The electrode double layer

Although double layers are a general interfacial phenomena, we shall first consider only electrode-electrolyte interfaces because of their importance in electrode kinetics and because the theory leads on to a general treatment of all such phenomena. 

For the case of an electrode dipping into a solution of an electrolyte, we see that, for electroneutrality, the excess charge residing on the electrode surface must be exactly balanced by an equal charge of opposite sign on the solution side. It is the distribution of this latter charge that we are interested in. When only electrostatic interaction operates, ions from the solution phase may approach the electrode only so far as their inner solvation shells will allow. The surface array of ions is thus cushioned from the electrode surface by a layer of solvent molecules (Fig. 7.1). The line drawn through the centre 

Variation of potential with distance from the electrode surface. 

Relative positions of inner and outer Helmholtz planes of electrode double layer. 

Uncharged species, if they are less polar than the solvent or are attracted to the electrode material by van der Waals or chemical forces, will accumulate at the interface. Such species are known as surfactants. Where specific adsorption occurs, the charge distribution in the diffuse layer will change to maintain electroneutrality. 

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Within this framework, by considering the physical situation of the electrode double layer, the free energy of activation of an electron transfer reaction can be identified with the reorganization energy of the solvation sheath around the ion. This idea will be carried through in detail for the simple case of the strongly solvated... 

An increase in pressure will also affect the rate of the diffusion of molecules to and from the electrode surface it will cause an increase in the viscosity of the medium and hence a decrease in diffusion controlled currents. The consequences of increased pressure on the electrode double layer and for the adsorption of molecules at the electrode surface are unclear and must await investigation. 

Double integration with respect to EA yields the surface excess rB+ however, the calculation requires that the value of this excess be known, along with the value of the first differential 3TB+/3EA for a definite potential. This value can be found, for example, by measuring the interfacial tension, especially at the potential of the electrocapillary maximum. The surface excess is often found for solutions of the alkali metals on the basis of the assumption that, at potentials sufficiently more negative than the zero-charge potential, the electrode double layer has a diffuse character without specific adsorption of any component of the electrolyte. The theory of diffuse electrical double layer is then used to determine TB+ and dTB+/3EA (see Section 4.3.1). 

In a CV measurement, the current output always contains two components the Faradaic current, /F, due to the reaction of the redox species and the capacitive charging current, /c, which results from the charging of the electrode double layer and the diffusion layer. (This diffusion layer contains all charged and polar species in the solution and therefore differs from that of the redox species.) While /F changes linearly with vm as determined by diffusion, Ic is directly proportional to v as shown below, where CD is the total electrode capacitance and q the added capacitance charge ... 

To appreciate that a majority of non-faradaic currents are caused by the effects of adsorption, capacitance and the electrode double-layer, or by competing side reactions such as solvent splitting. 

The Effects of Absorption, Capacitance and the Electrode Double-Layer... 

In solution, all electrodes are surrounded by a layer of water molecules, ions, and other atomic or molecular species. We will not look in depth at this topic, except to refer to the two principle layers, which are named after one of the original pioneers of electrochemistry, namely the nineteen-century great, Hermann Helmholtz. The two Helmholtz layers are often said to comprise the electrode double-layer (or electric double-layer ). 

We recall from Section 7.5.2 and equation (7.17) that the exchange current relates to the rate constant of electron transfer, k<./. The redox process described is the flow of electrons into and out of the layer of solid WO3 via the electrode double-layer. 

The first problem is that any ion needs to be brought from the bulk solution to the electrode surface before it can be discharged. On approaching the electrode, the ion needs to cross a boundary layer called the diffusion layer. This layer is about 0.1 mm (or 100 (tm) thick and is distinguished from the electrode double layer which is 100000 times smaller (Fig. 6.7). 

Residual currents, also referred to as background currents, are the sum of faradaic and nonfaradaic currents that arise from the solvent/electrolyte blank. Faradaic processes from impurities may be practically eliminated by the careful experimentalist, but the nonfaradaic currents associated with charging of the electrode double layer (Chap. 2) are inherent to the nature of a potential sweep experiment. Equation 23.5 describes the relationship between this charging current icc, the double-layer capacitance Cdl, the electrode area A, and the scan rate v ... 

Charging current subtraction assumes that the electrode double-layer capacitance does not change greatly in the presence of the test compound. See D.O. Wipf, E. W. Kristensen, M. R. Deakin, and R. M. Wightman, Anal. Chem. 60 306 (1988). 

