Thermal hysteresis loop in the elastic incoherent scattering function of vinylidene fluoride and trifluoroethylene ferroelectric copolymers

Abstract

A thermal hysteresis loop was measured in the normalized elastic incoherent scattering function $F(T,Q)$ of vinylidene fluoride and trifluoroethylene copolymers during a heating cooling scan across the ferroelectric phase transition. Three vinylidene fluoride copolymers with molar fractions $p=0.60$, 0.70, and 0.75 were studied. In addition, for the molar fraction 0.70 three crystallinities $c=0.35$, 0.61, and 0.70 were investigated. The hysteresis loop was interpreted in terms of a dynamical entropy defined by ${S}_{d}(T,Q)=\ensuremath{-}R\phantom{\rule{0.2em}{0ex}}\mathrm{ln}[F(T,Q)]$ that can be factorized as a temperature-dependent entropy factor and a $Q$ dependent form factor with two characteristic lengths ${\ensuremath{\lambda}}_{1}$ the control parameter of the entropy and ${\ensuremath{\lambda}}_{2}$ the control parameter of the confined volume. The thermal hysteresis loop observed in the entropy is attributed to the change in the confined volume of the dynamic relaxation. The dynamical entropy could be a useful concept for the analysis of the complex dynamic of macromolecular systems such as polymers.