Commun. Comput. Phys., 7 (2010), pp. 383-402.


A Nonhomogeneous Kinetic Model of Liquid Crystal Polymers and Its Thermodynamic Closure Approximation

Haijun Yu 1*, Guanghua Ji 2, Pingwen Zhang 1

1 LMAM, School of Mathematical Sciences and CCSE, Peking University, Beijing 100871, China.
2 Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China.

Received 12 February 2009; Accepted (in revised version) 12 June 2009
Available online 24 August 2009
doi:10.4208/cicp.2009.09.202

Abstract

A general nonhomogeneous extension of the Doi's kinetic theory with translational diffusion and nonlocal potential is proposed to describe the microstructures and defect dynamics of Liquid Crystal Polymer (LCP) solutions. The long-range elasticity of polymer molecules is depicted by a kernel type potential, from which one can derive the well-known Marrucci-Greco potential with weak spatial distortion assumption. Applying quasi-equilibrium closure approximation, we get a second-order moment model for isotropic long-range elasticity, and this reduced moment model maintains the energy dissipation. Implemented by the invariant-based fitting method, the moment model is a decent tool for numerical simulations of defect dynamics and texture evolution in LCP solutions. The numerical results of in-plane rotational case show that the reduced second-order moment model qualitatively predicts complicated nonhomogeneous director dynamics under moderate nematic potential strength, and the translational diffusion plays an important role in defect dynamics.


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PACS: 61.30.Cz, 61.30.Dk, 61.30.Vx
Key words: LCP, kinetic theory, energy dissipation, closure approximation, defect dynamics.

*Corresponding author.
Email: yuhaijun@gmail.com (H. Yu), ghji@bnu.edu.cn (G. Ji), pzhang@pku.edu.cn (P. Zhang)
 

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