Liquid crystals on deformable surfaces
Liquid crystals on deformable surfaces
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DOI：
10.1098/rspa.2020.0313
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
I. Nitschke;Sebastian Reuther;A. Voigt
中科院分区：
文献类型：
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作者：
I. Nitschke;Sebastian Reuther;A. Voigt
液晶分子约束到一个曲面的切向束显示有趣的现象，从紧耦合的弹性和散装自由能的液晶与表面的几何性质。我们导出了一个考虑Q张量场和表面同时弛豫的量子相容的Landau-de Gennes-Helfrich模型。由此产生的张量值表面偏微分方程和几何演化规律的系统数值求解，以解决这个系统的丰富的动力学，并计算由此产生的平衡形状。结果强烈依赖于内在和外在的曲率贡献，并导致意想不到的不对称形状。
Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk-free energies of the liquid crystal with geometric properties of the surface. We derive a thermodynamically consistent Landau-de Gennes-Helfrich model which considers the simultaneous relaxation of the Q-tensor field and the surface. The resulting system of tensor-valued surface partial differential equation and geometric evolution laws is numerically solved to tackle the rich dynamics of this system and to compute the resulting equilibrium shape. The results strongly depend on the intrinsic and extrinsic curvature contributions and lead to unexpected asymmetric shapes.