A comparison of open-loop and closed-loop strategies in colloidal self-assembly

Ordered colloidal crystals possess unique photonic properties for a wide range of applications in engineering, material science, communications, and medicine. However, ordered structures are hard to achieve even in small systems, due to the formation of defects during the process. In this paper, we focus on the control of a micron-sized SiO2 colloidal self-assembly process for defect-free crystal in an externally applied electric field batch system. Five control strategies including time-constant and time-varying, heuristic and model-based open-loop and closed-loop policies are investigated, to understand their control mechanisms. The model-based policies are designed using a reduced-order Markov state model, built with samples from Brownian dynamics simulations, and are calculated with dynamic programming. The performance of all the five strategies are evaluated on both the Brownian dynamics simulation and the experiments. Time-varying control strategies can improve the yield of grain-boundary-free crystals over that of their time-constant counterparts. Moreover, using feedback as “endpoint detection” to terminate the process can also shorten the process time, compared to open-loop strategies.