Studies On Temperature-dependent Mechanical Properties Of Monolayer Black Phosphorus By Molecular Dynamics Simulations

As a new type of two-dimensional material after grapheme,black phosphorus(BP)has attracted the attention of scientists from all over the world due to its excellent optical and electrical properties.BP is the most stable form of allotropes of phosphorus,its lattice is an orthogonal structure composed of six rings connected together.BP has been discovered by scientists and is still in the initial stage of the research on this new type of two-dimensional materials.Few reports and studies on its electrical and mechanical properties,especially for the mechanical properties have been carried out.According to the above,temperature-dependent stress-strain relations of monolayer black phosphorus(MBP)under biaxial and uniaxial tension as well as shear deformation are investigated using molecular dynamics(MD)simulations in five different gradient temperature(4.2K,100 K,200K,300 K,400K).In particular,for the bending mechanical properties of MBP have also been discussed.The main research contents and results are summarized as follows:1.The temperature-dependent mechanical properties of MBP under biaxial(armchair,zigzag)and uniaxial(armchair,zigzag)tension deformation have been addressed by MD simulations.The Young's modulus of MBP are obtained as 24 GPa and 105 GPa along the armchair and zigzag direction respectively under uniaxial tension deformation at 4.2K temperature.The results are in good agreement with available data from the first-principle method.In addition,the Young's modulus of MBP is 22.6GPa and 98.5GPa along the two directions under biaxial tension deformation at 4.2K temperature.At any temperature,the Young's modulus along the zigzag direction is almost 4.4 times more than that of the armchair,and with the increase of temperature,the Young's modulus of the two directions decrease continuously.In order to ensure the accuracy of the simulation process and the accuracy of the simulation results,we calculated the changes of the bond length,in-plane angle and out-ofplane angle of MBP in two directions at 4.2K temperature,so the simulation results are verified on the side.2.The temperature-dependent mechanical properties of MBP under shear(armchair,zigzag)deformation have been analyzed adopted MD simulations.The Shear modulus of MBP are observed to be 25.4GPa and 25.5GPa along the armchair and zigzag direction under shear deformation at 4.2K temperature.At any temperature,the shear modulus of MBP in the two directions are almost equal,with the increase of temperature,the shear modulus of MBP decreases slowly in addition.In order to explain the wrinkling behavior of MBP under shear deformation,the amplitude to wavelength ratio of wrinkles have been described by employing MD simulations and a good agreement with existing theory has been achieved.3.The mechanical properties of MBP under bending deformation have been investigated by MD simulations.The bending stiffnesses along the armchair and zigzag directions are 6.5eV and 8.8eV,respectively,which are agree well with those obtained from the first-principles calculations.Moreover the bending angles have a slight effect on the bending stiffness.This study provides physical insights into the origins of the temperature dependent mechanical properties of the MBP.The simulations results and theoretical results can provide a good theoretical support for the study of the mechanical properties of BP,and provide some theoretical support and technical support for the future application of BP in engineering.