Structure and piezoelectricity of poly(vinylidene fluoride)

A theoretical equation for calculating piezoelectric constants (dij) of polymer crystals has been derived and applied to poly(vinylidene fluoride) form 1. The calculated d 33 = -2.5 × 10−11 C/N, is in good agreement with the value of -2 × 10−11 C/N measured by the x-ray method. The calculated d 31, -0.025 × 10−11 C/N, is smaller by two digits than d 33, consistent with the experimental result that the x-ray (002) spot was not shifted nearly as much by the application of the electrostatic field as in the case of d 33 The macroscopic piezoelectric constants d M 31 and d M 33 have been estimated by using a model where the piezoelectric crystal form 1 is embedded in the nonpiezoelectric amorphous matrix; d M 31 = 0.6 × 10−11 C/N and d: = -1.4 × 10−11 C/N at room temperature and d M 31 = 6.8 × 10−13 C/N and d M 33 = -0.5 × 10−11 C/N below the glass transition temperature (Tg ), respectively. These are in the same order as the values observed both at room temperature and below Tg . In the present estimation the contribution of crystalline piezoelectric effect to the macroscopic piezoelectricity has been found to be negligible for d M 31 but significant for d M 33. d M 31 has been found to be controlled by the electric and mechanical heterogeneity between amorphous and crystalline regions.