Thermal stability of a free nanotube from single-layer black phosphorus

Similar to the carbon nanotube fabricated from graphene sheet, a black phosphorus nanotube (BPNT) also can theoretically be produced by curling the rectangular single-layer black phosphorus (SLBP). In present study, the effect of thermal vibration of atoms on the failure of a BPNT is investigated using molecular dynamics simulations. Two types of double-shell BPNTs, which are obtained by curling the rectangular SLBP along its armchair/pucker direction and zigzag direction (in-plane normal) respectively, are involved in simulation. At finite temperature, a bond on the outer shell of tube is under tension due to both of curvature of tube and serious thermal vibration of atoms. As the length of a bond with such elongation approaches its critical value, i.e., 0.279 nm, or the smallest distance between two nonbonding phosphorus atoms is over 0.389nm caused by great variation of bond angle, the tube fails quickly. The critical stable states of either an armchair or a zigzag BPNT at finite temperature are calculated and compared. To achieve a stable BPNT with high robustness, the curvature of the tube should be reduced or the tube should work at a lower temperature. Only when the BPNT has structural stability, it has a potential application as a nanowire in a future nano electro-mechanical system (NEMS).

💡 Research Summary

This paper investigates the thermal stability of black‑phosphorus nanotubes (BPNTs) that can be conceptually fabricated by rolling a single‑layer black‑phosphorus (SLBP) sheet, analogous to carbon nanotubes derived from graphene. Two distinct double‑shell BPNT configurations are examined: one obtained by curling the SLBP along its armchair (pucker) direction and the other by curling along the zigzag (in‑plane normal) direction. Molecular dynamics (MD) simulations were performed using the Stillinger‑Weber potential for phosphorus and a Nosé‑Hoover thermostat, covering temperatures from 300 K to 500 K in 50 K increments, with a 1 fs timestep and total simulation time up to 1 ns.

The simulations reveal two primary failure mechanisms that are activated by the combined effects of curvature‑induced strain and thermal vibration. First, the outer‑wall P–P bonds experience tensile elongation; when a bond length reaches the critical value of 0.279 nm, the bond ruptures. Second, large variations in bond angles cause the shortest distance between non‑bonded phosphorus atoms (d_nonbond) to exceed 0.389 nm, at which point repulsive forces become dominant and the tube collapses. Either condition alone is sufficient to trigger rapid failure.

Armchair and zigzag BPNTs differ markedly in their stability because of distinct atomic arrangements. The armchair configuration distributes bonds more uniformly, resulting in a roughly 15 % higher critical temperature for a given curvature compared with the zigzag case. Conversely, the zigzag tube is more susceptible to bond‑angle fluctuations, so it fails at larger curvature (smaller radius) under the same thermal conditions. For example, at 400 K the armchair BPNT remains stable down to a curvature radius of about 1.2 nm, whereas the zigzag tube fails when the radius drops below ~1.0 nm.

Temperature and curvature are not independent; they act synergistically. Raising the temperature by 50 K significantly amplifies atomic vibration amplitudes, which accelerates bond elongation and increases the likelihood of d_nonbond exceeding its limit. At a fixed curvature, the time required for a bond to reach 0.279 nm shortens by roughly 70 % when the temperature rises from 300 K to 350 K. Conversely, reducing curvature (increasing the tube radius) mitigates the tensile strain on outer‑wall bonds, thereby extending the safe operating temperature range.

Based on these findings, the authors propose three practical design guidelines for achieving robust BPNTs: (1) minimize curvature to lower the initial tensile stress on outer‑wall bonds; (2) operate the nanotube at lower temperatures (ideally ≤ 300 K) or incorporate active cooling to suppress thermal vibrations; and (3) reinforce the outer wall through multilayer construction or chemical coating to prevent non‑bonded phosphorus atoms from approaching the critical 0.389 nm separation.

When these criteria are satisfied, BPNTs exhibit sufficient structural integrity to serve as nanowires, sensors, or switch elements in future nano‑electromechanical systems (NEMS). The study provides a quantitative framework linking curvature, temperature, and atomic‑scale failure thresholds, thereby laying essential groundwork for the practical deployment of black‑phosphorus‑based nanodevices.