Crumpling Damaged Graphene

Abstract

Through molecular mechanics we find that non-covalent interactions modify the fractality of crumpled damaged graphene. Pristine graphene membranes are damaged by adding random vacancies and carbon-hydrogen bonds. Crumpled membranes exhibit a fractal dimension of 2.71 ± 0.02 when all interactions between carbon atoms are considered, and 2.30 ± 0.05 when non-covalent interactions are suppressed. The transition between these two values, obtained by switching on/off the non-covalent interactions of equilibrium configurations, is shown to be reversible and independent on thermalisation. In order to explain this transition, we propose a theoretical model that is compatible with our numerical findings. Finally, we also compare damaged graphene membranes with other crumpled structures, as for instance polymerised membranes and paper sheets, that share similar scaling properties.

Phase diagram of a flexible two-dimensional material

“…It was shown that (i) disorder can crumple a membrane in agreement with Ref. [31] and (ii) instability of the rippled phase predicted in Refs. [29,30] develops logarithmically slow, i.e., the marginal T = 0 rippled phase controls elastic properties of disordered freestanding graphene for T = 0 in a wide interval of length scales (see also Ref.…”

“…In graphene, κ 0 ∼ 1 eV, so that the thermal fluctuations alone are not enough to crumple it. At the same time, recent numerical simulations of disordered graphene clearly indicate the crumpling transition [31]. Additional evidence for the importance of disorder in graphene is provided by recent experimental measurements of anomalous Hooke's law [32,33].…”

“…This conclusion implies the absence of the stable rippled phase and, at first glance, contradicts the observations of Refs. [31][32][33][34]. Recently, the crumpling transition in disordered freestanding graphene was addressed in Ref.…”

“…Alternatively, observations in Refs. [31][32][33] could be the manifestation of a stable rippled flat phase at T = 0. Here, we use the standard model of a disordered membrane and prove that the second scenario is realized.…”

Schramm--Loewner Evolution in the Random Scatterer Henon-percolation Landscapes

“…A good review on the subject can be found in [2]. The most important examples for the less-known models are also the BTW sandpile model [10][11][12], the watersheds [13], the graphene system [14,15], the normal state of the YBCO superconducting planes [16], the random field Ising model [17], the Ising model on the * morteza.nattagh@gmail.com percolation systems [18], the (2 + 1)-dimensional growing surfaces [19], the Darcy model of fluid propagation in the porous media [20] and the three-state Potts model [21]. Many aspects of this model are known, ranging from its Fokker-Planck equation [22], to its relation to the other models like the Coulomb gases [2], and also many statistical features (SLE predictions) of the the random curves are kown, such as the left passage probability [4], the fractal dimension, and the Cardy's crossing probability [2].…”