Characteristic lengths measured by incoherent elastic and quasielastic neutron scattering within the thermal hysteresis loop in a ferroelectric copolymer

Abstract

A thermal hysteresis loop in the elastic incoherent scattering function $F(T,Q)$ of vinylidene fluoride and trifluoroethylene copolymer of molar fraction $p=0.70$ and crystallinity $c=0.61$ was observed by neutron scattering around the ferroelectric phase transition. We have performed three different measurements of $F(T,Q)$: incoherent elastic neutron scattering measurements using a backscattering spectrometer and incoherent quasielastic neutron scattering measurements with both a backscattering spectrometer and a time of flight spectrometer. The elastic measurements were analyzed using the concept of dynamical entropy defined by ${S}_{d}(T,Q)=\ensuremath{-}R\phantom{\rule{0.2em}{0ex}}\mathrm{ln}[F(T,Q)]$. From the $Q$ dependence of the dynamical entropy, two characteristic lengths were obtained: the thermal diffusion length ${\ensuremath{\lambda}}_{1}(T)$ related to the diffusion constant or, alternatively, to an effective vibrational motion and the localization length ${\ensuremath{\lambda}}_{2}(T)$ associated with the confined volume. The thermal hysteresis loop of the dynamical entropy is attributed to a change in the available volume associated with the structural phase transition, which is different in the heating and cooling scans.