While many of the standard electroanalytical techniques utilized with metal electrodes can be employed to characterize the semiconductor-electrolyte interface, one must be careful not to interpret the semiconductor response in terms of the standard diagnostics employed with metal electrodes. Fundamental to our understanding of the metal-electrolyte interface is the assumption that all potential applied to the back side of a metal electrode will appear at the metal electrode surface. That is, in the case of a metal electrode, a potential drop only appears on the solution side of the interface (i.e., via the electrode double layer and the bulk electrolyte resistance). This is not the case when a semiconductor is employed. If the semiconductor responds in an ideal manner, the potential applied to the back side of the electrode will be dropped across the internal electrode-electrolyte interface. This has two implications (1) the potential applied to a semiconducting electrode does not control the electrochemistry, and (2) in most cases there exists a built-in barrier to charge transfer at the semiconductor-electrolyte interface, so that, electrochemical reversible behavior can never exist. In order to understand the radically different response of a semiconductor to an applied external potential, one must explore the solid-state band structure of the semiconductor. This topic is treated at an introductory level in References 1 and 2. A more complete discussion can be found in References 3, 4, 5, and 6, along with a detailed review of the photoelectrochemical response of a wide variety of inorganic semiconducting materials. 

The chemical system at the surface will be quite complex. There will be strongly bound species at various sites on the metal surface. Where these are ionic, the electric field established at the surface will tend to attract ions of opposite charge from the solution. The first layer has been termed the electrode double layer, while the gegenion distribution in the solution is called the diffuse double layer. A theoretical analysis of the double layer has been made by Gouy and Chapman and adapted to kinetic analysis by Stern. For references, and discussion see paper by D. C. Grahame, J. Chem, Phys, 21, 1054 (1953). 

Since water is the species always present in all solutions at an approximately constant concentration, it may be inferred that the rate-determining stage in the evolution of hydrogen is the transfer of a proton across the electrode double layer. For reasons which will appear later, it is suggested that the proton transferred in this way passes to a molecule of water attached to the surface of the electrode the proton is immediately discharged by an electron to form a hydrogen atom, and a hydroxyl ion is left in solution. The essential discharge mechanism may thus be represented by... 

The measured adsorption effect at the electrode is influenced by all dissolved and/or dispersed surface-active substances according to their concentration in the solution, adsorbability at the electrode, kinetics of adsorption, structure of the adsorbed layer, and some other factors. Adsorption of organic molecules on electrodes causes a change of the electrode double-layer capacitance. It is the result of an exchange between the counterions and water molecules from solution, followed by changes in the dielectric properties and the thickness of the double layer on the electrode surface, that is, parameters that determine the electrode capacitance (Bockris et al., 1963 Damaskin and Petrii, 1971). 

No adsorption of cytochrome c was evident at gold in a.c. impedance measurements reported by Eddowes et at ". No detectable change in the electrode double layer capacitance was found upon addition of cytochrome c to an electrolyte solution. 

Ultrasonic agitation provides more even transport of ions across the electrode double layer Ultrasonic irradiation continuously cleans and activates the electrode surfaces... 

NAs, as well as NA bases, nucleosides, and nucleotides, are strongly adsorbed at the mercury electrodes [26-63]. Among bases, G is most strongly adsorbed at these electrodes [28]. The adsorption can be followed by measurement of the impedance and/or differential capacitance of the electrode double layer [26, 27, 31, 32, 34-39, 41, 42, 47]. In 1965, it was found by one of us (VV) [26, 27] that NA bases possess an extraordinarily high ability of... 

The adsorption of NAs can be followed by a number of physical and electrochemical methods such as voltammetry [184], a.c. polarography [31, 40, 185-187], measurements of the surface tension [40,188, 189], and of the impedance and/or differential capacitance of the electrode double layer [31, 37, 38, 88]. Differential capacitance C of the electrode double layer is a sensitive indicator of the adsorption. When the NAs are adsorbed at the... 

We studied the time dependence of the impedance of the electrode double layer around the potentials of the tensammet-ric peaks and around the potential of maximum adsorption of native and denatured calf thymus DNA (100 pg ml in 0.3 M NaCl with 0.05 M Na2HP04, pH 8.6). At potentials of maximum adsorption (around —0.7 V) the differential... 

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