Helmholtz compact

Without actually studying the whole mathematical equation of the potential profile in the double layer, one can remember that when the potential difference between the terminals of the diffuse double layer is moderate, then the variations inside the latter are close to an exponential function  

For concentrated solutions (for instance those involving a supporting electrolyte with a concentration higher than 0.1 mol L ), the Debye length is less than one nanometer and one can consider the double layer as being reduced to the compact layer. For very dilute solutions (for instance with an ionic strength of about 10 mol L ), the Debye length is about 0.1 pm and the diffuse layer represents most of the volume in the double layer. It should be remembered that the electrochemical double layer is typically about a few nanometers in thickness. 

This book will make little reference to phenomena relating to this double layer. Yet a number of applications in electrochemistry, such as electrophoresis, electroosmosis, supercapacitors, etc. are rooted in these same phenomena. 

In the following section we will focus on reactive interfaces. Here again, thermodynamic equilibrium corresponds to particular potential profiles in the interfacial zone. Although double layer phenomena do indeed also come into play for these reactive interfaces, here our analysis will be carried out on a much broader scale than merely the double layer alone. Therefore the potential profile appears simply as flat in both extreme phases, showing discontinuity when crossing the interface. This discontinuity, this potential difference between the two phases, is what thermodynamics connects up to the system s composition, as explained below. 

By analogy with the case of chemical reactions in volumes, the state of thermodynamic electrochemical equilibrium corresponds to a zero value for the electrochemical Gibbs energy of reaction  

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The simplest model of the structure of the metal-solution interphase is the Helmholtz compact double-layer model (1879). According to this model, all the excess charge... 

The simplest model of the structure of the metal-solution interphase is the Helmholtz compact double-layer model (1879). According to this model, all the excess charge on the solution side of the interphase, qs. is lined up in the same plane at a fixed distance away from the electrode, the Helmholtz plane (Fig. 4.4). This fixed distance xH is determined by the hydration sphere of the ions. It is defined as the plane of the centers of the hydrated ions. All excess charge on the metal, qM, is located at the metal surface. 

H = coverage of the electrode surface by the product of discharge, H Ch+,s = local concentration of H" " at electrode surface in the Helmholtz compact-layer region of the double layer k = rate constant for the process at a hypothetical V = 0 f and b = forward and backward reactions, respectively. 

Capacitance of the Helmholtz (compact) part of the double layer (F cm )... 

It is assumed that the concentration of ions present in a liquid is extremely low and that the ions present are formed exclusively in the autodissociation process. All ions and neutrals other than those originating from liquid solvent are removed by purification as impurities. Under such circumstances, the system can be considered as an ideally dilute solution i.e., the solvent mole fractions is 1. Hence, the system, the electrode and the solvent, is assumed to obey Henry s law. The surface concentration of specifically adsorbed anions can be estimated on this basis from the Henry isotherm. Assuming that the specific adsorption equilibrium constant for OH ions in pure water can range from 0.1 to 100 dm /mol, one can obtain the surface concentration of adsorbed anions in the range lO -lO mol/cm i.e., the ratio of the adsorbed anions to the metal atoms of the electrode surface is 10 -10 . Having this in mind and remembering that an amount of possible solvated cations in the bulk of solution is very low, it can hardly be believed that the Helmholtz compact layer is formed in pure liquid. Thus, the electrode-liquid interface seems to... 

Th se parameters represent capacitance and resistance to charge transfer for only the electroactive discharging species in the Helmholtz compact layer. The only mechanism of transporting electroactive reactants to the electrode is by di sion of discharging species, which is placed in series with Rbulk- reaction impedance Rb act should therefore be placed in... 

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

The traditional treatment of a double layer at electrode-electrolyte interfaces is based on its separation into two series contributions the compact ( Helmholtz ) layer and the diffusive ( dif ) layer, so that the inverse capacitance is... 

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. 

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). 

The diffuse layer of excess electrons and holes in solids is called the space charge layer and the diffuse layer of excess hydrated ions in aqueous solution is simply called the diffuse layer and occasionally called the Gouy layer [Gouy, 1917]. The middle layer of adsorbed water moleciiles, between the diffuse layer on the aqueous solution side and the space charge layer on the soUd side, is called the compact or the inner layer. This compact or inner layer is also called the Helmholtz layer [Helmholtz, 1879] or the Stem layer [Stem, 1924] the plane of the closest approach of hydrated ions to the solid surface is called the outer Helmholtz plane (OHP) [Graham, 1947]. 

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).

Chemisorption of anions at the electrode interface involves dehydration of hydrated anions followed by adsorption of dehydrated anions which, then, penetrate into the compact double layer to contact the interface directly, this result is called the contact adsorption or specific adsorption. The plane of the contact adsorption of dehydrated anions is occasionally called the inner Helmholtz plane... 

In the course of ionic contact adsorption on the interface of metal electrode, hydrated ions are first dehydrated and then adsorbed at the inner Helmholtz plane in the compact layer as shown in Fig. 5-27 and as described in Sec. 5.6.1. In the interfacial double layer containing adsorbed ions, the combined charge of motal and adsorbed ions = z eF on the metal side is balanced with the... 

Ionic contact adsorption on metallic electrodes alters the potential profile across the compact layer at constant electrode potential. If anions are adsorbed on the metal electrode at positive potentials, the adsorption-induced dipole generates a potential across the inner Helmholtz layer (IHL) as illustrated in Fig. 5-29. The electric field in the outer part (OHL) of the compact layer, as a result, becomes dififerent fi om and frequently opposite to that in the inner part (IHL) of the compact layer. 

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. 9-1. Potential energy profile for transferring metal ions across an interface of metal electrode M/S py. = metal ion level (electrochemical potential) x = distance fiom an interface au. = real potential of interfacial metal ions = real potential of hydrated metal ions - compact layer (Helmholtz layer) V = outer potential of solution S, curve 1 = potential energy of interfadal metallic ions curve 2 = potential energy of hydrated metal ions.

In the anodic dissolution of covalent semiconductors, the transfer of surface ions across the compact layer (Helmholtz la r) occurs following the ionization of surface atoms S, illustrated in Eqn. 9-33, as described in Sec. 9.2.1 ... 

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