Elastic properties of graphene and carbon nanoribbons: a combined continuum and atomistic approach

DIPC Seminars

Prof. Luciano Colombo (University of Cagliari)
Donostia International Physics Center (DIPC).Paseo Manuel de Lardizabal, 4 (nearby the Facultad de Quimica), Donostia
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Elastic properties of graphene and carbon nanoribbons: a combined continuum and atomistic approach ** ** A thorough theoretical picture about elastic properties of graphene and carbon nanoribbons, both under stretching and bending deformations, is presented and discussed by combining continuum elasticity theory and tight-binding atomistic simulations. As for stretching elasticity, the stress-strain nonlinear constitutive equation is worked out by continuum theory in both the small-strain and large- strain conditions. Then, by atomistic simulations we compute all the relevant linear and non-linear elastic moduli [1]. In particular, we discuss the physical meaning of the effective non-linear elastic modulus recently measured by nano-indentation of a free standing monolayer graphene sample [2], and we provide a robust interpretation of such an experiment. Through the stress- strain plot we also predict a very high failure stress, in excellent agreement with available experimental data reported in Ref. [2]. The corresponding effective three dimensional failure stress is then obtained to be as large as 130 GPa, exceeding that of most materials (even including multiwalled nanotubes). This result motivates the use of one-atom-thick carbon layers as possible reinforcement in advanced composites. As for bending elasticity, by continuum theory we identify the bending rigidity modulus and we characterize it in terms of the local curvature of a bended ribbon. Then, we calculate the above bending modulus by tight-binding atomistic simulations [3]. Finally, we investigate the elastic behavior of various curved nanoribbons, and we discuss the onset of nano-scale features which are out-of-rich of the continuum picture. In particular, we prove that atomic-scale relaxations upon bending induce an additional strain field of in- plane stretching, which provides new energy contributions. This intriguing result opens the problem of how to disentangle bending and stretching features, an especially important issue of considerable practical interest for small-width nanoribbons. To this aim we define a proof-of-concept computational procedure, based on a virtual process of unbending, and by means of it we put evidence on the stretching emergence in bended nanoribbons. We acknowledge financial and computational support by Cybersar (Cagliari, Italy), and computational support by CASPUR (Roma, Italy) [1] E. Cadelano, P. Palla, S. Giordano, and L. Colombo, Phys. Rev. Lett. 102, 235502 (2009). [2] C. Lee et al., Science, 321, 385 (2008). [3] E. Cadelano, S. Giordano, and L. Colombo, submitted for publication (2010).