467846 Towards Experimental Validation of a Multi-Resolution Approach for Directed Self-Assembly of Non-Periodic Structures: Spatial Control of Particle Densities
Self-assembly is the spontaneous association of components into patterns or structures.1 As a manufacturing technology of advanced materials, directly self-assembly is exciting as it enables molecular precision. External fields can be introduced to better control the self-assembly process, which is often referred to as directed self-assembly. The key challenge for practical implementation of directed self-assembly is to engineer the interactions between particles and between particles and external fields such that directed self-assembly proceeds in a desired direction.
Various external fields have been investigated to direct self-assembly. Electric fields are of particular interest due to the tunable strength and direction.2,3 For example, electric fields have been used as an actuator in automated feedback control methods to make advanced materials with low levels of defects.4
Self-assembly processes are prone to kinetic trapping and exhibit stochastic behavior, which complicates control of directed self-assembly to fabricate non-periodic structures.5 Furthermore, although important progress is being made in this direction,6 real-time observation of self-assembly processes is often not well possible in a non-invasive way, which complicates feedback control methods. Therefore, open-loop control methods are of particular interest for control of directed self-assembly. Several open-loop control methods have been proposed for control of directed self-assembly.7 Solis et al.7,8 proposed a novel multi-resolution approach to self-assemble non-periodic structures in a systematic way to avoid kinetic traps,8,9 This multi-resolution approach is inspired by protein folding and decomposes the dynamic self-assembly into a number of sequential resolutions in which the required number of particles are directed to a desired part of a domain. By dividing the domain into more parts when proceeding from resolution to resolution, the differences in particle density on the domain start to resemble the final structure more closely until the final structure can be assembled in the final resolution. This approach avoids kinetic traps since the local particle densities match the requirements of the final non-periodic structure. From a different perspective, the approach systematically breaks the ergodicity of the system in a number of steps such that undesired structures are not accessible anymore when the final structure is assembled. Dynamic simulations have demonstrated the potential of this method to self-assemble non-periodic structures reliably.10 However, the experimental validation of such multi-resolution approach has not been investigated to the best of our knowledge. Several challenges exist when implementing a multi-resolution approach experimentally. First, spatial control of the densities of the particles at different resolutions is needed. Second, the decomposition of the ergodicity of the system needs to be maintained when proceeding to lower resolutions. The former challenge may either require feed-back control or open-loop control when some form of predictive model is available.
The objective of this work is to validate an automated control strategy to control particle densities within different regions of a domain for a model system of directed self-assembly. Both open-loop and closed-loop control methods are investigated. Those methods can be used at a particular resolution to split a uniform particle population into two parts with desired densities. Ultimately, the ability to create different particle densities spatially and to maintain those divisions when proceeding to finer resolutions allows for the multi-resolution approach to be implemented experimentally.
Microscopic particles have been selected as the model system. The particles are suspended in a buffer solution and placed in a small cell under a microscope to observe the self-assembly process. Transparent electrodes on a glass substrate are patterned with non-conductive photoresist at the bottom of the cell to create an external field. A low-voltage AC electric field is used to direct the self-assembly of these microscopic particles. A dynamic analysis of this system has been conducted to quantify the diffusion and interaction of the particles with basic electrode shapes such as squares as function of electric field strength and frequency. Subsequently, an empirical input-output model is used to design an open-loop or closed-loop controller to separate a uniform particle population into various populations with different densities at specific regions of the domain. Figure 1 illustrates how the particles can be attracted to various electrodes and as such create density differences. Using automated image analysis (Matlab 2015b) for parallel experiments, the dynamics of the system can be quantified in terms of the density changes when applying step input changes in electric field properties, which are key for developing density control strategies to enable the experimental validation of a multi-resolution approach for control of directed self-assembly of non-periodic structures.
Figure 1: Dynamic analysis of the spatial particle densities in specific regions around square electrodes (indicated with row and column number) under AC electric fields with time-varying properties. The red line with circles represents the average particle density of the (inner) red area around the square electrodes computed from all 12 electrodes using image analysis. Similarly, the green line with triangles in the plotting represents the average particle density of the (outer) green area around the square electrodes.
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