We study the pressure induced collapse of single-, double- and triple-wall carbon nanotubes. Theoretical simulations were performed using density-functional tight-binding theory. For tube walls separated by the graphitic distance, we show that the radial collapse pressure, Pc, is mainly determined by the diameter of the innermost tube, din and that its value significantly deviates from the usual Pc∝din−3 Levy-Carrier law. A modified expression, Pcdin−3=α(1−β2∕din2) with α and β numerical parameters, which reduces the collapse pressure for low diameters is proposed. For din ≳ 1.5 nm an enhanced stability is found which may be assigned as due to the bundle intertube geometry-induced interactions. If the inner and outer tubes are separated by larger distances, the collapse process is found to be more complex. High-pressure resonant Raman experiments were performed in double-wall carbon nanotubes having inner and outer diameters averaging 1.5 nm and 2.0 nm, respectively. A modification in the response of the G-band and the disappearance of the radial breathing modes between 2 GPa and 5 GPa indicate the beginning and the end of the radial collapse process. Experimental results are in good agreement with our theoretical predictions, but do not allow to discriminate from those corresponding to a continuum mechanics model.

中文翻译：

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压力诱导的少壁碳纳米管径向塌陷：理论和实验相结合的研究

我们研究了单壁、双壁和三壁碳纳米管的压力诱导坍塌。使用密度泛函紧束缚理论进行了理论模拟。对于由石墨距离分隔的管壁，我们表明径向坍塌压力 Pc 主要由最里面管的直径 din 决定，并且其值显着偏离通常的 Pc∝din−3 Levy-Carrier 定律。提出了一个修改后的表达式，Pcdin−3=α(1−β2∕din2) 与 α 和 β 数值参数，它降低了小直径的坍塌压力。对于 din ≳ 1.5 nm，发现稳定性增强，这可能归因于束管间几何结构引起的相互作用。如果内管和外管相隔较大的距离，则发现塌陷过程更加复杂。高压共振拉曼实验在双壁碳纳米管中进行，内径和外径分别平均为 1.5 nm 和 2.0 nm。G 波段响应的改变和径向呼吸模式在 2 GPa 和 5 GPa 之间的消失表明径向塌陷过程的开始和结束。实验结果与我们的理论预测非常一致，但不允许与对应于连续介质力学模型的结果区分开来。