We report an extensive study of the properties of carbyne using first-principles calculations. We investigate carbyne's mechanical response to tension, bending, and torsion deformations. Under tension, carbyne is about twice as stiff as the stiffest known materials and has an unrivaled specific strength of up to 7.5 × 10(7) N·m/kg, requiring a force of ∼10 nN to break a single atomic chain. Carbyne has a fairly large room-temperature persistence length of about 14 nm. Surprisingly, the torsional stiffness of carbyne can be zero but can be "switched on" by appropriate functional groups at the ends. Further, under appropriate termination, carbyne can be switched into a magnetic semiconductor state by mechanical twisting. We reconstruct the equivalent continuum elasticity representation, providing the full set of elastic moduli for carbyne, showing its extreme mechanical performance (e.g., a nominal Young's modulus of 32.7 TPa with an effective mechanical thickness of 0.772 Å). We also find an interesting coupling between strain and band gap of carbyne, which is strongly increased under tension, from 2.6 to 4.7 eV under a 10% strain. Finally, we study the performance of carbyne as a nanoscale electrical cable and estimate its chemical stability against self-aggregation, finding an activation barrier of 0.6 eV for the carbyne-carbyne cross-linking reaction and an equilibrium cross-link density for two parallel carbyne chains of 1 cross-link per 17 C atoms (2.2 nm).
The morphology of graphene is crucial for its applications, yet an adequate theory of its growth is lacking: It is either simplified to a phenomenological-continuum level or is overly detailed in atomistic simulations, which are often intractable. Here we put forward a comprehensive picture dubbed nanoreactor, which draws from ideas of step-flow crystal growth augmented by detailed first-principles calculations. As the carbon atoms migrate from the feedstock to catalyst to final graphene lattice, they go through a sequence of states whose energy levels can be computed and arranged into a step-by-step map. Analysis begins with the structure and energies of arbitrary edges to yield equilibrium island shapes. Then, it elucidates how the atoms dock at the edges and how they avoid forming defects. The sequence of atomic row assembly determines the kinetic anisotropy of growth, and consequently, graphene island morphology, explaining a number of experimental facts and suggesting how the growth product can further be improved. Finally, this analysis adds a useful perspective on the synthesis of carbon nanotubes and its essential distinction from graphene.catalysis | Wulff construction | kinetics | growth shape R ecent years have seen development of ever simpler and cheaper methods to produce graphene on metal substrates (1, 2). Yet the quality of as-produced material suffers from defects and polycrystallinity (3-9), with electronic transport orders of magnitude inferior to mechanically exfoliated graphene (10,11). Understanding the atomistic mechanisms governing the sp 2 carbon growth remains a scientific challenge, critical for production of quality graphene, as well as controllable growth of nanotubes. Experimentally, graphene grows at very different conditions, on many different substrates, and from various precursors (12). In principle, this ubiquity is not surprising because graphene is a deep global minimum in the phase diagram of carbon. Overall carbon flow is often pictured as a VLS (vapor-liquid-solid, or vapor-solid-solid) model for nanowires (13,14) or tubes (15). Yet this flow from the higher chemical potential gas-feedstock (μ) into its product (μ 0 ) is mediated by various states of carbon atoms, first bound to the substrate-catalyst and then to the nanotube or graphene edge. The detailed atom-by-atom sequence of carbon accretion to the sp 2 lattice remains essentially unknown. How are these states ordered in space and in energy scale? Accordingly, which are populated or empty, and what serves as the bottleneck controlling the growth rates of different crystallographic faces? The answers to these questions determine how the equilibrium shape is replaced by its kinetic alternative, and how the excess nonequilibrium, Δμ ≡ μ − μ 0 > 0, might impose defects into the generally highly periodic lattice.These questions compel one to step from the VLS paradigm (13-15) up to a more detailed and quantitative view, by assigning specific energies to different locations of C-atoms, migrating toward the edge of graphene...
