Monodomain response of arbitrary aspect ratio nematic polymers in general linear planar flows

Forest, M. Gregory; Wang, Qi; Zhou, Ruhai; Choate, Eric P.

doi:10.1016/j.jnnfm.2004.02.004

Cited by 14 publications

(19 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…43 It is worthwhile to point out that even though the rigor of multi-scale asymptotic analysis has not yet been established, the method itself has become a powerful mathematical tool in recent applications. For example, Choate and Forest 12 applied it to study the viscoelastic response of nematic polymers to small amplitude oscillatory shear; Vicente Alonso et al 102 used it to investigate the nonlinear dynamics of a nematic liquid crystal in the presence of a plane Couette flow using a Landaude Gennes model; Chillingworth et al 11 employed it to describe the geometry and dynamics of nematic liquid crystal in a uniform shear flow.…”

Section: Effects Of Flow Fieldsmentioning

confidence: 99%

Mathematical Studies and Simulations of Nematic Liquid Crystal Polymers and Nanocomposites

Zhou

Forest²,

Wang

2010

Jnl of Comp & Theo Nano

View full text Add to dashboard Cite

Nematic liquid crystal polymers and nanocomposites have wide-ranging applications in modern technology including display devices, ultra-fast switches, high strength fibers, and materials with enhanced multi-functional properties including thermal, dielectric, electrical, and barrier properties. In this review article we provide an overview of selected mathematical issues and numerical simulations of nematic liquid crystal polymers and rigid rod nanocomposites. Some open questions will be addressed.

show abstract

Section: Effects Of Flow Fieldsmentioning

confidence: 99%

Mathematical Studies and Simulations of Nematic Liquid Crystal Polymers and Nanocomposites

Zhou

Forest²,

Wang

2010

Jnl of Comp & Theo Nano

View full text Add to dashboard Cite

show abstract

“…Later they extended the study in Ref. 36 to track the boundaries of the chaotic region of kinetic theory due to finite molecule aspect ratio and the addition of straining flow in the plane of shear. 25 It was predicted that sheared chaotic response persists up to a threshold straining flow strength and minimum aspect ratio, beyond which chaotic behavior is arrested.…”

Section: Introductionmentioning

confidence: 95%

“…Recently Forest's group did extensive research on various solutions of the 3D Smoluchowski equations under different kinds of conditions. 19,[22][23][24][25][26][27][28]36,37 In particular, in Ref. 36 they formulated a monodomain correspondence principle of kinetic and mesoscopic theory for arbitrary aspect ratio nematic polymers in general linear planar flow.…”

Section: Introductionmentioning

confidence: 99%

“…19,[22][23][24][25][26][27][28]36,37 In particular, in Ref. 36 they formulated a monodomain correspondence principle of kinetic and mesoscopic theory for arbitrary aspect ratio nematic polymers in general linear planar flow. From the principle, the monodomain response of nematic polymers for all linear flows in the plane of shear is identical to the mon-odomain response of another nematic polymer liquid with a renormalized molecular aspect ratio parameter in pure simple shear flow.…”

Section: Introductionmentioning

confidence: 99%

“…25 It was predicted that sheared chaotic response persists up to a threshold straining flow strength and minimum aspect ratio, beyond which chaotic behavior is arrested. Both 25,36 gave predictions on how steady and unsteady attractors are modified and eventually lost or persist in the presence of a variable extensional flow contribution.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Elongational perturbations on nematic liquid crystal polymers under a weak shear

Zhou

Wang

2007

Physics of Fluids

View full text Add to dashboard Cite

The two-dimensional Smoluchowski equation is employed to study the effect of elongational perturbations on nematic liquid crystal polymers under a weak shear. We use the multiscale asymptotic analysis to show that ͑1͒ when the elongational perturbation is small relative to the weak shear, the orientational probability density function ͑pdf͒ tumbles periodically only in an intermediate range of polymer concentration; outside this intermediate range ͑i.e., for very small and very large polymer concentration͒ the orientational pdf converges to a steady state and there is no tumbling. ͑2͒ When the elongational perturbation is about 20% of the shear rate or larger, the intermediate range of tumbling disappears and the orientational pdf always converges to a steady state regardless of the polymer concentration. Our theoretical predictions are consistent with various earlier results based on the Leslie-Ericksen theory ͓C.

show abstract

Exact Scaling Laws for Electrical Conductivity Properties of Nematic Polymer Nanocomposite Monodomains

Zheng¹,

Forest²,

Lipton³

et al. 2005

Adv. Funct. Mater.

View full text Add to dashboard Cite

The purpose of this paper is to connect two critical aspects of nanocomposite materials engineering: the knowledge of the orientational distribution of quiescent or flowing anisotropic macromolecules, and homogenization theory of composites with spheroidal inclusions at low volume fractions. The nano‐elements considered herein are derived from the class of high‐aspect‐ratio nematic polymers, either rod‐like or platelet spheroids. By combining the two features, we derive the effective electrical conductivity tensor in closed form. Scaling properties of enhanced conductivity versus volume fraction and weak shear rate become explicit. The most dramatic effect is that the effective conductivity tensor inherits hysteresis, bi‐stability, and discontinuous jumps from the isotropic–nematic first‐order phase transition. These formulas reveal finer estimates that depend on a competition between two inherently extreme parameters in nematic polymer nanocomposites: the molecular aspect ratio and the conductivity ratio of the inclusions and matrix. Herein, we confine our attention to steady monodomain orientational distributions at rest and in weak shear flows, which serve as benchmarks and guides for future extensions and numerical approaches.

show abstract

Monodomain response of arbitrary aspect ratio nematic polymers in general linear planar flows

Cited by 14 publications

References 25 publications

Mathematical Studies and Simulations of Nematic Liquid Crystal Polymers and Nanocomposites

Mathematical Studies and Simulations of Nematic Liquid Crystal Polymers and Nanocomposites

Elongational perturbations on nematic liquid crystal polymers under a weak shear

Exact Scaling Laws for Electrical Conductivity Properties of Nematic Polymer Nanocomposite Monodomains

Contact Info

Product

Resources

About