Helmholtz plane layer

Double layer models — The oldest model for the double layer at metal/solution interfaces was proposed by - Helmholtz. He suggested that an excess charge (- double layer, excess charge density) on the metal attracts an equivalent amount of counter ions to the interface, the two opposing layers are separated by a certain distance, which determines the capacity. His model gave rise to the concepts of the inner and outer Helmholtz planes (layers) (- Double layer). 

The compact layer can be structured into what is called an inner Helmholtz plane... 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

There is, or may be, an iimer layer of specifically adsorbed anions on the surface these anions have displaced one or more solvent molecules and have lost part of their iimer solvation sheath. An imaginary plane can be drawn tlirough the centres of these anions to fomi the inner Helmholtz plane (IHP). 

The layer of solvent molecules not directly adjacent to the metal is the closest distance of approach of solvated cations. Since the enthalpy of solvation of cations is nomially substantially larger than that of anions, it is nomially expected that tiiere will be insufBcient energy to strip the cations of their iimer solvation sheaths, and a second imaginary plane can be drawn tlirough the centres of the solvated cations. This second plane is temied the outer Helmholtz plane (OHP). 

Helmholtz layer Helmholtz layers Helmholtz planes... 

Fig. 1. Schematic representation of the electrochemical or diffuse double layer showing the inner (IHP) and outer (OHP) Helmholtz planes and the...

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. 

Fig. 1. The structure of the electrical double layer where Q represents the solvent CD, specifically adsorbed anions 0, anions and (D, cations. The inner Helmholtz plane (IHP) is the center of specifically adsorbed ions. The outer Helmholtz plane (OHP) is the closest point of approach for solvated cations or molecules. O, the corresponding electric potential across the double layer, is also shown.

FIGURE 1-11 Schematic representation of the electrical double layer. IHP = inner Helmholtz plane OHP = outer Helmoltz plane. 

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. 

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...

A rigorous solution of this problem was attempted, for example, in the hard sphere approximation by D. Henderson, L. Blum, and others. Here the discussion will be limited to the classical Gouy-Chapman theory, describing conditions between the bulk of the solution and the outer Helmholtz plane and considering the ions as point charges and the solvent as a structureless dielectric of permittivity e. The inner electrical potential 0(1) of the bulk of the solution will be taken as zero and the potential in the outer Helmholtz plane will be denoted as 02. The space charge in the diffuse layer is given by the Poisson equation... 

By means of the thermodynamic theory of the double layer and the theory of the diffuse layer it is possible to determine the charge density ox corresponding to the adsorbed ions, i.e. ions in the inner Helmholtz plane, and the potential of the outer Helmholtz plane 2 in the presence of specific adsorption. 

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 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. 

The electric field or ionic term corresponds to an ideal parallel-plate capacitor, with potential drop g (ion) = qMd/4ire. Itincludes a contribution from the polarizability of the electrolyte, since the dielectric constant is included in the expression. The distance d between the layers of charge is often taken to be from the outer Helmholtz plane (distance of closest approach of ions in solution to the metal in the absence of specific adsorption) to the position of the image charge in the metal a model for the metal is required to define this position properly. The capacitance per unit area of the ideal capacitor is a constant, e/Aird, often written as Klon. The contribution to 1/C is 1 /Klon this term is much less important in the sum (larger capacitance) than the other two contributions.2... 

The experimental data bearing on the question of the effect of different metals and different crystal orientations on the properties of the metal-electrolyte interface have been discussed by Hamelin et al.27 The results of capacitance measurements for seven sp metals (Ag, Au, Cu, Zn, Pb, Sn, and Bi) in aqueous electrolytes are reviewed. The potential of zero charge is derived from the maximum of the capacitance. Subtracting the diffuse-layer capacitance, one derives the inner-layer capacitance, which, when plotted against surface charge, shows a maximum close to qM = 0. This maximum, which is almost independent of crystal orientation, is explained in terms of the reorientation of water molecules adjacent to the metal surface. Interaction of different faces of metal with water, ions, and organic molecules inside the outer Helmholtz plane are discussed, as well as adsorption. 

Anions may exhibit a tendency toward specific adsorption at the O/S interface. This may be related in some way to the complexing affinity. This effect, occurring at the inner Helmholtz plane of the electrochemical double layer, may significantly change the charge transfer situation [cf. Section III(5(iii))]. 

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). 

Fig. 2. Schematic diagram of the tunnel gap between sample and tip, with the extension of the electric double layers indicated by the outer Helmholtz plane(OHP). (a) No tip interaction at large tip-sample separation, (b) Overlap of the electric double layers at a distance s = 0.6 nm, which can be achieved by conventional imaging conditions (e.g., Uj = 50 mV It = 2 nA Rt = 2.5 x 107 Q). Inset Dependence of the tunnel gap s on the tunnel resistance Rt for a tunnel barrier of 1.5 eV.

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). 

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