(741a) 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.

Reference

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