Effect of the Distribution of Free Volume on the β Relaxation in Poly (Vinylidene Fluoride)

Abstract

We extend the worldline description of vector and antisymmetric tensor fields coupled to gravity to the massive case. In particular, we derive a worldline path integral representation for the one-loop effective action of a massive antisymmetric tensor field of rank p (a massive p-form) whose dynamics is dictated by a standard Proca-like lagrangian coupled to a background metric. This effective action can be computed in a proper time expansion to obtain the corresponding Seeley-DeWitt coefficients a 0 , a 1 , a 2 . The worldline approach immediately shows that these coefficients are derived from the massless ones by the simple shift D → D + 1, where D is the spacetime dimension. Also, the worldline representation makes it simple to derive exact duality relations. Finally, we use such a representation to calculate the one-loop contribution to the graviton self-energy due to both massless and massive antisymmetric tensor fields of arbitrary rank, generalizing results already known for the massless spin 1 field (the photon).

Temperature dependence of positron-annihilation lifetime, free volume, conductivity, ionic mobility, and number of charge carriers in a polymer electrolyte polyethylene oxide complexed withNH4<

“…Further the concept of free volume 10 has been widely used over the last three decades for explaining some of the observed results in polymeric materials. 11 The observed temperature dependence of the electrical conductivity of ion-conducting polymers has also been explained 1 in terms of the free-volume theory. The study of thermally induced microstructural changes leading to free-volume changes in polyacrylonitrile 12 ͑PAN͒ or free-volume change associated with the amorphicity of polymer salt complexes, 13 have been reported using a positron annihilation technique.…”

Enhanced ferroelectric and pyroelectric properties of poly(vinylidene fluoride) with addition of graphene oxides

“…For both samples, there are internal friction (IF, Q À1 ) peaks around À50 C and 30 C corresponding to b and a relaxations in PVDF, respectively. 31,32 The b relaxation peak of PVDF-GO nanocomposite is broader than that of PVDF sample. Since the b peak is related with the Brownian motions of amorphous structures in PVDF, 33,34 it is suggested that the GO sheets could interact with the side chains or main chains of the amorphous phase of PVDF, increasing the viscosity of the amorphous PVDF structures.…”