Outer Helmholtz plane , electrode

F r d ic Current. The double layer is a leaky capacitor because Faradaic current flows around it. This leaky nature can be represented by a voltage-dependent resistance placed in parallel and called the charge-transfer resistance. Basically, the electrochemical reaction at the electrode surface consists of four thermodynamically defined states, two each on either side of a transition state. These are (11) (/) oxidized species beyond the diffuse double layer and n electrons in the electrode and (2) oxidized species within the outer Helmholtz plane and n electrons in the electrode, on one side of the transition state and (J) reduced species within the outer Helmholtz plane and (4) reduced species beyond the diffuse double layer, on the other. 

The inner layer (closest to the electrode), known as the inner Helmholtz plane (IHP), contains solvent molecules and specifically adsorbed ions (which are not hilly solvated). It is defined by the locus of points for the specifically adsorbed ions. The next layer, the outer Helmholtz plane (OHP), reflects the imaginary plane passing through the center of solvated ions at then closest approach to the surface. The solvated ions are nonspecifically adsorbed and are attracted to the surface by long-range coulombic forces. Both Helmholtz layers represent the compact layer. Such a compact layer of charges is strongly held by the electrode and can survive even when the electrode is pulled out of the solution. The Helmholtz model does not take into account the thermal motion of ions, which loosens them from the compact layer. 

Grahame introdnced the idea that electrostatic and chemical adsorption of ions are different in character. In the former, the adsorption forces are weak, and the ions are not deformed dnring adsorption and continne to participate in thermal motion. Their distance of closest approach to the electrode surface is called the outer Helmholtz plane (coordinate x, potential /2, charge of the diffuse EDL part When the more intense (and localized) chemical forces are operative, the ions are deformed, undergo partial dehydration, and lose mobility. The centers of the specifically adsorbed ions constituting the charge are at the inner Helmholtz plane with the potential /i and coordinate JCj < Xj. 

Reactant concentrations Cyj in the bulk solution, as well as the Galvani potential between the electrode and the bulk solution (which is a constituent term in electrode potential E), appear in kinetic equations such as (6.8). However, the reacting particles are not those in the bulk solution but those close to the electrode surface, near the outer Helmholtz plane when there is no specific adsorption, and near the inner Helmholtz plane when there is specific adsorption. Both the particle concentrations and the potential differ between these regions and the bulk solution. It was first pointed out by Afexander N. Frumkin in 1933 that for this reason, the kinetics of electrochemical reactions should strongly depend on EDL structure at the electrode surface. 

All factors influencing the potentials of the inner or outer Helmholtz plane will also influence the zeta potential. For instance, when, owing to the adsorption of surface-active anions, a positively charged metal surface will, at constant value of electrode potential, be converted to a negatively charged surface (see Fig. 10.3, curve 2), the zeta potential will also become negative. The zeta potential is zero around the point of zero charge, where an ionic edl is absent. 

Figure 4.3 Schematic diagram of the electrochemical metal—aqueous interface, with the electrode, inner layer, diffuse layer, outer Helmholtz plane (OHP), and inner-layer thickness Xji indicated.

In the simple case of electrostatic attraction alone, electrolyte ions can approach to a distance given by their primary solvation sheaths, where a monomolecular solvent layer remains between the electrode and the solvated ions. The plane through the centres of the ions at maximum approach under the influence of electrostatic forces is called the outer Helmholtz plane and the solution region between the outer Helmholtz plane and the electrode surface is called the Helmholtz or compact layer. Quantities related to the outer Helmholtz plane are mostly denoted by symbols with the subscript 2. 

Fig. 4.1 Structure of the electric double layer and electric potential distribution at (A) a metal-electrolyte solution interface, (B) a semiconductor-electrolyte solution interface and (C) an interface of two immiscible electrolyte solutions (ITIES) in the absence of specific adsorption. The region between the electrode and the outer Helmholtz plane (OHP, at the distance jc2 from the electrode) contains a layer of oriented solvent molecules while in the Verwey and Niessen model of ITIES (C) this layer is absent...

The introduction of the concept of the micropotential permits derivation of various expressions for the potential difference produced by the adsorbed anions, i.e. for the potential difference between the electrode and the solution during specific adsorption of ions. It has been found that, with small coverage of the surface by adsorbed species, the micropotential depends almost linearly on the distance from the surface. The distance between the inner and outer Helmholtz planes is denoted as xx 2 and the distance between the surface of the metal and the outer Helmholtz plane as jc2. The micropotential, i.e. the potential difference between the inner and... 

