Phase Equilibria in High Energy Density PVDF-Based Polymers

The phase diagrams of polyvinylidene fluoride (PVDF) and its copolymers with chlorotrifluoroethylene (CTFE) are investigated by first-principles calculations. Both PVDF and dilute P(VDF-CTFE) prefer nonpolar structures at zero field, but transform to a polar phase below the breakdown field. The critical field decreases with increasing CTFE content, facilitating the transformation. In disordered P(VDF-CTFE), a distribution of concentrations leads to a range of polar transitions, resulting in ultrahigh energy density. These results explain well experimental observations of very high-energy density in P(VDF-CTFE).

Figure 1

The unit cell of bulk PVDF in the (a) $\alpha$ and (b) $\beta$ phases. The carbon, fluorine, and hydrogen atoms are yellow, red, and white, respectively. The $\alpha$ phase is antipolar, since dipoles in the alternate chains cancel, while in the $\beta$ phase they are parallel to each other. The panels (c) and (d) show the trans-gauche arrangement in the $\alpha$ phase and all trans arrangement in the $\beta$ phase, respectively.

Figure 2

(a) Free energy as a function of the electric field for $\alpha$- and $\beta$-PVDF. $\alpha$-PVDF is lower in energy at zero field, but $\beta$-PVDF becomes the favored phase at $\sim 800\mathrm{MV}/\mathrm{m}$. (b) Electric displacement field $D$ versus applied electric field for $\alpha$- and $\beta$-PVDF. The vertical line at $\sim 800\mathrm{MV}/\mathrm{m}$ marks the transition from $\alpha$- to $\beta$-PVDF, when $D$ undergoes a discontinuous change.

Figure 3

Calculated thermodynamic properties P(VDF-CTFE) as functions of CTFE concentration: (a) difference between the total energies of $\alpha$ and $\beta$ phases, (b) polarization in the $\beta$ phase ($\alpha$ phase has zero polarization).

Figure 4

(a) Displacement field as a function of the electric field for ordered PVDF-CTFE $90/10\mathrm{mol}\%$ (dashed line) and for a Gaussian distribution of nanodomains in P(VDF-CTFE) centered at $90/10\mathrm{mol}\%$, with $\sigma =8\%$ (solid line). The blue-shaded area is the energy density for the disordered structure at $350\mathrm{MV}/\mathrm{m}$, whereas the red-shaded area is for the ordered structure. (b) The dielectric constant (dashed line) and the energy density (solid line) for $\sigma =8\%$. The diamonds are experimental results from Ref. 7. The dotted line is the energy density for $\sigma =5\%$. See text.