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Polymers relative permittivity

In the model, Xp is determined by a temperature dependent electrophoretic mobility factor [123] which contains the viscosity of the solvent as well as its relative permittivity, Xc °, the radius of the polymer chain and the Debye screening length 1D. The following equation holds for the case that electrolyte and polyelectrolyte are in the same concentration range ... [Pg.152]

Equation (10.6), formulated in the previous section, defines the relative permittivity tensor in terms of the mean orientation of certain uniformly distributed anisotropic elements, which we shall interpret here as the Kuhn segments of the model of the macromolecule described in Section 1.1. We shall now discuss the characteristic features of a polymer systems, in which the segments of the macromolecule are not independently distributed but are concentrated in macromolecular coils. [Pg.202]

In this situation, which is also discussed in Section 7.5, we refer to experimental evidence according to which components of the relative permittivity tensor are strongly related to components of the stress tensor. It is usually stated (Doi and Edwards 1986) that the stress-optical law, that is proportionality between the tensor of relative permittivity and the stress tensor, is valid for an entangled polymer system, though one can see (for example, in some plots of the paper by Kannon and Kornfield (1994)) deviations from the stress-optical law in the region of very low frequencies for some samples. In linear approximation for the region of low frequencies, one can write the following relation... [Pg.205]

In the simplest cases, the optical anisotropy of polymer systems is studied under the conditions of simple elongation, when the elongation velocity gradient i/ii is given. The system investigated then becomes, generally speaking, a triaxial dielectric crystal with components of the relative permittivity tensor... [Pg.206]

Let us consider the anisotropy of polymer system undergoing simple steady-state shear. This situation can be realised experimentally in a simple way (Tsvetkov et al. 1964). The quantity measured in experiment are the birefringence An and the extinction angle x which are defined by formulae (10.19) and (10.20), correspondingly, through components of the relative permittivity tensor. [Pg.209]

One can turn to equation (10.10) to find the components of the relative permittivity tensor. Using expressions for the moments (2.42), one determines the gradient dependence of the quantities for dilute polymer solutions to within second-order terms... [Pg.209]

Now we refer to formula (10.13) for the relative permittivity tensor to determine the characteristic quantities in this case of strongly entangled linear polymers. We use expansions (7.32) and (7.43) for the internal variables to obtain the expression for the components of the tensor through velocity gradients... [Pg.211]

Given that the appropriate relative permittivities of the ceramic and the polymer are respectively 1500 and 3.5, and that the d33 coefficient for the ceramic is 375 pCN-1, calculate a value for the hydrophone figure of merit and show that the units are m2 N 1. For this estimate it may be assumed that the composite has been structurally modified so that the d33 contribution is negligible. Comment on the realism or otherwise of the calculated value. [Pg.409]

In this expression, q> is the volume fraction of water, Ct is the capacitance after some exposure time t, C0 is the capacitance of a dry film, which is usually measured at the outset of an exposure experiment. The relative permittivity of water at 25°C is reflected in the denominator of the expression. This expression applies only when water is homgeneously dispersed in the polymer, no water-... [Pg.322]

Z values have been widely used to correlate other solvent-sensitive processes with solvent polarity, e.g. the a absorption of haloalkanes [61], the n n and n n absorption of 4-methyl-3-penten-2-one [62], the n n absorption of phenol blue [62], the CT absorption of tropylium iodide [63], as well as many kinetic data (Menschutkin reactions, Finkelstein reactions, etc. [62]). Copol5mierized pyridinium iodides, embedded in the polymer chain, have also been used as solvatochromic reporter molecules for the determination of microenvironment polarities in synthetic polymers [173]. No correlation was observed between Z values and the relative permittivity e, or functions thereof [317]. Measurement of solvent polarities using empirical parameters such as Z values has already found favour in textbooks for practical courses in physical organic chemistry [64]. [Pg.413]

We can then treat e as a scalar quantity, which is independent of the orientation of the electric field vector, as in Equation (2.6). This will not be true if the polymer has a preferred orientation conferred either by mechanical deformation or solid-state polymerisation. In this situation the relative permittivity will be a tensor so that... [Pg.30]

The situation is much more complicated in solids because the intermolecular effects can no longer be ignored, i.e. the approximation EM = 0 inherent in the simple formula for the local field (2.29) is not generally true. Consequently, although we can predict the molecular dipole moment from known group moments, it is not possible to calculate the molar polarisation and thereby the relative permittivity, without further elaboration of the dielectric model. In the case of a polymer there are further complications which arise from the flexibility of the long chains. [Pg.44]

Conjugated polymers, which contain multiple carbon-carbon bonds, can be expected to have somewhat higher relative permittivities, since the bond polarisabilities of multiple bonds are higher than those of single C-C bonds, see Table 2.2. Most measurements of relative permittivities have been made on the conductive forms of these polymers, but these are outside the scope of this chapter and will be discussed later. The intrinsic energy gap in the... [Pg.48]

The development of polymers with low relative permittivity provides an informative and instructive exercise in polymer design using the principles... [Pg.52]

An additional benefit of fluorination is an increase in hydrophobicity through the effect of the highly polar C-F groups. This means that the level of absorbed water in the polymer at typical ambient humidity is much reduced. Water has a very high relative permittivity, so that its presence can significantly increase the relative permittivity of a material, and the level will also be liable to vary with ambient conditions, bringing uncertainty into design considerations for electronic systems. [Pg.54]

An increase in fractional free volume will reduce the number of polarisable groups per unit volume, and thereby reduce the relative permittivity of the polymer. Quantitatively, the effect may be estimated by means of the Clausius-Mossotti/Lorenz-Lorentz model for dielectric mixing (Bottcher, 1978) ... [Pg.54]

Table 2.5 Change of relative permittivity attributable to change in fractionalfree volume Polymer pair %Afr due to Ai/ff... Table 2.5 Change of relative permittivity attributable to change in fractionalfree volume Polymer pair %Afr due to Ai/ff...
Generally, we must conclude that control of free volume is just as important as selection of groups with low polarisability, in order to achieve polymer molecular structures with low relative permittivities. [Pg.55]

The presence of the relative permittivity in the exponent of Equation (8.8) means that it will exert a strong influence on conductivity. In this way the absorption of water, which has a relatively high relative permittivity, generally enhances the conductivity of a polymer greatly, and polymer-water systems frequently conform to the equation... [Pg.253]

The use of polymers with a low relative permittivity, see Section 2.7, as the FET gate insulator has been found to result in higher carrier mobility and improved device performance (Veres et al., 2003). The authors developed stable semiconductive polymers, poly(triarylamines), and used them to fabricate FETs with silicon dioxide and poly(methylmethacrylate) gate insulators. Values of the carrier mobilities measured in the FETs were about 10 times smaller than those determined by TOF experiments. A dramatic increase in FET mobility was observed when a low permittivity fluoropolymer (e = 2.1) was employed as gate insulator. The FET mobilities for devices with gate insulators with relative permittivities in the range 2-18 are shown in Fig. 10.12(a). The devices were made with two different poly(triarylamines)... [Pg.419]


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