Diffusion Potential Drop

The use of reference electrodes frequently poses the problem of an additional potential drop between the electrolytes of the electrode under study and of the reference one. For liquid electrolytes, this drop arises at the solution/solution interface (liquid junction). The symbol conventionally denotes an interface of two solutions with a diffusion potential drop in between if this drop is eliminated (see later), then the 

The Henderson equation that has gained wider acceptance can be written as follows for concentrations c having the units of normality  

The solution is given for the case of a smeared out boundary and linear spatial distributions of concentrations. 

Generally, Eqs. (20)-(22) yield similar results however, for junctions with a pronounced difference in ion mobilities 

In practice, in place of model calculations and corresponding corrections, the elimination of the diffusion potential is conventionally applied. This is achieved by introducing the so-called salt bridges filled with concentrated solutions of salts, which contain anions and cations of close transport numbers. A widely known example is saturated KCl (4.2 M) in aqueous solutions, potassium and ammonium nitrates are also suitable. However, the requirement of equal transport numbers is less important as compared with that of high concentration of electrolyte solution, which fills the bridge [33, 34]. A suitable version of the salt bridge can be chosen for any type of cells, when taking into account the kind of studies and the features of chosen electrodes. 

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The potential difference can be seen to be made up of two terms. The first term represents the ohmic potential drop due to the flow of current through a medium of given electrical conductance. The second term, called the diffusion potential drop, is associated with a region in which there is a concentration gradient (concentration polarization region). This term does not disappear in the absence of a current and is due to unequal rates of diffusion of the charged particles, thus giving rise to a diffusional electric field. 

The expression for potential difference consists of two terms. The first term has the meaning of ohmic potential drop caused by the resistance of the medium to propagation of electric current of density i. The second term, called the diffusion potential drop, is related to the gradient of concentration, that is, to the presence of regions of concentration polarization. This term is caused by the difference in diffusion rates of charged particles and the occurrence of diffusion flux (the second term in Eq. (5.98)). 

A LJP resulting exclusively from concentration gradients of ions is most frequently called a diffusion potential drop If the solvent from both sides of junction is... 

The region of the gradual potential drop from the Helmholtz layer into the bulk of the solution is called the Gouy or diffuse layer (29,30). The Gouy layer has similar characteristics to the ion atmosphere from electrolyte theory. This layer has an almost exponential decay of potential with increasing distance. The thickness of the diffuse layer may be approximated by the Debye length of the electrolyte. 

Fig. 20.18 Concentration gradient and potential gradient in the diffusion layer for a cathodic process (note that the potential drop through the solution has not been included)...

Influence of the Diffusional Potential Drop In the case being considered, a potential difference % is established across the diffusion layer whose value can be found by integrating Eq. (4.20) from x = 0 to x = 5 ... 

The trends of behavior described above are found in solutions containing an excess of foreign electrolyte, which by definition is not involved in the electrode reaction. Without this excess of foreign electrolyte, additional effects arise that are most distinct in binary solutions. An appreciable diffusion potential q) arises in the diffusion layer because of the gradient of overall electrolyte concentration that is present there. Moreover, the conductivity of the solution will decrease and an additional ohmic potential drop will arise when an electrolyte ion is the reactant and the overall concentration decreases. Both of these potential differences are associated with the diffusion layer in the solution, and strictly speaking, are not a part of electrode polarization. But in polarization measurements, the potential of the electrode usually is defined relative to a point in the solution which, although not far from the electrode, is outside the diffusion layer. Hence, in addition to the true polarization AE, the overall potential drop across the diffusion layer, 9 = 9 + 9ohm is included in the measured value of polarization, AE. ... 

It is the major aim of diffuse EDL theory to establish the relation between the charge and potential /o at point x = 0 (the total potential drop across this layer). 

The ideal conductor model does not account for diffuseness of the ionic distribution in the electrolyte and the corresponding spreading of the electric field with a potential drop outside the membrane. To account approximately for these effects we apply Poisson-Boltzmann theory. The results for the modes energies can be summarized as follows [89] ... 

This result was taken as an experimental eonfirmation of the model developed by Sehmiekler [7]. However, it appeared somehow eontradictory with other results obtained with SECM. It was also suggested that eoneentration polarization phenomena occurring at the aqueous side are negligible as the whole potential drop is presumably developed in the benzene phase. This assumption can be qualitatively verified by evaluating a simplified expression for the potential distribution based on a back-to-back diffuse double layer [40,113],... 

The description of the ion transfer process is closely related to the structure of the electrical double layer at the ITIES [50]. The most widely used approach is the combination of the BV equation and the modified Verwey-Niessen (MVN) model. In the MVN model, the electrical double layer at the ITIES is composed of two diffuse layers and one ion-free or inner layer (Fig. 8). The positions delimiting the inner layer are denoted by X2 and X2, and represent the positions of closest approach of the transferring ion to the ITIES from the organic and aqueous side, respectively. The total Galvani potential drop across the interfacial region, AgCp = cj) — [Pg.545]

When the ITIES is polarized with a potential difference 0, there is a separation of electrical charge across it. According to the Gouy-Chapman theory, the charges in the aqueous and organic diffuse layers are related to the potential drops and A0 in the respective layers by the equations... 

For a long time, the electric double layer was compared to a capacitor with two plates, one of which was the charged metal and the other, the ions in the solution. In the absence of specific adsorption, the two plates were viewed as separated only by a layer of solvent. This model was later modified by Stem, who took into account the existence of the diffuse layer. He combined both concepts, postulating that the double layer consists of a rigid part called the inner—or Helmholtz—layer, and a diffuse layer of ions extending from the outer Helmholtz plane into the bulk of the solution. Accordingly, the potential drop between the metal and the bulk consists of two parts ... 

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