Collective polarization effects in $\beta$-polyvinylidene fluoride and its copolymers with tri- and tetrafluoroethylene

The polar properties of the $\beta$ phase of polyvinylidene fluoride (PVDF) and its copolymers with tri- and tetrafluoroethylene are investigated theoretically at different VDF-to-copolymer ratios. The calculations show that polarization in such polymers is described by cooperative, quantum-mechanical interactions between polymer chains, which cannot be viewed as a superposition of rigid dipoles. For $\beta$-PVDF, the monomer dipole moment is increased by 50% (from $2\text{to}3\mathrm{D}$) as the isolated chains are brought together to form a crystal. In PVDF crystals containing copolymers, we observe a weakly parabolic dependence of monomer dipole moments on copolymer concentration.

Figure 1

(Color online) The structure of the crystalline $\beta$ phase of PVDF. The polar-covalent nature of the $\mathrm{F}\mathrm{C}$ and $\mathrm{C}\mathrm{H}$ bonds leads to polarization in the VDF monomer, directed perpendicular to the carbon backbone; ${\mathit{d}}_{\mathrm{F}\mathrm{C}}$ and ${\mathit{d}}_{\mathrm{C}\mathrm{H}}$ are the bond-dipole moments. The unit cell coordinate system is shown at the bottom with “2” and “3” being the backbone and polarization directions, respectively.

Figure 2

(Color online) Chain models for PVDF and copolymers. (a) PVDF chain in all-trans conformation. (b) Poly-TrFE chain with alternating hydrogens. (c) Poly-TeFE chain.

Figure 3

(Color online) MLWFs and their charge centers computed for an isolated infinite $\beta$-PVDF chain. (a) Diamonds mark the positions of the MLWF charge centers on the chain. (b)–(d) Typical MLWFs localized on carbon-carbon, carbon-fluorine, and carbon-hydrogen bonds, respectively.

Figure 4

(Color online) Variation of the dipole moment $D_3$ in VDF, TrFE, and TeFE monomer units in finite chains with increasing numbers of units. Dipole moments obtained by averaging over all $n$ monomers in a chain are shown as circles, while diamonds represent the average moments when the end units (i.e., those in direct contact with terminating hydrogens) are excluded. The dipole moments of the monomers in infinite chains are shown on the right.

Figure 5

(Color online) Structural unit dipole moment components $D_1$ (squares), $D_2$ (circles), and $D_3$ (diamonds) in infinite isolated $\beta$-PVDF chains where one of the units (number 5 in this figure) was substituted by TrFE (top panel), TeFE (middle panel), and inverted VDF (bottom panel). Horizontal lines at $2\mathrm{D}$ in each panel mark the $D_3$ value of the VDF unit in a $\beta$-PVDF chain with no substitutions.

Figure 6

(Color online) Average $D_3$ component of the VDF unit dipole moment in an infinite $\beta$-PVDF chain as the chains are brought together to form a crystal. See text.

Figure 7

(Color online) Evolution of an elementary two-unit orthorhombic cell lattice constants with changing copolymer concentration. Circles and diamonds represent the P(VDF-TrFE) and P(VDF-TeFE) families, respectively.

Figure 8

(Color online) Evolution of the average dihedral angle between monomers in the P(VDF-TrFE) (circles) and P(VDF-TeFE) (diamonds) families with changing copolymer concentration.

Figure 9

(Color online) Changes in the values of average dipole moments of VDF, TrFE, and TeFE structural units in the crystalline P(VDF-TrFE) and P(VDF-TeFE) models with increasing copolymer concentration. The limiting values of unit dipole moments in the isolated infinite $\beta$-PVDF, PTrFE, and PTeFE chains are shown for comparison.

Figure 10

(Color online) Changes in total polarization in the crystalline P(VDF-TrFE) and P(VDF-TeFE) models with increasing copolymer concentration. The dashed lines represent the fitted curves of Eqs. (6). Extrapolations of experimental polarizations to 100% crystallinity are shown for comparison: (a) $\beta$-PVDF film of Ref. 15, (b) polycrystalline 75-25% P(VDF-TrFE) film of Refs. 20, 21, (c) 73-27% P(VDF-TrFE) sample of Ref. 18, (d) 70-30% P(VDF-TrFE) film of Ref. 41, and (e) 80-20% P(VDF-TeFE) sample of Ref. 19. See text for discussion.