Steady states and their stability of homogeneous, rigid, extended nematic polymers under imposed magnetic fields
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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.nematic liquid crystalkinetic theorypolymersmagnetic ﬁeldelectric ﬁeldbifurcationsteady statephase transitionpolaritystability
Communications in Mathematical Sciences, 5(4), 917-950, 2007
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