Stability of Equilibria of Nematic Liquid Crystalline Polymers
NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF APPLIED MATHEMATICS
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We provide an analytical study on the stability of equilibria of rigid rodlike nematic liquid crystalline polymers LCPs governed by the Smoluchowski equation with the Maier-Saupe intermolecular potential. We simplify the expression of the free energy of an orientational distribution function of rodlike LCP molecules by properly selecting a coordinate system and then investigate its stability with respect to perturbations of orientational probability density. By computing the Hessian matrix explicitly, we are able to prove the hysteresis phenomenon of nematic LCPs when the normalized polymer concentration b is below a critical value b 6.7314863965, the only equilibrium state is isotropic and it is stable when b b 152, two anisotropic prolate equilibrium states occur together with a stable isotropic equilibrium state. Here the more aligned prolate state is stable whereas the less aligned prolate state is unstable. When b 152, there are three equilibrium states a stable prolate state, an unstable isotropic state and an unstable oblate state.
- Physical Chemistry
- Polymer Chemistry
- Electricity and Magnetism