Equilibrium Interfacial Electrical Potentials

Double Layer Potential for a Charged Flat Surface 

Let us consider an infinite flat surface, which has a surface charge density r it is also assumed that phases separated by the surface are a nonaqueous phase having a dielectric constant e, and an electrolyte phase with dielectric constant e. In this situation, the electrical potential at a distance x in the electrolyte solution from the surface is given by the Poisson-Boltzman equation [Eq. (7)]. 

The electrical potential at such a membrane surface, with respect to the potential at infinite distance as zero, can be obtained under the following ideal conditions (1) the surface charge is uniformly distributed, (2) ions in the aqueous solution are considered as point charges, (3) the dielectric constant of the aqueous phase is e everywhere up to the boundary plane. 

It is obvious from Eq. (70) that if all bulk ionic concentrations, Cj(oo), and the surface charge density a are given, the magnitude of the surface potential, il/(0), at the membrane surface can be calculated analytically or numerically. 

The double layer potential at a finite point away from the membrane is difficult to obtain except for a few special cases, such as uni-univalent, and uni-univalent and one divalent electrolyte cases. 

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Consider now the partitioning of both cations and anions. Electroneutrality coupling requires c k Ick - c x jcx- Thus the system adjusts the interfacial electric potential drop in such a way that at equilibrium the condition... 

The analysis of oxidation processes to which diffusion control and interfacial equilibrium applied has been analysed by Wagner (1933) who used the Einstein mobility equation as a starting point. To describe the oxidation for example of nickel to the monoxide NiO, consideration must be given to the respective fluxes of cations, anions and positive holes. These fluxes must be balanced to preserve local electroneutrality throughout the growing oxide. The flux equation for each species includes a term due to a chemical potential gradient plus a term due to the electric potential gradient... 

Hence, two phases in contact can only be at a difference of electric potential V when the electrical distribution in the interfacial layer gives rise to the necessary moment. Thus, although the equilibrium value of V is determined solely by the chemical composition of the two homogeneous phases, a particular molecular and ionic arrangement must be established in the intervening non-homogeneous layer in order that the conditions of chemical and electrical equilibrium may be simultaneously obeyed. 

From what has been described so far, there can be a flow of cathodic current, or of anodic current at an electrode/solution interface, according to the value (and particularly the sign) of the overpotential, i.e., of the displacement from equilibrium of the electric potential of the electrode. The equilibrium referred to is that of some specific interfacial electron transfer reaction (e.g., the cathodic reduction of 02 (02 + 4H+ + e —> 2H20)) or the anodic oxidation of ethylene, C2H4 + 4H20 — 2C02 + 12H+ + 12e. 

Interface between two liquid solvents — Two liquid solvents can be miscible (e.g., water and ethanol) partially miscible (e.g., water and propylene carbonate), or immiscible (e.g., water and nitrobenzene). Mutual miscibility of the two solvents is connected with the energy of interaction between the solvent molecules, which also determines the width of the phase boundary where the composition varies (Figure) [i]. Molecular dynamic simulation [ii], neutron reflection [iii], vibrational sum frequency spectroscopy [iv], and synchrotron X-ray reflectivity [v] studies have demonstrated that the width of the boundary between two immiscible solvents comprises a contribution from thermally excited capillary waves and intrinsic interfacial structure. Computer calculations and experimental data support the view that the interface between two solvents of very low miscibility is molecularly sharp but with rough protrusions of one solvent into the other (capillary waves), while increasing solvent miscibility leads to the formation of a mixed solvent layer (Figure). In the presence of an electrolyte in both solvent phases, an electrical potential difference can be established at the interface. In the case of two electrolytes with different but constant composition and dissolved in the same solvent, a liquid junction potential is temporarily formed. Equilibrium partition of ions at the - interface between two immiscible electrolyte solutions gives rise to the ion transfer potential, or to the distribution potential, which can be described by the equivalent two-phase Nernst relationship. See also - ion transfer at liquid-liquid interfaces. 

Pratt, L. R., Contact potentials of solution interfaces phase equilibrium and interfacial electric fields. J. Phys. Chem. 96, 25- 33 (1992). 

When the current does not flow through battery the measurable diflerence in electric potential between the terminals of the two electrodes is the result of all the equilibrium potential differences at the interphase between the conducting phases in contact. In the example of the Daniell cell, with both electrodes having copper terminals, there are three interfacial potential differences (apart from the small liquid junction potential difference at the contact between the two electrolyte phases) one potential difference at the contact between the zinc rod and the copper terminal (Zn/Cu) and two potential differences at the metal-solution interphases (Zn/Zn + and Cu/Cu +), which are mainly due to the charge transfer processes. 

