  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.

Materials Science