Geometry, topology, and liquid crystals: The materials applications
Jul 16, 2019 1065 views 
“Geometry is perhaps the most elementary of the sciences”. Geometry is concerned with the properties of configurations of points, lines, and circles, and topology is concerned with space, dimension, and transformation. We will discuss our journey of discovering the beauty and power of geometry, and applications in a wide variety of materials at all scales. Through designs of geometric surface patterns, here, micropost arrays, we program topological defects, and thus the orientational elasticity in liquid crystal assemblies. When coupling chemical patterning and surface topography, we demonstrate symmetry breaking, allowing for multi-state optical switching. Geometry is materials independent. Taking the knowledge in small molecule liquid crystals, we preprogram arbitrary 3D shapes in 2D sheets of liquid crystal elastomers. By coupling with soft forces, we vertically aligned atomically thin 2D nanosheets of titanium carbide from the MXene family up to 200 m to store more energy. Geometry is also scale invariant. Lastly, we will show the prospective of taking geometry to create smart fabrics.