Dielectric Decrements

In Figure 6 we show that good theoretical representations are obtained for different temperatures with a small change in the parameter a. On such evidence we might expect to obtain a consistent description of partial molal enthalpies and entropies. However, discussion of these quantities, along with a fuller consideration of solvation aspects, the a parameters, and the dielectric decrements (27, 28), is deferred until a later stage. 

Nevertheless, in spite of these warnings, values of dielectric decrements have a sufficiently clear basis to allow their use in discussing the elusive solvation numbers. 

The rotation of large molecules in solution together with their hydration is the basis of many of the properties of solutions containing polyions. One has to ask questions, however, about the decrement of the dielectric constant in the case of linear polyelectrolytes, which include DNA. Substances such as this exhibit dielectric decrements as expected but it is difficult to account for their magnitude in terms of hydration. Thus, there might be a rotation but this cannot be about the long axis because in such a case <5 (Section 2.24) should increase when the molecules are oriented perpendicularly to the electric field and this is not found to be the case. 

Table 5 Comparison of dielectric decrements calculated on Glueckauf s discontinuous model with bracketed) experimental values... 

It would seem, from an examination of the four cases pyridine, acetone, tetrahydrofuran, and tetrahydrofurfuryl alcohol, that values of dipole moments of the order 2—4 D are likely to be up to 50% too high when calculated from the permittivity of their aqueous solutions. However, some confidence in the internal consistency of the calculations is to be derived from the fact that, although the dielectric decrements are temperature-dependent, the calculated dipole moments are not. Thus the correlation between the dipoles of solute and water molecules does not change with temperature. Since the correlation between dipoles in pure liquids and pure alcohols changes quite markedly with temperature, the... 

It may be remarked that large polyatomic ions will exhibit only very small dielectric saturation effects, but will contribute to the dielectric decrement by reason of thdr large volume. Such ions, of volume fraction v and zero dipole moment, have been treated " by the mixture relation of... 

Representative plots of as a function of concentration are shown in fig. 4.10. The principal feature depending on electrolyte concentration is the initial slope which is called the dielectric decrement. In addition all plots are curved, suggesting that a limiting permittivity is reached at high electrolyte concentration. The dependence of on electrolyte concentration c. has been examined by Friedman [30], who derived the following relationship ... 

Information about the bound water fraction in some colloid systems, silica gels, and biological systems is usually inferred on die basis of the frequency- and time-domain DS measurements from the analysis of the dielectric decrements or die relaxation times (64, 150-152). However, the nonionic microemulsions are characterized by a broad relaxation specfrum as can be seen from the Cole-Cole plot (Fig. 33). Thus, these dielectric methods fail because of the difficulties of deconvoluting die relaxation processes associated widi the relaxations of bound water and surfactant occurring in the same frequency window. 

As seen from Table 3.1, the permittivity of water is reduced by the addition of electrolytes. This dielectric decrement Ae is for 1 mol/L concentration —17 for HT ", —8 for Na and K, —3 for CP, and —13 for OH . It is directly related to the hydration of the ion, because these water molecules are more tightly bound and therefore not so easily polarized as free water molecules. The number of hydrated water molecules around a monovalent ion is of the order of 5 (see Table 2.4). 

The relaxation time for proteins in water is typically in the micro- to picosecond range (MHz—GHz), and the dielectric decrement of the order of 8q per gram per liter. 

The addition of electrolytes such as NaCl or KCl lowers the permittivity proportionally to concentration (e.g., with a dielectric decrement, Acr, of 4 for a 250 mmol/L concentration of KCl cf. Section 3.1.1). 

Ionic Dielectric Decrements Ions in dilute aqueous solutions diminish the permittivity of the solution, in a manner proportional to the concentration, an effect called the dielectric decrement. The permittivity of electrolyte solutions is measured as a function of both the concentration c and the frequency of the applied electric field co and extrapolated to zero values of both, hence obtaining the static decrement = lim c->0,(o- 0)d ldc. The infinite dilution electrolyte values at 25°C are additive in the ionic contributions and Marcus [130] proposed to split them into the latter, 5, on the assumption adopted for the viscosity B-coefficients (Section 2.3.2.3), namely (Rb ) = 5 (Br ), with results shown in Table 2.12. The uncertainties of the values are 2M . The values of 5., are approximately linearly... 

Dielectric decrement has been observed in bulk electrolytes and reflects structural rearrangement of water due to the presence of salt. For salt concentrations between 0 and 1.5 M, the dielectric constant was found to depend linearly on the salt concentration, e (c ) = e + ac [5,6, 31]. The orientation of water dipoles within the hydration shell around a dissolved ion is fixed by field lines originating from ion centers, so that these dipoles respond poorly to an external field. This behavior can be quantified with a crude model. Because the tightly bound dipoles within the hydration shell are excluded from screening an external electrostatic field, the effective density of free water dipoles becomes reduced, - (M c + M c ), where is the solvation number of water molecules in a hydration shell around either a cation or an anion. In the linear regime the dielectric constant of water is g = -i- Pc pll3. After the addition of salt the effective... 

The limiting slope, -S, the so-called dielectric decrement, is the quantity considered in theoretical concepts. The underlying models roughly can be classified into equilibrium approaches based on dielectic saturation, and dynamical theories based on kinetic depolarization. 

Chernenko has investigated the effect of a counterion-induced dielectric decrement on the solution of the Gouy-Chapman equation. Sansom et al. have studied the effect of a local dielectric coefficient in an ion channel pore (in the absence of ions), and others have analyzed cylindrical models of Kozak and co-workers and Frahim and Diekmann have... 

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