"...we limit the term to processes that involve pre-existing components (separate or distinct parts of a disordered structure), are reversible, and can be controlled by proper design of the components."

G.M. Whitesides and B. Grzybowski, Science, March 2002

 

What is self assembly?
Simply put, we're talking about collections of objects that put themselves together. Imagine holding a box containing a jigsaw puzzle, giving the box a shake, and peeking inside to find that the puzzle had assembled itself! While such behavior would be shocking in a jigsaw puzzle, a little reflection reveals that it's not so surprising to find self assembling systems in the natural world. After all, no one put you together did they? Biological systems as well as a variety of inorganic physical systems exhibit self assembling or self ordering behavior. Drawing on these systems for inspiration, scientists from numerous disciplines, chemistry, physics, biology, engineering, and mathematics, to name a few, have begun to investigate the self assembly process in hopes of learning to design and control the behavior of self assembling systems. Much of this work is motivated by recent advances in micro- and nanoscale science. On one hand, fabrication methods in micro- and nanoscience allow for batch processing. That is, we have the ability to make many copies of the same device simultaneously. How do we design these devices so that they spontaneously assemble themselves into a useful working structure? On the other hand, traditional fabrication methods are limited in resolution. To make smaller structures, i.e., true nanoscale structures, requires the development of new methods. Taking their cue from nature, coaxing nanostructures into self assembling is an avenue many scientists are exploring. Ultimately, a deeper understanding of self assembly may shed light on the nature of life itself.

 

 

Self assembly in the kitchen (and other parts of the house)
A variety of very simple systems exhibit self assembling behavior. In addition to being fun to play with, these systems serve as "toy models" allowing us to study self assembly in a simple setting. We can divide these systems into classes according as the forces that cause assembly to happen. Let's look at these classes and some examples you can carry out in your own kitchen.

Assembly by capillary forces

G.M. Whitesides and his group at Harvard University have designed and studied various self assembling systems. Many of these are based on the so-called "capillary bond." This "bond" exploits two properties of objects in water. First, small objects resting on the surface of water attract one another. In this way, interacting particles feel a force of attraction. Second, when two hydrophobic surfaces come into contact they remain in contact. In other words, they bond. In their experiments Whitesides et. al. have used the polymer polydimethylsiloxane (PDMS) to fabricate their self assembling shapes. PDMS is naturally hydrophobic and its surface properties can be easily changed from hydrophobic to hydrophilic by treating with an oxygen plasma. In this way interacting particles with varying surface properties can be fabricated. Whitesides et. al. have designed planar systems that self assemble to tile the plane, tile the plane with gaps, and form chain-like structures. See especially [1], [3-4] below.

Others have exploited the capillary bond using more prosaic materials to construct the interacting particles. Perhaps the most novel of these is the self-assembling hot dog system of Dr. Dean Campbell. Hot dogs? Yes, hot dogs. To see photo's of his system follow this link. At the University of Wisconsin researchers at the Materials Research Science and Engineering Center (MRSEC) have developed several novel demonstrations using LEGO bricks including a self assembling system of floating LEGO's. Descriptions of these demonstrations can be found here. In [7] Dungey et. al. introduce self assembled "Kixium" monolayers. What is Kixium? Isn't that the stuff that disabled Superman? No! Kixium refers to "Kix" the breakfast cereal from General Mills. They also report that Cheerios can be induced to self assemble. In [8] Campbell et. al. (yes the hot dog Campbell) introduce soda straws as a self assembling system. Like PDMS, soda straws are made of a hydrophobic polymer. They float easily on the surface of water and can be induced by light shaking to self assemble. The soda straw system demonstrates another important aspect of assembly by capillary forces - by controling the "height" of interacting particles the capillary force can be made repulsive. The idea was exploited by Hosokawa et. al. in [5].

Assembly by electrostatic forces

Assembly by capillary forces relies upon particle-particle interaction and interaction between particles and their enviornment. The particles have surface properties (hydrophobic or hydrophillic) and the enviornment is water. Place the particles in oil or alcohol and assembly stops. Make the particles entirely hydrophillic and assembly stops. Thinking of the capillary self assembly process in these terms naturally leads to the question of whether or not a different set of particle-particle and particle-enviornment interactions can be used to create a self assembling system. One natural alternative is to use electrostatic forces to induce self assembly. Anyone who's ever opened a package full of packing "peanuts" knows they hold a charge quite well. Toss a bunch of packing peanuts at a Van de Graff generator and some will self assemble into long chains. A more refined version of this demonstration using rice and corn oil is often used to illustrate the principle behind electrorheological fluids: dielectric particles in a fluid assemble into chains upon the application of an electric field.

