Bulk Electrolytes

The most favorable conditions for equation 9 are temperature from 60—75°C and pH 5.8—7.0. The optimum pH depends on temperature. This reaction is quite slow and takes place in the bulk electrolyte rather than at or near the anode surface (44—46). Usually 2—5 g/L of sodium dichromate is added to the electrolysis solution. The dichromate forms a protective Cr202 film or diaphragm on the cathode surface, creating an adverse potential gradient that prevents the reduction of OCU to CU ion (44). Dichromate also serves as a buffering agent, which tends to stabilize the pH of the solution (45,46). Chromate also suppresses corrosion of steel cathodes and inhibits O2 evolution at the anode (47—51). 

The cathodic reduction of dissolved oxygen contained in a thin condensed electrolyte layer is much less severely polarised than the reduction of dissolved oxygen in the corresponding bulk electrolyte. 

The reversible voltage is 2.8-3.0 V and the operating voltage is >7 Y. Details about electron transfer from the bulk electrolyte into the carbon base of the anode are not clear. 

The popular and well-studied primitive model is a degenerate case of the SPM with = 0, shown schematically in Figure (c). The restricted primitive model (RPM) refers to the case when the ions are of equal diameter. This model can realistically represent the packing of a molten salt in which no solvent is present. For an aqueous electrolyte, the primitive model does not treat the solvent molecules exphcitly and the number density of the electrolyte is umealistically low. For modeling nano-surface interactions, short-range interactions are important and the primitive model is expected not to give adequate account of confinement effects. For its simphcity, however, many theories [18-22] and simulation studies [23-25] have been made based on the primitive model for the bulk electrolyte. Ap-phcations to electrolyte interfaces have also been widely reported [26-30]. 

More realistic treatment of the electrostatic interactions of the solvent can be made. The dipolar hard-sphere model is a simple representation of the polar nature of the solvent and has been adopted in studies of bulk electrolyte and electrolyte interfaces [35-39], Recently, it was found that this model gives rise to phase behavior that does not exist in experiments [40,41] and that the Stockmeyer potential [41,42] with soft cores should be better to avoid artifacts. Representation of higher-order multipoles are given in several popular models of water, namely, the simple point charge (SPC) model [43] and its extension (SPC/E) [44], the transferable interaction potential (T1PS)[45], and other central force models [46-48], Models have also been proposed to treat the polarizability of water [49],... 

The Nernst equation is of limited use at low absolute concentrations of the ions. At concentrations of 10 to 10 mol/L and the customary ratios between electrode surface area and electrolyte volume (SIV 10 cm ), the number of ions present in the electric double layer is comparable with that in the bulk electrolyte. Hence, EDL formation is associated with a change in bulk concentration, and the potential will no longer be the equilibrium potential with respect to the original concentration. Moreover, at these concentrations the exchange current densities are greatly reduced, and the potential is readily altered under the influence of extraneous effects. An absolute concentration of the potential-determining substances of 10 to 10 mol/L can be regarded as the limit of application of the Nernst equation. Such a limitation does not exist for low-equilibrium concentrations. 

It must be pointed out that in a diffusion layer where the ions are transported not only by migration but also by diffusion, the effective transport numbers t of the ions (the ratios between partial currents ij and total current t) will differ from the parameter tj [defined by Eq. (1.13)], which is the transport number of ion j in the bulk electrolyte, where concentration gradients and diffusional transport of substances are absent. In fact, in our case the effective transport number of the reacting ions in the diffusion layer is unity and that of the nonreacting ions is zero. 

In porous separators the pore radii are large compared to the size of molecules. Hence, interaction between the electrolyte and the pore walls has practically no qualitative effects on the ionic current through the separator the transport numbers of the individuaf ions have the same vafues in the pores as in the bulk electrolyte, hi swollen membranes the specific interaction between individuaf ions and macromofecufes is very pronounced. Hence, these membranes often exhibit sefectivity in the sense that different ions are affected differentfy in their migration. As a resuft, the transport numbers of the ions in the membrane differ from those in the efectrofyte outside the membrane. In the limiting case, certain types of ion are arrested completely, and the membrane is called permselective (see Chapter 5). 

