Molecular Mechanism of the Piezoelectric Response in the β-Phase PVDF Crystals Interpreted by Periodic Boundary Conditions DFT Calculations

A theoretical approach based on Periodic Boundary Conditions (PBC) and a Linear Combination of Atomic Orbitals (LCAO) in the framework of the density functional theory (DFT) is used to investigate the molecular mechanism that rules the piezoelectric behavior of poly(vinylidene fluoride) (PVDF) polymer in the crystalline β-phase. We present several computational tests highlighting the peculiar electrostatic potential energy landscape the polymer chains feel when they change their orientation by a rigid rotation in the lattice cell. We demonstrate that a rotation of the permanent dipole through chain rotation has a rather low energy cost and leads to a lattice relaxation. This justifies the macroscopic strain observed when the material is subjected to an electric field. Moreover, we investigate the effect on the molecular geometry of the expansion of the lattice parameters in the (a, b) plane, proving that the rotation of the dipole can take place spontaneously under mechanical deformation. By band deconvolution of the IR and Raman spectra of a PVDF film with a high content of β-phase, we provide the experimental phonon wavenumbers and relative band intensities, which we compare against the predictions from DFT calculations. This analysis shows the reliability of the LCAO approach, as implemented in the CRYSTAL software, for calculating the vibrational spectra. Finally, we investigate how the IR/Raman spectra evolve as a function of inter-chain distance, moving towards the isolated chain limit and to the limit of a single crystal slab. The results show the relevance of the inter-molecular interactions on the vibrational dynamics and on the electro-optical features ruling the intensity pattern of the vibrational spectra.