Poly(vinylidene fluoride) under finite electric displacement fields: a removable $α\!\to\!δ$ reorientation barrier and a persistent first-order $δ\!\to\!β$ conformational change
The $α$, $δ$, and $β$ phases of PVDF are interconverted by electrical poling and mechanical drawing, yet the thermodynamics under a controlled electrical boundary condition has not been established from first principles. We evaluate the zero-temperature free energy at fixed electric displacement $D$ from van der Waals density-functional calculations along two constrained coordinates in a common 24-atom cell: a tilt of the gauche C--C bonds that maps antipolar $α$ onto polar $δ$ (cell change $<1\%$), and a backbone torsion that straightens TG$^+$TG$^-$ chains into all-trans $β$ (chain-repeat strain $10.6\%$). As $D$ increases from 0 to $0.30$~C\,m$^{-2}$, the lowest homogeneous free energy switches from $α$ to $δ$ at $D_{c1}=0.046$~C\,m$^{-2}$ and from $δ$ to $β$ at $D_{c2}=0.157$~C\,m$^{-2}$. At $T=0$ with domain-wall energy neglected, a $δ$ multidomain state lies $14.3$~meV per cell below homogeneous $α$ at every $D$. A $Γ$-point harmonic estimate suggests that vibrations reverse this ordering at room temperature. $δ$ and $β$ coexist for $0.11<D<0.21$~C\,m$^{-2}$ at $E^*=0.69$~GV\,m$^{-1}$, independent of the screening constant. The tilt barrier falls from $0.66$~eV per cell at $D=0$ to $17$~meV at $D=0.30$~C\,m$^{-2}$ (below $k_BT$ at $300$~K), while the torsion barrier remains $0.66$~eV at $D_{c2}$ and $0.34$~eV at $D=0.30$~C\,m$^{-2}$, so $δ\toβ$ stays first order. Much of the difference traces to the path effective charge ($0.28e$ for the tilt, $0.18e$ for the torsion). Scaling shows the tilt barrier would survive with the torsion charge; the smaller torsion charge accounts for about half the barrier it retains. The landscape accounts for why a field produces $δ$ and why $β$ is reached by drawing, and suggests that raising that charge could let a field alone produce $β$.