Prediction of Dielectric Constant

The basic regression equation for the dielectric constant employed for the polymers cited in this text is 

Equation (15) has a standard deviation of 0.0871 and a correlation coefficient of 0.979. It is based on a data set containing 61 polymers chosen in such a way as to avoid incorporation of the effects of additives and fillers. Further analysis of the data set gave the following results  

Anatomic is dependent on the total number of atoms of given types, with electronic configurations specified by appropriate pairs of atomic indexes. The terms on the right-hand side of Eq. (18) not been defined earlier are as follows  

N -(C=O)- in-carboxyiic-acid, ketone, aldehyde is the total number of carbonyl groups in carboxylic acid, ketone, and aldehyde. 

N other-(c=o)- is the number of C=O groups in ester and carbonate moieties as well as in anhydride groups. 

7 backbone(o, 12A sidegroup(o, s) the Contribution of the total number of oxygen and (divalent only) sulfur atoms in the main chain and in side groups, respectively. 

TVgroup is, like TVdc above, a correction factor that improves the statistical correlation. Its terms are as follows TVhydroxyl is the number of OH groups in alcohols and phenols. Contributions from OH groups in carboxylic or sulfonic acid groups are not incorporated in this term. 

TV amide is the total number of amide groups in the repeat unit. 

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Fig. 6. Maxwell-Garnett theory used for the prediction of dielectric constant containing dispersed regions of low dielectric polymer (e = 2.0,0) or air (e = 1.0, )...

Liu A, Wang X, Wang L et al. (2007) Prediction of dielectric constants and glass transition temperatures of polymers by quantitative structure-property relationships. Eur Polym J 43 989-995... 

Dielectric polarizabilities are useful for prediction of dielectric constants of new materials and compounds whose dielectric constants have not been measured, and in calculations of energies of the formation and migration of defects. In addition, deviations from the polarizability additivity rule are useful in understanding certain physical properties such as thermodynamic functions and ionic and electronic conductivity." ... 

Schweitzer, R.C. and Morris, J.B. (1999). The Development of a Quantitative Structure Property Relationship (QSPR) for the Prediction of Dielectric Constants Using Neural Networks. Anal. Chim.Acta, 384,285-303. 

Fig-1 Maxwell-Garnett theory used for the prediction of dielectric constant containing dispersed regions of air... 

The dielectric constant of the pure cyanurate network under dry nitrogen atmosphere at 20 °C is 3.0 (at 1 MHz). For the macroporous cyanurate networks, the dielectric constant decreases with the porosity as shown in Fig. 57, where the solid and dotted lines represent experimental dielectric results together with the prediction of the dielectric constant from Maxwell-Garnett theory (MGT) [189]. The small discrepancies between experimental results and MGT might be due to the error in estimated porosities, which are calculated from the density of the matrix material and cyclohexane assuming that the entire amount of cyclohexane is involved in the phase separation. It is supposed that a small level of miscibility after phase separation would result in closer agreement of dielectric constants measured and predicted. Dielectric constant values as low as 2.5 are measured for macroporous cyanurates prepared with 20 wt % cyclohexane. 

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. 

The temperature dependence of the dielectric properties of foods has been extensively measured and reviewed by Bengtsson and Risman (1971) and Buffler (1993). Mudgett et al. (1977) has pioneered the prediction of dielectric properties of foods as a function of constituency and temperature. Prediction of the temperature behavior of dielectric properties is crucial for accurate mathematical modeling of foods. Many workers today still use constant room temperature values or a look-up table at best. In the author s opinion, dielectric prediction of food properties is still a very fertile and useful research field. 

A number of attempts have been made to predict thermodynamic functions for ionizations on the basis of electrostatic theory (Benson, 1960d Frost and Pearson, 1961a). The simple Born treatment, which considers the solvent as a continuous dielectric, gives for the free energy of separation of a pair of spherical charges, ZK e and ZB e, in a medium of dielectric constant D,... 

