Solvent relative permittivity

Interaction Formulae for ru Typical solvent relative permittivity, e (nm) -Reff (nmf Attractive Repulsive... 

When dissolved in nonpolar solvents such as benzene or diethyl ether, the colourless (2a) forms an equally colourless solution. However, in more polar solvents [e.g. acetone, acetonitrile), the deep-red colour of the resonance-stabilized carbanion of (3a) appears (1 = 475... 490 nm), and its intensity increases with increasing solvent polarity. The carbon-carbon bond in (2a) can be broken merely by changing from a less polar to a more polar solvent. Cation and anion solvation provides the driving force for this heterolysis reaction, whereas solvent displacement is required for the reverse coordination reaction. The Gibbs energy for the heterolysis of (2a) correlates well with the reciprocal solvent relative permittivity in accordance with the Born electrostatic equation [285], except for EPD solvents such as dimethyl sulfoxide, which give larger values than would be expected for a purely electrostatic solvation [284]. 

The failure of the solvent relative permittivity to represent solute/solvent interactions has led to the definition of polarity in terms of empirical parameters. Such attempts at obtaining better parameters of solvent polarity by choosing a solvent-dependent standard system and looking at the changes in parameters of that system when the solvent is changed e.g. rate constants of solvent-dependent reactions or spectral shifts of solvatochromic dyes) are treated in Chapter 7. 

Eq. (4-10) can be used only for solvents of equal acid and base strength, because only the effect of the solvent relative permittivity on the degree of ionization is considered. Under these conditions, Eq. (4-10) predicts that the logarithm of the ionization constant of HA should be inversely proportional to the relative permittivity of the solvent in which HA is dissolved. However, one has to take into account the fact that the relative permittivities near solute ions can differ considerably because of the effect of dielectric saturation, which hinders the precise calculation of electrostatic interactions. Because of these restrictions, Eq. (4-10) can be expected to yield only semiquantitative results. Nevertheless, it allows us to predict qualitatively how the charge type of an acid affects the ionization constant in solvents of different relative permittivities. 

Laidler has pointed out [11, 242] that Eq. (5-88) is best considered as a semi-quantitative formulation, which gives only a rough prediction of the effect of a change in fir on the rate of dipole-dipole reactions. This also applies to Eqs. (5-87) and (5-90). Nevertheless, in many cases a satisfactory correlation between rate constants and function of solvent relative permittivity has been obtained, as, for instance, in the Men-schutkin reaction between trialkylamines and haloalkanes forming quaternary tetra-alkylammonium salts [2, 56, 58, 60, 61, 64, 65, 245-247]. 

Solvent Relative permittivity Percentage of conformative diads ... 

When acetaldehyde is polymerized at low temperatures in polar solvents (relative permittivity greater than 4) with alkali metal alcoholates as initiators, poly(vinyl alcohol) is produced. However, this process is not used industrially. 

Solvent Relative permittivity AAbT (solvent) sls/Ialumina particles in the solvent) Observed Stability behaviour... 

K is the inverse radius of the ionic atmosphere d is the minimum distance between the anion and cation 8, is the solvent relative permittivity (dielectric constant)... 

Solvent relative permittivity (dielectric constant) [dimensionless]... 

They argued that this trend could not be e>q)lained by copolymerization through the solvent or transfer to the solvent because there was no correlation with the solvent relative permittivity or polarity, or with the rate constants for transfer to solvent. However, there was a correlation with the calculated delocahzation stabilization energy for complexes between the radical and the solvent, which suggested that the propagating radical was stabilized by the solvent or monomer, but the solvent did not actually participate in the reaction. 

Electrostatic attraction causes formation of ion pairs. The lower is the solvent relative permittivity, and the smaller are ion radii, the larger is the ion pair formation. The degree of ion association can be very significant even in solvents of high relative permittivity, eg., in aqueous solution. Bjerrum calculated that univalent ions, having a diameter of 0.282 nm, are about 14% associated in aqueous solutions if the diameter is 0.176 nm, the ion association is about 29%. It may be concluded that ion association is important even in aqueous solutions, and of very great importance in solvents of low permittivity. 

The refractive index of a medium is the ratio of the speed of light in a vacuum to its speed in the medium, and is the square root of the relative permittivity of the medium at that frequency. When measured with visible light, the refractive index is related to the electronic polarizability of the medium. Solvents with high refractive indexes, such as aromatic solvents, should be capable of strong dispersion interactions. Unlike the other measures described here, the refractive index is a property of the pure liquid without the perturbation generated by the addition of a probe species. 

The uncharged ion is transferred into a solvent with permittivity e = De0y where D is the relative permittivity (dielectric constant) of the medium. No work is gained or lost in this process. In the solvent, the ion is again recharged to the value of the electric potential at its surface,... 

Dielectric constant (or relative permittivity), er, is an indication of the polarity of a solvent, and is measured by applying an electric field across the solvent between... 

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. 

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. 

Solvent-separated ion pairs, in which the first solvation shells of both ions remain intact on pairing may be distingnished from solvent-shared ion pairs, where only one solvent molecule separates the cation and the anion, and contact ion pairs, where no solvent separates them (Fig. 2.6). The parameter a reflects the minimum distance by which the oppositely charged ions can approach each other. This eqnals the sum of the radii of the bare cation and anion pins 2, 1, and 0 diameters of the solvent, respectively, for the three categories of ion pairs. Since a appears in Eq. (2.49), and hence, also in Q(b), it affects the value of the equilibrium constant, K s- The other important variable that affects K ss is the product T and, at a given temperature, the value of the relative permittivity, e. The lower it is, the larger b is and, hence, also K s-... 

When the relative permittivity of the organic solvent or solvent mixture is e < 10, then ionic dissociation can generally be entirely neglected, and potential electrolytes behave as if they were nonelectrolytes. This is most clearly demonstrated experimentally by the negligible electrical conductivity of the solution, which is about as small as that of the pure organic solvent. The interactions between solute and solvent in such solutions have been discussed in section 2.3, and the concern here is with solute-solute interactions only. These take place mainly by dipole-dipole interactions, hydrogen bonding, or adduct formation. 

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... 

Self-assembly of highly charged colloidal spheres can, under the correct conditions, lead to 3D crystalline structures. The highly charged spheres used are either polystyrene beads or silica spheres, which are laid down to give the ordered structures by evaporation from a solvent, by sedimentation or by electrostatic repulsion (Figure 5.34). The structures created with these materials do not show full photonic band gap, due to their comparitively low relative permittivity, although the voids can be in-filled with other materials to modify the relative permittivity. 

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