Structure and Born effective charge determination for planar-zigzag β-poly(vinylidene fluoride) using density-functional theory

Two structures have been proposed in the literature for the β-phase of the ferroelectric polymer, poly(vinylidene fluoride) (β-PVDF); planar-zigzag and alternatively-deflected forms. Using density-functional theory, we have found the planar-zigzag structure is the preferred form and upon atomic relaxation, the alternatively-deflected structure attains a structure very similar to the planar-zigzag structure. In order to better understand the atomic origin of the ferroelectricity in β-PVDF, we have for the first time determined the dynamic Born effective charges (Z*) for the planar-zigzag structure using a Berry-phase approach. When compared to their nominal ionic values, the Z* show anomalous differences. Using these effective charges, we describe the polarity of the bonds with β-PVDF and show the extent of atomic-motion-induced (or dynamic) charge transfer within this ferroelectric material. In addition, our effective charges are different to previously-determined Mulliken charges, due to the inherent differences between static and dynamic charges.