Electrolyte permittivity

FIGURE 2.32 Schematic, dimensions, and coordinate system of the computational domain simulated for carbon spheres with (a) simple cuhic, (h) hody-centered cubic, and (c) face-centered cubic packings. Shaded areas represent carhon spheres of diameter d. Five unit cells are shown here for illustration purposes. (Reprinted from Electrochimica Acta, 56, Wang, H. N., J. Varghese, and L. Pilon, Simulation of electric double layer capacitors with mesoporous electrodes Effects of morphology and electrolyte permittivity, 6189-6197, Copyright 2011, with permission from Elsevier.)... 

Wang, H. N., J. Varghese, and L. Pilon. 2011. Simulation of electric double layer capacitors with mesoporous electrodes Effects of morphology and electrolyte permittivity. Electrochimica Acta 56 6189-6197. 

The intrinsic properties of an electrolyte evaluated at low concentrations of the salt and from the viscosity and permittivity of the solvent also determine the conductivity of concentrated solutions. Various systems were studied to check this approach. The investigated parameters and effects were ... 

The main problem in the study of the role of these parameters in electrolyte conductivity is their interdependence. A change in composition of a binary solvent changes viscosity, along with the permittivity, ion-ion association, and ion solvation, which may be preferential for one of the two solvents and therefore also changes the Stokes radii of the ions. 

Ion pairs can form only when the distance of closest approach, a, of the two ions is less than r . For 1 1 electrolytes for which = 0.357 nm, this condition is not always fulfilled, but for others it is. The fractions of paired ions increase with increasing concentration of solutions. In nonaqueous solutions which have lower values of permittivity e than water, the values of and the fractions of paired ions are higher. In some cases the values of coincide with the statistical mean distance between the ions (i.e., the association of the ions is complete). 

In aqueous electrolyte solutions the molar conductivities of the electrolyte. A, and of individual ions, Xj, always increase with decreasing solute concentration [cf. Eq. (7.11) for solutions of weak electrolytes, and Eq. (7.14) for solutions of strong electrolytes]. In nonaqueous solutions even this rule fails, and in some cases maxima and minima appear in the plots of A vs. c (Eig. 8.1). This tendency becomes stronger in solvents with low permittivity. This anomalons behavior of the nonaqueous solutions can be explained in terms of the various equilibria for ionic association (ion pairs or triplets) and complex formation. It is for the same reason that concentration changes often cause a drastic change in transport numbers of individual ions, which in some cases even assume values less than zero or more than unity. 

An interface between two immiscible electrolyte solutions (ITIES) is formed between two liqnid solvents of a low mutual miscibility (typically, <1% by weight), each containing an electrolyte. One of these solvents is usually water and the other one is a polar organic solvent of a moderate or high relative dielectric constant (permittivity). The latter requirement is a condition for at least partial dissociation of dissolved electrolyte(s) into ions, which thus can ensure the electric conductivity of the liquid phase. A list of the solvents commonly used in electrochemical measurements at ITIES is given in Table 32.1. 

Much attention has been directed since olden times towards ion solvation, which is a key concept for understanding various chemical processes with electrolyte solutions. In 1920, a theoretical equation of ion solvation energy (AG ) was first proposed by Born [1], who considered the ion as a hard sphere of a given radius (r) immersed in a continuous medium of constant permittivity (e), and then defined AG as the electrostatic energy for charging the ion up to ze (z, the charge number of the ion e, the elementary charge) ... 

The species appearing as strong electrolytes in aqueous solutions lose this property in low-permittivity solvents. The ion-pair formation converts them to a sort of weak electrolyte. In solvents of very low-permittivity (dioxan, benzene) even ion triplets and quadruplets are formed. 

