Emergent Phenomena in Active Polymer Arrays
Three active matter systems involving long, flexible molecules (which we often refer to generally as polymers) are examined. Phenomena arising from these systems -- be it pure prediction (as in chapters 2 and 4) or based on a known experiment (chapter 3) -- are analyzed theoretically and through simulation. The first system we consider is a plate resting on a tilted polymer brush, where the ends of the polymers bind to sites on the plate and unbind in response to an incoming photon. We show that, under the right conditions, the plate will move in the direction of the polymer tilt, converting incoming light energy directly to mechanical energy. This mechanism was inspired by a similar mechanism already present in biology: the actin-myosin interface in muscle tissue. The second system is that of microtubule bundles confined between two parallel plates with one end bound to a surface, as studied experimentally by Sanchez et al. In this experiment, the spontaneous formation of metachronal waves was observed. We show that this result can be reproduced using first-principles hydrodynamic simulations, and argue that these basic interactions are sufficient to explain the observed behavior. Finally, we propose an experiment in which microtubules are not bound to a surface, but rather confined to an optical trap. We show that, under the right conditions, drifting microtubules exhibit various phases, and can even align, circling the trap uniformly.