Calculations of the elastic compliance and piezoelectric constants of PVDF and P(VDF-TrFE) crystals using molecular mechanics

Abstract

The selection and/or design of projector materials for ultrasonic transducers requires knowledge of their elastic, piezoelectric, and dielectric properties. These properties can be measured directly; however, in order to minimize the fabrication and measurement of many different materials, it would be useful to compute these properties from the chemical composition and structure of the material. In molecular mechanics, a force field is used to describe short- and long-range interactions between atoms in a crystal. The most favored state occurs when the total energy, i.e., the sum of the interaction energies, is minimized. This paper presents calculated compliance and piezoelectric constants for β-phase crystals of polyvinylidene fluoride (PVDF) and its copolymer with trifluoroethylene, P(VDF/TrFE). The constants were derived by minimizing the energy of the unit cell while varying the stress. The model was validated using experimental and theoretical values for the properties of PVDF. The behavior of the compliance and piezoelectric constants of P(VDF/TrFE) are examined as a function of the molecular percentage of VDF. It was found that an optimum value for d33 exists between 55 and 65 mol % VDF. The implications of these results for the use of P(VDF/TrFE) copolymer in ultrasonic projectors will be discussed.