essential coupling between the electric properties and the density profile. Limiting behavior at small and large charges at the interface is discussed.

Field theoretical approach to inhomogeneous ionic systems: thermodynamic consistency with the contact theorem, Gibbs adsorption and surface tension

Using a statistical field approach we investigate the structure of an electrolyte solution in contact with a neutral impenetrable wall. The Hamiltonian contains the Coulomb interaction and the ideal entropy. At the level of the quadratic approximation, the Hamiltonian yields the Debye-Hückel theory in the bulk. Analytic expressions of the charge-charge and potential-potential inhomogeneous correlation functions are obtained. Exact asymptotic results for point ion charge correlation functions are obtained and the profile for the fluctuation of the electric potential is calculated. We also consider the term beyond the quadratic expansion of the ideal entropy in the Hamiltonian. With this term a higher order coupling between charge density and number density produces a non-trivial profile for the total ion density. This density profile is consistent with the contact theorem and the related surface tension calculated from the Gibbs adsorption isotherm.

Cytochrome-c in reverse micelles: Small angle x-ray scattering measurements, percolation process, and critical behavior: An interpretation with an association model

It has been shown that solubilization of cytochrome-c in water in oil reverse micellar systems induces a change in the small angle x-ray scattering (SAXS) spectrum which suggests an increase in the attractive part of the intermicellar potential. In addition, from conductivity measurements a percolation threshold appears for a micellar concentration which is smaller than that observed without protein. Finally, for the liquid–liquid phase transition, a decrease in the critical temperature and concentration is observed. To explain these results, we introduce a pairing sticky hard sphere model. In this approach, the empty micelles are described by the sticky hard sphere model as is usually done. The presence of cytochrome-c is represented by an additional attractive potential characterized by an association parameter that leads to the pair formation of micelles. The association parameter was determined by fitting the experimental structure factors and from this parameter the decrease in the percolation thresh...

Localized adsorption at solid-liquid interfaces: the sticky site-hard wall model

Abstract The interface between a structured solid and a liquid is modelled by a flat surface with sticky sites placed on a regular lattice. It is shown that this three-dimensional adsorption model can be mapped into a two-dimensional lattice-gas model with the interaction energies of the particles on the sites related to the potential of mean force in the inhomogeneous fluid. In the simple case of a liquid of hard spheres, the first layer of liquid at contact with the solid exhibits an order-disorder phase transition and the total surface excess shows a maximum as the bulk density increases.

Effect of an association potential on percolation. Applications to reverse micelles containing proteins

Abstract We mimic the presence of proteins inside reverse micelles by an association potential. This potential shifts the percolation threshold which exists for empty micelles. The statistical mechanics of this system is solved using Wertheims theory. In particular, the theory predicts that the shift of the percolation threshold which depends on the solvent may exhibit an absolute maximum value.