Commun. Comput. Phys., 7 (2010), pp. 250-282.


A 2-D Kinetic Theory for Flows of Monodomain Polymer-Rod Nanocomposites

M. Gregory Forest 1, Qingqing Liao 2, Qi Wang 3*

1 Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA.
2 Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA.
3 Department of Mathematics and NanoCenter at USC, University of South Carolina, Columbia, SC 29208, USA.

Received 5 September 2008; Accepted (in revised version) 7 May 2009
Available online 24 August 2009
doi:10.4208/cicp.2009.08.204

Abstract

We merge classical kinetic theories [M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, 1986] for viscous dispersions of rigid rods, extended to semi-flexibility [A. R. Khokhlov and A. N. Semenov, Macromolecules, 17 (1984), pp. 2678-2685], and for Rouse flexible chains to model the hydrodynamics of polymer nano-rod composites (PNCs). A mean-field potential for the polymer-rod interface provides the key coupling between the two phases. We restrict this first study to two-dimensional conformational space. We solve the coupled set of Smoluchowski equations for three benchmark experiments. First we explore how rod semi-flexibility and the polymer-rod interface alter the Onsager equilibrium phase diagram. Then we determine monodomain phase behavior of PNCs for imposed simple elongation and shear, respectively. These results inform the effects that each phase has on the other as parametric strengths of the interactions are varied in the context of the most basic rheological experiments.

AMS subject classifications: 82D60, 82C31, 76T20, 76A05

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Key words: Kinetic theory, polymer, nanorod, nanocomposites, monodomains, equilibrium, elongation, shear.

*Corresponding author.
Email: forest@amath.unc.edu (M. G. Forest), liaoq@mailbox.sc.edu (Q.-Q. Liao), qwang@math.sc.edu (Q. Wang)
 

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