Dielectric data

Transitions. Samples containing 50 mol % tetrafluoroethylene with ca 92% alternation were quenched in ice water or cooled slowly from the melt to minimise or maximize crystallinity, respectively (19). Internal motions were studied by dynamic mechanical and dielectric measurements, and by nuclear magnetic resonance. The dynamic mechanical behavior showed that the CC relaxation occurs at 110°C in the quenched sample in the slowly cooled sample it is shifted to 135°C. The P relaxation appears near —25°C. The y relaxation at — 120°C in the quenched sample is reduced in peak height in the slowly cooled sample and shifted to a slightly higher temperature. The CC and y relaxations reflect motions in the amorphous regions, whereas the P relaxation occurs in the crystalline regions. The y relaxation at — 120°C in dynamic mechanical measurements at 1 H2 appears at —35°C in dielectric measurements at 10 H2. The temperature of the CC relaxation varies from 145°C at 100 H2 to 170°C at 10 H2. In the mechanical measurement, it is 110°C. There is no evidence for relaxation in the dielectric data. 

Dipole moments seem to exert a sort of fascination on theoretical chemists, who often check their calculations by comparing their calculated values of the dipole moment with the experimental ones. This is particularly startling since the experimental dipole moments generally arise from dielectric data (63PMH(1)189) and thus only the modulus is known. 

The pioneering work of Von Hippel [15] and his coworkers, who obtained dielectric data for organic and inorganic materials, still remains a solid basis. Study of dielectric permittivity as a function of temperature is, however, less well developed, particularly for solids. 

A similar analysis in terms of conformational dynamics can be performed as well for the interpretation of neutron scattering data in the picosecond time window159 and dielectric data.156 How do these findings then... 

Dielectric data came from a Tetrahedron dielectrometer operated at a 5°/min heating rate in air. 

Figure 4.2 is a plot of log(cr) versus log(viscosity) constructed from dielectric data of Figure 4.1 and measurements on a dynamic rheometer. The figure shows that at a viscosity less than 1 Pas (10P), a is proportioned to l/tj because the slope of log(n) versus log( j) is approximately — 1. The gel point of the polymerization reaction occurs at 90 min based on the crossover of G and G" measured at 40rad/s. This is very close to the time at which rj achieves 100 Pas, which is also often associated with gel. The region of gel marks the onset of a much more rapid change in viscosity than with a. This is undoubtedly due to the fact that as gel occurs the viscoelastic properties of the resin involve the cooperative motion of many chains, whereas the translational diffusion of the ions continues to involve motions over much smaller molecular dimensions. 

The dielectric constant is affected in different ways by a number of different mechanisms. Some of these mechanisms are interdependent and so it is difficult to ascertain their individual dependencies on fluorine incorporation. For instance, the increased hydrophobicity caused by fluorination decreases the ambient dielectric constant by elimination of water from the polymer, while the incorporation of fluorine also affects the intrinsic properties of the polymer irrespective of the moisture effect. Most published dielectric data were measured under ambient conditions and thus the distinction between these effects is lost. 

Density and dielectric data were obtained from the literature (23) or from experimental measurements. 

Ignoring the potential limitations of the dielectric data, we can evaluate the Debye-Onsager model for a number of apparently roughly Debye solvents, like propylene carbonate, the alkyl nitriles, the alkyl acetates, and other solvents. First of all, C( ) is often strongly nonmonoexponential, in contradiction to the theoretical prediction. Second, the observed average solvation time is often much different from xt. 

Dielectric data are from references found in Kahlow et al. [32]. 

Fuoss, R. M. Electrical properties of solids. VI. Dipole rotation in high polymers. J. Am. Chem. Soc. 63, 369—378 (1941). Note The dielectric data of Fig. 15 were taken from Document No. 1460, Amer. Documentation Inst. Library of Congress, Washington, D. C. 

The upper and lower curves for the dynamical mechanical data (110 Hz) correspond to the maxima in the resolvable loss curves. Dielectric data at 100 Hz. 

The present dielectric results show that for corresponding frequencies the temperatures of the y loss maxima for pure PPO and PS are extremely close. At 100 Hz, for example, these occur at —116° and —119°C, respectively. Further, the temperature but not intensity of the PPO y peak is somewhat sensitive to sample preparation and could be shifted upwards by 5°-10° by increasing the annealing temperature from 180° to 210 °C. Even though annealing was conducted in vacuo, this indicates the possibility of the y peaks arising at least in part from polar species introduced as a result of oxidation. As has already been observed, the dynamic mechanical y loss peaks are uniformly weak, but as far as can be observed, the peak temperatures again are consistent with the dielectric data. 

