Exactly 300 years after Guillaume Amontons produced the classic laws of friction, physicists at Johns Hopkins have accounted for the notable endurance of Amontons' equations by identifying the molecular origins of static friction.

It's that stuff in the middle.

"Typically, when someone measures friction, what they will report is the ratio of force to the load, which is the coefficient of friction," said Mark Robbins, professor of physics. "But it's never been understood at the molecular level how we get this linear relationship, or why it should hold for a wide array of materials and geometries. Our work now shows that the gunk in the middle--typically hydrocarbon molecules that are almost always present between two surfaces--provides an explanation."

The findings are reported in the June 4 issue of the journal Science by Robbins and his colleagues Gang He and Martin Muser.

Amontons' laws, relied upon extensively and routinely by engineers for three centuries, state that the frictional force needed to slide one body over another is proportional to the load that presses them together and is also independent of the areas of the surfaces. Scientists have argued, however, about the relative importance of surface roughness, chemistry and other factors that might contribute to friction.

Simple theories that leave out the "stuff in the middle" predict that static friction, the force needed to initiate sliding, should vanish between almost any pair of solids. In reality, if that were true, every piece of furniture in a room would slide to one corner and buildings would collapse. The data compiled by Robbins and his colleagues show that hydrocarbon molecules that adsorb on any surface exposed to air resolve this problem. The molecules actually rearrange to lock contacting surfaces together and produce the static friction force that satisfies Amontons' laws.

Scientists have known for centuries that hydrocarbons and other so-called "third bodies" play a significant role in friction. Only in the last decade, however, has a flurry of new experimental probes allowed scientists to study the origins of friction at the atomic scale. At the same time, more powerful computers have given researchers like Robbins and his colleagues an opportunity to simulate accurately the motion of thousands of atoms and determine more about the fundamental nature of friction.

On the whole, Robbins said, "the natural inclination for people approaching the problem has been to try to simplify the analysis as far as possible by disregarding the so-called 'dirt' between surfaces. Normally, you would think that, by introducing these other molecules, your analysis would just be made more complex. But the fact is, this 'dirt' makes something that would be very complicated quite simple."

Using molecular dynamics models, Robbins and his colleagues simulated the presence of third body hydrocarbons along the interface of a variety of contact surfaces. Interestingly, they discovered that varying the length of the molecular chain produced little change in the coefficient of friction. Increasing the number of hydrocarbon layers had no real effect either.

"Friction is a very, very complicated thing," Robbins observed, "and I want to be careful not to suggest that we've now explained it all. But I think most people who have heard about this work seem interested that such a simple picture can give a nice general result that's consistent with Amontons' laws.

"Clearly our model doesn't have all the complexity of the real world--the roughness of real surfaces, the chemical properties of different materials and actual molecules--but it does show how important these third bodies are. From now on, people who do simulations will have to look very carefully at the stuff in the middle."

The research was funded by the National Science Foundation and Intel Corp.