Communications in Mathematical Sciences

Steady states and their stability of homogeneous, rigid, extended nematic polymers under imposed magnetic fields

Guanghua Ji, Qi Wang, Pingwen Zhang, Hongyun Wang, and Hong Zhou

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Abstract

We study the steady state phase behavior of homogeneous, rigid, extended (polar) nematic polymers or nematic dispersions under imposed magnetic (or electric fields), in which the intermolecular dipole-dipole and excluded volume interaction as well as external field contribution are accounted for. We completely characterize the phase diagram for polar nematics with and without permanent magnetic moments (or dipoles). For nematics without magnetic moments, the steady state is either purely nematic or polar depending on the strength of the excluded volume and the dipole-dipole interaction, in which the nonzero polarity vector (the first moment vector) is coaxial with the second moment tensor; thereby the steady state pdf is determined essentially by up to three scalar order parameters and a rotational group of SO(2) transverse to the imposed field direction. For nematics with permanent magnetic moments (or dipoles), the steady states are polar and the polarity vector is parallel to the external field direction when a necessary condition for parameters is met. When the condition is violated, only stable steady states have their polarity vector parallel to the external field direction and there are thermodynamically unstable nonparallel states. The stability of the steady states is inferred from the minimum of the free energy density.

Article information

Source
Commun. Math. Sci., Volume 5, Issue 4 (2007), 917-950.

Dates
First available in Project Euclid: 3 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.cms/1199377558

Mathematical Reviews number (MathSciNet)
MR2375054

Zentralblatt MATH identifier
1152.82005

Subjects
Primary: 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 70K50: Bifurcations and instability 82B26: Phase transitions (general) 82B27: Critical phenomena

Keywords
nematic liquid crystal kinetic theory polymers magnetic field electric field bifurcation steady state phase transition polarity stability

Citation

Ji, Guanghua; Wang, Qi; Zhang, Pingwen; Wang, Hongyun; Zhou, Hong. Steady states and their stability of homogeneous, rigid, extended nematic polymers under imposed magnetic fields. Commun. Math. Sci. 5 (2007), no. 4, 917--950. https://projecteuclid.org/euclid.cms/1199377558


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