Structure, phase transition and electric properties of poly(vinylidene fluoride-trifluoroethylene) copolymer studied with density functional theory

The geometry, energy, internal rotation, vibrational spectra, dipole moments and molecular polarizabilities of poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) of α- and β-chain models were studied with density functional theory at B3PW91/6-31G(d) level and compared with those of the poly(vinylidene fluoride) (PVDF) homopolymer. The chain length and the trifluoroethylene (TrFE) concentration were examined to discuss the copolymer chain stabilities, chain conformations and electric properties. The asymmetrical internal-rotation potential energy curve shows that the angles for the g and g′ conformations in the α-chain (tg and tg′) models are 53° and −70°, respectively, and the β-chain (ttt) conformation is a slightly distorted all-trans plane with dihedral angle at 177°. The energy differences, Eβ − Eα(g) and Eβ − Eα(g′), between the β- and the α-conformation are 2.1 and 7.8 kJ/mol, respectively. These values are smaller than that in PVDF (8.4 kJ/mol), suggesting that the β-conformation in the copolymer will be more stable than in PVDF. The energy barriers for β → α(g) and β → α(g′) transitions are 16.2 and 5.8 kJ/mol, respectively. The former is almost twice of the energy barrier in PVDF by 8.2 kJ/mol and the latter is slightly smaller (by 2.4 kJ/mol) than that in PVDF. The respective energy barriers for α(g) → β and α(g′) → β transitions are 18.3 and 13.6 kJ/mol compared with the value 16.3 kJ/mol in PVDF. The asymmetrical energy barriers may be one of the reasons for the copolymers with 0.5-0.6 (mole fraction) VDF exhibiting complicated phase transition behavior. The conformation of α-chain P(VDF-TrFE) exhibits from a helical (containing higher TrFE) to a nearly beeline (containing lower TrFE). This behavior is different from that in the PVDF and the nearly beeline conformation might be responsible for the increasing crystallizability. The helical might also be associated with the complicated phase transition behavior and the larger lattice strain in the P(VDF-TrFE)s with higher TrFE concentration. The energy difference per monomer unit between the β- and α-chain decreases with increasing TrFE content. The ideal β-chain is curved with a radius of about 30 Å, which is similar to that in PVDF. The chain curvature and the TrFE content will affect the dipole moment contribution per monomer. The chain length and TrFE content will not significantly affect the mean polarizability. The calculations indicated that there are some additional characteristic vibrational modes that may be used in identification of the α- or β-phase P(VDF-TrFE)s with different TrFE contents.