Theory of linear viscoelasticity of cholesteric liquid crystals

The theory of linear viscoelasticity of rod-like cholesteric liquid crystal s subjected to small-amplitude oscillatory shear flow is formulated and app lied to the cholesteric helix along the flow, velocity gradient, and vortic ity directions. Expressions for the zero- and infinite-frequency viscositie s are derived and their ordering is predicted. Based on the classical order ing of the Miesowicz shear viscosities and anisotropies of torque coefficie nts, it is found that the largest (smallest) zero-frequency viscosity obtai ns with the helix along the flow (gradient) direction. In addition, the dif ference between the zero- and infinite-frequency viscosities is found to be sensitive to the helix orientation, such that it is largest (smallest) whe n the helix is along the flow (gradient) direction. The complex viscosity c orresponds to a viscoelastic material with a single relaxation time. The re laxation time depends on the Frank elastic constants involved in the deform ation, such that when the helix is along the vorticity it is twist dependen t, and splay-bend otherwise. The strength of the viscoelasticity is largest (smallest) when the helix is along the flow (gradient) direction. The hard -rod theory of Doi is used to confirm the predicted dependence of the stren gth of the viscoelastic response on the cholesteric helix orientation. (C) 2000 The Society of Rheology. [S0148-6055(00)00204-2].