Brillouin scattering study of elastic properties in ferroelectric copolymer single-crystalline films

The in-plane elastic properties of as-grown random copolymer poly (vinylidene fluoride-trifluoroethylene) single-crystalline films with 75/25 molecular ratio have been studied by Brillouin light scattering up to approximately 140 degrees C from room temperature, covering the D6h-C2v ferroelectric phase transition at approximately 126 degrees C. The in-plane longitudinal acoustic (LA) phonons propagating parallel and perpendicular to the polymer chains were examined. In spite of the strongly first-order nature of the phase transition, both LA velocities exhibit only a broad down step in the temperature range between approximately 100 degrees C and approximately 130 degrees C, depending on the propagation direction, with increasing temperature. The LA phonon width perpendicular to the polymer chains increases with increasing temperature, and exhibits a broad maximum centered at approximately 120 degrees C. On the other hand, the LA phonon width along the polymer-chain axis is much wider than the width perpendicular to the polymer chains, and continues to increase even in the paraelectric phase. Treating the E(u) symmetry electric polarizations (Px,P(y)) of the D6h point group as the macroscopic order parameter, a Laudau free energy was developed to discuss the elastic properties. Using the free energy, we found that the elastic anomalies expected through the electrostrictive couplings between the order parameter and the elastic strains are strongly suppressed by the intrinsic electrical nature of the ferroelectric polymer. For both LA phonons, the temperature development of the phonon frequency and width can be reasonably reproduced by the Cole-Davidson relaxation model for the velocity dispersion with an exponent of betaCD=0.4. The relaxation time was found to obey the Arrhenius law tau=tau(0) exp(DeltaE/k(B)T) with DeltaE=0.55+/-0.01 eV and tau(0)=(4.0+/-0.6)x10(-18) s. At 24.0 degrees C in the ferroelectric phase, the in-plane phonon width anisotropy can be reasonably described by gammaB(straight theta)/2pi=0.18+0.72 sin4 straight theta for the LA phonon and gammaB(straight theta)/2pi=0.02+0.095 sin2 2straight theta for the transverse acoustic phonon, where the phonon propagation angle straight theta is measured from the perpendicular direction with respect to the polymer-chain axis. The straight theta dependence is strongly related to the one-dimensional freedom constrained in each copolymer chain.