Regarding the electrode/electrolyte interface, it is important to distinguish between two types of electrochemical systems thermodynamically closed (and in equilibrium) and open systems. While the former can be understood by knowing the equilibrium atomic structure of the interface and the electrochemical potentials of all components, open systems require more information, since the electrochemical potentials within the interface are not necessarily constant. Variations could be caused by electrocatalytic reactions locally changing the concentration of the various species. In this chapter, we will focus on the former situation, i.e., interfaces in equilibrium with a bulk electrode and a multicomponent bulk electrolyte, which are both influenced by temperature and pressures/activities, and constrained by a finite voltage between electrode and electrolyte. 

Before we will discuss the electrochemical system, it is important to define the properties and characteristics of each component, especially the electrolyte. In the following, we assume macroscopic amounts of an electrolyte containing various ionic and nonionic components, which might be solvated. In the case that this bulk electrolyte is in thermodynamic equilibrium, each of the species present is characterized by its electrochemical potential, which is defined as the free energy change with respect to the particle number of species i ... 

The second term on the right-hand side of (5.1) is the energy required to transfer the charge qt associated with each particle of the ith species from a reference potential < ref to the electrostatic potential of the bulk electrolyte (solution), reference potential can be chosen freely, throughout this chapter we use as energy zero for the electrostatic potential. Further discussion on the importance of this aspect will be provided later. 

Figure 5.4 Atomistic model of the electrochemical half-cell, showing the electrode/electrolyte interface (xi < x < X2), which is connected to the hulk electrode and electrolyte (reservoirs). The lower panel indicates the electrostatic potential within the electrode and the bulk electrolyte (solid lines), and possible shapes for the potential drop between them (dashed lines).

Within the interfaces, the explicit prohle of the electrostatic potential electrode distance is unknown (possible shapes are indicated in Fig. 5.4 as dashed hnes) and the only well-dehned values are the as5mptotic limits, which ate the potential values of the electrode < e and the bulk electrolyte (f>s, respectively, and their difference (electrode potential)... 

Now having specified the bulk electrode, the bulk electrolyte, and the interface between them, our aim in this section is to quantify the atomistic structure of the interface and derive an expression that allows us to evaluate its stabUity. Based on (5.5), we wUl extend the ab initio atomistic thermodynamics approach to electrochemical systems. 

The term G T, a,, A/, ) is the Gibbs free energy of the full electrochemical system x < x < X2 in Fig. 5.4). It includes the electrode surface, which is influenced by possible reconstructions, adsorption, and charging, and the part of the electrolyte that deviates from the uniform ion distribution of the bulk electrolyte. The importance of these requirements becomes evident if we consider the theoretical modeling. If the interface model is chosen too small, then the excess charges on the electrode are not fuUy considered and/or, within the interface only part of the total potential drop is included, resulting in an electrostatic potential value at X = X2 that differs from the requited bulk electrolyte value < s-However, if we constrain such a model to reproduce the electrostatic potential... 

The last term comes from the assumption that every oxygen atom adsorbing on the surface originates from a water molecule of the bulk electrolyte reservoir ... 

Figure 13.9 Reaction scheme for Ci molecule oxidation on a Pt/C catalyst electrode, including reversible diffusion from the bulk electrolyte into the catalyst layer, (reversible) adsorption/ desorption of the reactants/products, and the actual surface reactions. The different original reactants (educts) and products are circled. For removal/addition of H, we do not distinguish between species adsorbed on the Pt surface and species transferred directly to neighboring water molecule (H d, H ) therefore, no charges are included (H, e ). For a description of the individual reaction steps, see the text.

The results have been compared with the earlier proposal of a dual-pathway mechanism for Cl oxidation, and, together with previous experimental and theoretical results, summarized in a comprehensive reaction scheme that explicitly includes also the (reversible) exchange between adsorbed species, dissolved product species in the catalyst layer, and similar species in the bulk electrolyte. The traditional dualpathway mechanism, where both the direct and indirect pathways lead to CO2 formation, has beenextended by adding a third pathway that accounts for formation and desorption of incomplete oxidation products. In the mechanistic discussion, we have focused on the role in and contribution to the Ci oxidation process of the formation/desorption and re-adsorption plus further oxidation of incomplete oxidation products. This not only leads to faradaic currents exceeding that for CO2 formation, but may result in additional COad and CO2 formation, via adsorption and oxidation of the incomplete oxidation products. 

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