Forest and co-workers report on p. 2029 that nematic polymer nanocomposite (NPNC) films can be processed in steady shear flows, which generate complex orientational distributions of the nanorod inclusions. Distribution functions for a benchmark NPNC (11 vol.-% of 1 nm × 200 nm rods) are computed for a range of shear rates, yielding a bifurcation diagram with steady states at very low (logrolling) and high (flow-aligning) shear rates, and limit cycles (tumbling, wagging, kayaking) at intermediate shear rates. The orientational distributions dictate the effective conductivity tensor of the NPNC film, which is computed for all distribution functions, and extract the maximum principal conductivity enhancement (Emax, averaged in time for periodic distributions) relative to the matrix. The result is a “property bifurcation diagram” for NPNC films, which predicts an optimal shear rate that maximizes Emax.
Nematic, or liquid-crystalline, polymer nanocomposites (NPNCs) are composed of large aspect ratio, rod-like or platelet, rigid macromolecules in a matrix or solvent, which itself may be aqueous or polymeric. NPNCs are engineered for high-performance material applications, ranging across mechanical, electrical, piezoelectric, thermal, and barrier properties. The rods or platelets possess enormous property contrasts relative to the solvent, yet the composite properties are strongly affected by the orientational distribution of the nanophase. Nematic polymer film processing flows are shear-dominated, for which orientational distributions are well known to be highly sensitive to shear rate and volume fraction of the nematogens, with unsteady response being the most expected outcome at typical low shear rates and volume fractions. The focus of this article is a determination of the ranges of anisotropy and dynamic fluctuations in effective properties arising from orientational probability distribution functions generated by steady shear of NPNC monodomains. We combine numerical databases for sheared monodomain distributions[1,2] of thin rod or platelet dispersions together with homogenization theory for low-volume-fraction spheroidal inclusions to calculate effective conductivity tensors of steady and oscillatory sheared mesophases. We then extract maximum scalar conductivity enhancement and anisotropy for each type of sheared monodomain (flow-aligned, tumbling, kayaking, and chaotic).