Controlling assembly of colloidal particles into structured objects: Basic strategy and a case study

A computational study is presented in which real-time manipulation of the interaction potential between particles in a colloidal system is used to control their assembly into a close-packed crystalline object. The basic model used throughout the study is a high-fidelity representation of a real experimental system in which 32 colloidal silica particles are suspended in aqueous solution with polymer hydrogel providing a temperature-tunable attractive force between the particles. Diffusion mapping is used to determine a set of coarse variables that provide an appropriate low-dimensional representation of this system at four discrete values of the attraction strength. In this case the diffusion mapping process identified two dimensions; one correlates well with the radius of gyration of the entire set of particles and the other correlates well with the average distance between distinct clusters of particles. Two different stochastic models are then built in the two-dimensional (2D) space of these variables, using data from a large number of short Brownian dynamics simulations of the full 32-particle system. The first 2D model is based on a Smoluchowski framework and is used to characterize the overall equilibrium and diffusive properties of the system. The second 2D model is based on a transition rate matrix and is used for process control. A control policy based on an infinite-horizon Markov decision process is developed using the four different attraction strengths as the input variables. The resulting policy is non-trivial; rather than simply selecting the strongest level of attraction, some mix of weak and strong attractions generally provides the optimal approach to the target close-packed state. This study, while focused on the particular mechanism of tunable depletion attraction, suggests a general strategy that could be adapted to different mechanisms of actuating colloidal assembly.