Dielectric relaxation dynamics of high-temperature piezoelectric polyimide copolymers

Polyimide co-polymers have been prepared based on different diamines as co-monomers: a diamine without CN groups and a novel synthesized diamine with two CN groups prepared by polycondensation reaction followed by thermal cyclodehydration. Dielectric spectroscopy measurements were performed and the dielectric complex function, ac conductivity and electric modulus of the co-polymers were investigated as a function of CN group content in the frequency range from 0.1 Hz to 107 Hz at temperatures from 25 to 260 °C. For all samples and temperatures above 150ºC, the dielectric constant increases with increasing temperature due to increaseing conductivity. The α-relaxation is just detected for the sample without CN groups, being this relaxation overlapped by the electrical conductivity contributions in the remaining samples. For the copolymer samples and the polymer with CN groups an important Maxwell-Wagner-Sillars contribution is detected. The mechanisms responsible for the dielectric relaxation, conduction process and electric modulus response have been discussed as a function of the CN groups content present in the samples.

Vanishing spin stiffness in the spin-1/2 Heisenberg chain for any nonzero temperature

Whether at the zero spin density m = 0 and finite temperatures T > 0 the spin stiffness of the spin-1/2 XXX chain is finite or vanishes remains an unsolved and controversial issue, as different approaches yield contradictory results. Here we explicitly compute the stiffness at m = 0 and find strong evidence that it vanishes. In particular, we derive an upper bound on the stiffness within a canonical ensemble at any fixed value of spin density m that is proportional to m2L in the thermodynamic limit of chain length L → ∞, for any finite, nonzero temperature, which implies the absence of ballistic transport for T > 0 for m = 0. Although our method relies in part on the thermodynamic Bethe ansatz (TBA), it does not evaluate the stiffness through the second derivative of the TBA energy eigenvalues relative to a uniform vector potential. Moreover, we provide strong evidence that in the thermodynamic limit the upper bounds on the spin current and stiffness used in our derivation remain valid under string deviations. Our results also provide strong evidence that in the thermodynamic limit the TBA method used by X. Zotos [Phys. Rev. Lett. 82, 1764 (1999)] leads to the exact stiffness values at finite temperature T > 0 for models whose stiffness is finite at T = 0, similar to the spin stiffness of the spin-1/2 Heisenberg chain but unlike the charge stiffness of the half-filled 1D Hubbard model.