Grain boundary control in colloidal self-assembly with dynamic programming

We propose a Markov decision based dynamic programming method to manipulate the self-assembly of a quadrupole colloidal system for grain-boundary-free two-dimensional crystals. To construct the optimal control policy, we developed a Markov chain model, based on information extracted from a Langevin dynamics simulation model, which originated from a more complicated Brownian dynamics model. An infinite-horizon Markov decision process is defined, and the optimal control policy is solved with dynamic programming using policy iteration. Both the Markov chain Monte Carlo and the Langevin dynamics simulation results demonstrate that the control strategy is able to significantly accelerate the crystallization of a SiO₂ colloidal self-assembly process for a grain-boundary-free, highly ordered crystal. Future work will focus on implementation of the control policy on the Brownian dynamics simulation and the experiments.