Bending-induced extension in two-dimensional crystals

Abstract

We find by ab initio simulations that significant overall tensile strain can be induced by pure bending in a wide range of two-dimensional crystals perpendicular to the bending moment, just like an accordion being bent to open. This bending-induced tensile strain increases in a power law with bent curvature and can be over 20% in monolayered black phosphorus and transition metal dichalcogenides at a moderate curvature of 2 nm −1 but more than an order weaker in graphene and hexagon boron nitride. This accordion effect is found to be a quantum mechanical effect raised by the asymmetric response of chemical bonds and electron density to the bending curvature.Keywords Monolayer black phosphorus · Bending to extension · Accordion effect · Density functional theory Douxing Pan and Yao Li have contributed equally to this work. Electronic supplementary materialThe online version of this article

Self-assembled chiral phosphorus nanotubes from phosphorene: a molecular dynamics study

“…All these energies decrease gradually with respect to time and reach a stable minimum (at t 0 ~ 0.16 ns as denoted in the figure for the total energy), which is similar to that of GNR 2,12,14,15 . The free energy of zPNR self-assembly after equilibrium is much larger than that of GNR 14,15,16 , since the configuration energy of graphene is -9.214eV/atom, which is much smaller than that of phosphorene, -5.365eV/atom, according to density functional theory (DFT) calculations 3,5,22 . The potential curve is coincided with that of the vdW interaction indicating that the self-assembly process is actually driven by the vdW force.…”

“…properties are desirable 3,4,5 . The corrugated crystal structure of phosphorene not only leads to novel physical properties, but also produces anisotropic mechanical behaviors 4,5,6 , for example, apparent nonlinear Young's modulus and ultimate strain 6 , prominent anisotropic elasticity 7 , negative Poisson's ratio 8 and highly anisotropic ripple pattern 4 and bending-induced extension 5 .…”

“…properties are desirable 3,4,5 . The corrugated crystal structure of phosphorene not only leads to novel physical properties, but also produces anisotropic mechanical behaviors 4,5,6 , for example, apparent nonlinear Young's modulus and ultimate strain 6 , prominent anisotropic elasticity 7 , negative Poisson's ratio 8 and highly anisotropic ripple pattern 4 and bending-induced extension 5 . Recently, the fracture behaviors of phosphorene at finite temperatures are explored and the failure crack propagates preferably along the groove in the corrugated structure when uniaxial tension is applied in its armchair direction 9 .…”

“…where d c =2(r+h+σ) is the diameter of the cPNT(n, m c ) and [x] denotes the nearest integer of x. Note that more precise lattice constants based on the DFT results |a 1 |=0.462 nm and |a 2 |=0.330 nm are adopted for convenience of theoretical predictions 5 , which are in agreement with that obtained from our MD calculations (the average lattice constants are 0.441nm and 0.331nm, respectively). According to the Eq.…”

“…Due to the anisotropic nature of phosphorene and the bending instability along its zigzag direction 5,10 , the zPNRs prefer moving forward in a spiral way outside the aPNTs to bend themselves directly, and finally form chiral tubes with different radii, as shown in Fig. 4a-c.…”