A generalization of the Coulomb’s friction law: from graphene to macroscale

Abstract

At the nanoscale, differently to what happens at the macroscale, friction even without an applied normal pressure and spontaneous adhesion take place. In particular, the nanotribology between two layers of graphene, or other two-dimensional nanomaterials (even curved, such as nanotube walls), remains controversial. It is sufficient to say that friction between two graphene layers or nanotube walls is described in the current literature giving as "material property" a constant friction force or a constant friction shear strength, even if such views are obviously mutually exclusive. Is friction dominated by a strength, by a force or by an energy? Coupling elasticity and energy balance we solve this paradox deriving a generalization of the celebrated Coulomb's friction law, reconciling the two current views. Molecular dynamics simulations on graphene are conducted to verify its validity at the nanoscale whereas statistical simulations confirm its validity even at the macroscale.

Mechanical behavior and properties of hydrogen bonded graphene/polymer nano-interfaces

“…Our result about the value of interfacial stiffness, strength as well as its relation with the frictional stress (a ¼ 1) are similar to that reported previously for a graphene/PET interface [11]. Particularly, in the terms of frictional stress to strength ratio, the related mechanism was also revealed through molecular dynamics (MD) simulations about vdW interaction dominated graphene interfaces where adhesion and sliding force would spontaneously take place even without an applied normal pressure, resulting in the unique frictional behavior of graphene-based vdW interfaces rather than shear-type interfacial delamination observed in macroscopic interfaces [19]. Meanwhile, its high frictional stress to strength ratio of graphene-based vdW interfaces can also result in huge interfacial energy dissipation during deformation [41,47], as macroscopically achieved high damping performance in nanocarbon based nanocomposites [48e50].…”

“…Nanoscale frictional behavior beyond the well-established linear interfacial mechanics in fiber-based composites should thus be carefully considered for pristine graphene-based nano-interfaces, in order to experimentally evaluate their mechanical behavior and properties. Similar results were also revealed through molecular dynamics (MD) simulations about vdW interaction dominated graphene interfaces where adhesion and sliding force would spontaneously take place even without an applied normal pressure [19]. More recently, Zhu et al also developed a nonlinear shear-lag model by assuming a constant frictional/sliding stress (i.e.…”

“…And the applied strain and length of damaging region could be given by the combination of Eqs. (18) and (19). (iii) During the elastic-damagingfrictional stage, the controlling behavior becomes the propagation of the sliding region from the edge to the center of interface.…”

Static and dynamic friction of hierarchical surfaces

“…This model was first introduced by Burridge and Knopoff [22] in the study of the elastic deformation of tectonic plates. Despite its simplicity, the model is still used not only in this field [23][24][25], but also to investigate some aspects of dry friction on elastic surfaces, e.g., the static to dynamic friction transition [26][27][28][29][30], stick-slip behavior [31][32][33], and the role of regular patterning [34].…”

Understanding and strain-engineering wrinkle networks in supported graphene through simulations

“…2(b), many more short wrinkles nucleate and the reorganization of the wrinkle network is hindered, leading to smaller subdomains. Friction could be modulated experimentally by controlling the pressure difference across the graphene sheet (Kitt et al, 2013;Pugno et al, 2013), since graphene is impermeable to common gases (Bunch et al, 2008). On the other hand, strain anisotropy leads to ripples and wrinkles aligned with the principal directions of anisotropy (Huang et al, 2005;Kim, P. et al, 2011), see Fig.…”