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

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)=−R ln[F(T,Q)]. From the Q dependence of the dynamical entropy, two characteristic lengths were obtained: the thermal diffusion length λ₁(T) related to the diffusion constant or, alternatively, to an effective vibrational motion and the localization length λ₂(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.