Electrical double layer Stern model

In the electrochemical literature one finds the Gouy-Chapman (GC) and Gouy-Chapman-Stern (GCS) approaches as standard models for the electric double layer [9,10]. 

Gouy-Chapman, Stern, and triple layer). Methods which have been used for determining thermodynamic constants from experimental data for surface hydrolysis reactions are examined critically. One method of linear extrapolation of the logarithm of the activity quotient to zero surface charge is shown to bias the values which are obtained for the intrinsic acidity constants of the diprotic surface groups. The advantages of a simple model based on monoprotic surface groups and a Stern model of the electric double layer are discussed. The model is physically plausible, and mathematically consistent with adsorption and surface potential data. 

To complement the models for the surface reactions, a model for the electric double layer is needed. Current models for the electric double layer are based on the work of Stern (21), who viewed the interface as a series of planes or layers, into which species were adsorbed by chemical and electrical forces. A detailed discussion of the application of these models to oxide surfaces is given by Westall and Hohl (2). 

Two models of surface hydrolysis reactions and four models of the electrical double layer have been discussed. In this section two examples will be discussed the diprotic surface group model with constant capacitance electric double layer model and the monoprotic surface group model with a Stern double layer model. More details on the derivation of equations used in this section are found elsewhere (3JL). ... 

The representation of the data for TiC in terms of the monoprotic surface group model of the oxide surface and the basic Stern model of the electric double layer is shown in Figure 5. It is seen that there is good agreement between the model and the adsorption data furthermore, the computed potential Vq (not shown in the figure) is almost Nernstian, as is observed experimentally. 

The variation of the electric potential in the electric double layer with the distance from the charged surface is depicted in Figure 6.2. The potential at the surface ( /o) linearly decreases in the Stem layer to the value of the zeta potential (0- This is the electric potential at the plane of shear between the Stern layer (and that part of the double layer occupied by the molecules of solvent associated with the adsorbed ions) and the diffuse part of the double layer. The zeta potential decays exponentially from to zero with the distance from the plane of shear between the Stern layer and the diffuse part of the double layer. The location of the plane of shear a small distance further out from the surface than the Stem plane renders the zeta potential marginally smaller in magnitude than the potential at the Stem plane ( /5). However, in order to simplify the mathematical models describing the electric double layer, it is customary to assume the identity of (ti/j) and The bulk experimental evidence indicates that errors introduced through this approximation are usually small. 

Figure 7.4. Schematic model of the Electrical Double Layer (EDL) at the metal oxide-aqueous solution interface showing elements of the Gouy-Chapman-Stern-Grahame model, including specifically adsorbed cations and non-specifically adsorbed solvated anions. The zero-plane is defined by the location of surface sites, which may be protonated or deprotonated. The inner Helmholtz plane, or [i-planc, is defined by the centers of specifically adsorbed anions and cations. The outer Helmholtz plane, d-plane, or Stern plane corresponds to the beginning of the diffuse layer of counter-ions and co-ions. Cation size has been exaggerated. Estimates of the dielectric constant of water, e, are indicated for the first and second water layers nearest the interface and for bulk water (modified after [6]).

From the discussion so far it can be appreciated that the Stern model of the electric double layer presents only a rough picture of what is undoubtedly a most complex situation. Nevertheless, it provides a good basis for interpretating, at least semiquantitatively, most experimental observations connected with electric double layer phenomena. In particular, it helps to account for the magnitude of... 

One other aspect of nonprimitive electric double layer theories which is particularly relevant to the inner Stern region are the models for the water molecule and the ions. The simplest models for a water molecule and an ion are a hard-sphere point dipole and point charge, respectively. A more realistic model of the hard-sphere water molecule would include quadrupoles and octupoles and also polarizability. However the hard-sphere property is best avoided and replaced, for example, by a Lennard-Jones potential. An alternative to a multipolar water model are three point charge sites associated with the atoms within the water molecule. 

Finally we shall argue that present-day theories of the nonprimitive models of the electric double layer have considerable difficulty in treating properly ion adsorption in the Stern inner region at metal-aqueous electrolyte interfaces and we suggest that this region is a useful concept which should not be dismissed as unphysical. Indeed Stern-like inner region models continue to be used in colloid and electrochemical science, for example in theories of electrokinetics and aqueous-non-metallic (e.g., oxide) interfaces. 

Many electrical double-layer and adsorption models have been proposed to account for experimental data dealing with the adsorption of ions on oxides. Stern suggested separation of the solution region near the surface into two parts, the first consisting of a layer of... 

Many more-sophisticated models have been put forth to describe electrokinetic phenomena at surfaces. Considerations have included distance of closest approach of counterions, conduction behind the shear plane, specific adsorption of electrolyte ions, variability of permittivity and viscosity in the electrical double layer, discreteness of charge on the surface, surface roughness, surface porosity, and surface-bound water [7], Perhaps the most commonly used model has been the Gouy-Chapman-Stem-Grahame model 8]. This model separates the counterion region into a compact, surface-bound Stern" layer, wherein potential decays linearly, and a diffuse region that obeys the Poisson-Boltzmann relation. 

The inner layer is a concept within the framework of the classical Gouy-Chap-man-Stern model of the double layer [57]. Recent statistical-mechanical treatments of electrical double layers taking account of solvent dipoles has revealed a microscopic structure of inner layer" and other intriguing features, including pronounced oscillation of the mean electrostatic potential in the vicinity of the interface and its insensitivity at the interface to changes in the salt concentration [65-69]. 

The dependence of the electro-osmotic flow on the specific adsorption of counterions in the electric double layer can be described by a model which correlates the electro-osmotic mobility to the charge density in the Stern part of the electric double layer (arising from the adsorption of counterions) and the charge density at the capillary wall (resulting from the ionization of silanol groups) [5]. According to this model, the dependence of the electro-osmotic mobihty on the concentration of the adsorbing ions (C) in the electrolyte solution is expressed as... 

The behavior of simple and molecular ions at the electrolyte/electrode interface is at the core of many electrochemical processes. The substantial understanding of the structure of the electric double layer has been summarized in various reviews and books (e.g., Ref. 2, 81, 177-183). The complexity of the interactions demands the introduction of simplifying assumptions. In the classical double layer models due to Helmholtz [3], Gouy and Chapman [5, 6], and Stern [7], and in most of the studies cited in the reviews the molecular nature of the solvent has been neglected altogether, or it has been described in a very approximate way, e.g., as a simple dipolar fluid. Computer simulations can overcome this restriction and describe the solvent in a more realistic fashion. They are thus able to paint a detailed picture of the microscopic structure near a metal electrode. 

We see that there is a complex structure in the solution, changing as we move from the electrode surface to the bulk solution. There have been several theories over the years attempting to explain this structure and they all provide a model of the electrical double layer. Fig. 1.3b resembles the model proposed by Stern in 1924 and is sufficiently advanced for our purposes. We see that there are three zones reaching out from the electrode, each zone having a potential defined by electrode potential, ie difference in potential between the electrode and the bulk solution). 

O. STERN (1888-1969) publishes his model of the electrical double layer (1924) Z Elektrochem 30 508... 

FIGURE 6. The arrangement of water molecules and counterions near to a negatively charged membrane surface according to the Stern model. Within the Stern layer of polarized water molecules the electric potential falls linearly, and for distances further than this the potential profile follows that predicted by the Gouy-Chapman theory of electrical double layers. For ascites cells the potential drop between the surface potential and the zeta potential has been determined to be around... 

Figure 7.10 Stern s model of the diffuse electric double layer.

---