The dynamics of systems that contain very large numbers of variables (e.g. oceans, weather, forests, cells) are difficult to study experimentally. The complex spatial and temporal interdependency of their many elements renders the systematic interrogation of individual variables intractable. To study complex systems, we take a constructionist approach we call “synthetic complexity”. The steps are simple: first, we characterize individual system elements (e.g., polymer beads, droplets, flames); then, we allow those elements to interact (in different numbers and under different environmental conditions). This approach allows us to observe emergent—or unexpected—phenomena, and the systems that we develop, in their tractability, enable us to determine the physical origins of those phenomena.
Crystals of electrostatically-charged macroscopic beads
Atoms and molecules are composed of particles – the nuclei and the electrons – that have electrostatic charge. The electrical interaction between these charges is responsible for the structure of much of the macroscopic matter around us. We have developed a system (Figure 1) in which ensembles of electrically charged macroscopic particles (millimeter-sized spheres) interact and organize into ordered structures . The appeal of this system is that we can follow both the position and the motion of single particles; today we cannot do the same for atoms and molecules.
We are shaking in a pan on the order of 100 spheres made from different plastic materials. Due to friction between the pan and the spheres, and the one between different spheres, different types of spheres acquire positive or negative charges of various and measurable amounts. After mechanical agitation (a surrogate for the thermal motion of atoms and molecules) the spheres assemble into regular lattices with cubic, pentagonal, and hexagonal symmetries (Figure 2), depending on the composition of the mix of beads and on the surface coverage. Surprisingly, some of these lattices possess a net electrical charge; we believe that such lattices are being stabilized by induced dipole interactions between spheres.
Experiments with two types of oppositely-charged beads are analogous to the crystallization of an ionic solid from its melt. We can also model the nucleation of ionic crystals from a solvent [2, 3]; the model for a solvent molecule is a plastic sphere that is coated with a thin layer of conductive material (gold in our case). Gold-coated spheres do not charge triboelectrically, but charge capacitively when close to an uncoated charged sphere, therefore the gold-coated spheres model a polarizable solvent. After agitation, charged particles separate from the ‘solvent’ and form regular lattices while a system of uncharged spheres mixes (Figure 3a). We have also investigated phase separation in systems of bound and dissimilarly-charged spheres mixed with gold-coated spheres joined in pairs (Figure 3b). This system models the nucleation of a molecular crystal from a polarizable molecular solvent.
Beads-on-a-string: a macroscopic model for polymer science
In another program whose goal is to model molecular interactions using systems of millimetrically-sized, charged beads, we have created an experimental system for the study of linear polymers . We assembled beads of dissimilar materials (nylon, Teflon, Poly(methyl methacrylate)) along a string, and we agitated the beads-on-a-string on a flat surface (Figure 4). Different types of beads acquired electric charges of different signs by tribocharging; the electrostatic interactions (attractive or repulsive) between different beads led to the folding of the string to configurations that were specific to the sequence of beads along the string (Figure 5). This folding process is a model for the folding of polymers that contains monomers that can interact with each other - such as proteins or RNA. The folding of proteins is a very difficult problem that is usually approached with computational models. Our beads-on-a-string model is the simplest we could design, yet it includes the inevitable nonlinearities of a real system, therefore it should give us new insight into the folding of polymers. Our system is, in effect, an analog computer for the study of polymer folding.
Interacting bubbles and drops in microfluidic channels
We have demonstrated a wide range of remarkable, emergent phenomena in single and multiple bubbles in microfluidic systems. These include coupling of drop formation from multiple flow-focusing nozzles , the generation of unexpectedly complex periodic patterns of bubbles , and the possibility of coding and decoding of the spacing between drops moving in a channel .
We have generated bubbles of nitrogen in water and drops of water in hexadecane using hydraulically-connected flow-focusing nozzles  (Figure 6). Under the regime of rates of flow that we investigated, a single flow-focusing nozzle would produce monodisperse drops or bubbles at constant frequency. Coupled bubble generators can produce bubbles of different sizes from a single nozzle (Figure 7a), and the generation of bubbles from different nozzles is synchronized. The formation of drops (Figure 7b) can be also synchronized but in general the generation of droplets was independent. These observations led us to conclude that the compressibility of the disperse phase (drops or bubbles) was the most important factor in achieving a synchronized production of the disperse phase.
We have produced trains of droplets at a T-junction, and sent them through a loop such that the drops could take two different paths through the loop (Figure 8). The droplets choose a path based on the number of droplets that occupy each branch. The presence of a drop in one of the paths influences which path the next droplet will take. This interaction between droplets changes the pattern of drops after the loops in a complex but reversible fashion . The output pattern is a function of the lengths of the two possible paths. The reversibility of this system is a consequence of its linearity. We could retrieve the original uniform pattern of drops by either reversing the flow, or by adding a second loop with reversed paths. If we regard the drops as information carriers, the manipulation of the drop pattern is equivalent to the coding and decoding of a signal encoded in the pattern.
We have extended the flow-focusing device to include five inlets for liquid on either side of the gaseous thread . In a simple flow-focusing device, the gaseous thread advances into the orifice region where it is squeezed closed by the buildup of pressure in the liquid around it. In the five-inlet system, as the gaseous thread advances through the orifice region, it blocks the orifices sequentially, thereby increasing the rate of flow of liquid through the unblocked orifices. The advancing gaseous thread thus creates a mechanism of feedback in the system. Bubbles are squeezed off by the downstream orifices as the thread is slowly squeezed at the most upstream orifice, leading to the production of bursts of bubbles (Movie 1). By varying the pressure of gas in the system, for a constant rate of flow of liquid, we can tune the number of bubbles produced by the device in each burst from one up to 40 and back down to ~10. We observe highly stable periodic behavior over a range of pressures in which 29 bubbles are produced per period.
In engineering, and in many other human activities, the simplest solution to a problem is often the best one, and simplicity is actively sought after. Much of science is a sophisticated craft nowadays, and doing science requires so much energy to learn and apply the craft that none is left to look for creative and simple solutions. Much of the work that we do consists in a search for simple – and not expensive – scientific systems. The work on complex systems outlined above is an example of this approach. Another one is our surface science studies of self-assembled monolayers ; these experiments can be carried out using the basic equipment present in a chemistry lab, in contrast with the expensive approach of studying extremely clean surfaces in an ultra-high vacuum environment. More examples can be found in most of the research areas we are active in.
There is a well-established and active science of complexity; there is no science of simplicity. How do we rationalize the process of creating a simple system, how does one quantify simplicity, and how does one plan a study of simplicity? We are interested in providing answers to such questions.
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2. Kaufman, G. K., Thomas, S. W. III, Reches, M., Shaw, B. F., Feng, J., and Whitesides, G. M. Phase separation of 2D meso-scale Coulombic crystals from meso-scale polarizable "solvent". Soft Matter 5, 1188-1191 (2009).
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4. Reches, M., Snyder. P.W., and Whitesides, G. M., Folding of Electrostatically Charged Beads-on-a-String: An Experimental Realization of a Theoretical Model, Proceedings of the National Academy of Sciences USA, 106, 17644-17649 (2009).
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