Controlled Formation of Nanostructures with Desired Geometries. Part 4. Multiresolution Optimal Control in Dynamically Directed Self-Assembly of Nanoparticles

Abstract

This paper presents an optimal control strategy that can guide any initial random configuration of nanoparticles to a final structure of desired geometry, in minimum time. It employs a multi-resolution view of the dynamically evolving configurations of nanoparticles, which are described through the Adaptive Finite State Projection (AFSP) approach introduced in Part 3 of this series. External charges, attracting or repelling the nanoparticles, are the controls, whose location and intensity are determined by the optimality conditions of the optimal control strategy. To ensure analytic consistency of the parametric sensitivities, during the computation of the optimal controls, and thus guarantee the optimality of the resulting control policy, a priori determination of enlarged constant projection spaces is shown to be essential. A case study illustrates the use of the proposed optimal control strategy and illuminates several of its features, such as: superiority over a static optimal solution; evasion of kinetic

Gain scheduling PID control for directed self‐assembly of colloidal particles in microfluidic devices

“…The method can potentially be combined with self‐assembly systems that require control over local particle density to assemble final structures with reduced defects. The current method can also be extended to include several hierarchical density control steps to self‐assemble complicated nonperiodic structures, which has been proposed in the framework of a multiresolution control approach …”

“…The current method can also be extended to include several hierarchical density control steps to self-assemble complicated nonperiodic structures, which has been proposed in the framework of a multiresolution control approach. [34][35][36][37][38] The current work is based on scheduling of the controller gain only by using an empirical steady-state model. Although the devel- be reached that colloidal crystallization could be induced.…”

Feedback control for defect-free alignment of colloidal particles

“…The spatial resolution of the domain becomes finer as the directed self-assembly process proceeds and control steps at a higher resolution restrict the steps at lower resolutions. [35,36] A multi-resolution approach has the potential to avoid kinetic traps by essentially decomposing the ergodicity of the system to systematically guide the self-assembly process, which has been demonstrated to be effective via dynamic simulations, but not yet via experiments. [37] The objective of this work is to present a novel integrated feedback control strategy to align colloidal particles reliably.…”

Staged Assembly of Colloids Using DNA and Acoustofluidics

“…Such external-field-directed self-assembly also allows extensions toward open- or closed-loop control schemes that dynamically tune the force fields to account for design uncertainty and mitigate disturbances. Essentially, it provides a sort of “external programmability” to achieve reliable assembly of materials. − Although AC electric fields (AEFs) are most widely used, it is challenging to apply AEFs for DNACC assembly. DNACC assembly requires saline buffer, while AC electrokinetic mechanisms need a low ion concentration (e.g., less than 2 mM NaCl or 8 mM KCl), which is typically insufficient for stabilizing the DNA hybridization. ,, Magnetic fields work in a saline buffer solution, but the paramagnetic colloids should be used, limiting the properties of the assembled DNACC-based materials. , In comparison, acoustic fields render a promising option to externally program the assembly of DNACCs, yet their potential has not been explored experimentally.…”