(767h) Open-Loop Optimal Control of Directed Self-Assembly of Colloidal Particles in a Microfluidic Device

Self-assembly is defined as the spontaneous and reversible association of molecules or particles into organized structures.1 Self-assembly offers a relatively inexpensive route for the fabrication of micron and nanoscale structures with unique properties at high resolutions2. The formation of robust structures from micron and sub-micron materials requires intervention through externally applied electric or magnetic fields. Electric fields are most commonly used in the directed self-assembly of colloidal particles as their magnitudes and directions can be easily tuned in the manipulation and assembly of micron and nano-sized particles into desired structures at specific locations in microfluidic cells.3 The control of local particle densities may be necessary for the formation of defect-free structures when specific features need to be self-assembled.4 The control of a local density of colloidal particles is challenging due to the nonlinear process behavior and inherent randomness.



Feedback control has been demonstrated for the electric field assisted crystallization of colloidal particles5–8 and in the alignment of colloidal particles into defect-free lines.9,10 However, the performance of feedback controllers is highly dependent on the availability and accuracy of measured variables. In addition, satisfactory performance of model-free controllers can only be achieved in a limited range due to the nonlinear relationship between electric field properties and the dielectrophoretic forces acting on particles.10 Model-based optimal control is well suited to handle process nonlinearities and can obviate some of the challenges associated with model-free feedback control of colloidal particle density during directed self-assembly. In addition, constraints on the directed self-assembly process can be explicitly handled in the formulation of the optimal control policy while simultaneously considering multiple control objectives.



The objective of this work is to present an open-loop optimal control strategy to guide the assembly of colloidal particles to a desired particle density in a given region of a microfluidic device. Optimal input trajectories of AC field frequency and voltage as a function of local colloidal particle density are determined by solving an off-line optimization problem governed by an experimentally validated dynamic model which accounts for the effects of dielectrophoresis, drag force and electrostatic particle-particle interactions. The performance of the proposed optimal control is experimentally examined.



Acknowledgement: The work described in this paper was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, People's Republic of China (Project No. 16214617).



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