Dielectric concentration dependence

Rudolph, R., Francke, K.P. and Miessner, H. (2002) Concentration dependence of VOC decomposition by dielectric barrier discharges, Plasma Chem. Plasma Process. 220, 401-12. 

The DTO model predicts that rmax is relatively insensitive to polymer concentration, in distinction to the results of Rouse and Bueche. The concentration dependence of the dielectric should therefore be a most interesting point of study and should distinguish between the two mechanisms. 

Kakizaki, M. and Hideshima, T., Effect of distribution of free volume on concentration dependence of dielectric relaxation in water mixtures with poly(ethylene glycol) and glucose, Jpn. J. Appl. Phys., Part 1, 1998, 37, 900. 

In concluding this section on liquid-liquid phase transitions, we briefly consider the available experimental information on the ion distribution near criticality. In the absence of scattering experiments, most experimental data come from electrical conductance data [72, 137, 138]. Moreover, there are some data on the concentration dependence of the dielectric constant in low-s solutions [139] and near criticality [138]. 

The concentration dependence of ionic mobility at high ion concentrations and also in the melt is still an unsolved problem. A mode coupling theory of ionic mobility has recently been derived which is applicable only to low concentrations [18]. In this latter theory, the solvent was replaced by a dielectric continuum and only the ions were explicitly considered. It was shown that one can describe ion atmosphere relaxation in terms of charge density relaxation and the elctrophoretic effect in terms of charge current density relaxation. This theory could explain not only the concentration dependence of ionic conductivity but also the frequency dependence of conductivity, such as the well-known Debye-Falkenhagen effect [18]. However, because the theory does not treat the solvent molecules explicitly, the detailed coupling between the ion and solvent molecules have not been taken into account. The limitation of this approach is most evident in the calculation of the viscosity. The MCT theory is found to be valid only to very low values of the concentration. 

The preceding discussion assumed a pure liquid was used for the measurement. Most molecules of interest, however, are not in the liquid state at room temperature. In this case it is common to dissolve the compound in an appropriate solvent and conduct the measurement. Contributions to the second harmonic signal are therefore obtained from both the solvent and solute. Since r and the local field factors that are related to e and n, (the dielectric constant and refractive index respectively) are concentration dependent, the determination of p for mixtures is not straightforward. Singer and Garito (15) have developed methods for obtaining r0, eQ, and nQ, the values of the above quantities at infinite dilution, from which accurate values for p can be obtained in most cases. 

The dipole moments were determined from the concentration dependence of the dielectric constant and the refractive index of the solutions in the low concentration limit (mol fraction ca. 0.001). 

Ps) and a nanoparticle concentration-dependent increase in the dielectric permittivity [371]. 

The inclusion of activity coefficients into the simple equations was briefly considered by Purlee (1959) but his discussion fails to draw attention to the distinction between the transfer effect and the activity coefficient (y) which expresses the non-ideal concentration-dependence of the activity of solute species (defined relative to a standard state having the properties of the infinitely dilute solution in a given solvent). This solvent isotope effect on activity coefficients y is a much less important problem than the transfer effect, at least for fairly dilute solutions. For example, we have already mentioned (Section IA) that the nearequality of the dielectric constants of H20 and D20 ensures that mean activity coefficients y of electrolytes are almost the same in the two solvents over the concentration range in which the Debye-Hiickel limiting law applies. For 0-05 m solutions of HC1 the difference is within 0-1% and thus entirely negligible in the present context. Of course, more sizeable differences appear if concentrations are based on the molality scale (Gary et ah, 1964a) (see Section IA). 

As with normal electrolytes (Section 2.12.1), the dielectric constant depends linearly on concentration ... 

In any event, some ions are produced, the ionic concentration depending on both the original concentration of the acid or base, the respective dissociation constant and the physical properties of the solvent, e.g. the pH and dielectric constant. Under the influence of a potential gradient, the ions in solution can carry an electric charge consequently, if a potential is applied across two electrodes situated in the solvent, a current will flow and the solvent is said to be conducting. It is clear that such a system could be used to detect ionic species in LC. 

Viscosity of aqueous cesium chloride (CsCl) solution was measured in the range of 0.1-5.0 mol kg-i and 0.1-375 MPa at 25 °C. The Jones-Dole B coefficient of CsCl was obtained from the concentration dependence of the viscosity. It is negative not only at atmospheric pressure but also at high pressure, having a maximum against pressure at about 160 MPa. Similar maximum of the B was observed for aqueous sodium chloride (NaCl) solution. The similarity is discussed in terms of the water structure and dielectric friction theory. 

The values obtained from eqn (7.24), which includes the correction for the concentration dependence of the dielectric constant (from ref. 46), are lowered by between 5 and 10% compared to the uncorrected values. The more frequently used approximation appears to be that of eqn (7.25). 

