(427e) Model-Based Optimal Feedback Control of Colloidal Self-Assembly

The ability to control the structure of a material at micro- and nano-meter scales could enable the design of new material properties.  For example, when micron-scale colloidal particles are arranged in a regular crystalline structure, they interact with light in novel ways, for use in optoelectronic devices [1].  However, the rapid manufacture of defect-free materials over large length scales is challenging.  The crystalline lattice is the low energy thermodynamic ground state, but in a finite time assembly process, defects are created stochastically and can be locked in.  This tradeoff between thermodynamics and kinetics could potentially be circumvented using dynamic processing inputs and feedback control.  Defects could be corrected in their early stages as they begin to form, by temporarily lowering the attractive potential that drives the assembly.  Once the defect is healed, the voltage can be raised again to further drive the assembly.

Here we demonstrate feedback control in a colloidal assembly process consisting of about 300 micron-size particles.  The assembly is driven by an applied electric field, which creates dielectrophoretic forces on the particles.  Real-time optical microscopy provides the information for feedback, by tracking the individual particle locations throughout the process [2].  A Brownian dynamics model and simulation describes the forces on each particle, and is used to generate a reduced-order Markov state model for a select number of discrete voltage inputs.  This Markov state model is then used to calculate the optimal feedback policy via dynamic programming, specifically through the framework of the Markov decision process [3].   This policy was implemented experimentally, and in a period of 1000 s, it was able to achieve defect-free assembly in 100 out of 100 cases, compared to 70/100 with a constant voltage input.

[1] K. A. Arpin, A. Mihi, H. T. Johnson, A. J. Baca, J. A. Rogers, J. A. Lewis, and P. V. Braun, Multidimensional Architectures for Functional Optical Devices. Adv. Mater., 2010. 22(10): p. 1084-1101.

[2] J. J. Juarez and M. A. Bevan, Feedback Controlled Colloidal Self-Assembly. Adv. Funct. Mater., 2012. 22(18): p. 3833-3839.

[3] Y. Xue, D. J. Beltran-Villegas, X. Tang, M. A. Bevan, and M. A. Grover, Optimal Design of a Colloidal Self-Assembly Process, IEEE Trans. on Cont. Sys. Tech., 2014.   22(5): p. 1956-1963.