Dielectric constant mean value

A similarly transparent explanation is available for the effect of temperature. If T is increased (at fixed dielectric constant), the value of decreases, and hence the number 9 of condensed counterions also decreases. A smaller number of condensed counterions means that the charge density of the condensed layer is less. The free volume, which scales like the charge density of the condensed layer, compensates by contracting. A negative thermal expansion coefficient of the condensed layer (again, at fixed dielectric constant) may be interesting, but it is also easily understood. 

In Section 4.8 we decided that such a high value of dielectric constant means that many monomers dissociate in water solutions. In other words, the corresponding pol3rmers are polyelectrolytes. In particular, the polyelectrolyte nature of the main biopolymers, DNA and proteins, is crucial for their biological functioning. 

The polarity of IL is one of the spedfic properties that distinguishes it from molecular solvents. The variation of the polarity of IL before and after its covalent immobilization on different polymers was semiquantitatively investigated by means of steady-state fluorescence spectroscopy using pyrene as a probe. Scheme 2.15 [69]. It suggested that the static dielectric constant (e) values deduced from the fluorescence experiments revealed an increase in the polarity of the polymers from e < 5 to e > 10-20 after immobilization of IL. Hence, an IL supported covalently on a polymer exhibits similar polarity as that of the bulk room-temperature IL. For example, the e of the IL [EMIm][NTf2 is 15.76. 

For gases the values of the dielectric constant can be adjusted to somewhat different conditions of temperature and pressure by means of the equation... 

Dielectric constant The dielectric constant of anodic oxide films has been found to be 5-0-5-9 for sulphuric films, and 7-8 for oxalic films. A mean value of 7-45 has been quoted for barrier-layer films, but more recent work favours a value of 8-7 . 

At large distances the curve of Fig. 8b is a plot of — (c2/ r)> where t is the macroscopic dielectric constant of the solvent at the temperature considered. For small values of r the curve deviates from this value but at every point the slope of the curve must represent the mean intensity of the mutual attraction or repulsion at the particular temperature considered. If the curve of Fig. 86 for dissociation in solution is to be useful, every point on this curve must belong to the same temperature T. That is to say, when we consider any change in the distance r between the ions, we are interested in an isothermal change in r. 

Correlations among solvent polarity scales, dielectric constant and dipole moment, and a means to reliable predictions of polarity scale values from current data. T. R. Griffiths and D. C. Pugh. Coord. Chem. Rev., 1979, 29,129-211 (130). 

However, the equilibrium of the indicator adsorbed at an interface may also be affected by a lower dielectric constant as compared to bulk water. Therefore, it is better to use instead pH, the interfacial and bulk pK values in Eq. (50). The concept of the use at pH indicators for the evaluation of Ajy is also basis of other methods, like spin-labeled EPR, optical and electrochemical probes [19,70]. The results of the determination of the Aj by means of these methods may be loaded with an error of up to 50mV [19]. For some the potentials determined by these methods, Ajy values are in a good agreement with the electrokinetic (zeta) potentials found using microelectrophoresis [73]. It is proof that, for small systems, there is lack of methods for finding the complete value of A>. 

We have seen in Chapter 2 that the frequency of an EPR spectrum is not a choice for the operator (once the spectrometer has been built or bought) as it is determined by the combined fixed dimensions of the resonator, the dewar cooling system, and the sample. Even if standardized sample tubes are used and all the samples have the same dielectric constant (e.g., frozen dilute aqueous solutions of metalloproteins), the frequency will still slightly vary over time over a series of consecutive measurements, due to thermal instabilities of the setup. By consequence, two spectra generally do not have the same frequency value, which means that we have to renormalize before we can compare them. This also applies to difference spectra and to spectra... 

Dielectric constants of these materials can be further lowered by known means such as by incorporating air bubbles into the materials or by inhibiting crystallization. A difference of a couple of hundredths in the DE value may be important when one is at the low extremes. Recently Singh et al. calculated the DEs ofpolyimide films from the measured free volume fraction and found that the calculated values, are close to the experimental result.1415 ... 

The predicted distribution corresponds to an unskewed Gaussian curve. Distributions for the other programs and MM3 with the vacuum dielectric constant were similar, but their maxima were located at about 4.55 A. We judged that distance to be too long, in part because the mean observed value is about 0.14 A (7.4 standard deviations) smaller. Also, those predicted distributions based on vacuum dielectric constants called for a large fraction of... 

The evaluation of the interaction term is done with the prescriptions given in Section V,B. The chief difficulty in evaluating electrostatic terms is the indeterminate dielectric constant at the surface which has been estimated as the mean value of the dielectric constants for the solvent and the material forming the stationary phase layer. Therefore, the apparent dielectric at the surface, e., may be expressed as... 

Dielectric constants are determined for pure liquid dimethylsiloxane oligomers. Mean-square dipole moments, calculated from the Onsager equation, are in good agreement with predicted values based on the RIS model (S 117) with neighbor dependence and chain conformational energies obtained in an independent analysis of the random-coil dimensions of such chains. In addition, the observed temperature coefficients of are in qualitative agreement with calculated results. 

The mean-square dipole moments of POE and POMg are determined from dielectric constant measurements on dilute solutions in benzene. The values obtained are in good agreement with those predicted using the RIS models for these chains. In addition, the unperturbed dimensions of POMg are calculated as a function of molecular weight using the RIS theory. 

Polypropylene sulfide) is synthesized in both the iosotactlc and atactic stereochemical forms. They are investigated by means of dielectric constant measurements in benzene and CCI4. The experimental results are in good agreement with values predicted from RIS calculations. 

Values of the mean-square dipole moment of PNA are determined from measurements of dielectric constants and refractive indices of the polymer in benzene. The dipole moment ratio and the temperature coefficient of both the dipole moment and the unperturbed dimensions are critically interpreted using the RIS model. Good agreement between theory and experiment is obtained by assuming that the gauche states about C(CH3)2— CH2 bonds have an energy 2.5 kJ mol-1 lower than the alternative trans states. 

PCCS and PTCS are synthesized by condensation of the corresponding c/s and Vans isomers of 1,4-cyclohexanedimethanol with sebacic acid. Values of the mean-square dipole moments of both polyesters are determined from dielectric constant measurements on dilute solutions of the polymers in benzene. Theoretical calculations carried out with the RIS model give values of d (In 0) / d Tin very good agreement with the experimental results. Fair agreement between theory and experiment is also found in the case of the dipole moments of the chains. 

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