Abstract Analytical solution of the associative mean spherical approximation (AMSA) and the modified version of the mean spherical approximation - the mass action law (MSA-MAL) approach for ion and ion-dipole models are used to revise the concept of ion association in the theory of electrolyte solutions. In the considered approach in contrast to the traditional one both free and associated ion electrostatic contributions are taken into account and therefore the revised version of ion association concept is correct for weak and strong regimes of ion association. It is shown that AMSA theory is more preferable for the description of thermodynamic properties while the modified version of the MSA-MAL theory is more useful for the description of electrical properties. The capabilities of the developed approaches are illustrated by the description of thermodynamic and transport properties of electrolyte solutions in weakly polar solvents. The proposed theory is applied to explain the anomalous properties of electrical double layer in a low temperature region and for the treatment of the effect of electrolyte on the rate of intramolecular electron transfer. The revised concept of ion association is also used to describe the concentration dependence of dielectric constant in electrolyte solutions. 

In the series Ba2+, Cu2+, Y3+ the cation size increases. These cations do not create the ion pairs with anion NO3 and the dependence of es on the ion strength for nitrate salts is in agrement with our previous conclusions about the dependence of the solvent dielectric constant on the ion concentration with change of 5. For the formate salts, these cations create ion pairs with anions CHOO- due to hydrogen bonds between anion and water molecules from the hydration shell of cation thus, the degree of association increases with the decrease of ion size. As a result, we obtaine the concentration dependence for es that is opposite to nitrate salts. Since the considered theory is elaborated for the symmetrical electrolytes and experimental data concern the asymmetri-... 

Some results of the application of such theory for the description of concentration dependence of the dielectric constant of electrolyte solution will be published elsewhere [78],... 

Figure 53. The dielectric loss of 2-picoline in mixtures with tri-styrene at different concentrations obtained at different temperatures but similar a-relaxation times of the 2-picoline component. For clarity, each spectrum is shifted by a concentration-dependent factor kc. Data from T. Blochowicz and E. A. Rossler, Phys. Rev. Lett. 92, 225701 (2004).

Figure 54. Dielectric loss spectra with the same maximum peak frequency for different concentrations of tert-butylpyridine (wt%) in tristyrene. For clarity, each spectrum is shifted vertically by a concentration dependent factor K. K = 1, 2, 1.3, 1, and 0.98 for 100%, 60%, 40%, 25%, and 16% TBP, respectively. The x axis is the real measurement frequency, except for the spectra of 100% and 16% TBP, where horizontal shifts of frequency by factors of 1.75 and 0.80, respectively, have been applied.

Figure 4 presents the variation of with p for different metal/dielectric composites, measured at different excitation wavelengths and with different pulsewidths, as selected from the literature [74, 139, 163, 180, 190-193]. The influence of both X and t on the nonlinear response will be discussed in Section 8. Nevertheless, one can already notice that the concentration dependence of ... 

Molle et al. (243) synthesized the 22-residue transmembrane segment of the essential subunit 8 of the Saccharomyces cerevesiae H+ ATP synthetase and observed weakly voltage-dependent conductance levels on different planar lipid bilayers. CD spectra show 60% a-helix for this peptide in low dielectric solvents. The conductance exhibited a second-order concentration dependence, suggestive of antiparallel dimers as the conducting unit (243). 

Dielectric and conductivity measurements of NHs-doped ice were discussed by Arias, Levi, and Lubart (I). They observed a dielectric dispersion which, for all concentrations (2 X 10"5M to lO M), and temperatures (— lO C. to —40°C.) was qualitatively similar to that for pure ice or ice of slight impurity content (Figure 18). The a.c. conductivity curves also look like those of Figure 18. Above lO M the conductivity was independent of concentration and about equal to the d.c. conductivity. No specific expressions were given for the temperature and concentration dependence. These results point to a role for NH3 in ice quite different from HF. Ionization appears to be much smaller in ice doped with the former or the difference is caused by the smaller mobility of hydroxide ions as compared to hydrogen ions. 

In HF doped ice, Kopp (personal communication) found exponents of 0.4 and 0.6 for the concentration dependence of the dielectric relaxation and of the nuclear magnetic relaxation, respectively. He suggests that the mass-action law does not hold for the relaxations. 

Steinemann (140) found that, at a given temperature, the dielectric relaxation time was inversely proportional to the HF concentration if the concentration was high, and inversely proportional to the square root of the concentration if it was lower. (The relations are listed in Table III.) Thus, the concentration dependence of the dielectric relaxation time does not follow a simple law. The formulation depends on the assumptions one makes about the nature of the relaxation process or processes (ion translation or molecular rotation), carrier concentration and dissociation, and the energies involved. 

Fig. 7.15 Hydrogen concentration dependence of (a) the complex ( -2) and (b) the real (ei) part of the dielectric function for YH - Similar dependences are observed in Lai-zYzH alloys although the trihydrides Lai-zYzHs with z< 0.67 remain cubic while for z> 0.86 they are hexagonal. (From Van Gogh et al. (2001), Ref [56].)...

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