Polyvinylidene fluoride (PVDF) is a piezoelectric polymer that has been used in many applications including microphones, transducers, sensors and actuators. The electromechanical properties of PVDF are commonly defined by the constitutive equations of piezoelectricity. This paper presents experimental evidence that the assumptions underlying the theory of piezoelectricity have certain limitations in terms of representing adequately the electromechanical properties of PVDF. It is shown that PVDF tends to demonstrate time-dependent behavior in the form of viscoelastic creep and dielectric relaxation, and measurable energy losses under cyclic loading conditions. Moreover, the response of PVDF strongly depends on temperature and cyclic frequencies.

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With a numerical relaxation method and Landau-de Gennes theory, we have calculated the continuous dependence of structure and shape of tangentially anchored liquid crystal microdroplets on the parameters of anchoring strength W0 and radius r, at. fixed temperature. The structure is characterized by order parameter field S and director field n and the shape is described by a prolateness parameter x. For structure, we find that there exists an order/disorder first-order transition induced by r, a distortion/uniform first-order transition of S induced by w0, and a distortion/uniform continuous transition of n induced by both W0 and r. For shape, we find that the change of bulk free energy due to deviations from spherical shape can never compete with that of the surface energy. The surface interaction itself can induce prolateness, which becomes greater and approaches to a limiting value as the size gets smaller, and which is almost proportional to W0/ς None of the above predictions have been reported before. Our physical explanations show they are reasonable and not the outcomes of approximations made in the work.

The syntheses, crystal structures, and powder magnetic studies of several new quasi-planar bibridged CunX2n+22õ ligomers (n = 3, 4, 6, and 7; X = Cl or Br) are reported, based on the 1 -methylpyridinium (CftHsN'U and 1,2-dimethylpyridinium (C7H|0N)+ cations. These include (C7HioN)2Cu3Br8, (C6H8N)2Cu4C1io, (C7H|0N)2Cu6-Clu, and (C7H|0N)2Cu7Bri6. Crystallographic data: (C7HioN)2Cu3Br8, triclinic, space group PI, a = 7.947(2) A,b = 8.799(2) A, c = 9.840(2) A, a = 86.95(2)°, = 76.23(2)°, y = 71.54(2)°, V = 633.6(3) A3, Z=2,dx = 2.78 g/cm3, and R = 0.0483; (CeHgN^CmClio, monoclinic, space group P2\!n, a = 11.759(2) A, b = 9.056(2)A, c = 12.048(3) k,J = 106.21(2)°, V = 1232.1(5) A3, Z = 2, dx = 2.15 g/cm3, and 7? = 0.0321; (C7HI0N)2-Cu6Cl|4, triclinic, PI, a = 8.997(3) A, b = 9.288(3) A, c = 11.540(4)A, a = 80.53(2)°, /? = 67.82(2)°, y = 60.22(2)°, V = 714.7(4) A3, Z = 1, dx = 2.34 g/cm3, and R = 0.0363; (C6H8N)2Cu7Bri6, triclinic, PI, a = 7.237(2) k,b= 10.880(2) A, c = 12.880(2) A, a = 89.47(2)°, /? = 75.08(2)°, y = 79.48(2)°, V = 962.7(3) A3, Z = 1, dx = 3.35 g/cm3, and R = 0.0520.A common feature of the structures is the existence of oligomers containing quasi-planar symmetric bibridged finite chains of edge-sharing CuXa (X = halide) monomeric units.The n = 3 oligomers aggregate into chains through the formation of asymmetric bibridged linkages between terminal copper ions on adjacent trimers. In the n = 4 salt, the oligomers aggregate into stacks in which pairs of the copper ions extend their coordination sphere by forming a long, semicoordinate bond to a halide ion from a neighboring oligomer. For both the n = 3 and n = 4 salts, the pyridinium cations lie parallel to and directly above and below the anionic oligomers, separating the chains. In the n = 6 and n = 7 salts, the stacks formed in this manner interdigitate, forming two-dimensional slabs. The slabs are separated by the organic cations. The magnetic properties of compounds are dominated by antiferromagnetic intraoligomer interactions. Thus, the n = 4 and n = 6 salts depopulate into singlet ground states at low temperature. In contrast, the n = 3 and n -7oligomers have S = '/2 ground states. Expressions for the magnetic susceptibility of the n = 6 and n = 1 oligomers were obtained by diagonalization of a nearest neighbor Heisenberg Hamiltonian. The data were fit to these expressions, with inclusion of a mean field correction for interoligomer exchange. The intra-oligomer exchange coupling constants are

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