Self-Assembly at the Macroscale Simulates the Microscale

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Self-assembly is the process in which a disorganized system spontaneously assembles into an organized specific product without external interference. The properties of the assembled product are determined by the properties of the individual parts and the connection between them. “Self-assembly is the science of things that put themselves together” as once famously stated by mathematician John Pelesko.

One of the most promising applications of Self-assembly will arise in the semiconductor industry.

Per A. Löthman

Self-assembly is used extensively by nature; for example, in crystal growth, protein folding, the assembly of molecules into larger compounds, and the creation of complex organs such as the human brain. It is a prospective candidate for use in areas where conventional production and assembly methods are problematic. Although it is not limited to specific dimensions [2], self-assembly is especially applicable to small scales [3]; for example, because conventional machining tools for three-dimensional construction are limited to larger feature sizes, while photo-lithography processes are two-dimensional in nature. Mastrangeli et al.’s [4] review gives an excellent summary of this area, ranging from nanosized DNA origami [5] to magnetically folded milli-scale structures [6].

Due to the continuous down scaling of fabrication processes, non-volatile data storage systems will at, some point, run into their limits to store and process bits of information using only a few atoms.

Per A. Löthman

Arguably, one of the most promising applications of Self-assembly will arise in the semiconductor industry. As a result of the continuous down scaling of fabrication processes, non-volatile data storage systems will at some point run into their limits to store and process bits of information using only a few atoms [7]. To achieve higher data densities, it is necessary to move to the third dimension. The first steps in this direction have been taken by stacking wafers [8] or layers [9]. However, the stacking approach is not suitable to achieve truly three-dimensional structures, in which both the resolution and extent of the features is identical in all directions [10]. The most promising production method may well be based upon three-dimensional self-assembly.

Magnetic forces have been used extensively as driving forces in self-assembly on all scales, together with various sources of agitating energy.

Per A. Löthman

Moreover, it has been demonstrated that microscopic spherical particles can form regular
structures up to centimeter-sized dimensions [11]. By tuning the particle properties and/or the driving force of self-assembly, one can control the size and dimensions of the resulting structures [12, 13].

Although major progress has been made in three-dimensional microscopic self-assembly, observing the dynamic behavior during the assembly process remains a challenge due to the small size and time constants involved. Several approaches have been explored to model and simulate these processes [14, 15, 16]. However, these approaches rely on exhaustive Monte-Carlo simulations, scaling unfavorably with the number of particles involved.

Magnetic forces have been used extensively as driving forces in self-assembly on all scales, together with various sources of agitating energy. When exposed to an external magnetic field, it has been demonstrated that nanoscopic magnetic rods form bundles [17] or multimers when driven by ultrasound [9].

A “macroscopic self-assembly reactor” has been introduced by Leon Abelmann’s research group in Saarbrücken, Germany.

Macroscopic self-assembly processes on a centimeter scale are dominated by two-dimensional structures, where mechanical shaking is the most widely used source of disturbing energy. Hacohen et al., [17] demonstrated DNA-inspired patterned bricks with embedded magnets, self-assembling into a programmed structure, but report gravity bias. Stambaugh et al., [18] reported self assembled 2D structures of centimeter-sized spherical particles with internal magnets that were shaken vertically, and observed different resulting structures that were based on particle concentration and magnet shape. Ilievsky et al., [19] demonstrated self-assembly of centimeter-sized magnetic cubes into chains in a turbulent flow by submerging them in a rotating reactor filled with water, this way introducing eddy flows as a disturbing energy. They also introduced the concept of effective temperature, describing the motion of particles as if Brownian by nature. Even though the assembly process is three-dimensional, the resulting structures are limited to a single dimension and the dynamics involved have not been studied. Trajectories of particles or the energies involved have not been studied in the previous mentioned examples of macroscopic self-assembly. This is, however, a crucial part for the successful implementation of self-assembly.

In order to address the above-mentioned questions, a “macroscopic self-assembly reactor” was introduced by Leon Abelmann’s research group in Saarbrücken, Germany. This reactor functions as a simulator for microscopic self-assembly and has been introduced in order to study the fundamentals of self-assembly in a turbulent water flow representing the microscopic thermal energy [20,21,22]. Motion and interaction of centimeter-sized magnetic polymeric objects was characterized and evaluated. By increasing particle size from micrometers to centimeters, not only the ease of observation but also the characteristic time constants increase decidedly. This makes the self-assembly process visible using conventional cameras. As a result of scaling up the system, the environment also changes; laminar flows become turbulent while inertia effects become dominant. At the same time, Brownian motion becomes negligible. Therefore, it is crucial to study to what extent the macroscopic system is a good simulator for microscopic environments. By observing the trajectories of a single particle in the reactor, we quantify the similarity between Brownian motion of said dynamics.

Surprisingly, the particles conduct a random walk and a Brownian motion like behavior, similar to what microscopic particles experience at the microscopic scale.

Per A. Löthman

By observing the interaction of two particles in the reactor, we can characterize the most fundamental building block of the self-assembly process, which is the interaction of magnetic spheres in a turbulent environment. Surprisingly, the particles conduct a random walk and a Brownian motion like behavior, similar to what microscopic particles experience at the microscopic scale. A turbulence dependent thermal energy could be calculated which further underlines the similarities to the microscopic scale.

For a successful implementation of self-assembly it is necessary to understand the underlying mechanism of self-assembly. Macroscopic self-assembly seem to deliver valuable data in this respect and may contribute decidedly to the self-assembly of future advanced materials.


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