If the electrolyte components can react chemically, it often occurs that, in the absence of current flow, they are in chemical equilibrium, while their formation or consumption during the electrode process results in a chemical reaction leading to renewal of equilibrium. Electroactive substances mostly enter the charge transfer reaction when they approach the electrode to a distance roughly equal to that of the outer Helmholtz plane (Section 5.3.1). It is, however, sometimes necessary that they first be adsorbed. Similarly, adsorption of the products of the electrode reaction affects the electrode reaction and often retards it. Sometimes, the electroinactive components of the solution are also adsorbed, leading to a change in the structure of the electrical double layer which makes the approach of the electroactive substances to the electrode easier or more difficult. Electroactive substances can also be formed through surface reactions of the adsorbed substances. Crystallization processes can also play a role in processes connected with the formation of the solid phase, e.g. in the cathodic deposition of metals. 

The value of the electric potential affecting the activation enthalpy of the electrode reaction is decreased by the difference in the electrical potential between the outer Helmholtz plane and the bulk of the solution, 2, so that the activation energies of the electrode reactions are not given by Eqs (5.2.10) and (5.2.18), but rather by the equations... 

The Frumkin theory of the effect of the electrical double layer on the rate of the electrode reaction is a gross simplification. For example, the electrode reaction does not occur only at the outer Helmholtz plane but also at a somewhat greater distance from the electrode surface. More detailed considerations indicate, however, that Eq. (5.3.20) can still be used to describe the effect of the electrical double layer as a good approximation. 

Most cations are strongly solvated, since their radii are small, and the free energy of solvation is approximately proportional to z2/r +, where ze0 is the cation charge in coulombs and r+ its ionic radius. The result of this is that even if the charge on the electrode is negative, there is usually little tendency for these cations to shed their water molecules and adsorb directly on the metal surface. Thus, the distance of closest approach of cations is determined by the radius of the inner solvent coordination sphere, and if the metal surface itself constitutes a plane, then the cation nuclei, at the distance of closest approach, will also constitute a plane termed the outer Helmholtz plane (OH P). 

Figure 2.2 (a) The structure of the electrode/electrolyte interface, assuming a single layer of solvated ions adjacent to the electrode. The distance of closest approach of the ions to the electrode is a, and the ion sheet forms the outer Helmholtz plane (OHP). (b) The variation of the potential as a function of the distance from the metal surface for the interface shown in (a). 

As a result of the above considerations, the Helmholtz model of the interface now shows two planes of interest (see Figure 2.8). The inner Helmholtz plane (IHP) has the solvent molecules and specifically adsorbed ions (usually anions) the outer Helmholtz plane (OHP), the solvated ions, both cations and anions. It can be seen from Figure 2.8 that the dielectric in the capacitor space now comprises two sorts of water that specifically adsorbed at the electrode surface and that lying between the two Helmholtz planes. Continuing the analogy with capacitance, these two forms of water act as the dielectric in two capacitors connected in series. 

That volume within which the ions having charge opposite to that on the electrode have a concentration higher than those in the bulk of the solution (in the absence of specific adsorption). Under the conditions typically employed in electrochemical measurements, i.e. high ionic strength, this would correspond simply to a volume bounded by the outer Helmholtz plane, a few angstroms (see section on electrocapillarity). 

Alkali 10ns in aqueous solution are probably the most typical and most widely studied representatives of non-specific adsorption. The electrochemical term of non-specific adsorption is used to denote the survival of at least the primary hydration shell when an ion is interacting with a solid electrode. As pointed out previously, the generation of such hydrated ions at the gas-solid interface would be of great value because it would provide an opportunity to simulate the charging of the interfacial capacitor at the outer Helmholtz plane or perhaps even in the diffuse layer. 

The electrified interface is generally referred to as the electric double layer (EDL). This name originates from the simple parallel plate capacitor model of the interface attributed to Helmholtz.1,9 In this model, the charge on the surface of the electrode is balanced by a plane of charge (in the form of nonspecifically adsorbed ions) equal in magnitude, but opposite in sign, in the solution. These ions have only a coulombic interaction with the electrode surface, and the plane they form is called the outer Helmholtz plane (OHP). Helmholtz s model assumes a linear variation of potential from the electrode to the OHP. The bulk solution begins immediately beyond the OHP and is constant in potential (see Fig. 1). 

It is important to stress that the activity coefficients (and the concentrations) in equation 16.18 refer to the species close to the surface of the electrode, and so can be very different from the values in the bulk solution. This is portrayed in figure 16.6, which displays the Stern model of the double layer [332], One (positive) layer is formed by the charges at the surface of the electrode the other layer, called the outer Helmholtz plane (OHP), is created by the solvated ions with negative charge. Beyond the OHP, the concentration of anions decreases until it reaches the bulk value. Although more sophisticated double-layer models have been proposed [332], it is apparent from figure 16.6 that the local environment of the species that are close to the electrode is distinct from that in the bulk solution. Therefore, the activity coefficients are also different. As these quantities are not... 

