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Relation between interfacial shear and friction force in 2D materials


Understanding the interfacial properties between an atomic layer and its substrate is of key interest at both the fundamental and technological levels. From Fermi level pinning to strain engineering and superlubricity, the interaction between a single atomic layer and its substrate governs electronic, mechanical and chemical properties. Here, we measure the hardly accessible interfacial transverse shear modulus of an atomic layer on a substrate. By performing measurements on bulk graphite, and on epitaxial graphene films on SiC with different stacking orders and twisting, as well as in the presence of intercalated hydrogen, we find that the interfacial transverse shear modulus is critically controlled by the stacking order and the atomic layer–substrate interaction. Importantly, we demonstrate that this modulus is a pivotal measurable property to control and predict sliding friction in supported two-dimensional materials. The experiments demonstrate a reciprocal relationship between friction force per unit contact area and interfacial shear modulus. The same relationship emerges from simulations with simple friction models, where the atomic layer–substrate interaction controls the shear stiffness and therefore the resulting friction dissipation.

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Fig. 1: Interfacial transverse shear modulus experiment.
Fig. 2: Interfacial shear modulus measurements.
Fig. 3: Correlation between friction force and interfacial shear modulus.
Fig. 4: Friction force and interfacial shear modulus relationship.
Fig. 5: Friction force FK modelling.

Data availability

The data that support the findings of this study are available from the Figshare repository at This repository contains the data presented in all figures, including those in the Supplementary Information.

Code availability

The source simulation codes are available from the Figshare repository at


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This work was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under award no. DE-SC0018924 and the US Army Research Office under award no. W911NF2020116. We also acknowledge W. de Heer and C. Berger for providing the twisted 10 L epitaxial graphene samples. We thank A. Bongiorno for stimulating discussions.

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Authors and Affiliations



M.R. and F.L. performed the friction force measurements and analysis. M.R. designed and conducted the interfacial shear modulus experiments, performed the PT simulations and analysed the data. E.R. conceived and designed all the experiments and the PT simulations, and analysed the data. A.K. and E.T. designed and carried out the FK simulations. J.K. and M.S. synthesized the epitaxial graphene samples. All the authors contributed to writing the manuscript.

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Correspondence to Elisa Riedo.

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Nature Nanotechnology thanks Michael Urbakh, Stefano Zapperi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information, Figs. 1–15 and Tables 1–3.

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Rejhon, M., Lavini, F., Khosravi, A. et al. Relation between interfacial shear and friction force in 2D materials. Nat. Nanotechnol. 17, 1280–1287 (2022).

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