Graphene is one of the most researched materials in the world today. The explanation is simple: consisting of a single layer of carbon atoms arranged in a two-dimensional honeycomb lattice of repeating hexagons, graphene is extremely thin, light and tough. In view of its other properties, such as transparency, flexibility, high electric and thermal conductivity, and low production cost, the number of potential applications is practically unlimited.
Despite the vast amount of research conducted on graphene to date, however, a significant trait has only just been discovered by Brazilian researchers, who recently published their findings in Scientific Reports, an online journal published by Springer Nature.
As evidenced by the title of their article, “Giant and tunable anisotropy of nanoscale friction in graphene”, graphene exhibits an extraordinary degree of friction anisotropy when scanned in different directions by the tip of an atomic force microscope (AFM).
If the properties of a material are anisotropic, their values differ when measured along axes in different directions.
“Observation showed that the friction force between the microscope tip and the graphene sheet was highly dependent on the scanning direction,” said physicist Douglas Soares Galvão, a co-author of the article, in an interview with Agência FAPESP.
“The energy dissipated along the armchair direction is as much as 80% greater than the energy dissipated along the zigzag direction.”
Galvão is Full Professor at the University of Campinas’s Physics Institute (IF-UNICAMP) in São Paulo State and a researcher at the Center for Computational Engineering and Sciences (CCES), one of the 17 Research, Innovation and Dissemination Centers (RIDCs) supported by FAPESP.
Armchair and zigzag are crystallographic terms referring to graphene lattice edge geometry and were the two main directions considered in the study.
“In graphene, crystallographic directions are determined with an atomic force microscope using the friction force mode,” said physicist Clara Muniz da Silva Almeida, lead author of the article. “We used this technique to establish the directions in the graphene sheet and measure friction at the nanoscale.”
Almeida heads the Atomic Force Microscopy Laboratory in the Material Metrology Division of the National Institute of Metrology, Quality & Technology (INMETRO), based at its Xerém campus in Duque de Caxias, Rio de Janeiro State.
According to the article, the “giant anisotropy” in values of the friction force, and hence in the energy dissipated along the different directions, is surprising because the linear elastic properties of graphene are isotropic. A small difference in dissipated energy between crystal directions would have been expected, as in graphite, which is essentially a stack of graphene sheets. However, the researchers’ experimental measurements confounded this expectation, showing a difference of up to 80% between the two directions in terms of dissipated energy.
“This is due to deformation of the graphene sheet by the tip of the microscope. The deformation is amplified differently in each direction, determining different values of friction force. A simple analogy of this phenomenon is the way a piece of cloth forms waves while being ironed,” Galvão said.
“It was a surprise to find that friction force increased in proportion to the number of graphene layers. But the analogy with ironing also helps explain this. When several pieces of cloth are laid on top of one another, the result is a rigid structure that practically doesn’t deform at all as the iron passes over it. Similarly, in the case of graphite, which consists of many layers of graphene, deformation is minimal. However, as the number of layers diminishes down to a single sheet, deformation becomes very significant.”
For Almeida, “the flexural deformation produced in the graphene sheet by the microscope tip determines different undulations depending on the direction. Moving this undulation in the zigzag direction is much easier than in the armchair direction.”
Put like that, it sounds simple. To explain the experimentally detected difference, however, the researchers had to call on a combination of three robust theoretical frameworks: the Prandtl-Tomlinson model, used in the description of atomic-scale friction mechanisms; atomistic molecular dynamics; and density functional theory, which is derived from quantum mechanics.
According to the researchers, the effect can be understood as a nanoscale manifestation of the classical phenomenon of “Euler buckling”. The great Swiss mathematician and physicist Leonhard Euler (1707-83) is well known in structural engineering for his critical buckling load formula.
Graphene’s unique electronic, thermal and mechanical properties make it a strong candidate for inclusion in the production process of next-generation electronic devices and nanoelectromechanical systems (NEMS). Such applications require a profound understanding of the mechanical and tribological properties of this and other two-dimensional materials (tribology covers the design, friction, wear and lubrication of interacting surfaces in relative motion).
“The anisotropy we found could be a determinant in the fabrication of NEMS, since their design requires prior knowledge of crystal orientation,” Almeida stressed. “Most of the time, the properties of a 2D material such as graphene are very different from the well-known properties of the 3D configuration, which in this case is graphite.”
Almeida’s group at INMETRO started working with graphene in 2010. Since then, they have researched graphene defect metrology, performed AFM determination of graphene sheet crystal orientation, and used AFM for graphene manipulation to create new nanostructures and, now, graphene nanotribology.