The process is illustrated in the cartoon animation above. The particles float freely in a fluid, the particle and fluid have different dielectric properties. In the cartoon, the top and bottom boundaries are electrodes. A voltage difference is applied between the electrodes, the particles begin to move back and forth between the plates transferring charge and assembling themselves into chain-like structures. In our laboratory, we've conducted this experiment using pieces of resistance paper as the particles. The fluid is vegetable oil and the applied voltage is about 15kV. The system starts in a disordered state like so:

Here only a handful of rectangular shaped particles are used. Note that the depth of the oil is much greated than any length scale of the particles, hence they are free to move in three dimensions. The field is applied between parallel aluminum electrodes residing on the left and right of the container. A short time after applying the field, the system becomes ordered:

Observe that the particles become oriented in the direction of the field. Also, note that the particles "cluster" and begin to form long chain-like structures. Individual chains attract one another leading to a coarse-graining effect. In the system above the number of particles is limited. We can start with more:

and see complete chains forming:

Or, we can use disk shaped particles and get the same behavior:

If you'd like to watch this process in action, you can download a 20 second zipped MPEG here. The file is about 20MB, so please only attempt a download if you have a fast connection! When playing with these systems many questions arise. How does changing particle shape change the assembled structures? What happens if you make different parts of the particles from different materials? What happens if you change from the parallel plate geometry? We're investigating many of these question in our lab. References [9-10] below provide a entry point into the literature on this subject. The link to Argonne National Labs contains another electrostatic assembly setup.

Assembly by magnetic forces

A simple to construct, yet interesting, self assembling system involves magnets. In its simplest incarnation, the system is no more than a collection of disk shaped magnets randomly strewn about a inside a container. Here, simple shaking is enough to cause formation of a more highly ordered state:

What do we mean by "more highly ordered"? Well, in the animation above, the ordering is clear. Initially, the magnets are randomly placed in some closed region of the plane. Upon shaking, they form a chain-like structure. How should we make this notion of ordering or of complexity precise? One idea is to use the Kolmogorov definition - the complexity is the length of the shortest computer program needed to produce the pattern we see. Above, before shaking, our program would need to specify the location of every particle. After shaking, we need only specify the location of one magnet and the fact that all others are arrayed in a chain behind it. This system is more "ordered." It is worth observing that even after assembly is completed in the system above, a good deal of disorder remains. We can visualize the disorder by painting a colored stripe on the side of our magnets:

Upon repeated the experiment we see that rotational orientation is not preseved, there is still rotational "disorder" in the system:

Further, if we numbered each disk, we would see that there was no preferred order for the position of disks in the chain.

 

 

How does a mathematician think about self assembly?

There is a joke about mathematicians that ends with the punchline "First, assume the cow is spherical..." To quote Homer (Simpson that is, not the Greek one), "It's funny because it's true!" Let me describe some of our thinking about self assembly, but keep in mind that old spherical cow. The systems described above lead us to several observations about the self assembly process. Each system involves particles that are able to interact and to bind. Above we saw particles that interacted via capillary attraction, electrostatic charge, and magnetic fields. The interaction depends both on the particles themselves and on the interaction with the enviornment. In the electrostatic example the enviornment supplied the background electric field. If the field is turned off assembly stops. The interaction of particles with the enviornment creates the particle-particle interaction. In the magnetic example we observed that a system could become ordered in one "direction" but remain disordered in other respects. In all examples we observed that chain-like structures are easy to form. The question becomes - How to go beyond chains? How do we self assemble structures with more complexity? The PDMS experiments of Whitesides et. al., give us one clue. Change the properties of the particles, i.e., give them additional structure. Said another way - the information about the final structure has to be encoded in the particle-enviornment system. To explore this notion of information encoding in a one dimensional self assembling system we built an "alphabet" from plastic cubes:

These 1cm^2 cubes are available at education stores such as The Learning Station.

 

 

Related Links

 

 

References and Suggested Reading
[1] G.M. Whitesides and B. Grzybowski, "Self-assembly at all scales," Science, v. 295, March 2002, pp. 2418-2421.
[2] R.C. Merkle, "Molecular building blocks and development strategies for molecular nanotechnology," Nanotechnology, v. 11, 2000, pp. 89-99.
[3] G.M. Whitesides and M. Boncheva, "Beyond molecules: self-assembly of mesoscopic and macroscopic components," PNAS, v. 99, 2002, pp. 4769-4774.
[4] N. Bowden, A. Terfort, J. Carbeck, and G.M. Whitesides, "Self-assembly of mesoscale objects into ordered two-dimensional arrays," Science, v. 276, April 1997, pp. 233-235.
[5] K. Hosokawa, I. Shimoyama, and H. Miura, "Two-dimensional micro-self-assembly using the surface tension of water," Sensors and Actuators, v. 57, 1996, pp. 117-125.
[6] K. Saitou and M. Jakiela, "On classes of one-dimensional self-assembling automata," Complex Systems, v. 10, 1996, pp. 391-416.
[7] K.E. Dungey, G. Lisensky, and S.M. Condren, "Kixium monolayers: A simple alternative to the bubble raft model for close-packed spheres," J. of Chemical Education, v. 77, 2000, pp. 618.
[8] D.J. Campbell, E.R. Freidinger, J.M. Hastings, and M.K. Querns, "Spontaneous assembly of soda straws," J. of Chemical Education, v. 79, 2002, pp. 201-202.
[9] M.P. Hughes, "AC electrokinetics: applications for nanotechnology," Nanotechnology, v. 11, 2000, pp. 124-132.
[10] A. Bezryadin, R.M. Westervelt, and M. Tinkham, "Self-assembled chains of graphitized carbon nanoparticles," Appl. Phys. Lett., v. 74, 1999, pp. 2699.