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August 17th, 2012

The yin and yang of entropy: When disorder begets organized nanostructures

Published on August 17th, 2012 | By: pwray@ceramics.org


Shapes can arrange themselves into crystal structures through entropy alone, new research from the University of Michigan shows. Credit: P. Damasceno, M. Engel, S. Glotzer.

Oddly enough (at least at first glance), a new paper in Science reports that computer simulations show the effects of entropy can lead to useful, ordered structures at the nano level, and the resulting particle structures can even be predicted with some level of certainty.

The unexpected entropy outcomes, discovered by University of Michigan scientists and engineers, could have some odd-but-valuable applications, including “designer materials with wild capabilities such as shape-shifting skins to camouflage a vehicle or optimize its aerodynamics,” according to a university news release.

One of the researchers Sharon Glotzer, a physicist and chemical engineering professor at the school, argues that one approach to making such materials is to start with a set of sought-after properties and then work backward to generate a blueprint for specific nanostructures.

How to make the nanostructures? That, according to the group, is where entropy can play a role in helping provide direction for the right type of precursor nanoparticles. The tendency of some nanoparticles to self-organize under certain conditions (e.g., at particular concentrations when particles start to “crowd”) is well known. For Glotzer and the other researchers, this tendency may be a help or hindrance, so one of their major challenges is “persuading” the nanoparticles to match the blueprint of target shapes and structures.

Glotzer reports in the release that one tactic they used was to aggregate a lot of data about spontaneous structures and then develop some statistical analysis. She says, “We studied 145 different shapes, and that gave us more data than anyone has ever had on these types of potential crystal-formers. With so much information, we could begin to see just how many structures are possible from particle shape alone, and look for trends.”

To tease out the trends, two member of Glotzer’s team, Michael Engel and Pablo Damasceno, crunched the numbers. Engel, a research chemical engineer, developed computer modeling code and Damasceno, an applied physics graduate, ran thousands of simulations. Engel’s program could handle any polyhedral shape, such as dice with any number of sides, and Damasceno particularly played with crowding variables to see how they affected different final shapes.

As Glotzer and others tell the story, they set the stage by first affirming that random particles will find the arrangements with the highest entropy: If there is enough space for the particles, a high level of disorder will occur with particles settling in a random arrangement, however, if the particles are forced to be crowded more tightly, they will begin forming crystal-like structures (that lack normal atomic bonding found in crystals) but still represent high-entropy arrangements.

In other words, the group’s simulations show that nanoparticles of certain shapes have a certain probability of arranging themselves into crystal-like structures driven only by entropy alone

Glotzer emphasizes that their virtual experiments are really about measuring possibilities. “It’s all about options. In this case, ordered arrangements produce the most possibilities, the most options. It’s counterintuitive, to be sure,” Glotzer says in the release. Here is the analogy she uses

If you could turn off gravity and empty a bag full of dice into a jar, the floating dice would point every which way. However, if you keep adding dice, eventually space becomes so limited that the dice have more options to align face-to-face. The same thing happens to the nanoparticles, which are so small that they feel entropy’s influence more strongly than gravity’s.

Let’s take a look at the group’s results. They looked at the 145 polyhedra found that 70 percent of the shapes tested were capable of forming crystal-like structures under entropy alone. As yet, they are uncertain why the other 30 percent essentially create a disordered glass-like material. Damasceno is quoted as saying, “The geometry of the particles themselves holds the secret for their assembly behavior.”

Moreover, they discovered that 52 of the initial particle shapes were able to form structures that contained repeating patterns. These synthetic structures fall into three familiar categories: regular crystals, liquid crystals and plastic crystals. Glotzer says in the release that any one of these is “an extraordinarily complex crystal structure even for atoms to form, let alone particles that can’t chemically bond,”

The benefit of the groups work is that by first analyzing the shape of a particle, one can predict how groups of them are likely behave and the probabilities for the resultant type of crystal-like structure, Damasceno said that it is possible to predict which type of crystal the particles would make.

The team says it is going to delve more into why some shapes resist order, but in the meantime, they think they have developed a valuable predictive tool. In a Science podcast, Glotzer says

Without having to do an experiment or do a simulation, we can take a particle’s shape and predict whether or not it will form say, a very simple type of crystal with a very small repeat unit, or a much more complex crystal with a much more complex repeat unit, or whether it will form a liquid crystal… There are many types of crystal structures that nanotechnologists would like to be able to obtain through self-assembly because it’s just not practical to build them by placing every nanoparticle where you want it in some mechanical process. So you just want them to self-assemble by the bucket. And so now we can tell them, “Well, if you want this particular kind of structure, then your nanoparticle should have this kind of a shape.” That was not possible before. So the greater significance is that we now understand that entropy can get you a lot in the way of complexity and so that we can go back and look at many of these types of self-assembled materials especially in biology and think about what the role of entropy might be there. It also has applications in the field of granular matter—processing of particles of sand grains, packaging of pharmaceuticals…

Hungry for more on this topic? Glotzer recently discussed these concepts at a TEDx talk:

The groups paper is titled, “Predictive Self-Assembly of Polyhedra into Complex Structures” (doi:10.1126/science.1220869).


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