From Topology to Morphology: Defects, Shape Evolution, and Auto-origami in Soft Matter
We explore novel mechanisms of pattern formation in soft matter, examining why a lipid membrane crumples during a phase transition and how stimuli-responsive liquid crystal polymer films can be patterned to induce programmed shape transformations . In both of these materials, whose constituent molecules align to form orientationally ordered phases, topological defects play a key role: they drive changes in morphology by inducing curvature. In lipid membranes cooled through a phase transition into the tilted “gel” phase, we theorize that defects nucleate spontaneously and then coarsen via kinetic competition between defect pair-annihilation and membrane shape evolution. We explore this process via simulation using a coarse-grained model and also study membranes with nematic order. Next we examine the role of defects in stimuli-responsive liquid crystal polymers, which flex when exposed to light or a change of temperature. If a precise pattern of defects is induced in the sample when it is cross-linked, a process known as “blueprinting,” then under stimulus an initially flat film will twist, curl, or fold into a complex shape, a form of programmed auto-origami. We use 3-d nonlinear finite element simulation studies to explore the mechanism by which the complete trajectory of motion is encoded in the sample’s nematic director field, and compare with relevant experiments.