Electrical double-layer, basic properties

It can be observed that the above two types of electric double layer, which have basically similar properties, differ principally in the manner of establishing the potential difference across the electric double layer. One type is fixed by the solubility and other interactions of the solid in contact with solution of electrolyte. In the other type, polarizable interface, the experimenter applies any desired potential difference between one liquid surface and a reference electrode. The resulting Volta potential is fixed by the specific adsorbability of the electrolyte. 

In this chapter, mathematical procedures for the estimation of the electrical interactions between particles covered by an ion-penetrable membrane immersed in a general electrolyte solution is introduced. The treatment is similar to that for rigid particles, except that fixed charges are distributed over a finite volume in space, rather than over a rigid surface. This introduces some complexities. Several approximate methods for the resolution of the Poisson-Boltzmann equation are discussed. The basic thermodynamic properties of an electrical double layer, including Helmholtz free energy, amount of ion adsorption, and entropy are then estimated on the basis of the results obtained, followed by the evaluation of the critical coagulation concentration of counterions and the stability ratio of the system under consideration. 

Electric double layers at phase boundaries pervade the entire realm of Interface and colloid science. Especially in aqueous systems, double layers tend to form spontaneously. Hence, special precautions have to be taken to ensure the absence of charges on the surfaces of particles. Insight into the properties of double layers is mandatory, in describing for Instance electrosorption, ion exchange, electrokinetics (chapter 4), charged monolayers (Volume III), colloid stability, polyelectrolytes and proteins, and micelle formation of ionic surfactants, topics that are intended to be treated in later Volumes. The present chapter is meant to Introduce the basic features. 

Since this book is dedicated to the dynamic properties of surfactant adsorption layers it would be useful to give a overview of their typical properties. Subsequent chapters will give a more detailed description of the structure of a surfactant adsorption layer and its formation, models and experiments of adsorption kinetics, the composition of the electrical double layer, and the effect of dynamic adsorption layers on different flow processes. We will show that the kinetics of adsorption/desorption is not only determined by the diffusion law, but in selected cases also by other mechanisms, electrostatic repulsion for example. This mechanism has been studied intensively by Dukhin (1980). Moreover, electrostatic retardation can effect hydrodynamic retardation of systems with moving bubbles and droplets carrying adsorption layers (Dukhin 1993). Before starting with the theoretical foundation of the complicated relationships of nonequilibrium adsorption layers, this introduction presents only the basic principles of the chemistry of surfactants and their actions on the properties of adsorption layers. 

Before starting with dynamic effects at a liquid interface, the equilibrium state of adsorption is described and adsorption isotherms as basic requirements for theories of adsorption dynamics are reviewed. Chapter 2 presents the transfer from thermodynamics to macro-kinetics of adsorption. As Chapter 7 deals with the peculiarities of ionic siu-factant adsorption and introduces some properties of electric double layers. 

Tlie discussions of the basic features of filtration given thus far illustrate that the unit operation involves some rather complicated hydrodynamics that depend strongly on the physical properties of both fluid and particles, as well as interaction with a complex porous medium. The process is essentially influenced by two different groups of factors, which can be broadly lumped into macro- and micro-properties. Macrofactors are related to variables such as the area of a filter medium, pressure differences, cake thickness and the viscosity of the liquid phase. Such parameters are readily measured. Micro-factors include the influences of the size and configuration of pores in the cake and filter medium, the thickness of the electrical double layer on the surface of solid particles, and other properties. 

An activated carbon in contact with a salt solution is a two-phase systan consisting of a solid phase that is the activated carbon surface and a liquid phase that is the salt solution containing varying amounts of different ionic and molecular species and their complexes. The interface between the two phases acts as an electrical double layer and determines the adsorption processes. The adsorption capacity of an activated carbon for metal cations from the aqueous solutions generally depends on the physico-chemical characteristics of the carbon surface, which include surface area, pore size distribution, electro-kinetic properties, the chemistry of the carbon surface, and the nature of the metal ions in the solution. Activated carbons are invariably associated with acidic and basic carbon-oxygen surface groups. 

Among different liquid-solid interfaces, fhe boundary between an electrolyte and a metal electrode is the one which has been most investigated in surface science. This is dictated by its importance for elecfrochemisfry and by a rich variety of interesting phenomena. In some respect the relevant processes are similar to those at the gas-solid interface. On the other hand, the electrified character of the electrolyte-solid interface resulfs in some peculiarities. One can control interface properties through external manipulation of the interfacial potential difference. All reactions that involve charge transfer respond directly to this quantity. In this section we shall consider the structure of the electric double layer which takes place at an electrolyte-solid interface and the basic principles of control for various reactions at this boundary. 

The distribution of fixed acidic and basic groups in membrane layer contributes critical influences on the variations in electrical properties of interacting double layers, rendering a variety of performances for the behavior related to biological phenomena. If the concentration of nonuniformly distributed functional groups in the membrane is defined by... 

In this section we describe the equations required to simulate the electrochemical performance of porous electrodes with concentrated electrolytes. Extensions to this basic model are presented in Section 4. The basis of porous electrode theory and concentrated solution theory has been reviewed by Newman and Tiedemann [1]. In porous electrode theory, the exact positions and shapes of aU the particles and pores in the electrode are not specified. Instead, properties are averaged over a volume small with respect to the overall dimensions of the electrode but large with respect to the pore structure. The electrode is viewed as a superposition of active material, filler, and electrolyte, and these phases coexist at every point in the model. Particles of the active material generally can be treated as spheres. The electrode phase is coupled to the electrolyte phase via mass balances and via the reaction rate, which depends on the potential difference between the phases. AU phases are considered to be electrically neutral, which assumes that the volume of the double layer is smaU relative to the pore volume. Where pUcable, we also indicate boundary conditions that would be used if a Uthium foil electrode were used in place of a negative insertion electrode. 

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