Complete Pockels tensor component analysis of ferroelectric copolymers of vinylidene fluoride and trifluoroethylene

Abstract

The first copolymer of vinylidene fluoride (VDF) and trifluoroethylene (TrFE) (P(VDF/TrFE)) was synthesized about 20 years ago [1–3]. At that time, the changes in the physical constants of P(VDF/TrFE) with temperature were measured, and it was recognized that P(VDF/TrFE) underwent a ferroelectric-to-paraelectric phase transition [4–6]. Broussoux and MiCheron [7] and Spector and Stein [8] conducted pioneering research on the birefringence and Pockels effects of ferroelectric polymers. However, no one-to-one correspondence was found between the macrooptical properties and crystal characteristics, because the ferroelectric polymer film has a complex, highly ordered structure with intermingled crystalline and amorphous regions [1–3]. Recently, a highly double-oriented film, which was described as a “single-crystalline” film (SCF) of P(VDF/TrFE) with a VDF/TrFE molar ratio of 75/25 was reported by Ohigashi et al. [9]. SCFs exhibit the following characteristics: single-crystal-like orientation, near-100% crystallinity and no lamellar structure in highly ordered structures. SCF does not have a singlecrystal structure, but has many more single-crystal-like features than any other solid polymeric material. Therefore, SCFs are suitable materials for investigating the characteristics of ferroelectric polymer crystals, which cannot be clarified conventionally due to the existence of higher-order structures. In this study, all Pockels tensor components of SCF of P(VDF/TrFE) with a molar ratio of 71/29 have been measured at room temperature under constant stress. We prepared SCFs following the previously described method [9]. The SCF sample used had a thickness of 60μm. Indium tin oxide (ITO) or Au was used for the electrode and was vapor-deposited onto the SCFs. For the SCFs used the orientation coefficient of the crystallographic c axis (molecular chain axis) of the P(VDF/TrFE) crystal was more than 0.996 along the drawn axis X1 and the crystallinity of the SCF was close to 100%, as determined by X-ray measurements. On application of the electric field parallel to the film thickness along the poling axis X3, the amount of remanent polarization was about 100 mC/m2. SCF thus had macro-symmetry with the point group C2v [3, 10, 11]. Hence, in a right-handed Cartesian coordinate system with X1, X2, and X3, the equation of the indicatrix, under constant stress T , is [10–13], ( 1 n1 + γ T 13 E3 ) X 1 + ( 1 n2 + γ T 23 E3 ) X 2