One can address this issue more rigorously by considering the work of Rovere and Tosi [73]. The authors show that, in the limit of a salt composed of monovalent, nonpolarizable ions of uniform size, linear response theory predicts the dielectric constant e(k) should be... 

We see now that the effect of dielectric constant is not separable from the influence of ms and rg, the dipole moment and distance of closest approach of a solvent molecule to the ion. When msAI = mb/ b, there should be no effect of changes in solvent, while, depending on which of these is greater, opposite effects may be predicted."... 

It may be concluded that electrostatic models may be successfully applied only so far as interactions between weakly coordinating or noncoordinating species (such as tetraalkylammonium ions) are concerned. This is illustrated by Table X which shows that variations of association constants for tetrabutylammonium iodide as a function of dielectric constant roughly correspond to the trends predicted by the Bjerrum theory. When iodide, which is a comparatively weak base, is... 

Finally, Shannon obtained 61 sets of ionic polarizabilities for 129 oxides and 25 fluorides using the Clausius-Mosotti equation and least square refinements, and suggested the periodic table of ionic polarizabilities. Therefore the dielectric constant of materials with compositional changes can be successfully predicted by Equation 22.17 and Equation 22.18. Erom another arrangement of Equation 22.16, the theoretical dielectric constant can be obtained from the total ionic polarizabilities in Equation 22.19. Erom Equation 22.17 through Equation 22.19, the theoretical values of dielectric constant and polarizabilities can be obtained as well as the measured values ... 

Table 17.7. Cohesive energy Ecohl (Equations 5.10-5.12), van der Waals volume Vw, the term N(jc used in predicting the dielectric constant e, and predicted e values at room temperature, for low-hydroxyl" grade of poly(vinyl butyral) containing roughly 12% by weight of poly(vinyl alcohol). The subscript 1 denotes poly(vinyl butyral), while the subscript 2 denotes poly(vinyl alcohol), for weight fractions and mole fractions which are denoted by w and m, respectively.

Davies model (Equation 20.3 with the dielectric constant replacing the shear modulus G [58]) can be used to predict the dielectric constants of materials containing co-continuous interpenetrating phases (as in interpenetrating networks) at all volume fractions. 

The relative dielectric constant of O2 gas at 0°C was measured to be 1.000523. Using this result, predict the dielectric constant of liquid O2 if its density is 1.19 g/cm. Compare your answer with the experimentally determined value of 1.507. State all assumptions and discuss implications of your results vis a vis the assumptions made. 

Capacitance Methods. Capacitance methods have been used to measure solids concentration in slurry pipelines (79). This method requires the dielectric constant of the solids and the carrying fluid to be significantly different. Sand-water slurry is a good example to use the capacitance method. In this case, the dielectric constant for water is 80, whereas that of the sand particles is 5. The method relies on the variation of the dielectric constant of the mixture, Em, with the solids concentration, C. For homogeneous slurries of spherical particles at low solids concentration, Maxwell s correlation can be used to predict the dielectric constant of the mixture. However, several investigators assumed that the relationship of the dielectric constant of the mixture and solids concentration was linear, as follows ... 

The conductivity of a single pore is determined by the charge density of protons p and the proton mobiUty p,. As discussed above, p and are fimctions of the position within the pore. In highly hydrated PEMs, p, is highest in the bulk and smallest close to the surface. The proton distribution from simple Poisson-Boltzmann theory decreases monotonously from the interface towards the pore center. Refined calculations of the proton distribution take into accoimt the finite size of protonated complexes and a repulsive part of the intermolecular potential near the pore surface. This modified PB approach predicts an excluded region for the hydrated protons close to the surface (mainly related to the finite size of proton complexes). A maximum in exists at about 1.5 A away from the interface. From this position p decreases continuously towards the center of the pore. This density profile is in reasonable agreement with results from MD simulations [84]. Further possible refinements, such as incorporating variations of dielectric constant with position within the pore and with pore size, were not included in these calculations. 

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