It is shown that at weak alternating stress the relationship between the piezoelectrically induced charge and applied stress in ferroelectric ceramics has the same form as the Rayleigh law for magnetization versus magnetic field in ferromagnetic materials. Applicability of the Rayleigh law to the piezoelectric effect is demonstrated in detail for lead zirconate titanate (PZT) ceramics. Experimental results indicate that the dominant mechanism responsible for piezoelectric hysteresis and the dependence of the piezoelectric coefficient on the applied ac stress is the pinning of non-180 degrees domain walls. The dependence of the piezoelectric coefficient on the frequency of the driving stress is examined and is shown to be due to the frequency dispersion of both reversible and irreversible components of domain-wall displacement. Analysis of the stress dependence of the piezoelectric phase angle reveals piezoelectric hysteresis contributions that are not necessarily due to Rayleigh-type displacement of domain walls. Piezoelectric properties of a modified lead titanate composition that exhibits non-Rayleigh type behavior are examined and compared with the properties of PZT ceramics. (C) 1997 American Institute of Physics.

Stress and frequency dependence of the direct piezoelectric effect in ferroelectric ceramics

Piezoelectricity describes interconversion between electrical charge and mechanical strain. As expected for lattice ions displaced in an electric field, the proportionality constant is positive for all piezoelectric materials. The exceptions are poly(vinylidene fluoride) (PVDF) and its copolymers with trifluoroethylene (P(VDF-TrFE)), which exhibit a negative longitudinal piezoelectric coefficient. Reported explanations exclusively consider contraction with applied electric field of either the crystalline or the amorphous part of these semi-crystalline polymers. To distinguish between these conflicting interpretations, we have performed in situ dynamic X-ray diffraction measurements on P(VDF-TrFE) capacitors. We find that the piezoelectric effect is dominated by the change in lattice constant but, surprisingly, it cannot be accounted for by the polarization-biased electrostrictive contribution of the crystalline part alone. Our quantitative analysis shows that an additional contribution is operative, which we argue is due to an electromechanical coupling between the intermixed crystalline lamellae and amorphous regions. Our findings tie the counterintuitive negative piezoelectric response of PVDF and its copolymers to the dynamics of their composite microstructure.

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The negative piezoelectric effect of the ferroelectric polymer poly(vinylidene fluoride)

Keywords: hysteresis ; ferroelectric ; piezoelectric Reference LC-CHAPTER-2006-001 Record created on 2006-08-03, modified on 2017-05-10

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Hysteresis in Piezoelectric and Ferroelectric Materials

A miscible homopolymer–copolymer pair viz., poly(ethyl methacrylate) (PEMA)–poly(styrene-co-butyl acrylate) (SBA) is reported. The miscibility has been studied using differential scanning calorimetry. While 1 : 1 (w/w) blends with SBA containing 23 and 34 wt % styrene (ST) become miscible only above 225 and 185 °C respectively indicating existence of UCST, those with SBA containing 63 wt % ST is miscible at the lowest mixing temperature (i.e., Tg's) but become immiscible when heated at ca 250 °C indicating the existence of LCST. Miscibility for blends with SBA of still higher ST content could not be determined by this method because of the closeness of the Tg's of the components. The miscibility window at 230 °C refers to the two copolymer compositions of which one with the lower ST content is near the UCST, while the other with the higher ST content is near the LCST. Using these compositions and the mean field theory binary interaction parameters between the monomer residues have been calculated. The values are χST-BA = 0.087 and χEMA-BA = 0.013 at 230 °C. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 369–375, 2000

https://onlinelibrary.wiley.com/doi/pdf/10.1002/%28SICI%291099-0488%2820000201%2938%3A3%3C369%3A%3AAID-POLB3%3E3.0.CO%3B2-W

Miscibility of poly(styrene-co-butyl acrylate) with poly(ethyl methacrylate): Existence of both UCST and LCST

This article reviews the theoretical and experimental material accumulated in recent years on water-soluble and water-swelling polyampholytes of integral and pendant types. The theory of polyampholytes in comparison with experimental results, acid-base equilibrium, hydrodynamic, conformational, and the molecular and colloidal properties of amphoteric copolymers are considered. The responsibility of Coulomb forces, hydrogen bonds and hydrophobic interactions in the formation of compact structures is shown. Basic attention is paid to the specific structure and behaviour of polyampholytes at or near the isoelectric point (IEP), in particular to the “forcing out” phenomenon found at the IEP. The ability of polyampholytes to associate with various low- and high-molecular-weight substances as well as to be absorbed on dispersed particles is discussed. An attempt to show the closeness of structural organization or molecular recognition of synthetic polyampholytes to natural ones is undertaken.

Recent Advances in the Study of Synthetic Polyampholytes in Solutions

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Copolymer/copolymer blends: effect of sequence distribution on miscibility

La temperature critique est plus faible lorsque la difference des teneurs en chlore dans le melange diminue, ce qui indique une meilleure compatibilite

Upper critical solution temperatures in blends of chlorinated polyethylenes

The influence of electrical conductivity on the piezoelectricity of polymers was studied using a three‐phase model The model consists of a continuous nonpiezoelectric phase (phase 1) surrounding a spherical piezoelectric phase (phase 2), which is itself bounded by an electrically conductive shell (phase 3) The piezoelectric constants for the system can be expressed as d=d2KPKT and e=e2KPKS, where d2 and e2 are the piezoelectric strain and stress constants of phase 2, respectively, and KP is a function of the dielectric constants of phases 1, 2, and 3 KT and KS are expressed as functions of the elastic constant of each phase The piezoelectric constants d and e decrease with decreasing elastic constant of phase 3 and with increasing dielectric constant of phase 3 The three‐phase system shows a Maxwell–Wagner piezoelectric relaxation with a relaxation time given by τ=(2e1+e2+ηe3)/(2σ1+σ2+ησ3), where η=2δ/a In these expressions ei and σi are the dielectric constant and the electrical conductivity of pha

Piezoelectricity in three-phase systems: effect of the boundary phase

Miscibility in blends of chlorinated polyethylene (CPE) and chlorinated poly(vinyl chloride) (CPVC) has been determined as a function of polymer composition at 170°C. The phase state was determined by differential scanning calorimetry to observe glass transition behavior. Experimental results were analyzed using a first-order mean-field treatment for binary mixtures of random copolymers in which it was assumed that both polymers could be regarded as containing only two randomly disposed repeating units. The miscibility-immiscibility boundary was calculated to provide a best fit of the experimental results and fitted to a segment of an ellipse as predicted by theory. A major result was that mixtures of CPEs and CPVCs with identical chlorine content were found to be immiscible; this effect arises from differences in the microstructures of these polymers.

Hiroyoshi Ueda

Papers

Copolymer/copolymer blends: effect of sequence distribution on miscibility

Upper critical solution temperatures in blends of chlorinated polyethylenes

Piezoelectricity in three-phase systems: effect of the boundary phase

Miscibility in Blends of Chlorinated Polyethylene and Chlorinated Poly(vinyl chloride).

Miscibility in chlorinated polybutadiene/chlorinated polyethylene blends: effect of chain microstructure