Relaxed remanent polarization

Prrei+ positive state of relaxed remanent polarization, relaxed for one second in the Pr+ state. Equal to the positive state of remanent polarization of the quasi statically measured loop (see Section 3.3.4)... 

Pmax+ — Prrei—) change of polarization when the sample is switched from the negative state of the relaxed remanent polarization into the positive saturation -switching case... 

The third loop establishes the sample into the positive remanent polarization state without sampling data. The fourth loop now starts in the positive relaxed remanent polarization state (Prrei+), turns into the negative saturation (Pmax-), then crosses the polarization axis at zero volts excitation signal in the negative remanent polarization state (Pr ). Afterwards the sample is driven into the positive saturation (Pmax+) and ends up in the positive remanent polarization state (Pr+) when the voltage is zero again. Subsequently, the hysteresis loop is balanced respectively to the values P(+Vmax) and P(-Vmax). From the data of the second loop the parameters Vc-, Pr, Prrei- are determined and from the data of the fourth loop the parameters Vc+, Pr+, Prrei+ The closed hysteresis loop (continuous loop) can be calculated from the second half of the second loop and the second half of the fourth loop. 

Yamada et al. [9,10] demonstrated that the copolymers were ferroelectric over a wide range of molar composition and that, at room temperature, they could be poled with an electric field much more readily than the PVF2 homopolymer. The main points highlighting the ferroelectric character of these materials can be summarized as follows (a) At a certain temperature, that depends on the copolymer composition, they present a solid-solid crystal phase transition. The crystalline lattice spacings change steeply near the transition point, (b) The relationship between the electric susceptibility e and temperature fits well the Curie-Weiss equation, (c) The remanent polarization of the poled samples reduces to zero at the transition temperature (Curie temperature, Tc). (d) The volume fraction of ferroelectric crystals is directly proportional to the remanent polarization, (e) The critical behavior for the dielectric relaxation is observed at Tc. 

Relaxor ferroelectrics can be prepared either in polycrystalline form or as single crystals. They differ from the previously mentioned normal ferroelectrics in that they exhibit a broad phase transition from the paraelectric to ferroelectric state, a strong frequency dependence of the dielectric constant (i.e. dielectric relaxation) and a weak remanent polarization. Lead-based relaxor materials have complex disordered perovskite structures. 

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) ... 

Piezo- and pyroelectric coostanls and dielectric relaxation strengths VDCN copolymers are listed in TU>ie 1 [1438]. Piezoelectric constant seems to be dneedy pn>-poitional to residual polarization (F,), and further related to dielectric lelaxathm strength. Generally, piezoelectric constant in polymer electreta is proportional to the remanent polarization as related by following equatioo ... 

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