Stern-Helmholtz layer

Equation (2.33) now defines the double layer in the final model of the structure of the electrolyte near the electrode specifically adsorbed ions and solvent in the IHP, solvated ions forming a plane parallel to the electrode in the OHP and a dilfuse layer of ions having an excess of ions charged opposite to that on the electrode. The excess charge density in the latter region decays exponentially with distance away from the OHP. In addition, the Stern model allows some prediction of the relative importance of the diffuse vs. Helmholtz layers as a function of concentration. Table 2.1 shows... 

Streaming potential The interface of a mineral (rock) in contact with an aqueous phase exhibits surface charge. The currently accepted model of this interface is the EDL model of Stem. Chemical reactions take place between the minerals and the electrolytes in the aqueous phase, which results in a net charge on the mineral. Water and electrolytes bound to the rock surface constitute the Stern (or Helmholtz) layer. In this region, the ions are tightly bound to the mineral, while away from this layer (the so-called diffuse layer), the ions are free to move about. 

Most solid surfaces in water are charged. Reason Due to the high dielectric permittivity of water, ions are easily dissolved. The resulting electric double layer consist of an inner Stern or Helmholtz layer, which is in close contact with the solid surface, and a diffuse layer, also called the Gouy-Chapman layer. 

Fig. 3. The structure of the EDL at the mineral-water-electrolyte interface. 1-Layer of charging ions 2j-inner and 2,-outer Helmholtz layer (Grahame and Stem plane, resp.) 3-diffuse layer and 4-slipping or shear plane [after Ref. 16]. V o-phase potential and -Stern s poten-tial.a - H20 dipols, b - hydrated counterions, c - negatively charged ions, d - thickness of the G-S layer o - charge density...

The Stern model modifies the Gouy-Chapman model and divides ions present in the solution into two groups a part of the ions is placed near the solid surface, forming the so-called Stern layer (similar to the Helmholtz layer), and the other part having a diffuse distribution (Gouy-Chapman layer). It implies that the surface potential is linear in the Stern layer, and the exponential in the Gouy-Chapman layer. 

The solvent molecules form an oriented parallel, producing an electric potential that is added to the surface potential. This layer of solvent molecules can be protruded by the specifically adsorbed ions, or inner-sphere complexed ions. In this model, the solvent molecules together with the specifically adsorbed, inner-sphere complexed ions form the inner Helmholtz layer. Some authors divide the inner Helmholtz layer into two additional layers. For example, Grahame (1950) and Conway et al. (1951) assume that the relative permittivity of water varies along the double layer. In addition, the Stern variable surface charge-variable surface potential model (Bowden et al. 1977, 1980 Barrow et al. 1980, 1981) states that hydrogen and hydroxide ions, specifically adsorbed and inner-sphere... 

The model introduced by Stern (2), which is in best agreement with all experimental facts, combines a distribution of charges in a space charge layer (diffuse part of the double layer) and the Helmholtz layer (rigid part of the double layer). Ions are assumed to be adsorbed on the electrode and thus bound to the surface by chemical forces. If strongly adsorbed ions are present at the interface, the rigid double layer predominates in determining the electrical properties of the interface. 

Figure 3.21. Gouy-Stern double layer model with specific adsorption at the outer Helmholtz plane. The inner layer has a constant capacit mce C. ...

In all situations discussed so far only one Stern layer capacitance is required. In literature it is however often assumed [7, 8, 22] that diffuse ions can approach the surface up to the Stern plane and that s.a. ions are located at a newly defined adsorption plane, the inner Helmholtz plane. The inner Helmholtz plane is located in between the surface plane and the Stern or outer Helmholtz plane. The double layer model composed of an inner and outer Helmholtz layer plus a diffuse layer is generally called the triple layer (TL) model. 

On the metal side of the oHp, there is the so-called inner layer (the compact layer, or Stern or Helmholtz layer) which is a molecular-diameter thick and in which short-range interactions as well as long-range interactions exist. 

Helmholtz Double Layer A simplistic description of the electric double layer as a condenser (the Helmholtz condenser) in which the condenser plate separation distance is the Debye length. The Helmholtz layer is divided into an inner Helmholtz plane (IHP) of adsorbed, dehydrated ions immediately next to a surface, and an outer Helmholtz plane (OHP) at the center of a next layer of hydrated, adsorbed ions just inside the imaginary boundary where the diffuse double layer begins. That is, both Helmholtz planes are within the Stern layer. 

