Parallel systems, electrical properties polymers

If the medium is isotropic, is a scalar, i.e. the relationship between E and Plinear IS independent of the direction of the field vector E and the polarization is parallel to E. Many polymers possess amorphous structures and their optical properties are isotropic. However, electro-optic polymeric systems containing polar moieties can be made anisotropic by orienting these moieties, for example, by electric field-induced or optical alignment. In this case, the polarization is not necessarily parallel to the direction of E and its component in one direction is related to the field components in all three directions ... 

Typical nonidealities such as polydispersity in filler size and conductivity, filler waviness and entanglements, and impurities impact the measured electrical properties of polymer nanocomposites. Most analytical and simulation studies of these nonidealities have been conducted for highly simplified systems, so that the extent to which these factors can modify composite properties, particularly within the context of more dominant factors such as filler dispersion and network stmcture, is unclear. To clarify the importance of these effects, theoretical analysis or modeling of more complex systems is required. Conducting parallel experiments in model systems can enhance the efficacy of such studies. 

Piezoelectricity links the fields of electricity and acoustics. Piezoelectric materials are key components in acoustic transducers such as microphones, loudspeakers, transmitters, burglar alarms and submarine detectors. The Curie brothers [7] in 1880 first observed the phenomenon in quartz crystals. Langevin [8] in 1916 first reported the application of piezoelectrics to acoustics. He used piezoelectric quartz crystals in an ultrasonic sending and detection system - a forerunner to present day sonar systems. Subsequently, other materials with piezoelectric properties were discovered. These included the crystal Rochelle salt [9], the ceramics lead barium titanate/zirconate (pzt) and barium titanate [10] and the polymer poly(vinylidene fluoride) [11]. Other polymers such as nylon 11 [12], poly(vinyl chloride) [13] and poly (vinyl fluoride) [14] exhibit piezoelectric behavior, but to a much smaller extent. Strain constants characterize the piezoelectric response. These relate a vector quantity, the electrical field, to a tensor quantity, the mechanical stress (or strain). In this convention, the film orientation direction is denoted by 1, the width by 2 and the thickness by 3. Thus, the piezoelectric strain constant dl3 refers to a polymer film held in the orientation direction with the electrical field applied parallel to the thickness or 3 direction. The requirements for observing piezoelectricity in materials are a non-symmetric unit cell and a net dipole movement in the structure. There are 32-point groups, but only 30 of these have non-symmetric unit cells and are therefore capable of exhibiting piezoelectricity. Further, only 10 out of these twenty point groups exhibit both piezoelectricity and pyroelectricity. The piezoelectric strain constant, d, is related to the piezoelectric stress coefficient, g, by... 

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