Dielectric polar amorphous polymer

As can be seen from Figure 1.2, the typical dielectric response of a polar amorphous polymer at constant temperature is characterized by a succession of descending steps in e and a corresponding series of " peaks. 

Figure 1.2 Typical dielectric response of a polar amorphous polymer. Frequency dependence of e and e" atconstanttemperature. Adapted with permission from Ref [3] 1996, Pergamon/Elsevier.

It is interesting to note that, in the case of amorphous polar polymers, the temperature dependence of e and e" reflects alterations in the physical state of the system. This is due to the fact mentioned above that the absorption of sub-THz radiation is based on the orientation polarization of polar groups, which is determined by their mobility. As a polymeric system is heated up from low to high temperatures, various physical stages related to the mobility of structural elements are surpassed. As demonstrated in Figure 1.4, the temperature dependence of the dielectric response at constant frequency, typical for a polar amorphous polymer, is characterized by a succession of ascending steps in e and a corresponding series of e" peaks. 

FIGURE 3.59 Variation of dielectric constant with temperature (schematic), (a) Crystalline material, (b) Amorphous polymer. A crystalline polymer containing polar group would behave as shown by dashed lines. 

The commercially important properties of Et>-Nb copolymers include low density, high transparency and low color, high moisture barrier and low moisture absorption, low optical distortion, excellent feature replication, resistance to polar solvents, high purity, shatter resistance, good biocompatibiUty, extremely low dielectric loss, high temperature capability, and compatibility with polyethylenes. The resins also have the low shrinkage and warpage typical of amorphous polymers. 

It can be concluded that remanent polarization and hence the piezoelectric response of a material are determined by Ae this makes it a practical criterion to use when designing piezoelectric amorphous polymers. The Dielectric relaxation strength Ae may be the result of either free or cooperative dipole motion. Dielectric theory yields a mathematical approach for examining the dielectric relaxation Ae due to free rotation of the dipoles. The equation incorporates Debye s work based on statistical mechanics, the Clausius-Mossotti equation, and the Onsager local field and neglects short-range interactions (43) ... 

This is the Langevin equation which describes the degree of polarization in a sample when an electric field, E, is applied at temperature T. Experimentally, a poling temperature in the vicinity of Tg is used to maximize dipole motion. The maximum electric field which may be applied, typically 100 MV/m, is determined by the dielectric breakdown strength of the polymer. For amorphous polymers p E / kT 1, which places these systems well within the linear region of the Langevin function. The following linear equation for the remanent polarization results when the Clausius Mossotti equation is used to relate the dielectric constant to the dipole moment 41). 

Designing an amorphous polymer with a large dielectric relaxation strength and hence piezoelectric response would require the ability to incorporate highly polar groups at high concentrations and cooperative dipole motion. 

Bauer S, Bauer-Gogonea S, Ploss B, Ploss B (2005) Nonlinear dielectric response of poled amorphous polymer dipole glasses. J Non-Cryst Sol 351 2759—2763 Bauer-Gogonea S, Bauer S, Gerhard(-MuHhaupt) R (1999) Monomorphs, bimorphs, and multimorphs from polar polymer electrets. Braz J Phys 29 306-317 Broadhurst MG, Davis GT (1984) Physical basis for piezoelectricity in PVDF. Fenoelectrics 60 3-13... 

We will now discuss expansion functions of the general pair correlation function which are controlled by orientation correlations, starting with the function which represents the relative orientation of vector quantities such as the dipolar moments of molecular groups. The spatial integral over this function is directly related to the Kirkwood correlation factor, g, well-known from the theory of dielectric relaxation. The Kirkwood correlation factor was found to be of the order of 1 to 3 for strongly polar fluids such as water, methanol, etc., and to be of the order of 1 or less than 1 for less polar fluids, including nematic fluids. Similar results were obtained for amorphous polymers such as poly(methyI methacrylate), where the correlation factor is less than 1... 

For investigating the transition spectra of amorphous polymers, TSC spectra have been recorded after polarization at various temperatures for two minutes. Before each TSC spectra, the sample was cooled down to 0 C under the electrical field (E = 1.6 x 10 V/m). After polarization at 120°C, only one TSC peak was recorded at 9TC (see Figure 1, dashed line). This is the dielectric manifestation of the glass transition, Tg. After polarization at 140°C, a new, additional TSC peak at... 

Relaxation functions for fractal random walks are fundamental in the kinetics of complex systems such as liquid crystals, amorphous semiconductors and polymers, glass forming liquids, and so on [73]. Relaxation in these systems may deviate considerably from the exponential (Debye) pattern. An important task in dielectric relaxation of complex systems is to extend [74,75] the Debye theory of relaxation of polar molecules to fractional dynamics, so that empirical decay functions for example, the stretched exponential of Williams and Watts [76] may be justified in terms of continuous-time random walks. 

Table 9.2. Experimental molar volumes V(exp) at 298K in cc/mole, predicted molar volumes V(pred) at 298K calculated by using equations 3.13 and 3.14, and experimental and predicted values of the molar polarization PLL in cc/mole, for 61 polymers. The calculations also utilize the experimental and fitted values of the dielectric constant, which are listed in Table 9.1. The V(exp) values listed for semicrystalline polymers are extrapolations to the amorphous limit. LL(exP) was not calculated for six polymers because V(exp) was not known.

Veres et al. have shown that the field-effect mobilities of amorphous PTAA [18] and other polymers are higher in contact with low-k dielectrics with 8 < 3 than dielectrics with higher k [19]. The latter usually contain polar functional groups randomly oriented near the active interface, which is believed to increase the energetic disorder at the interface beyond what naturally occurs due to the structural disorder in the organic semiconductor film resulting in a lowering of the field-effect... 

Orientational polarization is not a resonant process since the molecular dipoles have inertia. The response of the orientational polarization to a charge of the electric field is, therefore, always retarded. This process is called dielectric relaxation. The characteristic time constant of such a relaxation process—this is the time for reaching new equilibrium after changing the excitation—is called relaxation time (r). It is strongly temperature dependent, since it is closely related to the viscosity of the material. At room temperature, the relaxation times of the orientational polarization in crystals are of 10 -10 s. In amorphous solids and polymers, however, they can reach a few seconds or even hours, days, and years, depending on the temperature. 

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