Viscoelastic nematodynamics

Nematic liquid crystals exhibit both crystallike and fluidlike features. In particular, the propagation of an acoustic wave shows an interesting occurrence of some of the solidlike features at the hydrodynamic level, namely, the frequency-dependent anisotropy of sound velocity and acoustic attenuation. The non-Newtonian behavior of nematics also emerges from the frequency-dependent viscosity coefficients. To account for these phenomena, we put forward a viscoelastic model of nematic liquid crystals, and we extend our previous theory to fully include the combined effects of compressibility, anisotropic elasticity, and dynamic relaxation, at any shear rate. The low-frequency limit agrees with the compressible Ericksen-Leslie theory, while at intermediate frequencies the model correctly captures the relaxation mechanisms underlying finite shear and bulk elastic moduli. We show that there are only four relaxation times allowed by the uniaxial symmetry.

Figure 1

Decomposition of the deformation gradient into its relaxing and effective parts.

Figure 2

Frequency dependence of the velocity anisotropy. The solid line represents our fit to the four relaxation times and the model parameters listed in Table 1. Experimental points are taken from [2].

Figure 3

Frequency dependence of the attenuation anisotropy. The solid line represents our theoretical estimate obtained with the model parameters listed in Table 1. Experimental points are taken from [19].

Figure 4

Temperature dependence of the Miesowicz coefficients for 5CB. Solid lines represent the theoretical estimates of ${\eta }_1$ and ${\eta }_2$; the dashed lines show ${\gamma }_1$ and $-{\gamma }_2$. Experimental values are extracted from [40]. The isotropic viscosity ${\alpha }_4$ is taken from [41]. The isotropic-nematic transition temperature is $T_{\mathrm{NI}}=35.5^{\circ }\mathrm{C}$.