Antipolar ordering of topological defects in active liquid crystals

Abstract

ATP-driven microtubule-kinesin bundles can self-assemble into two-dimensional active liquid crystals (ALCs) that exhibit a rich creation and annihilation dynamics of topological defects, reminiscent of particle-pair production processes in quantum systems. This recent discovery has sparked considerable interest but a quantitative theoretical description is still lacking. We present and validate a minimal continuum theory for this new class of active matter systems by generalizing the classical Landau–de Gennes free-energy to account for the experimentally observed spontaneous buckling of motor-driven extensile microtubule bundles. The resulting model agrees with recently published data and predicts a regime of antipolar order. Our analysis implies that ALCs are governed by the same generic ordering principles that determine the non-equilibrium dynamics of dense bacterial suspensions and elastic bilayer materials. Moreover, the theory manifests an energetic analogy with strongly interacting quantum gases. Generally, our results suggest that complex nonequilibrium pattern-formation phenomena might be predictable from a few fundamental symmetry-breaking and scale-selection principles.

Keywords

• active liquid crystals
• Landau-de Gennes free-energy
• Stokes flow
• 87.10.Pq
• 46.70.Hg
• 89.75.Da