Structural and effective charge determination for planar-zigzag beta-poly(vinylidene fluoride)

We present the computation of structural and polarization for a ferroelectric polymer, specifically, the beta-phase of poly(vinylidene fluoride) or (-CH$_2$-CF$_2$-)$_n$. Two structures have been described in the literature: one containing an undistorted carbon backbone (planar-zigzag) and the other containing alternatively deflected -CF$_2$- groups. Previous studies have indicated that these deflections have no significant effect on calculated elastic properties. We employ density functional theory within the generalized gradient approximation to find relaxed atomic positions for the planar-zigzag structure. The relaxed structure is in good agreement with the X-ray studies. In addition, we have computed the spontaneous polarization and Born effective charges for this structure using a Berry-phase approach. The spontaneous polarization agrees well with results from other density functional theory studies. The effective charges are considerably smaller as compared to those in inorganic ferroelectric materials and show a small amount of charge transfer between the -CH$_2$- and -CF$_2$- moieties.