Mechanical properties of phosphorene nanotubes: a density functional tight-binding study

Using the density functional tight-binding method, we studied the elastic properties, deformation and failure of armchair (AC) and zigzag (ZZ) phosphorene nanotubes (PNTs) under uniaxial tensile strain. We found that the deformation and failure of PNTs are very much anisotropic. For ZZ PNTs, three deformation phases are recognized: the primary linear elastic phase-which is associated with interactions between neighboring puckers, succeeded by the bond rotation phase-where the puckered configuration of phosphorene is smoothed via bond rotation, and lastly the bond elongation phase-where the P-P bonds are directly stretched up to the maximally allowed limit and failure is initiated by the rupture of the most stretched bonds. For AC PNTs, the applied strain stretches the bonds up to the maximally allowed limit, causing their ultimate failure. For both AC and ZZ PNTs, their failure strain and failure stress are sensitive-while the Young's modulus, flexural rigidity, radial Poisson's ratio and thickness Poisson's ratio are relatively insensitive-to the tube diameter. More specifically, for AC PNTs, the failure strain decreases from 0.40 to 0.25 and the failure stress increases from 13 GPa to 21 GPa when the tube diameter increases from 13.3 angstrom to 32.8 angstrom; while for ZZ PNTs, the failure strain decreases from 0.66 to 0.55 and the failure stress increases from 4 GPa to 9 GPa when the tube diameter increases from 13.2 angstrom to 31.1 angstrom. The Young's modulus, flexural rigidity, radial and thickness Poisson ratios are 114.2 GPa, 0.019 eV . nm(2), 0.47 and 0.11 for AC PNTs, and 49.2 GPa, 0.071 eV . nm(2), 0.07 and 0.21 for ZZ PNTs, respectively. The present findings provide valuable references for the design and application of PNTs as device elements.