Inverse Friction Force – Load Dependence of Graphene

Atomistic Simulation of Gold-Graphene Interface


When the bodies slide against each other, the classic Amonton’s law states that the friction force is directly proportional to the applied normal load. This law holds true for various if not most of the engineering materials, like metals, ceramics etc. At the same time, the law is in agreement with the experiments across all the length scales (although at nanoscale the nonlinear behavior maybe observed).

Two-dimensional carbon based material, known as graphene, is unique in many senses and particularly may exhibit a negative normal load – friction force dependence, e.g., its friction decreases with the increase of the applied normal load. This behavior was observed experimentally, however, the exact mechanism responsible for such a peculiar behavior was not understood. To add more, this behavior was observed only for suspended graphene (a sheet deposited on a substrate with holes for example), and not for the supported (deposited on a substrate).

Recently, for the first time researchers from the University of California Merced could reproduce the peculiar behavior of the friction force – normal load behavior of the suspended graphene using molecular dynamic simulations. They found that the area of contact increased with the increase of load for both, suspended and supported graphene. The increase in the area of contact typically leads to an increase in friction force. However, in case of the suspended material, this was not the case.

Instead, the out-of-plane deformation of the graphene sheet, forming a puckered region in front of the sliding tip, called wrinkle, was found to be well correlated with the negative load behavior. The wrinkle first increased with the applied load, the same way as the friction force, but with further increase of the load, it started to decrease. It was therefore concluded, that in case of supported graphene, the area of contact dominates the friction, whereas in the suspended material, its the wrinkle height responsible for the friction.

The details of the simulations can be found in the original paper: “Atomistic Simulation of the Load Dependence of Nanoscale Friction on Suspended and Supported Graphene” Langmuir, DOI: 10.1021/la503329u.

Credit for image: Zhijiang Ye and Ashlie Martini, “Atomistic Simulation of the Load Dependence of Nanoscale Friction on Suspended and Supported Graphene”.

Founder of TriboNet, Editor, PhD (Tribology), Tribology Scientist at ASML, The Netherlands. Expertise in lubrication, friction, wear and contact mechanics with emphasis on modeling. Creator of Tribology Simulator.


  1. Aydar, I wonder if this “negative normal load” behavior would be seen on the surface of a curved graphene shell, “suspended” about a solid core? Such a situation might be the case in an endohedral metallofullerene such as an SGAN synthesized from Phantaslube®. In addition, has anybody suggested that the observed “negative normal load” effect is from interactions between pi orbitals (possibly curved and out of 90 degree plane) at the point of contact? I seem to remember that geometry was important to Bent’s Rule-type discussions.

  2. It would be a good MD simulation to try to answer the question. But as long as I understand, the condition for this strange behavior is the absence of the substrate beneath the graphene layer. I dont know, if that would be possible, for graphene covering the solid core. I am not familiar with the Bent’s rule, actually. What do you think is the mechanism for the negative load dependence?

    • Upon reflection (relative to your comments above) and a bit of study, I think I have a classical thermodynamics/CFD answer. I am somewhat trepidatious in typing this, and hope some more-qualified CFD people will chime in on this soon!

      I think the reason that this “strange behavior” is only seen in “suspended” graphene relates to the creation thereby of an “adiabatic system” where by heat generated by friction cannot be transferred to a substrate, and is instead converted to work (see generally, the work of W.J.M. Rankine in his theories regarding Rankine-Hugoniot conditions in one-dimensional deformation of solids).
      In short, the idea is that heat generated from the frictional compression of the elastic solid cannot get transferred (due to the theoretical adiabatic system), so it is converted directly to work on its surroundings.
      This idea began while I considered the analogy of the suspended graphene conditions to formation of low-pressure “bow waves” in front of ships (“constructive interference “) and the work done by release of the pressure differential.
      I am now looking at so-called ” MCE” (magnetocaloric effect) with regard to this observed phenomenon, but would really like to defer to a quantum mechanics person on this.
      p.s. sorry I was not logged-in to tribonet at the time I typed this at home.

      • Now, looking at graphene’s negative thermal expansion coefficient (TEC) and high thermal conductivity, I am intrigued by just having read about inhomogeneous strain in graphene inducing pseudo-magnetic fields! If work in = work out…with no losses due to heat transfer (adiabatic system), something’s gotta’ give!

  3. From the paper referenced above…
    “As mentioned above, such contraction of the edge bond induces the magnetism of [graphene nanoribbons in the armchair configuration]. The applied tensile strain brings about the variation of the bond length. When the strain is in the range of 9%, both L1 and L2 show fluctuations as the strain increases, which is consistent with the spin moment variation. However, when the strain rises to 10%, L1 sharply drops whileL2 keeps increasing as the tensile strain increases. This explains the dramatic transition of the magnetism in monolayer [armchair graphene nanoribbons] beyond the strain of 10%. It is because such sudden variations of the bond lengths, where the spin moment is localized, could reduce the stability of the edge-quantum well and lead to the redistribution of the excess electrons. Here an interesting point should be noticed, when the strain is in the range of 6% to 10%, the value of L1 decreases, although it should increase under the tensile strain.”

    Could this be part of the MD answer to the graphene friction paradox?

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