Time and Shear‐Rate Scaling Laws for Liquid Crystal Polymers

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Abstract
Recoverable strains were measured on isotropic and liquid crystalline solutions of PBLG [poly(γ‐benzyl‐L‐glutamate)] and HPC [hydroxypropylcellulose]. For isotropic PBLG, the strain recovery approaches the expected linear viscoelastic behavior in which the recovery is proportional to γ̇ 0 , as γ̇ 0 —the shear rate prior to recovery—becomes small. In the nonlinear regime for isotropic PBLG, the magnitude and shear‐rate dependence of the recoverable strain are qualitatively consistent with the Doi theory. In the liquid crystalline state, neither PBLG nor HPC show a regime of linear viscoelasticity even at strain rates low enough that the viscosity is nearly independent of γ̇ 0 . Instead, the total strain recovery is independent of γ̇ 0 , although the time over which this recovery occurs is inversely proportional to γ̇ 0 . Plots of recoverable strain versus the product of time t and γ̇ 0 for various values of γ̇ 0 nearly superpose. This scaling of recovery time with γ̇ 0 −1 is similar to a result obtained with PBLG by Moldenaers and Mewis and confirmed here in measurements of G′ and G″ after cessation of steady‐state shearing. Remarkably, not only do plots of recovered strain versus γ̇ 0 t for various γ̇ 0 superpose for each of the three liquid crystalline PBLG and HPC samples, but even curves for the three different materials come fairly close to superposing. Extending an idea of Marrucci, a simple phenomenological scaling equation for the evolution of domain size and domain distortion is proposed that can account for these phenomena.

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