Elsevier

Carbon

Volume 49, Issue 13, November 2011, Pages 4111-4121
Carbon

Mechanical properties of graphyne

https://doi.org/10.1016/j.carbon.2011.05.024Get rights and content

Abstract

Carbon nanotubes and graphene have paved the way for the next step in the evolution of carbon materials. Among the novel forms of carbon allotropes is graphyne – a two-dimensional lattice of sp–sp2-hybridized carbon atoms similar to graphene for which recent progress has been made in synthesizing dehydrobenzoannulene precursors that form subunits of graphyne. Here, we characterize the mechanical properties of single-atomic-layer graphyne sheets by full atomistic first-principles-based ReaxFF molecular dynamics. Atomistic modeling is carried out to determine its mechanical properties for both in-plane and bending deformation including material failure, as well as intersheet adhesion. Unlike graphene, the fracture strain and stress of graphyne depends strongly on the direction of the applied strain and the alignment with carbon triple-bond linkages, ranging from 48.2 to 107.5 GPa with ultimate strains of 8.2–13.2%. The intersheet adhesion and out-of-plane bending stiffnesses are comparable to graphene, despite the density of graphyne being only one-half of that of graphene. Unlike graphene, the sparser carbon arrangement in graphyne combined with the directional dependence on the acetylenic groups results in internal stiffening dependent on the direction of applied loading, leading to a nonlinear stress–strain behavior.

Introduction

The superlative properties and potential applications of synthetic carbon materials – particularly fullerenes [1], nanotubes [2] and graphene [3] – illustrate their unique scientific and technological importance and have motivated substantial research efforts in recent years. Recent investigations of “exotic” carbon allotropes – including the successful synthesis of carbyne [4] and graphdiyne [5], and the prediction of T-carbon [6], [7] – illustrate the continuing interest in all-carbon chemistries beyond already known (and well studied) allotropes such as fullerenes, nanotubes, and graphene [8]. Among the remaining predicted forms of carbon allotropes [9], graphyne has been the subject of little yet continuing interest among structural, theoretical, and synthetic scientists due to its unknown electronic, optical, and mechanical properties [10], [11], [12], [13], [14], [15], as well as proposed practical strategies of synthesis [14], [16], [17], [18]. Although currently, large homogenous sheets of graphyne with long-range ordered (periodic) internal structures have not yet been reported, there are increasing efforts in the synthesis and assembly of a class of molecules known as dehydrobenzoannulenes (DBAs), a precursor and subunit of graphyne [14], [18]. Indeed, new synthetic methods in annulene chemistry [19], [20] now enable the assembly of a diverse array of DBA topologies, leading to an increasing potential and inevitable synthesis of graphyne. For example, recently the first successful synthesis of thin films of graphdiyne was achieved on copper substrates via a cross-coupling reaction using hexaethynylbenzene [5]. There has been particular interest in terms of electronic properties, motivating previous theoretical, experimental and quantum-scale studies [13], [21], [22], [23]. However, the elastic and mechanical properties, critical to successful implementation, have yet to be explicitly determined. In addition, the search for new modifications of carbon has produced several new classes of macrocycles that feature conjugated all-carbon backbones without annellated benzene rings and display highly interesting properties [24]. These systems – including dehydroannulenes, expanded radialenes, radiaannulenes, expanded “Platonic” objects, and alleno-acetylenic macrocycles – may well serve as precursors to graphyne in the near future [24]. In the interim, the mechanical characterization approach outlined herein can equally be applied to such molecular substructures to exploit the combinatorial features of mixed carbon networks (such as unique molecular architectures based on expanded dehydroannulenes and expanded radialenes scaffolds).

The atomistic-level characterization techniques described herein are equally applicable to small, graphyne-like DBA substructures and can be immediately applied to various possible carbon geometries. To provide immediate quantitative comparison, there is an extensive catalogue of work currently available regarding the mechanics of carbon nanotubes and graphene facilitating a direct assessment of the mechanical performance of graphyne.

Naturally occurring carbon exists in only two allotropes, diamond and graphite, which consist of extended networks of sp3- and sp2-hybridized carbon atoms, respectively. Other ways to construct carbon allotropes are theoretically possible by altering the periodic binding motif in networks consisting of sp3-, sp2- and sp-hybridized carbon atoms [24], [25], [26]. Specifically, graphyne is a two-dimensional structure of spsp2-hybridized carbon atoms (Fig. 1a), and thus graphyne can be thought of as simply replacing one-third of the carbon–carbon bonds in graphene by triple-bonded carbon linkages. The presence of these acetylenic groups in these structures introduces a rich variety of optical and electronic properties that are quite different from those of graphene or carbon nanotubes. Although significantly large molecular segments of graphyne have been experimentally synthesized [14], large regular sheets of graphyne have yet to be achieved.

Section snippets

Methodology

A series of full atomistic calculations of mechanical test cases is implemented here by classical molecular dynamics (MD) to derive a simplified set of parameters to mechanically characterize monolayer graphyne. Similar approaches have been used for the characterization of carbon nanotubes [27] and graphene systems [28]. The test suite implemented consists of the following three loading cases: (i) a stacked assembly of two sheets to determine the adhesion energy per unit area, γ, as well as

Bond length analysis

The structure acetylene linked aromatic structure of graphyne is depicted in Fig. 1. There are a number of literature reports discussing the method and basis set dependency of the degree of bond length alternation (BLA) in conjugated π-systems – DFT methods in which ReaxFF is based tend to overly favor more delocalized structures with less BLA [41], [42], [43], and thus more consistent and homogeneous bond lengths are anticipated. Being said, it has been demonstrated that optimization of

Conclusion

The intensive study of carbon nanotubes and graphene has now paved the way for the next step in the evolution of carbon materials. Progress in carbon nanotube and graphene science has been driven by the theoretical predictions from first-principles-based simulations which were tested with experimental work, and vice versa. Similarly, the motivation for the determination of the properties of novel materials such as graphyne leads to important insights that drive the development of new models and

Acknowledgements

This work was supported primarily by the MRSEC Program of the National Science Foundation under award number DMR-0819762. The calculations and the analysis were carried out using a parallelelized LINUX cluster at MIT’s Laboratory for Atomistic and Molecular Mechanics (LAMM). Visualization has been carried out using the VMD visualization package [76]. We recognize Professor Eduardo Kausel (MIT) for providing the impetus of investigation.

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