By contrast, the charge of the solution, qs, is distributed in a number of layers. The layer in contact with the electrode, called the internal layer, is largely composed of solvent molecules and in a small part by molecules or anions of other species, that are said to be specifically adsorbed on the electrode. As a consequence of the particular bonds that these molecules or anions form with the metal surface, they are able to resist the repulsive forces that develop between charges of the same sign. This most internal layer is also defined as the compact layer. The distance, xj, between the nucleus of the specifically adsorbed species and the metallic electrode is called the internal Helmholtz plane (IHP). The ions of opposite charge to that of the electrode, that are obviously solvated, can approach the electrode up to a distance of x2, defined as the outer Helmholtz plane (OHP). 

Fig. 5-8. Diffuse charge layer on the solution side of metal electrode M = electrode metal S = aqueous solution HL = compact layer (Helmholtz layer) DL = diffuse charge layer x distance from the outer Helmholtz plane (OHP).

Pig. 5-27. Contact ion adsorption on metal electrodes in aqueous solution IHP = inner Helmholtz plane OHP = outer Helmholtz plane i,d = adsorbed ion ih = hy-dratedion oM = charge on the metal electrode o i = charge of adsorbed ions o i = charge of excess hydrated ions in solution. [From Bockris-Devanathan-MuUer, 1963.]... 

The reaction of electron transfer at electrodes in aqueous electrolytes proceeds either with hydrated redox particles at the plane of closest approach of hydrated ions to the electrode interface (OHP, the outer Helmholtz plane) or with dehydrated and adsorbed redox particles at the plane of contact adsorption on the electrode interface (IHP, the inner Helmholtz plane) as shown in Fig. 7-2. 

Fig. 7-2. Electron transfer of hydrated redox particles and of dehydrated adsorbed redox particles across an electrode interface (a) electron transfer of hydrated redox particles, (b) electron transfer of dehydrated and adsorbed redox particles on electrodes. (RED., OX,q) = hydrated redox particles (RED.d, OX.d) = dehydrated and adsorbed redox particles on electrode OHP = outer Helmholtz plane, IHP = inner Helmholtz plane.

The electron transfer of hydrated redox particles at the outer Helmholtz plane is occasionally called the outer-sphere electron transfer, while the electron transfer of dehydrated and adsorbed redox particles on electrodes is called the inner-sphere electron transfer. 

The plane of closest approach of hydrated ions, the outer Helmholtz plane (OHP), is located 0.3 to 0.5 run away from the electrode interface hence, the thickness of the interfacial compact layer across which electrons transfer is in the range of 0.3 to 0.5 nm. Electron transfer across the interfacial energy barrier occurs through a quantum tunneling mechanism at the identical electron energy level between the metal electrode and the hydrated redox particles as shown in Fig. 8-1. 

Fig. 8-1. Potential energy barrier for tunneling transfer of electrons across an interface of metal electrode (a) cathodic electron transfer from an occupied level of metal electrode to a vacant level of l drated oxidant particles, (b) anodic electron transfer fiom an occupied level of hjrdrated reductant particles to a vacant level of metal electrode. M. = electrode surface OHP = outer Helmholtz plane cfuh = Fermi level of electnms in metal electrode. [From Gerischer, I960.]...

Fig. 9-7. Ionization of surface at oms followed by ion tnnsfer across an electrode interface in anodic dissolution of covalent semiconductor S = covalently bonded atom in semiconductor S. = surface atom of semiconductor s = surface radical = surfisce ion 825 = hydrated ion OHP = outer Helmholtz plane.

Figure 5.4 Schematic representation of the double-layer around an electrode, showing the positions of the inner and outer Helmholtz planes, and the way that ionic charges are separated. The circles represent solvated ions.

Diffusion-Layer Model Let us consider again the general electrochemical reaction (6.6). Initially, at time before electrolysis, the concentration of the solution is homogeneous at all distances x from the electrode, equal to the bulk concentration of reactant Ox. In a more rigorous consideration, one would say that the concentration of the solution is homogeneous up to the outer Helmholtz plane (OHP), that is, up to x = xqhp-When a constant current is applied to the test electrodes and counterelectrodes such that the reaction... 

In a water solution, a proton (hydrogen ion) is hydrated, forming the hydroxonium ion H30. For the sake of simplicity we write H+ instead of H30. For further simplicity, we assume that the diffusion of protons from the bulk of the solution to the electrode [outer Helmholtz plane (OHP)],... 

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