Critical peeling scaling laws of tethered graphene nanoribbons*

Peeling of surface-deposited nanostructures is commonly executed by AFM pickup and lifting. Its theoretical description has important differences from, e.g., Kendall's theory for macroscopic peeling of adsorbed films [1], because unlike the macroscopic case, many nanostructures are superlubrical sliders.  An appropriate theory was recently put forward by Gigli el al. [2] for superlubric graphene nanoribbons (GNRs) on gold [3,4]. After an initial bending builds up, the system reaches a steady regime, where the peeling angle is π/2 and the curvature is fixed. In that regime, a lifting amount $h$ of the tip produces no advancement of the detachment front, and a simple retraction of the free tail end, opposite to Kendall’s limit, where the detachment point advances and the tail end stands still. A third intriguing situation is expected to arise when the nanoribbon, albeit structurally lubric, does not have a freely moving tail, which may instead be thethered by construction or by accident. Here we show, both analytically and by realistic simulations, novel nontrivial exponents exhibited in this case, that are absent in the  previous cases. As the tip is lifted, the peeling force increases as $h^{1/3}$ and the lifting angle asymptotically drops like $h^{−1/3)$.  As the detachment front advances and the tethered tail retracts, the adsorbed fraction shrinks as $h^{4/3}$. These exponents appear to prepare the final total detachment as a critical point, where the entire ribbon eventually hangs suspended between the tip and tethering spring.

[1] K. Kendall, J. Phys. D. Appl. Phys. 8, 1449 (1975).

[2] L. Gigli, A. Vanossi, and E. Tosatti, Nanoscale 11, 17396 (2019).

[3] S. Kawai, et al., Science 351, 957 (2016).

[4] L. Gigli, et al., ACS Nano 13, 689 (2019).