[Paper Review] Thermal stability of a free nanotube from single-layer black phosphorus

Kun Cai, Jing Wan+3 more|arXiv (Cornell University)|Dec 23, 2015

2D Materials and Applications23 references4 citations

TL;DR

This study investigates the thermal stability of free-standing black phosphorus nanotubes (BPNTs) derived from single-layer black phosphorus using molecular dynamics simulations. It identifies critical failure thresholds—bond elongation beyond 0.279 nm or nonbonding atom distance exceeding 0.389 nm—as indicators of structural collapse, concluding that reduced curvature and lower operating temperatures enhance stability for potential NEMS applications.

ABSTRACT

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).

Motivation & Objective

• To evaluate the thermal stability of free-standing black phosphorus nanotubes (BPNTs) under finite-temperature conditions.
• To investigate the structural failure mechanisms of BPNTs due to atomic thermal vibrations and curvature-induced strain.
• To compare the stability of armchair- and zigzag-oriented BPNTs under thermal loading.
• To determine critical geometric and energetic thresholds for structural failure in BPNTs.
• To establish design guidelines for robust BPNTs suitable for use in nano-electromechanical systems (NEMS).

Proposed method

• Employed classical molecular dynamics (MD) simulations to model the thermal behavior of double-shell BPNTs.
• Constructed BPNTs by curling rectangular single-layer black phosphorus (SLBP) along armchair and zigzag directions.
• Applied finite-temperature dynamics to simulate atomic thermal vibrations and their effects on bond elongation.
• Tracked bond length evolution and nonbonding atom distances to detect failure onset.
• Defined failure when bond length exceeded 0.279 nm or nonbonding P–P distance surpassed 0.389 nm.
• Compared critical stable states between armchair and zigzag BPNT configurations to assess directional stability differences.

Experimental results

Research questions

• RQ1 What are the critical thermal and geometric conditions that lead to structural failure in a free-standing BPNT?
• RQ2 How does the curvature direction (armchair vs. zigzag) influence the thermal stability of BPNTs?
• RQ3 To what extent do thermal vibrations and curvature jointly induce bond elongation and bond angle distortion in BPNTs?
• RQ4 What are the threshold values for bond elongation and nonbonding atom separation that trigger rapid failure in BPNTs?
• RQ5 Under what conditions can BPNTs maintain structural integrity for potential NEMS applications?

Key findings

• The critical bond length beyond which failure occurs in a BPNT is 0.279 nm, corresponding to a tensile stress state induced by curvature and thermal motion.
• Failure is also triggered when the minimum distance between nonbonding phosphorus atoms exceeds 0.389 nm due to excessive bond angle distortion.
• The zigzag-oriented BPNT exhibits lower thermal stability compared to the armchair variant under identical thermal conditions.
• Thermal vibrations significantly amplify strain on outer-shell bonds, making them the primary failure initiation point.
• Reducing tube curvature or operating at lower temperatures enhances the structural robustness of BPNTs.
• Structural stability is a prerequisite for any practical application of BPNTs in nano-electromechanical systems (NEMS).