Critical peeling of tethered nanoribbons

The peeling of an immobile adsorbed membrane is a well-known problem in engineering and macroscopic tribology. In the classic setup, picking up at one extreme and pulling off result in a peeling force that is a decreasing function of the pickup angle. As one end is lifted, the detachment front retracts to meet the immobile tail. At the nanoscale, interesting situations arise with the peeling of graphene nanoribbons (GNRs) on gold, as realized, e.g., by atomic force microscopy. The nanosized system shows a constant-force steady peeling regime, where the tip lifting h produces no retraction of the ribbon detachment point, and just an advancement h of the free tail end. This is opposite to the classic case, where the detachment point retracts and the tail end stands still. Here we characterise, by analytical modeling and numerical simulations, a third, experimentally relevant setup where the nanoribbon, albeit structurally lubric, does not have a freely moving tail end, which is instead elastically tethered. Surprisingly, novel nontrivial scaling exponents appear that regulate the peeling evolution. As the detachment front retracts and the tethered tail is stretched, power laws of h characterize the shrinking of the adhered length, the growth of peeling force and the peeling angle. These exponents precede the final total detachment as a critical point, where the entire ribbon eventually hangs suspended between the tip and the tethering spring. These analytical predictions are confirmed by realistic MD simulations, retaining the full atomistic description, also confirming their survival at finite experimental temperatures.