Curvature-driven stability of defects in nematic textures over spherical disks

Abstract

Stabilizing defects in liquid-crystal systems is crucial for many physical processes and applications ranging from functionalizing liquid-crystal textures to recently reported command of chaotic behaviors of active matters. In this work, we perform analytical calculations to study the curvature driven stability mechanism of defects based on the isotropic nematic disk model that is free of any topological constraint. We show that in a growing spherical disk covering a sphere the accumulation of curvature effect can prevent typical +1 and +1/2 defects from forming boojum textures where the defects are repelled to the boundary of the disk. Our calculations reveal that the movement of the equilibrium position of the +1 defect from the boundary to the center of the spherical disk occurs in a very narrow window of the disk area, exhibiting the first-order phase-transition-like behavior. For the pair of +1/2 defects by splitting a +1 defect, we find the curvature driven alternating repulsive and attractive interactions between the two defects. With the growth of the spherical disk these two defects tend to approach and finally recombine towards a +1 defect texture. The sensitive response of defects to curvature and the curvature driven stability mechanism demonstrated in this work in nematic disk systems may have implications towards versatile control and engineering of liquid crystal textures in various applications.

Liquid crystals on deformable surfaces

“…The shape significantly differs from the proposed equilibrium shape in [27], where n-atic order on deformable surfaces is considered, but with a much simpler and purely intrinsic model. More recently, it has been demonstrated that besides these intrinsic curvature terms also extrinsic curvature terms, i. e. curvatures related to the geometry of the embedding space, are relevant [16,18,21,22,24,25,[41][42][43][44][45][46][47]. It has been demonstrated that the intrinsic geometry tends to confine topological defects to regions of maximal Gaussian curvature, while extrinsic couplings tend to orient the director field along minimal curvature lines.…”

Anomalous Chained Turbulence in Actively Driven Flows on Spheres

“…Over the past two decades, important breakthroughs have been made in characterizing activestress driven matter flows in planar Euclidean geometries both theoretically [12][13][14][15][16][17][18][19][20][21][22][23] and experimentally [24][25][26][27][28][29][30]. More recently, theoretical work has begun to focus on incorporating curvature effects into active matter models [31][32][33][34][35][36][37][38][39][40]. Despite some promising progress, the hydrodynamic description of pattern-forming non-equilibrium liquids in non-Euclidean spaces continues to pose conceptual challenges, attributable to the difficulty of formulating exactly solvable continuum models and devising efficient spectral methods in curved geometries.…”

Liquid Crystals on Deformable Surfaces

“…Both shapes significantly differ from the proposed equilibrium shapes in 32 , where n−atic order on deformable surfaces is considered, but with a much simpler and purely intrinsic model. More recently, it has been demonstrated that besides these intrinsic curvature terms also extrinsic curvature terms, i. e. curvatures related to the geometry of the embedding space, are relevant 21,23,26,27,29,30,[45][46][47][48][49][50] . It has been demonstrated that the intrinsic geometry tends to confine topological defects to regions of maximal Gaussian curvature, while extrinsic couplings tend to orient the director field along minimal curvature lines.…”