At present it is impossible to formulate an exact theory of the structure of the electrical double layer, even in the simple case where no specific adsorption occurs. This is partly because of the lack of experimental data (e.g. on the permittivity in electric fields of up to 109 V m"1) and partly because even the largest computers are incapable of carrying out such a task. The analysis of a system where an electrically charged metal in which the positions of the ions in the lattice are known (the situation is more complicated with liquid metals) is in contact with an electrolyte solution should include the effect of the electrical field on the permittivity of the solvent, its structure and electrolyte ion concentrations in the vicinity of the interface, and, at the same time, the effect of varying ion concentrations on the structure and the permittivity of the solvent. Because of the unsolved difficulties in the solution of this problem, simplifying models must be employed the electrical double layer is divided into three regions that interact only electrostatically, i.e. the electrode itself, the compact layer and the diffuse layer. 

The basic difference between metal-electrolyte and semiconductor-electrolyte interfaces lies primarily in the fact that the concentration of charge carriers is very low in semiconductors (see Section 2.4.1). For this reason and also because the permittivity of a semiconductor is limited, the semiconductor part of the electrical double layer at the semiconductor-electrolyte interface has a marked diffuse character with Debye lengths of the order of 10 4-10 6cm. This layer is termed the space charge region in solid-state physics. 

The interface is, from a general point of view, an inhomogeneous dielectric medium. The effects of a dielectric permittivity, which need not be local and which varies in space, on the distribution of charged particles (ions of the electrolyte), were analyzed and discussed briefly by Vorotyntsev.78 Simple models for the system include, in addition to the image-force interaction, a potential representing interaction of ions with the metal electrons. 

One way to achieve such improvements is by doping of aluminum oxide with properly selected impurities. These could be introduced by implantation into aluminum and subsequent transfer into the oxide during anodization.331 Alternatively, complex anions containing impurity atoms could be introduced into the anodizing bath [see Section IV(2)]. The incorporated anions influence the dielectric permittivity, E, of the oxide.176 Hence, one can manipulate the E value by changing the electrolyte concentration and anodization regime.91 According to the published data, rare-earth-doped... 

Here, e0 is the permittivity of vacuum, sel the dielectric constant of the electrolyte, z is the valency of the ions in the electrolyte, and I represents the ionic strength, which for a 1 1 salt, can be replaced by the electrolyte concentration n0. 

Knowledge of complex permittivities of appropriate electrolyte solutions is useful in assessing interactions of microwave radiation with biological tissues. A full study and analysis of complex permittivities of sodium chloride solutions as a function of concentration, temperature, and microwave frequency (207) has laid the foundations for a similar investigation of calcium salt solutions. 

Bosch, Roses and coworkers62 65 66 have used the dissociation of electrolytes in binary solvents of low permittivity using 2-methylpropanol or propan-2-ol as the main solvent... 

A similar conclusion arises from the capacitance data for the mercury electrode at far negative potentials (q 0), where anions are desorbed. In this potential range, the double-layer capacitance in various electrolytes is generally equal to ca. 0.17 F Assuming that the molecular diameter of water is 0.31 nm, the electric permittivity can be calculated as j = Cd/e0 = 5.95. The data on thiourea adsorption on different metals and in different solvents have been used to find the apparent electric permittivity of the inner layer. According to the concept proposed by Parsons, thiourea can be treated as a probe dipole. It has been cdculated for the Hg electrode that at (7 / = O.fij is equal to 11.4, 5.8, 5.1, and 10.6 in water, methanol, ethanol, and acetone, respectively. 

Although examining an ideal electrolyte is helpful in developing our understanding of dc polarisation, polymer electrolytes are not ideal systems since interactions between the ions of the salt are always likely to be significant in a medium of such low permittivity. It is therefore necessary to take into account two effects ... 

The nonideality of electrolyte solntions, cansed nltimately by the electrical fields of the ions present, extends also to any nonelectrolyte that may be present in the aqueous solution. The nonelecttolyte may be a co-solvent that may be added to affect the properties of the solntion (e.g., lower the relative permittivity, e, or increase the solubility of other nonelecttolytes). For example, ethanol may be added to the aqueous solution to increase the solnbility of 8-hydroxyqni-noline in it. The nonelectrolyte considered may also be a reagent that does not dissociate into ions, or one where the dissociation is snppressed by the presence of hydrogen ions at a sufficient concentration (low pH cf Chapter 3), snch as the chelating agent 8-hydroxyquinoline. 

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