Abstract
We analyze the interaction with uniform external fields of nematic liquid crystals within a recent generalized free energy posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i.e., uniform heliconical structures, which correspond to the so-called twist-bend nematic phase and we also study the transition between this phase and the standard uniform nematic one. The twist-bend phase is further reproduced by three-dimensional simulations. Moreover, we find liquid crystal configurations, which closely resemble some novel, experimentally detected, structures called Skyrmion tubes. Skyrmion tubes are characterized by a localized cylindrically symmetric pattern surrounded by either twist-bend or uniform nematic phase. We study the equilibrium differential equations and find numerical solutions and analytical approximations.
Highlights
The achiral nematic N phase is surely the most common state for thermotropic liquid crystals
In this paper we studied the interaction of external uniform magnetic fields with achiral liquid crystals according to a generalized fourth-order elasticity theory recently put forward in Ref. [19]
This theory is encoded in the free-energy density (10), which is parameterized by six elastic constants: k1, k2, k3 associated with the quadratic terms in the Frank free energy and k4, k5, k6 related to fourth-order contributions
Summary
The achiral nematic N phase is surely the most common state for thermotropic liquid crystals. The author focused on an achiral scenario where the NTB phase has been experimentally identified and deliberately built his generalized elastic free energy with the symmetry of the intended heliconical ground state, i.e., its double degeneration for right and left helicities. This choice makes the free energy depend on only six elastic constants: three for the quadratic part and three for the quartic one. We find Skyrmion-tube-like nematic textures that form when a uniform magnetic field is applied along the axis of a heliconical state.
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