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The main purpose of this paper is to evaluate the self-stress state ofsingle-wall carbon nanotubes (CNTs) and flat graphene strips (FGSs) in theirnatural equilibrium state, that is, the state prior to the application ofexternal loads. We model CNTs as discrete elastic structures, whose shape andvolume changes are governed by a Reactive Empirical Bond-Order interatomicpotential of second generation. The kinematical variables we consider are bondlengths, bond angles, and dihedral angles; to changes of each of thesevariables we associate a work-conjugate nanostress. To determine theself-stress state in a given CNT, we formulate the load-free equilibriumproblem as a minimum problem for the interatomic potential, whose solutionyields the equilibrium nanostresses; next, by exploiting the nonlinearconstitutive dependence we derive for nanostresses in terms of a list ofkinematical variables, we determine the equilibrium values of the latter;finally, from the equilibrium values of the kinematical variables we deduce thenatural geometry and, in particular, the natural radius. In the achiral case,when we can count on maximal intrinsic symmetries and hence the number ofindependent unknowns is reduced to a minimum, the stationarity conditionsimplied by energy minimization are relatively easy to derive and solvenumerically; for chiral CNTs, we prefer to solve the minimum problem directly.We surmise that our discrete mechanical model may serve as a source ofbenchmarks for MD simulation algorithms. We find that self-stress depends onchanges in both bond and dihedral angles in achiral CNTs and, in addition, onchanges in bond length in chiral CNTs. Our analysis applies also to FGSs, whoseself-stress and self-energy we evaluate; we find that, in FGSs self-stress isassociated exclusively with changes in bond angle.

Geometry and Self-Stress of Single-Wall Carbon Nanotubes and Graphene via a Discrete Model Based on a 2nd-Generation REBO Potential