Electrolyte model

Weak electrolytes in which dimerization (as opposed to ion pairing) is the result of chemical bonding between oppositely charged ions have been studied using a sticky electrolyte model (SEM). In this model, a delta fiinction interaction is introduced in the Mayer/-fiinction for the oppositely charged ions at a distance L = a, where a is the hard sphere diameter. The delta fiinction mimics bonding and tire Mayer /-function... 

Zhu J and Rasaiah J C 1989 Solvent effects in weak electrolytes II. Dipolar hard sphere solvent an the sticky electrolyte model with L = a J. Chem. Phys. 91 505... 

So far in our revision of the Debye-Hiickel theory we have focused our attention on the truncation of Coulomb integrals due to hard sphere holes formed around the ions. The corresponding corrections have redefined the inverse Debye length k but not altered the exponential form of the charge density. Now we shall take note of the fact that the exponential form of the charge density cannot be maintained at high /c-values, since this would imply a negative coion density for small separations. Recall that in the linear theory for symmetrical primitive electrolyte models we have... 

The results of the simple DHH theory outlined here are shown compared with DH results and corresponding Monte Carlo results in Figs. 10-12. Clearly, the major error of the DH theory has been accounted for. The OCP model is greatly idealized but the same hole correction method can be applied to more realistic electrolyte models. In a series of articles the DHH theory has been applied to a one-component plasma composed of charged hard spheres [23], to local correlation correction of the screening of macroions by counterions [24], and to the generation of correlated free energy density functionals for electrolyte solutions [25,26]. The extensive results obtained bear out the hopeful view of the DHH approximation provided by the OCP results shown here. It is noteworthy that in... 

Calcium-sodium-chloride-type brines (which typically occur in deep-well-injection zones) require sophisticated electrolyte models to calculate their thermodynamic properties. Many parameters for characterizing the partial molal properties of the dissolved constituents in such brines have not been determined. (Molality is a measure of the relative number of solute and solvent particles in a solution and is expressed as the number of gram-molecular weights of solute in 1000 g of solvent.) Precise modeling is limited to relatively low salinities (where many parameters are unnecessary) or to chemically simple systems operating near 25°C. 

Criddle CS, McCarty PL. 1991. Electrolytic model system for reductive dehalogenation in aqueous environments. Environ Sci Technol 25 973-978. 

Calculate the capacity of the Helmholtz layer per unit area for an interface of mercury in contact with a 0.0 XM NaF electrolyte. Model the value of the double layer thickness assuming a two-state water model, a positive charge on the electrode, and a local dielectric constant of six. (Bockris)... 

Although several single-crystal, wide-band gap semiconductors provide electrochemical and optical responses close to those expected from the ideal semiconductor-electrolyte model, most semiconducting electrodes do not behave in this manner. The principal and by far overriding deviation from the behavior described in the previous section is photodecomposition of the electrode. This occurs when the semiconductor thermodynamics are such that thermal or photogenerated valence band holes are sufficiently oxidizing to oxidize the semiconductor lattice [8,9]. In this case, kinetics routinely favor semiconductor oxidation over the oxidation of dissolved redox species. For example, irradiation of n-CdX (X = S, Se, or Te) in an aqueous electrolyte gives rise exclusively to semiconductor decomposition products as indicated by... 

The method has not taken on. One paper [168] reports the use of PSPICE, but for simulating actual resistance in an electrolyte, modelled as a resistance network. This is quite a different application, and much more directly relevant. 

The double-layer capacity depends strongly on the nature of the electrode material, even in cases where there is no specific adsorption of ions and solvent. It was therefore suggested, first by O.K. Rice, that the metal makes a direct contribution to the double-layer capacity. This idea was quantitatively pursued within the -> jel-lium model, in which the distribution of the electrons at the surface is affected by the double-layer field. In essence, the surface electrons form a highly polarizable medium, which enhances the capacity. In combination with the hard sphere electrolyte model, it gives the correct order of magnitude for the capacity at the -> point of zero charge also, it predicts correctly that the capacity of simple sp-metals should increase with the electronic density. An extension of the jellium-hard sphere elec-... 

Hard-sphere electrolyte model - double-layer models... 

Hard Sphere Electrolyte Model for Specific Adsorption... 

