Mechanisms of direct and converse piezoelectricity in ferroelectric polymers

Within the linear regime of mechanical and electrical responses, it is commonly accepted that direct and converse piezoelectric coefficients should be the same. However, we observed a consistently higher converse d 31 (∼54 pm/V) than the direct d 31 (∼42 pC/N) for a quenched, stretched, annealed, and electrically poled poly(vinylidene fluoride- co -trifluorethylene) [P(VDF-TrFE)] 52/48 mol.% sample (abbreviated as coP-52/48QSAP). On the contrary, the direct and converse d 31 values were the same for coP-65/35QSAP and coP-55/45QSAP. Small-angle X-ray scattering results showed that coP-52/48QSAP had a higher amount of relaxor-like secondary crystals (SCs) in the oriented amorphous fraction (OAF) (SC OAF ) than coP-55/45QSAP and coP-65/35QSAP. To explain the experimental observation, we performed molecular dynamics (MD) simulation of the pure PVDF (without TrFE) to estimate direct and converse piezoelectricity for the PVDF OAF. Based on the MD simulation, the direct d 31 had a plateau value around 350 pC/N for the transverse (i.e., along the chain direction) strain up to 1 %, whereas the simulated converse d 31 could be lower (for electric field E < 0.8 MV/m), equal (for E = 0.8 MV/m), or higher (for E > 0.8 MV/m) than the direct d 31 , depending on the poling electric field. From the MD simulation, both mechano-electrostriction and electrostatic interaction were identified in the OAF as the driving force for enhanced piezoelectricity in ferroelectric PVDF. When ferroelectric domains were formed in the OAF by electric poling, the simulated converse d 31 became higher than the direct d 31 . Combining both experimental and MD simulation results, the higher converse d 31 than direct d 31 for coP-52/48QSAP was understood qualitatively. • Different direct and converse piezoelectric coefficients are observed for P(VDF-TrFE) 52/48 mol.% copolymer (coP-52/48QSAP). • A large amount of relaxor-like secondary crystals (SCs) in the oriented amorphous fraction (OAF, i.e., SC OAF ), is observed for coP-52/48QSAP. • Computer simulation indicates that ferroelectric domain formation in SC OAF is the reason for different direct and converse piezoelectricity.