Dielectrics, quantitative relationships

In other chemical systems, such as tetrafunctional epoxies, polyimides, phenolics, and polyesters, there have been few attempts 64,65) to establish quantitative relationships between chemical kinetics and dielectric properties. 

Dielectric relaxation spectra of poly(methyl acrylate) (IfA) and poly(t-butyl acrylate) (tBA) were measured at temperatures above and below Tg, and both a- and 3-relaxation processes were observed. As for the 3-relaxation process, in order to clarify the quantitative relationship between the relaxation mechanism and the polymer structure, the effective dipole moment(Pg) was estimated by a method according to the 2-state transition theory. In the estimation, the average local configuration of the main chain was assumed to be in isotactic form or syndiotactic form. Since samples used were atactic polymers, the authors assume that Pg(atact) = Xi Pe(i) + (1 - X ) Pe(s)> where X denotes the tacticity, i represents isotactic form, and s, sytidiotactic form, respectively. And, the activation energy for the atactic form sample is examined in a similar way. From the results, it can be concluded that the 3-relaxation of samples is attributed to the restricted rotation of the side chain, especially, to the rotation of the first bond-axis connecting the side chain and main chain. 

Hence, it is possible to construct a standard curve relating viscometric measurements to steady-state anisotropy measurements for a particular fluid and use the quantitative relationship to determine the viscosity of the fluid by fluorescence polarization [4,9-11]. A standard curve in a reference calibration oil such as white paraffin oil can be used to determine the viscosity of another fluid as long as the calibration fluid is similar in dielectric constant and viscosity to the fluid being analyzed. It is important to keep in mind that the same fluorescent probe may display different behavior even in different hydrocarbon calibration oils, hence one must exercise caution when determining absolute values for microvis-... 

Ultimately physical theories should be expressed in quantitative terms for testing and use, but because of the eomplexity of liquid systems this can only be accomplished by making severe approximations. For example, it is often neeessary to treat the solvent as a continuous homogeneous medium eharaeterized by bulk properties such as dielectric constant and density, whereas we know that the solvent is a molecular assemblage with short-range structure. This is the basis of the current inability of physical theories to account satisfactorily for the full scope of solvent effects on rates, although they certainly can provide valuable insights and they undoubtedly capture some of the essential features and even cause-effect relationships in solution kinetics. Section 8.3 discusses physical theories in more detail. 

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... 

The quantitative interpretation of the dielectric relaxation times is still not on a satisfactory basis. The earliest attempt in this direction was made on the basis of an ion-oriented hydration sheath, for the formation of which a calculated number of hydrogen-bonds must be broken. This breakage changes the equilibrium of species in the liquid, and statistical relationships connect the proportion of bonds broken, the equilibrium populations, and the relaxation time. From the observed shift of relaxation time one can calculate the number of molecules in the sheath, and show that for temperatures between 276 and 298 K it is approximately the same as the number calculated from the depression of the static permittivity (comparison in Figure 4 of ref. 54). This treatment is open to criticism on the following grounds ... 

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. 

The quantitative definition of temperature is completed by establishing a partially arbitrary functional relationship between the temperature t and a suitably selected property P of the thermometer. The thermometric property P and those other properties of the thermometer which are held constant in the operation of measurement must determine the thermodynamic state of the thermometer. The care necessary in choosing the variables to be held constant is illustrated by the fact that p and v are not always sufficient to determine the thermodynamic states of a pure system. Thus, for example, in water at temperatures between 0°C and 8°C, the dielectric constant may have two different values at the same values of p and v. The relationship between t and P, t = t P), though partially arbitrary, must be such that t P) is a continuous, monotonic, and single-valued function of P. Single-valuedness is required so that a set of systems with the same value of P remain in equilibrium on contact with each other, i.e., there is only one value of t for each P monotonicity... 

A more quantitative assessment of the above data was attempted within the frame of several theoretical treatments of dielectric permittivity-composition relationships in composite materials, by the implicit assumption that the dielectric permittivities of the matrix and of spherical inclusions (e and e, respectively)... 

Finally, this chapter discussed the use of block copolymers to examine local relaxations. Relationships between polymer motion, polymer dynamic modes, and paths for extracting regiospecific dynamic information by use of dielectric relaxation spectroscopy were considered. Quantitative applications of the block copolymer approach presented in this chapter are very demanding on the calibration, accuracy, and sensitivity of the dielectric apparatus and on the synthetic precision of the polymer chemist. 

Between the two semi-infinite phases lies a Stem layer which contains continuum solvent with dielectric strength E, surface site ions, and adsorbed solute ions. The thickness of the Stem layer, Ug, corresponds to the diameter, a, of a single surface site ion, S . The surface site ions may or may not be bound to solute ions. The presence of adsorbed solute ions will not affect Ug, but will change the valence of the surface site. In general, the area of a surface site ion, A, will be > a. This relationship can be seen qualitatively in Fig. 2 and understood quantitatively when one consideres flrat ionic diameters are nominally 2— 3 A, while surface sites are nominally spaced 7—10 A (the electrostatic surface charge density on a fully ionized surface is of the order of 0.3 coulombs m [32], which corresponds to an electrostatic surface site density of50—100 A per surface site). The volume of a surface site not occupied by a surface site ion is filled with continuum solvent. The surface... 

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