Mixed permittivity

The mixed-solvent approach is a compromise, based on mixed solvents of moderate permittivity and moderate viscosity. The following example illustrates that. 

An alternative electrical method that has been used in the study of glass-ionomer cements has been the measurement of dielectric properties. Tay Braden (1981, 1984) measured the resistance and capacitance of setting cements at various times from mixing. From the results obtained, relative permittivity and resistivity were calculated. In general, as these cements set, their resistivity was found to fall rapidly, then to rise again. Both these results and the results of relative permittivity measurements were consistent with the cements comprising highly ionic and polar structures. 

When nonnegligible concentrations of the electrolyte are present in the organic solvent, ion-ion interactions superimpose on the ion-solvent ones, or the secondary medium ejfect. Although an equation similar to Eq. (2.43) may be used for determining the activity coefficient in the new medium, it is necessary to employ the appropriate value of A in this equation that depends on the relative permittivity of the medium A(org) = A(aq)(eaq/e ,g) Unless very water-rich mixed solvents are used, different numerical values of the parameters in the denominator and the second term on the right-hand side of Eq. (2.43) have to be employed. 

A further complication that sets in when organic or mixed aqueous-organic solvents are used, which is aggravated when the relative permittivity of the medium, e, falls below 40, is ion pairing. This phenomenon does occur in purely aqueous solutions, mainly with higher-valence-type electrolytes 2 2 and higher, and with 2 1 or 1 2 electrolytes only at high concentrations. Ion pairs may also form in aqueous solutions of some 1 1 electrolytes, provided the ions are poorly hydrated and can approach each other to within <0.35 nm. Such ion pairs are of major importance in solvents that are relatively poor in water or that are nonaqueous. 

A common sitnation is that the electrolyte is completely dissociated in the aqueons phase and incompletely, or hardly at all, in the organic phase of a ternary solvent extraction system (cf. Chapter 3), since solvents that are practically immiscible with water tend to have low valnes for their relative permittivities e. At low solnte concentrations, at which nearly ideal mixing is to be expected for the completely dissociated ions in the aqneons phase and the undissociated electrolyte in the organic phase (i.e., the activity coefficients in each phase are approximately nnity), the distribntion constant is given by... 

The problem of relative permittivity of mixed solvents (denoted by e for simplicity) was theoretically studied by Debye and Onsager [34], Onsager derived the following equation ... 

Here, volume fractions of A and B, respectively, Pi is the complex formation constant of XA , B that is obtained in solvent A, and the solvation in B should be stronger than that in A. These equations are important in showing that the data for the complexation between X and B in solvent A are applicable to predicting the solvation of X in solvent B and in mixed solvent (A+B). As discussed in detail in Section 6.3.6, these equations are valid as long as the permittivities of A and B do not differ significantly. 

Fig. 2.12 Relationship between the ion association constants (log KA) and the reciprocal of solvent permittivity (1 /er) (solid line) and between the degree of ion association (a) and log (c/(A) (dotted curve), (open circles Bu4NPic in AN, NB, MeOH, Ac, Py, DCE, o-dichlorobenzene, acetic acid, chlorobenzene and benzene closed squares KCI in ethanolamine, MeOH, EtOH, acetic acid and H20-dioxane mix-tures). The solid line was obtained using a Eq. (2.19) for 0 = 0.6 nm.

Among amphiprotic solvents of high permittivities, there are water-like neutral solvents (e.g. methanol and ethanol), more acidic protogenic solvents (e.g. formic acid), and more basic protophilic solvents (e.g. 2-aminoethanol). There are also amphiprotic mixed solvents, such as mixtures of water and alcohols and water and 1,4-dioxane. The acid-base equilibria in amphiprotic solvents of high permittivity can be treated by methods similar to those in aqueous solutions. If the solvent is expressed by SH, the acid HA or BH+ will dissociate as follows ... 

Notation o=e1ectrical conductivity, ic-real relative permittivity, subscripts mix, f and p denote soil-flu id mixture, fluid, and particle, respectively, /-ionic valence, c-ionic concentration, u=ionic mobility is, F =96485.3 C/mol is Faraday s constant, TDS= total dissolved salts in [mg. L], n=porosity, p=density, =surface conduction, S,=specific surface, a=degree of saturation, m=cementation factor, Gv=volumetric water content... 

Electric-force mixing is adequate for mixing flows at very low Reynolds number (-1). By lamination of two fluids with different electric conductivity and/or permittivity in a micro mixer, a steep cross-sectional gradient of the respective properties can be established [91]. The electric field may be parallel or perpendicular to the fluid interface, which is also a boundary where electric properties abruptly... 

An increase in fractional free volume will reduce the number of polarisable groups per unit volume, and thereby reduce the relative permittivity of the polymer. Quantitatively, the effect may be estimated by means of the Clausius-Mossotti/Lorenz-Lorentz model for dielectric mixing (Bottcher, 1978) ... 

A common form of discontinuity occurring in a solid dielectric is one where cracks or voids are present. The relative permittivity will then simply be reduced, depending on the amount and distribution of the enclosed space or air. A much more serious type of heterogeneity, however, is one where a relatively conductive component is mixed in an insulator. Common instances of this occur where a material is contaminated with metallic particles or droplets... 

The interaction energy between spheres at constant surface potential involves only the function G (0 (which depends only on the sphere radius a,), while the interaction at constant surface charge density is characterized by the function H (i) (which depends on both sphere radius u, and relative permittivity Ep,). The interaction energy in the mixed case involves both G (i) and // (/) ... 

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