Carbon nanotubes hold enormous technological promise. It can only be harnessed if one controls their chirality, the feature of the tubular carbon topology that governs all the properties of nanotubes-electronic, optical, mechanical. Experiments in catalytic growth over the last decade have repeatedly revealed a puzzling strong preference towards minimally chiral (near-armchair) tubes, challenging any existing hypotheses and making chirality control ever more tantalizing, yet leaving its understanding elusive. Here we combine the nanotube/ catalyst interface thermodynamics with the kinetic growth theory to show that the unusual near-armchair peaks emerge from the two antagonistic trends at the interface: energetic preference towards achiral versus the faster growth kinetics of chiral nanotubes. This narrow distribution is inherently related to the peaked behaviour of a simple function, xe À x .
Nanomaterials are anticipated to be promising storage media, owing to their high surface-to-mass ratio. The high hydrogen capacity achieved by using graphene has reinforced this opinion and motivated investigations of the possibility to use it to store another important energy carrier - lithium (Li). While the first-principles computations show that the Li capacity of pristine graphene, limited by Li clustering and phase separation, is lower than that offered by Li intercalation in graphite, we explore the feasibility of modifying graphene for better Li storage. It is found that certain structural defects in graphene can bind Li stably, yet a more efficacious approach is through substitution doping with boron (B). In particular, the layered C3B compound stands out as a promising Li storage medium. The monolayer C3B has a capacity of 714 mAh/g (as Li1.25C3B), and the capacity of stacked C3B is 857 mAh/g (as Li1.5C3B), which is about twice as large as graphite's 372 mAh/g (as LiC6). Our results help clarify the mechanism of Li storage in low-dimensional materials, and shed light on the rational design of nanoarchitectures for energy storage.
First-principles calculations for carbyne under strain predict that the Peierls transition from symmetric cumulene to broken-symmetry polyyne structure is enhanced as the material is stretched. Interpretation within a simple and instructive analytical model suggests that this behavior is valid for arbitrary 1D metals. Further, numerical calculations of the anharmonic quantum vibrational structure of carbyne show that zero-point atomic vibrations alone eliminate the Peierls distortion in a mechanically free chain, preserving the cumulene symmetry. The emergence and increase of Peierls dimerization under tension then implies a qualitative transition between the two forms, which our computations place around 3% strain. Thus, zero-point vibrations and mechanical strain jointly produce a change in symmetry resulting in the transition from metallic to insulating state. In any practical realization, it is important that the effect is also chemically modulated by the choice of terminating groups. Our findings are promising for applications such as electromechanical switching and band gap tuning via strain, and besides carbyne itself, they directly extend to numerous other systems that show Peierls distortion.Carbyne-the linear allotrope of carbon-is perhaps one of the most unusual materials due to its ultimate one-atom thinness. Although carbyne is elusively hard to prepare and has been perceived as an exotic or even completely fictitious material, the development of methods to synthesize carbon chains proceeds at a steady rate, with input from both experiments and theory. 1-7 Among the most notable recent achievements, chains with length of up to 44 atoms 8 and such complex molecular machines as carbyne-based rotaxanes 9,10 have been synthesized. This progress is driven by carbyne's attractive physical properties such as unusual electrical transport 11,12 and intriguing mechanics, 13 or its large specific area. 14 Accordingly, a better theoretical understanding of this material is becoming more and more relevant. 13 It has long ago been established by the quantum chemistry community 15 that carbyne undergoes the Peierls transition [16][17][18][19] that converts it from the cumulene (=C=C=) n to the polyyne (-C≡C-) n form. Later it has been suggested that the zero-point vibrations (ZPV) may substantially affect the Peierls instability 20 and even completely eliminate the distortion in carbyne. 21 As the symmetric and broken-symmetry forms have very distinct electronic properties (metallic and insulating, respectively), this issue becomes crucial from both the fundamental physicochemical perspective and for applications in 1D conducting systems.A whole new dimension is added to the situation by the unusual effects of stretching on carbyne that we have recently found through first-principles calculations 13 (also observed experimentally after the present study had been completed. 22 ) Specifically, stretching increases the bond length alternation (BLA, defined as the difference between the long and short bonds) and the ba...
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