Understanding friction laws at the nanoscale and their relation to the macroscale

Dr. Neil Canter, Contributing Editor | TLT Tech Beat July 2009

A new theoretical approach found that friction at the nanoscale is consistent with friction at the macroscale.

KEY CONCEPTS
• Friction at the nanoscale has been described by continuum mechanical theories, which treat the contact at the single-asperity level as contacting linear-elastic homogeneous spheres. This approach breaks down because surfaces at the nanoscale are, in fact, rough.
• Molecular dynamic simulations were used to determine how interactions between atoms and an AFM tip depend on the applied load and the contact area.
• Frictional laws observed between two sliding surfaces at the nanoscale have been found for the first time to be consistent with the fractional behavior of rough macroscale contacts.

A fundamental understanding of the nature of friction at the nanoscale is still sought so that we in the lubricant industry can better develop technologies to overcome it. We know that friction on the macroscopic scale occurs through a loss of energy as one object slides on a second object. The energy is lost through the generation of heat.

In a previous TLT article, research conducted by Robert Carpick described the connection between the vibrational properties of atoms and friction (1). Carpick evaluated the effectiveness of hydrogen and deuterium atoms at resisting the motion of the tip of an atomic force microscope (AFM). He found that hydrogen generated a 30% increase in friction over deuterium because atoms of the former collided more frequently with the AFM tip due to their lighter mass as compared to deuterium.

Izabela Szlufarska, assistant professor of materials science and engineering at the University of Wisconsin-Madison, says, “Friction at the nanoscale has been described by continuum mechanical theories. An example of such theories is the Hertz model, which treats the contact at the single asperity level as contacting linear-elastic homogeneous spheres. If the adhesion in contact plays an important role—which is often the case at the nanoscale—other continuum level theories are being used (e.g., the Maugis-Dugdale model).”

The continuum mechanics approach breaks down because of its assumption that surfaces at the nanoscale are smooth while, in fact, atomic roughness plays an important role at the nanoscale. This topic has been extensively studied by Robbins (2). Szlufarska adds, “Surfaces at the nanoscale are, in fact, rough with the topography being similar to a mountain range. Atoms and molecules are positioned at the tops of the peaks and act as rough objects rubbing against each other.”

A new theoretical approach is needed to determine the effect of atomic-scale roughness on friction laws (i.e., friction force dependence on the applied load). Such an approach has not been conducted until now.

SCANNING FORCE MICROSCOPY SIMULATIONS
Szlufarska and coworkers Kevin Turner, assistant professor of mechanical engineering, and Yifei Mo, materials science graduate student, used molecular dynamic simulations to gain a better understanding of the laws of friction at the nanoscale. Szlufarska says, “We are able to use molecular dynamics to track motion of individual atoms and to determine the friction force when an AFM tip slides across a sample. In conducting the simulations, we were able to determine how interactions between atoms across the contact contribute to friction and how friction depends on the applied load and the contact area.”

The simulation focused on using an amorphous carbon AFM tip that interacts with a diamond surface. Szlufarska says, “We chose these materials because experimental data has been generated for their interaction. Our objective is to be able to compare the molecular dynamic simulations with the experimental data.”

Both materials are terminated with hydrogen atoms. The AFM tip is spherical with a curvature radius of up to 30 nanometers.

Figure 1 shows the contact taking place between the spherical tip and the diamond surface. Carbon and hydrogen atoms are represented in gold and red, respectively. The close-up view of the interaction shows the rough nature of the surface. Atoms interact literally by rubbing against each other. Solid golden and red sticks represent covalent bonds. Repulsive interactions are represented by translucent pink sticks.


Figure 1. Frictional forces generated during the interaction between an amorphous carbon AFM tip and a diamond surface are directly proportional to the number of atoms interacting between the two rough surfaces. For the first time, frictional laws seen in this nanoscale study are consistent with frictional behavior between rough macroscale contacts. (Courtesy of the University of Wisconsin- Madison)

The system modeled contains between six million and 10 million atoms. Szlufarska says, “We used the model to describe interactions among atoms over time. Forces displacing atoms are measured accurately because resolution is achieved at the atomic scale.”

As the probe moves across the diamond surface, the frictional forces measured are directly proportional to the number of atoms that interact between the two surfaces. Through this discovery, the researchers were able to directly correlate fundamental properties of contact (e.g., number of interfacial bonds) with frictional response of the system.

The key in doing this analysis is to realize that a contact area between the AFM tip and the diamond surface is not defined by the edge of the contact, which is the continuum mechanics definition. Szlufarska says, “The real contact area is smaller than that and is defined as the number of atoms interacting across the interface multiplied by the average surface area per atom.”

Molecular dynamic simulations were done in the presence and absence of van der Waals forces, and it was shown that friction force dependence on the applied load changes from sublinear to linear as the adhesion of the contact is reduced. The scanning force microscopy simulations have been performed at the length scale comparable to the AFM experiments, and the simulations used highly accurate descriptions to compute interatomic forces. Consequently, for the first time molecular dynamics simulations have quantitatively reproduced experimental friction forces and shear strengths. Szlufarska adds, “The simulation results we have obtained correlate well with experimental work carried out with amorphous carbon tips on a diamond surface.”

The researchers have shown for the first time that frictional laws we observe between two sliding surfaces at the nanoscale are consistent with frictional behavior of rough macroscale contacts. Szlufarska says, “We have taken the roughness theories at the macroscale that were developed for macroscale contacts and applied them successfully to model behavior of contacts with atomic roughness.”

Future work will involve determining how to quantitatively predict friction forces and interfacial shear strengths and how to determine the dominant energy dissipation mechanisms that underlie friction in various environmental conditions.

Other systems that the research team is studying include silicon carbide and ultrananocrystalline diamond. They will be evaluated to determine which frictional behavior is material-specific and which is generally applicable to any material. Further information can be found in a recently published article (3).

REFERENCES
1. Canter, N. (2008), “The Nature of Friction,” TLT, 64 (2), pp. 14–15.
2. Luan, B. and Robbins, M. (2005), “The Breakdown of Continuum Models for Mechanical Contacts,” Nature, 435, pp. 929–932.
3. Mo, Y., Turner, K. and Szlufarska, I. (2009), “Friction Laws at the Nanoscale,” Nature, 457, pp. 1116–1119.

Neil Canter heads his own consulting company, Chemical Solutions, in Willow Grove, Pa. Ideas for Tech Beat items can be sent to him at neilcanter@comcast.net.