The presence of an electrical potential drop, i.e., interfacial potential, across the boundary between two dissimilar phases, as well as at their surfaces exposed to a neutral gas phase, is the most characteristic feature of every interface and surface electrified due to the ion separation and dipole orientation. This charge separation is usually described as the formation of the ionic and dipolar double layers. The main interfacial potential is the Galvani potential (termed also by Trasatti the operative potential), AJinner potentials chemical nature of the contacting phases in the equilibrium, but it is not a measurable quantity. 

To get the main idea of the charge effect on adsorption kinetics, it is sufficient to consider an aqueous solution of a symmetric (z z) ionic surfactant in the presence of an additional indifferent symmetric (z z) electrolyte. When a new interface is created or the equilibrium state of an interfacial layer disturbed a diffusion transport of surface active ions, counterions and coions sets in. This transport is affected by the electric field in the DEL. According to Borwankar and Wasan [102], the Gouy plane as the dividing surface marks the boundary between the diffuse and Stem layers (see Fig. 4.10). When we denote the surfactant ion, the counterion and the coion, respectively, with the indices / = 1, 2 and 3, the transport of the ionic species with valency Z/ and diffusion coefficient A, under the influence of electrical potential i, is described by the equation [2, 33] ... 

Surfactants play a crucial role in emulsification and emulsion stability. A first step in any quantitative study on emulsions should be to determine the equilibrium and dynamic properties of the oil-water interface, such as interfacial tension, Gibbs elasticity, sinfactant adsorption, counterion binding, siuface electric potential, adsorption relaxation time, etc. Useful theoretical concepts and expressions, which are applicable to ionic, nonionic, and micellar surfac-... 

Interfacial instability is a common phenomenon since in most cases the events occurring at the interface are in the region far from equilibrium [40, 41]. A typical example is Marangoni instability [44-47]. Electric potential oscillations have been observed in biphasic systems [48, 49], Self-induced oscillations in similar systems have also been observed [10]. Theoretical efforts have also been made to understand the mechanism in some cases [23, 27],... 

As can be seen in Figure 2.8, the metal M is coupled with the platinum (Ft) electrode and the electric potential of M at the surface is measured against the SHE. Recall that this potential is the resultant of several interfacial potentials described by eq. (2.7a). The junction potentials of the Pt and M electrodes are small, equd, and apposite so that they cancel out. The liquid junction potential is also small and negligible. The ceU potential is also Imown as the inteifacial cell potential, which depends on the chemical potential of the species (ions) in solution at equilibrium and it is predicted by eq. (2.28). The electrons flow toward the cathodic electrode M, where the metal cations M+ gain these electrons and enter the electrode lattice. This is a reduction process that strongly depends on the chemical potential of the M+ cations. 

Fig. 4 Electrical Potential Profiles (a) Two-electrode system. In the absence of current, two equilibrium interfacial potentials exist, and the cell potential measured between the two electrodes is the difference between these equilibrium potentials. As shown the equilibrium potentials are the same (as would be the case if the same metal was used for both electrodes), and the cell potential would be zero. Upon passing current, overpotentials develop at both interfaces (one interfacial potential becomes greater, one smaller). The net change in measured cell potential is due to three sources the voltage drop in solution i Rs and two overpotentials rji and r]2- (b) Three-electrode system. The measured potential is between the working electrode and reference electrode. Since no substantial overpotential can be developed at the reference electrode, any change in measured potential upon passing current is due to two sources the overpotential at the working electrodesolution interface, and the solution drop i Rjj, where the uncorrected resistance Rjj is the solution resistance between the WE interface and RE interface...

When a semiconductor electrode is immersed in an electrolyte, the semiconductor-liquid junction is thus established. As a result, electrons flow from semiconductor to the electrolyte rmtil the equilibrium is achieved (Fig. 2.4). The electrolyte solution contains redox couple. The charge transfer develops an interfacial electric held and thus electrostatic potential builds up. The electrostatic potential balances the electrochemical potential between electrolyte solution and semiconductor. The electrochemical potential is observed throughout the system after equilibrium stage is achieved. It is also referred as Fermi level [38, 39, 42]. 

When an aqueous phase (noted w) is brought in contact with a second immiscible phase (noted o), the different species dissolved in one or the two phases spontaneously distribute depending on their hydrophilic-lipophilic balance until the thermodynamic equilibrium is reached. The distribution of the charged species generates an interfacial region, in which the electrical field strength differs from zero, so that an electrical Galvani potential difference, is established across the interface ... 

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