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arXiv 0909.1917cond-mat.mtrl-sci
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碳纳米管和石墨烯的热膨胀:非平衡格林函数方法

Thermal expansion in carbon nanotubes and graphene: nonequilibrium Green's function approach

Jin-Wu Jiang, Jian-Sheng Wang, Baowen Li

摘要:

采用非平衡格林函数方法研究了单壁碳纳米管和石墨烯的热膨胀系数。结果表明,在T=0 K时,原子偏离平衡位置约1%,这是量子零点运动和非线性相互作用相互作用的结果。从不同振动模式之间的竞争角度对不同尺寸单壁碳纳米管的热膨胀系数进行了研究和分析。由于这种竞争,轴向CTE在整个温度范围内是正的,而径向CTE在低温下是负的。在石墨烯中,CTE对衬底非常敏感。在没有基底的情况下,CTE在低温下具有大的负区域,在高温极限下具有非常小的值,并且在T=300 K下的CTE值是$-6\times 10^{-6}$ K $^{-1}$,其非常接近最近的实验结果,$-7\times 10^{-6}$ K $^{-1}$(Nat.Nanotechnol. \textbf{10},1038(2009))。很弱的衬底相互作用(约为面内相互作用的0.06%)可以大大减小负CTE区域,并大大提高CTE值。当衬底相互作用足够强时,热膨胀系数在整个温度范围内均为正值,高温下的饱和值达到$2.0\times 10^{-5}$ K $^{-1}$。

英文摘要:

The nonequilibrium Green's function method is applied to investigate the coefficient of thermal expansion (CTE) in single-walled carbon nanotubes (SWCNT) and graphene. It is found that atoms deviate about 1% from equilibrium positions at T=0 K, resulting from the interplay between quantum zero-point motion and nonlinear interaction. The CTE in SWCNT of different sizes is studied and analyzed in terms of the competition between various vibration modes. As a result of this competition, the axial CTE is positive in the whole temperature range, while the radial CTE is negative at low temperatures. In graphene, the CTE is very sensitive to the substrate. Without substrate, CTE has large negative region at low temperature and very small value at high temperature limit, and the value of CTE at T=300 K is $-6\times 10^{-6}$ K$^{-1}$ which is very close to recent experimental result, $-7\times 10^{-6}$ K$^{-1}$ (Nat. Nanotechnol. \textbf{10}, 1038 (2009)). A very weak substrate interaction (about 0.06% of the in-plane interaction) can largely reduce the negative CTE region and greatly enhance the value of CTE. If the substrate interaction is strong enough, the CTE will be positive in whole temperature range and the saturate value at high temperature reaches $2.0\times 10^{-5}$ K$^{-1}$.

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