Tunable corrugated patterns in an active nematic sheet.

Active matter locally converts chemical energy into mechanical work and, for this reason, it provides new mechanisms of pattern formation. In particular, active nematic fluids made of protein motors and filaments are far-from-equilibrium systems that may exhibit spontaneous motion, leading to actively driven spatiotemporally chaotic states in 2 and 3 dimensions and coherent flows in 3 dimensions (3D). Although these dynamic flows reveal a characteristic length scale resulting from the interplay between active forcing and passive restoring forces, the observation of static and large-scale spatial patterns in active nematic fluids has remained elusive. In this work, we demonstrate that a 3D solution of kinesin motors and microtubule filaments spontaneously forms a 2D free-standing nematic active sheet that actively buckles out of plane into a centimeter-sized periodic corrugated sheet that is stable for several days at low activity. Importantly, the nematic orientational field does not display topological defects in the corrugated state and the wavelength and stability of the corrugations are controlled by the motor concentration, in agreement with a hydrodynamic theory. At higher activities these patterns are transient and chaotic flows are observed at longer times. Our results underline the importance of both passive and active forces in shaping active matter and demonstrate that a spontaneously flowing active fluid can be sculpted into a static material through an active mechanism.