Mechanics of 2D materials

Phosphorene, also known as monolayer black phosphorous, has been enjoying the popularity in electronic devices due to its superior electrical properties. However, it’s relatively low Young’s modulus, low fracture strength and susceptibility to structural failure has limited its application in mechanical devices. Therefore, in order to design more mechanically reliable devices that utilize phosphorene, it is necessary to explore the fracture patterns and energy release rate of phosphorene. In this study, molecular dynamics simulations are performed to investigate phosphorene’s fracture mechanism. Results indicate that fracture under uniaxial tension along the armchair direction is attributed to a break in the interlayer bond angles, while failure in the zigzag direction is triggered by the break in both the intra-layer angles and bonds. Furthermore, we developed a modified Griffith criterion to analyze the energy release rate of phosphorene and its dependence on strain rates and orientations of cracks. Simulation results indicate that phosphorene’s energy release rate remains almost unchanged in the armchair direction while it fluctuates intensively in the zigzag direction. Additionally, the strain rate was found to play a negligible role in the energy release rate. The geometrical factor α in the Griffith’s criterion is almost constant when the crack orientation is smaller than 45 degree, regardless of the crack orientation and loading direction. Overall, these findings provide helpful insights into the mechanical properties and failure behavior of phosphorene.

phosphorene structure
Geometrical configuration of phosphorene.
phosphrene fracture
Fracture path under the uniaxial tensile test along zigzag direction

Silicene, a silicon-based homologue of graphene, arouses great interest in nano-electronical devices due to its outstanding electronic properties. However, its promising electronic applications are greatly hindered by lack of understanding in the mechanical strength of silicene. Therefore, in order to design mechanically reliable devices with silicene, it is necessary to thoroughly explore the mechanical properties of silicene. Due to current fabrication methods, graphene is commonly produced in a polycrystalline form; the same may hold for silicene. Here we perform molecular dynamics simulations to investigate the mechanical properties of polycrystalline silicene. First, an annealing process is employed to construct a more realistic modeling structure of polycrystalline silicene. Results indicate that a more stable structure is formed due to the breaking and reformation of bonds between atoms on the grain boundaries. Moreover, as the grain size decreases, the efficiency of the annealing process, which is quantified by the energy change, increases. Subsequently, biaxial tensile tests are performed on the annealed samples in order to explore the relation between grain size and mechanical properties, namely Young’s modulus, fracture strength and fracture strain etc. Results indicate that as the grain size decreases, the fracture strain increases while the fracture strength shows an inverse trend. The decreasing fracture strength may be partly attributed to the weakening effect from the increasing area density of defects which acts as the reservoir of stress-concentrated sites on the grain boundary. The observed crack localization and propagation and fracture strength are well-explained by a defect-pileup model, which shows an intriguing inverse trend of the Hall-Petch effect of polycrystalline graphene reported in Song, 2013, 13, 1829-1833, Nano Letters.

silicene structure
Geometrical configuration of silicene.
fracture silicene
Probability density of atomic von Mises stress before crack initialization.

Folded graphene has exhibited novel electrical and mechanical properties unmatched by pristine graphene, which implies that morphology of graphene adds the dimensionality of design space to tailor its properties. However, how to overcome the energy barrier of the folding process to fold the graphene with the specific morphology remains unexplored. Here we propose a programmable chemical functionalization by doping a pristine graphene sheet in a certain pattern with hydrogen atoms to precisely control its folding morphology. Molecular dynamics simulation has been performed to create a cross-shaped cubic graphene nanocage encapsulating a biomolecule by warping the top graphene layer downward and the bottom graphene layer upward to mimic the drug delivery vehicle. Such a paradigm, programmable enabled graphene nanocage, opens up a new avenue to control the 3D architecture of folded graphene and therefore provides a feasible way to exploit and fabricate the graphene-based unconventional nanomaterials and nanodevices for drug delivery.

