Graphene, a two-dimensional form of carbon in sheets just one atom in thick, has been the subject of widespread research, in large part because of its unique combination of strength, electrical conductivity and chemical stability. But, despite many years of study, some of graphene’s fundamental properties are still not well understood, including the way it behaves when something slides along its surface.

Now, using powerful computer simulations, researchers at the University of Pennsylvania, the Massachusetts Institute of Technology and elsewhere have made significant strides in understanding that process, including why the friction varies as the object sliding on it moves forward, instead of remaining constant as it does with most other known materials.

​​​​​​​Robert Carpick, the John Henry Towne Professor and chair of the Department of Mechanical Engineering and Applied Mechanics in Penn’s School of Engineering and Applied Science, contributed to these findings.

The study, published in the journal Nature, was led by Ju Li, the Battelle Energy Alliance Professor of Nuclear Science and Engineering at MIT and a former adjunct professor in Penn Engineering’s Department of Materials Science and Engineering, and former visiting Penn student Suzhi Li, now a Humboldt Research Fellow at the Karlsruhe Institute of Technology, Germany. The research team also included Peter Gumbsch at Karlsruhe Institute of Technology, Xiangdong Ding and Jun Sun at Xi’an Jiaotong University, China, and Xin Liu and Qunyang Li, then-members of Carpick’s research group at Penn.  

Graphite, a bulk material composed of many layers of graphene, is a well-known solid lubricant; like oil, adding it in between contacting materials reduces friction. Recent research suggests that even one or a few layers of graphene can also provide effective lubrication. This may be used in small-scale thermal and electrical contacts and other nanoscale devices. In such cases, friction between two pieces of graphene, or between graphene and another material, is important to understand for maintaining a good electrical, thermal and mechanical connection.

Carpick and other collaborators had previously found that, while one layer of graphene on a surface reduces friction, having a few more was even better. However, the reason for this has not been well explained to date, Ju Li said.

“There is this broad notion in tribology that friction depends on the true contact area,” Li said, referring to the area of where two materials are really in contact, down to the atomic level. The “true” contact area is often substantially smaller than it would otherwise appear to be if observed at larger-size scales. Determining the true contact area is important for understanding not only the degree of friction between the pieces but also other characteristics such as the electrical conduction or heat transfer.

“When two parts in a machine make contact, like two steel gear teeth, the actual amount of steel in contact is much smaller than it appears,” Carpick said, “because the gear teeth are rough, and contact only occurs at the topmost protruding points on the surfaces. If the surfaces were polished to be flatter so that twice as much area was in contact, the friction would then be twice as high. In other words, the friction force doubles if the true area of direct contact doubles.”

But it turns out that the situation is even more complex than scientists had thought.

“We found that there are also other aspects of the contact that make a difference in the way friction force gets transferred across it. We call this the quality of contact, as opposed to the quantity of contact measured by the ‘true contact’ area,” said Li.

Experimental observations by Carpick and collaborators published in Science in 2010 had shown that when a nanoscale object slides along a single layer of graphene, where the graphene could be supported on top of a substrate like a piece of silicon, the friction force actually increases when sliding begins, and then levels off. This effect lessens, and the levelled-off friction force decreases when sliding on more and more graphene sheets; the effect was seen in other layered materials including molybdenum disulfide. Previous attempts to explain this variation in friction, not seen in anything other than these two-dimensional materials, had fallen short.

To determine the quality of contact, it is necessary to know the exact position of each atom on each of the two surfaces. The quality of contact depends on how well aligned the atomic configurations are in the two surfaces in contact and on the synchrony of these alignments. According to the computer simulations, this turned out to be more important than the traditional measure in explaining the materials’ frictional behavior, the true contact area.

“You cannot explain the increase in friction as the material begins to slide by just the contact area,” Li said. “Most of the change in friction is actually due to change in the quality of contact, not the true contact area.”

The researchers found that the act of sliding caused graphene atoms to make better contact with the object sliding along it. This increase in the quality of contact leads to the increase in friction as sliding proceeds and eventually levels off. The effect is strong for a single layer of graphene because the graphene is so flexible that the atoms are more free to displace and find locations of better contact with the tip. When more layers of graphene are underneath the top layer, they act to hold the topmost graphene atoms more still. The graphene is now less flexible, and friction stays low and constant as sliding proceeds.

A number of factors can affect that quality of contact, including rigidity of the surfaces, slight curvatures and gas molecules that get between the two solid layers. But, by understanding the way the process works, engineers can now take specific steps to alter that frictional behavior to match a particular intended use of the material. For example, “pre-wrinkling” of the graphene material can give it more flexibility and improve the quality of contact.

“We can use that to vary the friction by a factor of three, while the true contact area barely changes,” Li said.

In other words, it’s not just the material itself that determines how it slides but also its boundary condition, including whether it is loose and wrinkled or flat and stretched tight. And these principles apply not just to graphene but also to other two-dimensional materials, such as molybdenum disulfide, boron nitride or other single-atom or single-molecule-thick materials.

“One potential application that’s very exciting is in nanoelectromechanical systems, or NEMS,” Carpick said. “Switches made from NEMS can function as transistors but use mechanical, not electrical switching. The electrodes need robust surfaces to avoid failing, and a graphene coating could be ideal.” But that is still some ways off. While graphene is a promising material being widely studied, “such an application is years away, but it’s exciting to see that we can reduce friction at the nanoscale and understand how to optimize it.”

Xin Liu is now a process engineer at Intel Corporation. Qunyang Li is now an associate professor at Tsinghua University, China.

The work was supported by the National Science Foundation under grants CMMI-1401164 and MRSEC DMR-1120901.