D. di Caprio

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.

A FIELD THEORY STUDY OF THE EFFECT OF SPECIFIC INTERACTIONS IN IONIC SYSTEMS : A SIMPLE MODEL

The effect of specific ionic interactions on the Debye length has been studied using a simple model Hamiltonian for a binary mixture of anions and cations in the framework of the field theory. The Hamiltonian contains the Coulombic interaction and an independent non-Coulombic part describing a binary mixture of equivalent uncharged particles. We use a local and quadratic approximation to calculate the partition function via a functional integral. The Debye limiting law is obtained with a renormalized screening length. The screening is enhanced when the specific interactions favor demixion. This is illustrated on the example of an asymmetric hard sphere mixture.

New results from the contact theorem for the charge profile for symmetric electrolytes

In this paper the contact value of the charge profile at a charged interface is presented as the sum of the normal component of the Maxwell electrostatic tensor and a new electrostatic property defined by the integral from the product of the gradient of the electrical potential and the singlet distribution function of coions (ions with sign of the charge equal to that of the interface). On physical arguments, it is conjectured that this new property is a monotonic function of the electrical charge at the wall and is limited by the bulk electrolyte pressure for large electrical charges at the wall. Using the contact theorems for the density and the charge profiles, the exact expressions for the contact values of the profiles of coions and counterions are derived and some related general properties are discussed.

Field theory for ionic systems. From fluctuations and structure at a hard wall to thermodynamics

Abstract We use a field theoretical approach to study ionic systems. In this paper we illustrate this formalism in a grand canonical ensemble for the long range Coulomb potential. For the inhomogeneous system near a hard neutral plane wall we go beyond the well known Debye–Huckel electrolyte results and predict the existence of a desorption profile. The results are compared with well established sum rules for ionic systems and thermodynamic relations are verified. We also calculate the differential capacitance in a slab using the linear response theory. The capacitance is calculated from the charge–charge correlations for the neutral system using the fluctuation–dissipation theorem.

Density field theory for a fluid interacting with the Yukawa potential. Role of the ideal entropy

We present a field theory to describe liquids where the field represents the density. In terms of this field, the Hamiltonian contains the ideal entropy and the interaction between the density fields. The approach is illustrated with the Yukawa interaction and presented in the grand canonical ensemble formalism. In this framework, first, we derive a relation specific to the field theory. This relation is equivalent to the ‘equation of motion’ in field theory for interacting quantum particles. Then, focusing on the effect of the fluctuations, we calculate thermodynamic quantities beyond the mean field. The pressure, the density and the compressibility at a given chemical potential in the quadratic approximation and beyond are given. The aim of this paper is to illustrate the importance and the role of the ideal entropy in this type of approach. The density and the compressibility at a given chemical potential are calculated perturbatively in various ways. Whether from their field theoretical definition, or deriving them from one another using the thermodynamical relations or also using the ‘equation of motion’, the results are in all ways of calculation consistent. However, the different calculations require different levels of expansion of the ideal entropy term involving in our case three and four body coupling constants. The consistency is then closely related to the form of the functional of the ideal entropy.

Two-Yukawa fluid at a hard wall: Field theory treatment

We apply a field-theoretical approach to study the structure and thermodynamics of a two-Yukawa fluid confined by a hard wall. We derive mean field equations allowing for numerical evaluation of the density profile which is compared to analytical estimations. Beyond the mean field approximation, analytical expressions for the free energy, the pressure, and the correlation function are derived. Subsequently, contributions to the density profile and the adsorption coefficient due to Gaussian fluctuations are found. Both the mean field and the fluctuation terms of the density profile are shown to satisfy the contact theorem. We further use the contact theorem to improve the Gaussian approximation for the density profile based on a better approximation for the bulk pressure. The results obtained are compared to computer simulation data.

Cellular automata approach for morphological evolution of localised corrosion

Abstract We present a cellular automata approach to the morphology evolution of a corroding metal surface. In the model, we consider a morphology dependent corrosion probability of a site on the corrosion front. Selecting the model parameters we are able to reproduce a variety of different pit shapes and morphological regimes ranging from narrow pore-like channels to broader cavities. In the model, we control the ratio between localised and uniform corrosion. A diffusion process is also taken into account. The model is capable of predicting different scenarios for the evolution of the corrosion front in time.

A simple model to investigate the effects of non-Coulombic interactions on the structure of charged interfaces

A simple field theoretical model is considered for an electrified interface in which the electrolyte solution is in contact with a charged hard wall. The model for the electrolyte includes Coulombic interactions, local ideal entropy, functional and specific nonlocal interactions. For the specific nonlocal interactions, the simplest form of the square gradient term is selected. The charged hard wall is characterized by an additional short range potential reduced to the form of a Dirac function. An exact relation, analogous to Maxwell relations in thermodynamics, is derived describing the effect of the wall specificity on the electric properties. In the mean field theory, the consistency equations for the ionic profiles are solved analytically in the limit of small charge densities and weak wall potentials. The electric double layer structure is discussed in terms of two characteristic lengths—Debye length for electrostatics and the characteristic length for the specific interaction. We also present and dis...

Fluctuations of electric variables in Debye–Hückel electrolyte at a neutral hard wall

Abstract We analyse the fluctuations of electric variables in a simple case of semi-infinite electrolyte solution bound by a neutral hard wall. We use the statistical field theory with the effective Hamiltonian that yields the Debye–Huckel theory in the bulk. Although there is no profile for the average electrical quantities the fluctuations are influenced by the presence of the hard wall. We have calculated the profile for the electrical potential fluctuation at a given point across the interface. Analytic expression for the charge–charge and potential–potential correlation function is given. Some perspectives for a further study on the electric variables fluctuations in inhomogeneous electrolyte systems are presented.