Fig. 2: Orientation dependent Brillouin light spectroscopy from monodomain LCE film.
a Polarized BLS spectra of the monodomain LCE film at different orientation angles ϕ and a constant wave vector, q = 0.0167 nm−1, represented by Lorentzian shapes (green lines). The high and low frequency peaks are assigned to the quasi-longitudinal (Q-L) and quasi-transverse (Q-T) phonons, respectively. b VV and HH spectra of the monodomain LCE film recorded at backscattering geometry with incident angle β = 0o. At this geometry, q is normal to the x2-x3 plane of the film and hence normal to the director n. c The sound velocity, c, computed from the frequencies of Q-L (gray symbols), Q-T (red symbols) and pure-transverse (P-T, blue symbols) modes, as a function of the orientation angle ϕ. The solid and open symbols indicate the data obtained from polarized (VV) and depolarized (VH) BLS spectra, respectively. The solid lines denote the representation of sound velocities by Christoffel’s equation (Eq. 1 and 2 in Methods section), whereas the dashed lines indicate the experimental values of the longitudinal (LA) and transverse (TA) sound velocities of polydomain LCE film. d The elastic properties (Young’s modulus E|| and E⊥, shear modulus G12 and G13, Poisson’s ratio ν31 and ν21) for monodomain (red and blue columns) and (Er, Gr and νr) for polydomain LCE (shaded columns). The black arrow points to the right axis of the Poisson’s ratio, ν. The inset schemes illustrate the physical meanings of Young’s, shear and bulk moduli. e The linewidth Γ of Q-L (gray symbols) and Q-L (red symbols) modes, obtained from polarized BLS spectra in a and Supplementary Fig. 2, as a function of the orientation angle ϕ. The solid lines represent the best fits based on the nonlinear functions in Supplementary Section 2. f The viscosity coefficients, η|| = η33 along and η⊥ = η11 normal to the director of monodomain, ηr of polydomain LCE, ordinary and extraordinary refractive index (no and ne) of monodomain LCE, and refractive index nr of polydomain LCE. The black arrows point to the left viscosity and to the right refractive index on the left and right axis, respectively.
