Focus: Surface Grime Explains Friction

Published February 8, 2001  |  Phys. Rev. Focus 7, 6 (2001)  |  DOI: 10.1103/PhysRevFocus.7.6

Simple Microscopic Theory of Amontons's Laws for Static Friction

Martin H. Müser, Ludgar Wenning, and Mark O. Robbins

Published February 12, 2001
Figure 1
© 2001 Photodisc, Inc.

Old view of friction. The standard frictional force law makes sense only if the two surfaces are identical crystals, fitting together at the atomic level like a pair of gears. New theory and computer simulations show that for mismatched surfaces, a molecular coating of grit explains static friction.

Static friction is everywhere. It’s in that little extra shove at the beginning of a wild downhill sled ride and the first big push that starts a heavy piece of furniture rolling across the floor. But according to the modern microscopic theory of interacting surfaces, it shouldn’t exist at all. Now, in the 12 February PRL, a team of physicists has built an analytic theory, backed up with detailed numerical modeling, that may explain why virtually every pair of surfaces lock together and resist sliding. The key is that impurities like dust, dirt, and stray molecules, coat nearly every surface and prevent smooth motion.

The laws of static friction were first laid down by Guillaume Amontons, a 17th century French researcher who believed that surfaces have regular jagged edges like the teeth in a bicycle wheel gear. When two surfaces meet, his theory said, the teeth of the upper surface settle into the grooves of the lower surface. To get the upper surface sliding, a lateral force has to lift the teeth out of the grooves–that force is static friction. Accordingly, Amontons’ laws say that static friction is proportional to the weight of the upper plate and independent of the plate’s surface area.

The gears in a car transmission will grind and lock unless they line up precisely, but a mismatch at the molecular level has the opposite effect. Theoretical models predict zero static friction for mismatched surfaces. “You can also envision the surfaces as strands of balls with different diameters,” explains Mark Robbins of Johns Hopkins University in Baltimore. When a surface of ping-pong-ball-sized strands, for example, is placed on a surface of tennis-ball-sized strands, some ping pong balls sit perched on top of a tennis ball and others settle into the spaces between balls. To slide the upper surface, one expends energy to lift up the ping pong balls that are lying in the spaces, but recovers energy from the balls that drop from their perches. When you add up all the energy gains and losses for this theoretical model of a surface, they exactly cancel; no extra energy is required to start the sliding.

Now Robbins and his colleagues argue that previous models failed to explain static friction because they didn’t account for inevitable surface impurities–like dust, fingerprints, and even water vapor. These molecules are like marbles that roll to the open niches between the strands of ping pong and tennis balls, locking the two surfaces together. The team found that the marbles always find a local energy minimum, and so it always takes energy to start sliding. Both a simple analytic expression and detailed computer simulations of sliding surfaces show that this model explains Amontons’ laws. “It is the schmutz from the air that locks the surfaces and causes friction,” says Robbins.

“This is a general philosophy of friction that is very compelling,” says Miquel Salmeron of the Lawrence Berkeley National Laboratory in California. “The idea that [impurities] could influence friction had been floating around for years, but people hadn’t thought of it in this simple form until now.” Salmeron’s group is one of many that are trying to carry out the challenging experimental verification of the theory. “It is very difficult to make sure that no extra atoms are present,” he says. “But the challenge is there, so people will find a way.”

–Mark Sincell

Mark Sincell is a freelance science writer based in Houston, TX.


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New in Physics