It was taken into account in the models developed in Refs 75, 78 and 80 that some portion of the counter-ions is bound to surface-active ions within the Stern-Helmholtz (S-H) layer, while another (unbound) portion is located within the diffuse region of the DEL. The equivalent relations of Eqs (56)-(58) in this case contain the difference F — y"X instead of Fj, where F x is the adsorption of counterions localized within the monolayer. It follows from the model described by Eqs (56)-(58) that if all counterions are lo-... 

The outer Helmholtz plane is limiting the Stern s layer and determines the shortest distance available for the hydrated ions from the solution. Inside the internal layer an internal Helmholtz plane is also distinguished which determines the centers of gravity of ions adsorbed on the surface of solid phase. 

Grahame made a further division of the Stern layer into the inner Helmholtz layer and outer Helmholtz layer. These layers are separated by the inner Helmholtz plane at a distance from the surface corresponding to the radius of nonhydrated specifically adsorbed ions. These ions are smaller than the counterions, and the inner Helmholtz, plane is hence located between the Stern plane and the surface. The outer Helmholtz layer is limited by the outer Helmholtz plane, which is identical to the Stern plane. 

The Stern Model is a combination of the Helmholtz and Gouy-Chapman models (Figure 3.47). The potential difference between the metal and the solution is comprised of two terms A h. due to the compact Helmholtz layer and A0gc, due to the diffuse Gouy-Chapman layer. 

Figure 2. Three models of the electrochemical interface (a) the Helmholtz fixed (rigid) double layer, 1879 (b) the Gouy-Chapman diffuse double layer 1910-1913 (c)the Stern double layer, 1924, being a combination of the Helmholtz and the Gouy-Chapman concepts.

See color insert.) Electric double-layer models at interface of electrode and electrolyte solution. (a) Diffuse layer or Gouy-Chapman model, (b) Helmholtz layer or model the d represents the double-layer thickness, (c) Stern-Grahame layer or model in which the IHP represents the inner Helmholtz plane and the OHP represents the outer Helmholtz plane. 

A similar approach to the boundary condition for the potential at the metal-solution interface has been applied by Biesheuvel et al., in consideration of diffuse charge effects in galvanic cells, desalination by porous electrodes, and transient response of electrochemical cells (Biesheuvel and Bazant, 2010 Biesheuvel et al., 2009 van Soestbergen et al., 2010). However, their treatment neglected the explicit effect of In principle, the PNP model could be modified to incorporate size-dependent and spatially varying dielectric constants in nanopores, as well as ion saturation effects at the interface. However, in a heuristic fashion, such variations could be accounted for in the Helmholtz capacitance of the Stern double layer model. 

Equation [23] represents the GC solution for point ions. A key development in the theory of electrolytes was the introduction of a finite distance of closest approach of ions to a charged surface by Stern and further elaborated upon by Grahame. The layer of ions directly adsorbed onto the surface constitutes the inner Helmholtz layer those ions that make contact but do not adsorb define the abovementioned distance of closest approach and constitute the outer Helmholtz or Stern layer. These modifications still admit an analytical solution to the GC equation Laplace s equation is solved in the Stern layer with the (linear) potential and (constant) field matched at the polyelectrolyte surface and to the outer GC solution. The adsorbed ions serve to reduce the charge density of the surface. Identification of the inner and outer Helmholtz layers has been particularly helpful in improving agreement between GC theory and electrochemical data. If we assign a common radius a to all electrolyte ions, then the identification of the interface atx = a actually... 

The behavior of simple and molecular ions at the electrolyte/electrode interface is at the core of many electrochemical processes. The complexity of the interactions demands the introduction of simplifying assumptions. In the classical double layer models due to Helmholtz [120], Gouy and Chapman [121,122], and Stern [123], and in most analytic studies, 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... 

Fig. 1 Double layer model for a cathode, (a) Helmholtz model (b) Gouy-Chapman model (c) Stern model. 

Fig. 17.2. The distribution of charges at the internal wall of a silica capillary. x is the length in cm from the center of charge of the negative wall to a defined distance, 1 = the capillary wall, 2 = the Stern layer or the inner Helmholtz plane, 3 = the outer Helmholtz plane, 4 = the diffuse layer and 5 = the bulk charge distribution within the capillary.

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