Mechanisms of direct and converse piezoelectricity in ferroelectric polymers

Abstract

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 d₃₁ (∼54 pm/V) than the direct d₃₁ (∼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 d₃₁ 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 d₃₁ 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 d₃₁ 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 d₃₁, 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 d₃₁ became higher than the direct d₃₁. Combining both experimental and MD simulation results, the higher converse d₃₁ than direct d₃₁ for coP-52/48QSAP was understood qualitatively.