Annual Report [2018]

Cracking the Glass Problem

Mathematics and Physical Sciences

Glass has served humankind for millennia and is used in everything from windows to dishes to cell phones and high-speed internet cables. This ubiquitous material is so common that the fact that it is also something of a scientific mystery is surprising. Why don’t we have a handle on glass yet? 

The Simons Collaboration on Cracking the Glass Problem seeks to understand why glass behaves in all the myriad ways it does — rigidly at some temperatures and as a liquid at others — and how its properties might be engineered for everything from building materials to medical devices.

Household window glass is an amorphous solid, meaning it does not have a crystal structure and it exhibits certain property changes when its temperature is raised or lowered. But when collaboration researchers talk about glass, they are referring not only to this familiar silicon dioxide type but also to a host of other materials with two of the same properties: an amorphous structure and a transitional temperature at which its brittle structure becomes pliable and viscous. Non-silicate glasses include, for example, metals that have been heated and then supercooled to prevent them from forming crystals; plastics; the granular materials in between plates at an earthquake fault; and even many biological tissues. All are fair game for the collaboration.

A model of glucokinase, a glucose-processing protein in the liver and pancreas, produced by collaboration member Jason Rocks of the University of Pennsylvania. Proteins undergo transitions akin to the changes in viscosity and other properties that occur in liquids when they form a glass. This protein’s atoms are colored according to a so-called persistent-homology-based analysis. This analysis identifies the two regions of the molecule (red and blue) that are most important to the protein’s function. Image courtesy of Jason Rocks

The collaboration is divided into three main research directions. One is tasked with understanding jamming behaviors: When molecules are loosely packed in a space, the material is not rigid. As they are packed more tightly, they become rigid, whether they develop a crystal structure or not. The transition from a loose to a rigid state is called jamming. “There is new physics there, and it’s different from the kind of physics you get when a material suddenly becomes a crystal,” says Sidney Nagel, a physicist at the University of Chicago and director of the collaboration.

Another strand of research deals with what is called the mean-field transition. Projects in this area look at what happens in theoretical infinite-dimensional arrays of glass, where molecules interact with many more of their neighbors and local effects are not as important. The technique has been common in physics for decades, but with many materials, a lot of precision is lost in the transition from few to many dimensions. Not so with glass. “We found it quite astonishing,” says Giorgio Parisi, a physicist at Sapienza University in Rome and a principal investigator in the mean-field group. “These infinite-dimensional computations are much closer in the case of glasses than in other materials.” The jamming group and mean-field group study the extremes of glass behavior (zero temperature and infinite dimension); combining the two approaches can give insight into how glass behaves in more typical situations.

The final research area is dynamics of glass: how molecules flow past one another at high temperatures or under applied force. Lisa Manning, a physicist at Syracuse University and a principal investigator in the collaboration, says one of the most important avenues of research for the group is understanding how and where glasses are likely to fail. “They fail in interesting and unexpected ways,” she says. If members of the collaboration succeed in making better predictions about how glassy materials will behave, they can help materials scientists apply those insights and not only strengthen the materials they are creating but also develop materials with novel functionality.

Over the years, scientists have developed several different methods for understanding and predicting how the structure of glass impacts the dynamics, but until the collaboration was formed, there was little interaction among research groups. Now the collaboration has allowed more than 10 research groups to bring their techniques together to compare their merits and determine which ones are most powerful under which circumstances. For example, Manning’s team specializes in looking at vibrational patterns in glassy materials; a group led by collaboration principal investigator Andrea Liu uses machine-learning algorithms to make predictions; and so on. “I think this collaboration is a real breakthrough in our field,” Manning says.

When most of us look out of our windows, we don’t realize what a complex substance we are peering through. But collaboration researchers relish the mysteries in this seemingly mundane material.

Strength from disorder:

“So much of what we have been taught to do as physicists has been to treat ordered systems such as crystals,” says Nagel, “but glass’s disorder poses a challenge to traditional models of physical objects. Systems with disorder obey different laws of nature not found In ordered crystalline matter.” For example, a magnet has only two ground states because all the spins in the system are aligned. For glass, the number of ground states grows exponentially as the number of molecules present increases, requiring a whole new way to address the statistical mechanics of problems involving glass.

Disordered materials such as glass resist compression and shearing as well. But is the rigidity of glass the same as that of a crystal?

In an ideal setting, crystals are incredibly strong. The uniform structure holds the material together. But in the real world, crystals have slight chemical imperfections that weaken them. One region has a crystal structure aligned with a certain direction that bumps into another region with a crystal structure pointing another way. Along these fault lines, the material is susceptible to breakage or decay. (Perfectly crystalline iron would not rust; oxygen enters through defects in the crystal structure.) Glass, on the other hand, is uniformly disordered, so there are no discontinuities in the structure that can cause weaknesses. Therefore, understanding glass structures and discovering ways to make glass out of particular materials or with particular connections in their molecular structures can result in stronger, more resilient materials for all sorts of applications. 

Seeing clearly:

As is often the case in basic research, Cracking the Glass’s work will yield knowledge applicable to areas beyond just glass. “We think of understanding this glass state as a hub for understanding many new directions beyond that,” Nagel says. Where disorder plays a role in scientific questions, the collaboration’s work on disorder in glass could be applicable. For example, work on rugged energy landscapes in glass is relevant to diverse areas, such as questions in biology about cell differentiation and questions in physics about string theory. But perhaps the most unexpected outside connection is to computer science. The collaboration’s work on jamming is related to satisfiability problems in algorithms, where a collection of statements, sometimes unrelated to one another, must be simultaneously satisfied.

When most of us look out of our windows, we don’t realize what a complex substance we are peering through. But collaboration researchers relish the mysteries in this seemingly mundane material. “We love this kind of problem,” Nagel says. “You have things that you’ve dealt with every day, and then you stop and think about it and realize you don’t know how this thing manages to be the way it is. We are at a stage where we can formulate new principles and develop powerful mathematical tools that can be applied widely throughout science.”