Electrolytes diffusion planes

Figure 2.6 Schematic of diffusion planes in the electrolyte solution. (For color version of this figure, the reader is referred to the online version of this book.)...

The quantity 1 /k is thus the distance at which the potential has reached the 1 je fraction of its value at the surface and coincides with the center of action of the space charge. The plane at a = l//c is therefore taken as the effective thickness of the diffuse double layer. As an example, 1/x = 30 A in the case of 0.01 M uni-univalent electrolyte at 25°C. 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

The experimental data bearing on the question of the effect of different metals and different crystal orientations on the properties of the metal-electrolyte interface have been discussed by Hamelin et al.27 The results of capacitance measurements for seven sp metals (Ag, Au, Cu, Zn, Pb, Sn, and Bi) in aqueous electrolytes are reviewed. The potential of zero charge is derived from the maximum of the capacitance. Subtracting the diffuse-layer capacitance, one derives the inner-layer capacitance, which, when plotted against surface charge, shows a maximum close to qM = 0. This maximum, which is almost independent of crystal orientation, is explained in terms of the reorientation of water molecules adjacent to the metal surface. Interaction of different faces of metal with water, ions, and organic molecules inside the outer Helmholtz plane are discussed, as well as adsorption. 

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... 

Beyond the IHP is a layer of charge bound at the surface by electrostatic forces only. This layer is known as the diffuse layer, or the Gouy-Chapman layer. The innermost plane of the diffuse layer is known as the outer Helmholtz plane (OHP). The relationship between the charge in the diffuse layer, o2, the electrolyte concentration in the bulk of solution, c, and potential at the OHP, 2> can be found from solving the Poisson-Boltzmann equation with appropriate boundary conditions (for 1 1 electrolytes (13))... 

The charge at the diffuse layer plane is calculated from Gouy-Chapman-Stern-Grahame theory, which for a symmetrical monovalent electrolyte of concentration Cg is given by... 

In the presence of EOF, the observed velocity is due to the contribution of electrophoretic and electroosmotic migration, which can be represented by vectors directed either in the same or in opposite direction, depending on the sign of the charge of the analytes and on the direction of EOF, which depends on the sign of the zeta potential at the plane of share between the immobilized and the diffuse region of the electric double layer at the interface between the capillary wall and the electrolyte solution. Consequently, is expressed as... 

In the above equations, h is the film thickness, n is the munber concentration of z z symmetrical electrolyte and is the surface potential. The surface potential is the potential at the interface of stem and diffuse layers and is usually replaced by the zeta potential of the droplet determined from electrophoretic measurements. When the interface has an adsorbed layer of globular proteins, it may be reasonable to assume that the shear plane is located at the interface of protein layer. When xp > 2L, the disjoining pressure 11 / can be evaluated by replacing with potential and taking as (jCf - 2L,). 

Consider a plane electrode in an electrolytic solution dilute enough for there to be a thick diffuse layer, i.e., one that is hundreds or thousands of angstroms thick. Suppose now that a pressure difference is applied on the electrolytic solution in a direction parallel to the electrode. The electrolyte will begin to flow. When the liquid... 

For example, the treatment of diffusion that is to follow is solely restricted to semi-infinite linear diffusion, i.e., diffusion that occurs in the region between x = 0 and x —> +oo, to a plane of infinite area. Thus, diffusion to a point sink—called spherical diffusion—is not treated, though it has been shown to be relevant to the particular problem of the electrolytic growth of dendritic crystals from ionic melts. 

Figure 8.11—Effecl of diffusion on the efficiency obtained in HPLC and CE. Diffusion increases with the square of tube diameter. This is, thus, more important in HPLC. In CE. the electrolyte is repelled by the wall leading to an almost perfect plane-like flow contrary to the usual parabolic profile obtained under hydrodynamic flow. However, other factors that depend on the difference in conductivity between the electrolyte and solutes can lead to peak deformation.

In the absence of specific adsorption of anions, the GCSG model regards the electrical double layer as two plate capacitors in series that correspond respectively, to two regions of the electrolyte adjacent to the electrode, (a) An inner compact layer of solvent molecules (one or two layers) and immobile ions attracted by Coulombic forces (Helmholtz inner plane in Fig. 2). Specific adsorption of anions at the electrode surface may occur in this region by electronic orbital coupling with the metal, (b) An outer diffuse region of coulombically attracted ions in thermal motion that complete the countercharge of the electrode. 

Under the ribs, the species diffusion in the direction orthogonal to the cell plane, i.e. cross-plane diffusion, is obviously impossible. Hence, the reactant concentrations on the electrode/electrolyte site under the ribs are driven only by in-plane diffusion. Due to the strong diffusion property of H2, in-plane diffusion allows H2 to penetrate under the ribs, while in the case of O2, a relevant concentration reduction is noticed. The effect of the ribs is significant at all operating conditions, but it becomes predominant at high fuel utilization (not shown in the figures). 

Current density. Figure 4.16 shows the current density distribution at the an-ode/electrolyte interface. The current density is not uniform, as it is affected by the hydrogen and oxygen distributions and by the electrolyte resistance which is, in turn, dependent on the temperature. Because of the previously discussed reasons, as emphasized in Figure 4.17 where a 2D representation is shown, the produced current is smaller under the ribs than elsewhere. Furthermore, around the ribs, it is possible to observe that the produced current is characterized by a local increase. This effect is related to the local flow deceleration which, in turn, causes a local increase in the species concentrations together with a greater species diffusion perpendicular to the cell plane. 

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...

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