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Evolution of opening graphene nanocage as simulation time by reversing the direction of doped hydrogen on the gate sides.

Hydrogenated graphene has been emerging as the cynosure of the subject for numerous studies with their conductivity, ferromagnetism, and energy storage as well as drug delivery. However, how to find a decent way to overcome the graphene bending barrier and modify the graphene from planar structures to 3D structures remains to be further explored. By virtue of molecular mechanics/dynamics simulations, here we present the formation of carbon nanohelix from a pristine graphene nanoribbon by doping it with hydrogen atoms in a specific pattern. Meanwhile, we quantitatively investigate the effect of interatomic potential on the process of helical structure formation, thermal stability and mechanical properties of the carbon nanohelix as well as its potential application in molecule packing. Carbon nanohelix portrays an intriguing zigzag strain-stress curve and amazing extensibility under tension as well as relatively limited deformability under compression, which represents its unique signature of mechanical properties to differentiate the carbon nanohelix from the behavior of carbon nanotube and graphene. These findings lends compelling credence to envision that the carbon nanohelix opens up a viable avenue for nanofabrication and is perceived as a novel nanomaterial for a variety of applications such as electronics, sensors, energy storage, drug delivery and nanocomposites.

Programmable hydrogenation pattern enables the formation of novel 3D structures from a pristine graphene nanoribbon.

Single-walled carbon nanotubes (SWCNT) have demonstrated a remarkable capacity for self-assembly into nano-bundles through intermolecular van der Waals interactions, bestowing these agglomerates extraordinary mechanical, thermal, and electrical properties. However, how to improve the binding ability of SWCNT bundles to mitigate the delamination and sliding effects between individual nanotubes remains to be further investigated. By utilizing molecular dynamics simulation, here we present the construction of SWCNT bundles with discrete cylindrical and continuous helical binders by non-covalent coating of the bundle surface with sp2 hybridized carbon networks. Meanwhile, by modifying the binding potentials between the binder and SWCNT bundles to mimic the different binding types actually used, the bound SWCNT bundle presents a variety of distinct mechanical properties unmatched by unbound bundles. The pull-out tests with discrete binders portray an intriguing force-displacement curve which can help determine the number of discrete binders used in the system. SWCNT bundles with binders depict unique mechanical properties which can differentiate them from unbound SWCNT bundles. These findings provide compelling evidence that bound SWCNT bundles will open up novel avenues for a variety of applications, especially in nanocomposites.

nanotube bundles
Tensile performances of discontinuous SWCNT bundles with 7-binder and helical-binder combining with Type C binding potential.


N. Liu, J. Hong, R. Pidaparti and X. Wang, "Abnormality in Fracture Strength of Polycrystalline Silicene", 2D Materials, accepted.

N. Liu, J. Hong, R. Pidaparti and X. Wang, "Fracture Patterns and Energy Release Rate of Phosphorene", Nanoscale, 8: 5728-5736, 2016.

H. Chen, L. Zhang, J. Chen, M. Becton, X. Wang and H. Nie, "Energy Dissipation Capability and Impact Response of Carbon Nanotube Buckypaper: A Coarse-Grained Molecular Dynamics Study", Carbon, 103: 242-254, 2016.

M. Becton, X. Zeng and X. Wang, "Computational Study on the Effects of Annealing on the Mechanical Properties of Polycrystalline Graphene", Carbon, 86: 338-349, 2015.

L. Zhang and X. Wang, "Tailoring Pull-out Properties of Single-walled Carbon Nanotube Bondles by Varying Binding Structures through Molecular Dynamic Simulation", Journal of Chemical Theory and Computation, 10(8): 3200-3206, 2014.

L. Zhang, X. Zeng and X. Wang, "Programmable Hydrogenation of Graphene for Novel Nanocages", Scientific Reports, 3: 3162, 2013.


Dr. Changhong Ke (Bingham University)

Dr. Xiaowei Zeng (University of Texas at San Antonio)