Stern’s layer

Chemical complexation processes within Sterns layer run much slower and thereby slow down process of mass transfer as a whole. It is usually very difficult to separate processes of ion exchange and complexation. For this reason, their rates, as a rule, are studied together. They depend both on physical diffusion mass exchange within the Nernst layer and on chemical reactions within Stern s layer. 

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. 

Figure 7.2 Schematic representation of the structure of the electric double layer according to Stern s theory... 

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...

Earlier theories by Gouy, Chapman, and Hcrzfeld discussed the double layer as wholly of this diffuse type but Stem points out that these give far too high values for the capacity of the double layer, partly because in them the ions are supposed mathematically to be able to approach indefinitely close to the solid surface, which is impossible physically owing to the size of the ions. Stern s theory gives a complicated expression for the capacity of the double layer, but accounts reasonably well for the experimental values. Though the layer is largely diffuse in many cases, the capacity is usually of the same order as if the layer were of the plane parallel type, because most of the ions are fairly close to the fixed part of the layer. 

The adsorbed ions aid coagulation by reducing the net charge on the central, compact core of the particle, wrhich includes the fixed part of Stern s double layer. 

Up till about 1921, it was often supposed that the potential could be identified with the single potential difference at the phase boundary. Freundlich and his collaborators1 showed that this is quite impossible, since the variation with concentration, and the influence of adsorbed substances, are entirely different in the two cases sometimes indeed the two potentials may have different signs. The phase boundary potential, if defined as the Volta potential, is the difference between the energy levels of the charged component, to which the phase boundary is permeable, inside the two phases when these are both at the same electrostatic potential. We have seen that it is difficult, or impossible, to define the phase boundary potential in any other way (see 2 and 3). It includes the work of extraction of the charged component from each phase, and this includes the part of the double layer which according to Stern s theory is fixed. The potential is merely the potential fall in the mobile, diffuse part of the double layer, and is wholly within one phase. 

The influence of ions on electrokinetic effects can be readily explained with the aid of Stern s concept of the double layer. Substances like silicon carbide, cellulose, sulfur and carbon, which do not ionize, are negatively charged in contact with water and the addition of small amounts of uni-univalent electrolytes tends to increase this charge. It is probable that in these cases the negative zeta-potential is due in the first place to the firm attachment to the surface of hydroxyl ions from the water and possibly also of anions from the electrolyte. An equivalent number of positive ions, some closely held in the fixed part of the double layer and the remainder in the diffuse portion, will be left in the solution. The potential gradient between the solid surface and the bulk of the liquid, which is pure water or a dilute solution, is shown diagrammatically in Pig. 128,1. If the electrolyte concentration is increased, there will be... 

Planes 1 - Helmholtz s, 11 - slip layers - Stern s, - Gouy s, - Nernst s potentials q> -surficial, - of diffuse fayer, - efectrokinetic. 

Zie is the charge of the species. Stern assumed the location of the adsorption ion at the outer Helmholtz plane separating the compact and diffuse layer, so that the potential in the work term in Eq. (71) corresponds to the potential difference across the diffuse layer. The combination of Eqs. (70a) and (71) gives Stern s expression for the adsorption isotherm from a binary electrolyte solution for the case of a single ionic species being accumulated in the adsorbed state ... 

The second modification compared to the Stern theory was the introduction of the discreteness-of-charge factor , X. The electrostatic part of the work of ion transfer from the bulk solution into the adsorption plane across the EDL field in Stern s approximation may be represented as the sum of the contributions of the compact and diffuse layers ... 

In order to calculate this distribution equilibrium of the liquid charge between the two layers (which may be called the Stern-layer and the Gouy-layer, respectively). Stern proceeds in a way somewhat analogous to the derivation of the adsorption isotherm of Langmuir. We will simplify Stern s equations by considering only the counter-ions, i.e. 

It has long been recognized that the "Potential has quite a different character from that of the potential (the total potential difference of the double layer), s is usually considerably smaller than it reacts strongly to the addition of indifferent electrolytes, which leave Po unaltered. Although c is perhaps not identical with the potential (the potential in the diffuse layer according to Stern s picture), it is felt that will resemble ps much more than Pq. ... 

The quantitative effect of the use of Stern s concept of the double layer is illustrated in Fig. 33. This figure, again, contains a set of curves similar to those in Fig. 31, with the only difference that they now represent the combination of and logq, for which the maximum of the total potential energy curve (+ K.4) exactly coincides with the horizontal... 

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

Hence, knowing the charge of the compact layer the ion distribution can be modelled. The crux of Stern s treatment is the estimation to which extent ions enter the compact layer and reduce the surface potential. The ion distribution between compact and diffuse layer cannot be easily experimentally established, for example surface potential measurements cannot measure this distribution. 

The observation that bromide, and even iodide, can strongly adsorb on hydrophobic surfaces due to non-electrostatic forces, can also have a considerable impact in electrochemistry. There, for more than 80 years, Otto Stern s idea of an obscure non-electrostatically adsorbed layer is an ad hoc assumption that is not really explained. 

The most promising attempt to improve Stern s theory is due to Grahams Grahame s work is directed especially on the interpretation of the double layer on mercury He supplies evidence that in the STERN-layer only the unions are really chemisorbed with loss of a part of their hydration shells, whereas the cations remain hydrated and are only attracted to the surface by electrostatic forces. A distinction should therefore be made between what Grahams calls the outer Helmholtz plane, that is the locus of nearest approach of the centres of charge of cations to the wall and the inner Helmholtz plane that is the locus of the centres of charge of the chemisorbed anions. 

Fig. 7, Differential ca acity of the double layer according to Stern s theory. Capacity of the molecular condenser 3B [iF for positive surface and 20 pF for negative surface. (Taken from A. Frumkin, Trans. Faraday Soc., 36 (1940) 126).

Retaining for the moment Stern s theory it should be asked how the interaction is modified by the presence of a Stern layer. Considering again two flat plates approaching each other, the primary effect will be an interaction of the two diffuse double layers, c/. Fig. 11. A direct influence of the two Stern layers on each other will only occur when the distance between the plates becomes of the order of atomic dimensions and thus may usually be left out of consideration. 

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