Relative permittivity of polymers

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. 

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-... 

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. 

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) ... 

This table lists typical values of the dielectric constant (more properly called relative permittivity) of some important polymers. Values are given for frequencies of 1 kHz, 1 MHz, and 1 GHz in most cases the dielectric constant at frequencies below 1 kHz does not differ significantly from the value at 1 kHz. Since the dielectric constant of a polymeric material can vary with density, degree of crystallinity, and other details of a particular sample, the values given here should be regarded as only typical or average values. 

At the beginning of this section it was stated that the propensity of a textile polymer to accumulate static electrical charges is related to their electrical resistance. It has al.so been said that electrical resistance is related to the relative permittivity of the material. Relative permitivity or permittivity is sometimes (now incorrectly) called dielectric constant, as this used to be the common term before SI units became the fashion. Relative permittivity is therefore often used as a shorthand method of indicating the static electrical propensity of fibers and filaments. Its measurement is discussed in lEC 250. 

Sonoda et al. [155] observed an increase in relative permittivity of BST/polymer composites by introducing aliphatic carboxylic aids onto the BST surface. The modified nanoparticles with longer carboxylic acid chains had better compatibility with the polymer matrix. In addition, the mechanical properties of modified BST powder/polymer composites were not affected. 

The main operating principle of capacitance sensors is that changes can be made to the relative permittivity of the dielectric (e ), the area of the electrode (A), or the distance between the two electrodes (d), and therefore, by measuring the change in the capacitance, the presence of the measurand can be detected (Ishihara and Matsubara 1998). With reference to polymer coating, the mechanisms... 

In this, M is the molecular mass, p is density, is Avogadro s number, cq is the permittivity of free space, is the relative permittivity/dielectric constant and a is the molecular polarisability. For a full discussion of the dielectric behaviour of polymer-based materials, reference to the excellent works by Kremer (2003) and Jonscher (1983) is highly recommended. Nevertheless, simplistically, permittivity can be thought of in terms of the number and nature of the polarisable species present in the system, plus their dynamics. Since the dielectric response of a given moiety is affected by its environment, dielectric spectroscopy can provide local structural information. In practice, the relative permittivity of a material is a complex quantity ... 

This table lists typical values of the dielectric constant (more properly called relative permittivity) of some important polymers. Values are given for frequencies of 1 kHz, 1 MHz, and 1 GHz in... 

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 ... 

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. 

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... 

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... 

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. 

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