Even though this equation is based on an overly simple model, it illustrates well the double-layer properties that govern the electrosorption valency in the absence of pet. In particular, it shows that a fractional value of / need not necessarily indicate pet. We shall return to the hard-sphere electrolyte model when we discuss dipole moments of adsorbates. 

Table 1 summarizes a few values of the dipole moment fx and of the electrosorption valency l of halide and alkali metal ions adsorbed on mercury. The experimental values of l are relative to low coverages near the potential of zero charge and are taken from Schultze and Koppitz,50 while the corresponding // values were calculated from Eq. (75). The theoretical values in the last column are from a hard sphere electrolyte model. Further data can be found in the article by Schmickler49 Note that, in the electrochemical environment, the dipole moments are much smaller than in vacuo, where they can reach values of the order of 7 D for the alkali metal ions. No doubt, this difference is caused by the screening of the adsorbate dipole by the solvent molecules. 

The hard-sphere electrolyte model, presented in section n.4, can be used to estimate the dipole moment in the absence of charge transfer. The model can be improved by noting that, as mentioned before, the effective image plane of a metal usually sits at a distance xim in front of the geometrical surface. From Eq. (73), in which B and A are obtained by comparing Eq. (72) with Eq. (50), we get ... 

Figure 10. Q coefficients for Harness binary electrolyte model as a function of ionic strength...

Figure 2.4. Charge density as function of distance from electrode, for the electrolyte modelled in Fig. 2.3. The three cases represent positive, zero and negative electrode charge. Solid lines are total charge densities, longer dashes are ionic charge densities, and shorter dashes are aqueous charge densities. The curves have been smoothed. From E. Spohr (1999). Molecular simulation of the electrochemical double layer. Electrochimica Acta 44,1697-1705, reproduced with permission from Elsevier.

First, we need a predictive activity coefficient model for electrolyte systems. The electrolyte NRTL model is correlative, and it requires extensive experimental data sets from which NRTL binary interaction parameters can be identified. The OLI electrolyte model, with its extensive parameter database, has been serving as a pseudo-predictive model. However, use of the OLI electrolyte model is limited to dilute aqueous electrolytes, its parameter database is not open to the public, and its electrolyte speciation is not supported by experiments. 

K. Thomsen, Aqueous electrolytes model parameters and process simulation, Ph.D. Thesis, Department of Chemical Engineering, Technical University of Denmark, 1997,... 

Protsykevytch, I.A., Kalyuzhnyi, Yu.V., Holovko, M.F., and Blum, L. Solution of the polymer mean spherical approximation for the totally flexible sticky two-point electrolyte model. Journal of Molecular Physics, 1997, 73, No. 4, p. 1-20. 

The current efficiency in modern cells of aluminum electrolysis may exceed 95%. It is generally accepted that the major part of loss in current efficiency is due to the reaction between dissolved metal and electrolyte. Model studies by 0degard et al. (1988) indicates that sodium dissolves in the electrolyte in the form of free Na, while dissolved Al is predominantly present as the monovalent species ALF. Any electronic conductivity is most likely associated with the Na species, which may form trapped electrons and electrons in the conduction band. Morris (1975) ascribed the loss in current efficiency during Al production to electronic conduction. In a theoretical and experimental study. Dewing and Yoshida (1976) subsequently maintained that the electronic conductivity was too low to account for the loss in current efficiency in industrial aluminum cells. However, the existence of electronic conduction in NaF-AlF3 melts was demonstrated later by Borisoglebskii et al. (1978) also. 

Weak electrolyte model of RS has been employed to calculate activity coefficients and to use activity coefficients to detennine the activation barriers for conductivity. The agreement between the experimental and theoretical activation energies has been found to be satisfactory (Ravine and Souquet, 1977). 

Figure 8.4 Origin of the electro-osmotic flow in a capillary filled with an electrolyte. Model of the double layer. If the inner wall has not been treated (polyanionic layer of a silica or glass capillary) then a pumping effect arises from the anodic to the cathodic compartment this is the electro-osmotic flow which is reliant upon the potential which exists on the inner surface of the wall. If the wall is coated with a non polar film (e.g. octadecyl) then this flow no longer exists. The electro-osmotic flow is proportional to the thickness of the double cationic layer attached to the wall. It is reduced if the concentration of the buffer electrolyte increases. Ugos pH dependant between pH 7 and 8 can increase by as much as 35 per cent.

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