Mathematical descriptions of nematic polymers in the monolayer limit Public Deposited

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  • March 21, 2019
Creator
  • Lee, Joohee
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • Monolayer films of liquid crystalline polymers (LCPs) are modeled with a two dimensional (2D) analog of the Doi-Hess (1981, 1976) kinetic model. In this dissertation, we focus on the analysis of the Doi-Hess Smoluchowski equation for the orientational distribution of LCPs, and an understanding of the distinctions which arise due to 2D confinement relative to results for full orientational space distributions. In Chapter 2, we study the mesoscopic model which approximates the Doi-Hess kinetic model, based on a second-moment closure. In this setting, we establish a more complete solution to the classical problem of how orientational degeneracy of quiescent nematic equilibria breaks in weak shear, and we determine the distinctions between two versus three dimensional sheared nematic-liquids. We give the first proof that limit cycles, known as tumbling orbits, must arise beyond the parameter boundary for the steady-unsteady transition. Finally, we show the shear-perturbed 2D phase diagram is significantly more robust to closure approximations than the 3D system. In Chapter 3, we solve a two dimensional Smoluchowski equation which is the extended Doi-Hess model for magnetic nano-rod dispersions in linear flows. We obtain closed-form representations of all steady state solutions in terms of Boltzmann distributions of the Smoluchowski equation. This method yields an exact, finite-dimensional reduction of the infinite-dimensional PDE, from which we construct bifurcation diagrams for all equilibria without external fields.
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  • In Copyright
Advisor
  • Forest, M. Gregory
Degree granting institution
  • University of North Carolina at Chapel Hill
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