Passive defect driven morphogenesis in nematic membranes

Abstract

Topological defects are ubiquitous on surfaces with orientational order fields. Here, we study equilibrium states generated by the feedback between geometry and nematic order on fluid membranes with an integer topological defect. When the Frank elastic constants associated with the orientational field dominate, the surfaces spontaneously deform toward an conical shape featuring an aster topological defect at its apex. In the case of vanishing tension this is a solution to the normal force balance. We show that the stability of the surface depends on the balance of the elastic parameters and the phase of the defect. When boundary constraints are introduced, we observe three distinct modes of deformation. These deformation modes take advantage of the way in which splay, twist and bend distortions of the director field can be exchanged on a curved surface. We discuss how these deformation modes are distinguished by their response to the cost of twist distortions and the existence of inverted solutions. Our findings show that fusion of +1/2 topological defect pairs can reduce the total energy of deformable surfaces. Finally, we argue how these results can be relevant for biological systems.

6 pages, 4 figures, and SI with 3 additional figures

References in corpus (15)

• Spontaneous motion in hierarchically assembled active matter
• Topology and Dynamics of Active Nematic Vesicles
• Two-Dimensional Matter: Order, Curvature and Defects
• Morphogenesis of growing soft tissues
• Theory of defect-mediated morphogenesis
• Interplay of Structure, Elasticity and Dynamics in Actin-Based Nematic Materials
• Conical defects in growing sheets
• Probing the shear viscosity of an active nematic
• Defects in nematic membranes can buckle into pseudospheres
• Active morphogenesis of patterned epithelial shells
• Theory of nematic and polar active fluid surfaces
• Active nematic flows on curved surfaces
• Probing active nematics with in-situ microfabricated elastic inclusions
• Active nematodynamics on curved surfaces -- the influence of geometric forces on motion patterns of topological defects
• Membrane stress and torque induced by Frank's nematic textures: A geometric perspective using surface-based constraints