Reactive molecular dynamics simulations of the mechanical properties of various phosphorene allotropes.

Although various phosphorene allotropes have been theoretically predicted to be stable at 0 K, the mechanical properties and fracture mechanism at room temperature remain unclear for many of them. We investigate through reactive molecular dynamics simulations at room temperature the mechanical properties of phosphorene allotropes including: five sheets with hexagonal structures (β-, γ-, δ-, θ-, and α-phosphorene), one sheet with 4-8 membered rings (4-8-P), and two sheets with 5-7 membered rings. High, moderate and slight anisotropies in their mechanical properties are observed, depending on their crystal structures. Their Young's moduli and tensile strength are approximately in the range from 7.3% through 25%, and from 8.6% through 22% of those of graphene, respectively. At the early stage of fracture, eye-shaped cracks are formed by local bond breaking and perpendicular to the tensile direction in hexagonal and 4-8-P sheets. Complete fractures take place with straight cracks in these hexagonal sheets under tension along the zigzag direction and under tension along the square edge direction in the 4-8-P sheet. Crack meandering and branching are observed during the tension of α-, β-, and γ-phosphorene along the armchair direction; and along the square diagonal direction in the 4-8-P sheet. Under uniaxial tension of two phosphorene sheets with 5-7 atom rings, 12 and 10 membered rings are formed by merging two neighbor heptagons, and a heptagon and its neighbor pentagon, respectively. These 12 and 10 membered rings coalesce subsequently, causing the failure of these two sheets. The results are of great importance in the design of these novel phosphorene allotropes.