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

Zheng, Xiaoyu; Forest, M. Gregory; Lipton, Robert; Zhou, Ruhai; Wang, Qi

doi:10.1002/adfm.200400200

Cited by 26 publications

(49 citation statements)

References 21 publications

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“…[32,30,21,29]). Molecular orientation features in different flow regimes are of extreme importance for materials design, as they impart anisotropic and nonuniform material properties [34,18,19]. Another issue typical of non-Newtonian fluids is flow feedback, where elastic stresses alter apparent viscosity.…”

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confidence: 99%

On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles

Cui¹,

Forest²,

Wang³

et al. 2006

SIAM J. Appl. Math.

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On weak plane Couette and Poiseuille flows of rigid rod and platelet ensembles (with Z. Cui, M.G. Forest and Q. Wang), SIAM J. Appl. Math. , 66 (4), 2006 Abstract. Films and molds of nematic polymer materials are notorious for heterogeneity in the orientational distribution of the rigid rod or platelet macromolecules. Predictive tools for structure length scales generated by shear-dominated processing are vitally important: both during processing because of flow feedback phenomena such as shear thinning or thickening, and postprocessing since gradients in the rod or platelet ensemble translate to nonuniform composite properties and to residual stresses in the material. These issues motivate our analysis of two prototypes for planar shear processing: drag-driven Couette and pressure-driven Poiseuille flows. Hydrodynamic theories for high aspect ratio rod and platelet macromolecules in viscous solvents are well developed, which we apply in this paper to model the coupling between short-range excluded volume interactions, anisotropic distortional elasticity (unequal elasticity constants), wall anchoring conditions, and hydrodynamics. The goal of this paper is to generalize scaling properties of steady flow molecular structures in slow Couette flows with equal elasticity constants [M. G. Forest et al., J. Rheol., 48 (2004), pp. 175-192] in several ways: to contrast isotropic and anisotropic elasticity; to compare Couette versus Poiseuille flow; and to consider dynamics and stability of these steady states within the asymptotic model equations.

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confidence: 99%

On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles

Cui¹,

Forest²,

Wang³

et al. 2006

SIAM J. Appl. Math.

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“…how large is the fraction of free particles, is described by an appropriate kinetic equation. This fraction defines the enhancement of electrical conductivity of the polymer matrix given by the theory of effective electrical conductivity of composites with spheroidal inclusions at low volume fractions [18]. Presently, for the sake of simplicity, it is assumed that the particles belonging to the non-percolating phase are oriented randomly.…”

Section: Discussionmentioning

confidence: 99%

“…The electric enhancement factor, X, in Equation (1) can be calculated for the case of strong contrast, i.e. when the particle conductivity is considerably larger than the polymer conductivity, according to the Equation (2) [18]: (2) Here # is the volume fraction of particles (here CNTs), f # is the volume fraction of free particles and L = ln r/r 2 is the depolarization factor defined by the aspect ratio of rigid conductive particle, r. Equation (2) has been obtained from a general expression for the effective electrical conductivity tensor (see Equation (12) in ref. [18]) of composites with rod-like conductive inclusions in a slightly conductive matrix.…”

Section: Model Description 31 Electrical Conductivitymentioning

confidence: 99%

“…The first approach considers composites in which anisometric conductive particles are randomly distributed in a slightly conducting matrix. Assuming that filler particles do not interact with each other, it is possible to derive the effective electrical conductivity tensor if the second order orientation tensor is known [18]. One of the advantages of this approach is that it naturally accounts for the time evolution of anisotropic conductivity if the time dependence of orientation tensor can be determined (for example by the Folgar-Tucker equation [19,20]).…”

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Superposition approach for description of electrical conductivity in sheared MWNT/polycarbonate melts

Saphiannikova¹,

Skipa²,

Lellinger³

et al. 2012

Express Polym. Lett.

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The theoretical description of electrical properties of polymer melts, filled with attractively interacting conductive particles, represents a great challenge. Such filler particles tend to build a network-like structure which is very fragile and can be easily broken in a shear flow with shear rates of about 1 s–1. In this study, measured shear-induced changes in electrical conductivity of polymer composites are described using a superposition approach, in which the filler particles are separated into a highly conductive percolating and low conductive non-percolating phases. The latter is represented by separated well-dispersed filler particles. It is assumed that these phases determine the effective electrical properties of composites through a type of mixing rule involving the phase volume fractions. The conductivity of the percolating phase is described with the help of classical percolation theory, while the conductivity of non-percolating phase is given by the matrix conductivity enhanced by the presence of separate filler particles. The percolation theory is coupled with a kinetic equation for a scalar structural parameter which describes the current state of filler network under particular flow conditions. The superposition approach is applied to transient shear experiments carried out on polycarbonate composites filled with multi-wall carbon nanotubes

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“…The studies presented here afford a glimpse into the delicate morphology coupling that is possible in confined flows of nematic (rigid rod or platelet) dispersions. The authors and collaborators have only begun to use homogenization theory of high-aspect-ratio spheroidal inclusions to transfer these flow-induced morphologies in the orientation distribution and stored anisotropic stresses to infer bulk nano-composite material properties [23,24,25]. The anisotropic property tensors associated with structures shown here provide a theoretical basis for understanding performance features of high performance nematic polymer materials.…”

Section: Hong Zhou and M Gregory Forestmentioning

confidence: 98%

Anchoring distortions coupled with plane Couette & Poiseuille flows of nematic polymers in viscous solvents: Morphology in molecular orientation, stress & flow

Zhou

Forest²

2005

DCDS-B

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Abstract. The aim of this work is to model and simulate processing-induced heterogeneity in rigid, rod-like nematic polymers in viscous solvents. We employ a mesoscopic orientation tensor model due to Doi, Marrucci and Greco which extends the small molecule, liquid crystal theory of Leslie-Ericksen-Frank to nematic polymers. The morphology has various physical realizations, all coupled through the model equations: the orientational distribution of the ensemble of rods, anisotropic viscoelastic stresses, and flow feedback. Previous studies in plane Couette & Poiseuille flow (with the exception of [7]) have focused on the coupling between hydrodynamics and the orientational distribution of rigid rod polymers with identical anchoring conditions at solid boundaries; without flow, the equilibrium structure is homogeneous. Here we explore steady structures that emerge with mismatch anchoring conditions at the walls, which couple an equilibrium elastic distortion across the channel, short and long range elasticity potentials, and hydrodynamics. In plane Couette (where moving plates drive the flow) and Poiseuille flow (where a pressure gradient drives the flow), in the regime of weak flow and strong distortional elasticity, asymptotic analysis yields closed-form steady solutions and scaling laws with identical wall conditions. We focus simulations in this regime to expose the effects due to wall anchoring conflicts, and illustrate the induced morphology of the orientational distribution, stored viscoelastic stresses, and non-Newtonian flow. A remarkably simple diagnostic emerges in this physical parameter regime, in which salient morphology features are controlled by the amplitude and sign of the difference in plate anchoring angles of the director field at the two plates.

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

Cited by 26 publications

References 21 publications

On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles

On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles

Superposition approach for description of electrical conductivity in sheared MWNT/polycarbonate melts

Anchoring distortions coupled with plane Couette & Poiseuille flows of nematic polymers in viscous solvents: Morphology in molecular orientation, stress & flow

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