In order to get more detailed information about the motions associated with the p relaxation in PET and to understand the differences observed between mechanical and dielectric data, 13 C NMR was used, as well as 2H NMR on PET samples selectively deuterated either on the phenyl rings or on the ethylene glycol units [12]. Due to the higher frequency range corresponding to NMR experiments (105 Hz), the extrapolation of the dielectric results leads to the occurrence of the motions involved in the f3 relaxation around 25 °C, which is effectively observed. 

The dielectric y transition is observed for the xTyli-y copolyamides only. The transition temperature, determined at 105 Hz by extrapolating the dielectric data, is around - 60 °C. Such a temperature agrees with NMR observations of the motions of the C = O groups in an aliphatic environment (Fig. 86), as well as the motions of the lactam-12 methylene groups (Fig. 87). 

The mean activation energy for CMIM20 is 53 kj mol-1, significantly smaller than that obtained for PMMA (58 kj mol x). Such a trend agrees with the dielectric data (Sect. 8.2.2), in spite of the larger change observed experimentally. 

The parameters of Hamiltonians (1) and (2) are determined in our approach by pure theoretical way using different quantum chemical models and calculations unlike the traditional fitting the experimental thermodynamic and dielectric data. Our method of the many-pseudospin clusters [ 1,4] seems to be the most reliable way of determination. The latter are obtained in this case within the static approximation from the system of equations for a typical crystal fragment (cluster) for all possible proton distributions on H-bonds. The left-hand side of any equation expresses the cluster total energy in terms of Jy, while the right-hand side is determined by means of the quantum chemical calculation of this energy. 

As a general comment about the dynamic mechanical relaxational behavior of this polymer, the results are consistent with dielectric data [210] and with the fact that no glass transition phenomenon is observed, at least in the range of temperature studied. This is striking in an amorphous polymer. It is likely that the residual part of the molecule mechanically active above the temperature of the ft relaxation is only a small one, and this is the reason for the low loss observed in the a zone. 

C. M. Roth and A. M. Lenhoff, "Improved parametric representation of water dielectric data for Lifshitz theory calculations,"). Colloid Interface Sci., 179, 637-9 (1996), present another set of parameters for water. 

F. Buckley and A. A. Maryott, "Tables of dielectric data for pure liquids and dilute solutions." NBS Circular 589 (National Bureau of Standards, Gaithersburg, MD, 1958). 

Dispersion. Dispersion or London-van der Waals forces are ubiquitous. The most rigorous calculations of such forces are based on an analysis of the macroscopic electrodynamic properties of the interacting media. However, such a full description is exceptionally demanding both computationally and in terms of the physical property data required. For engineering applications there is a need to adopt a procedure for calculation which accurately represents the results of modem theory yet has more modest computational and data needs. An efficient approach is to use an effective Lifshitz-Hamaker constant for flat plates with a Hamaker geometric factor [9]. Effective Lifshitz-Hamaker constants may be calculated from readily available optical and dielectric data [10]. 

The dielectric spectroscopy study of conductive samples is very complicated because of the need to take into account the effect of dc-conductivity. The dc-conductivity c>o contributes, in the frequency domain, to the imaginary part of the complex dielectric permittivity in the form of additional function a0/(so ). The presence of dc-conductivity makes it difficult to analyze relaxation processes especially when the contribution of the conductivity is much greater than the amplitude of the process. The correct calculation of the dc-conductivity is important in terms of the subsequent analysis of the dielectric data. Its evaluation... 

It is known that in some cases the modulus representation M (oo) of dielectric data is more efficient for dc-conductivity analysis, since it changes the power law behavior of the dc-conductivity into a clearly defined peak [134]. However, there is no significant advantage of the modulus representation when the relaxation process peak overlaps the conductivity peak. Moreover, the shape and position of the relaxation peak will then depend on the conductivity. In such a situation, the real component of the modulus, containing the dc-conductivity as an integral part, does not help to distinguish between different relaxation processes. 

Software for dielectric data treatment and modeling in the frequency domain has been developed recently [132]. This program (MATFIT) was built around the software package MATLAB (Math Works Inc.), and it is available through an intuitive visual interface. Key features of the program include ... 

Usually, spin-lattice relaxation experiments are performed at one or a few magnetic fields. The spectral density can thus be determined at only a few Larmor frequencies, so that a detailed analysis of its temperature variation is not possible. Here, an analysis of the spin-spin relaxation times, T, can provide further information about the spectral density, since T2 1 S2(to = 0). Often, the Cole-Davidson distribution Gco(lnT2) [34] is chosen to interpolate the relaxation around the maximum. However, one has to keep in mind that the spectral density close to Tg contains additional contributions from secondary relaxations, such as the excess wing and/or the (i-process discussed in the following sections. In Section IV.C we give an example of a quantitative description of 7) (T) at T > 7 obtained by approximating the spectral density S2(co) using dielectric data. 

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