We employ a hydrodynamic theory for chiral liquid crystal polymers (CLCPs) to investigate the linear viscoelastic
response of CLCPs to small amplitude oscillatory permeation shear flow, when the helix is oriented
along the velocity direction and the orientation distortion retain the original planar structure. To predict the
linear viscoelasticity, we model the system with Stokes hydrodynamic equations with viscous and nematic
as well as cholesteric stresses coupled with orientational dynamics driven by the flow. The key findings
are the following: in low frequency limit, both the loss modulus (G") and storage modulus (Gi) exhibit a
classical frequency ω dependence (G" ∝ ω, Gi ∝ ω2 ) but their magnitudes are of order O(q/Er1/2 ), where
2π/q defines the pitch of the chiral liquid crystal and Er is the Ericksen number. In high frequency limit,
Gi = O(q2 /Er) is independent of ω while Gi = O(1)ω is independent of q and Er.
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