六角排列碳纳米管阵列的场增强因子的计算

Calculation of field enhancement factor of hexagonal array of carbon nanotubes

通过求解Laplace方程得到六角排列的碳纳米管(CNTs)阵列的管尖端电场强度和场增强因子,具体研究CNTs的自身线度、阵列密度及阵列形状对CNTs的场增强因子的影响.研究结果表明,场增强因子随CNTs长径比的增加而增加,对于长径比一定的CNTs阵列,对应着一个最佳阵列密度,如管长为6μm、管径分别为5 nm、13 nm、20 nm的CNTs阵列对应的最佳阵列密度为3.05×1011cm-2、4.83×1010cm-2、2.12×1010cm-2.在相同的阵列密度下,六角排列CNTs阵列的场发射性能要优于四方排列的CNTs阵列.计算得到六角排列CNTs阵列上端面的电势分布曲线.

The tip electric field intensity and field enhancement factor of the hexagonal carbon nanotubes （CNTs） array were calculated by solving the Laplace equation. The influences of the nanotube’s linearity proper, and array＇s shape as well as the density of the array on the enhancement factor was studied in the concrete. The result of investigation indicated that the field enhancement factor would increase with the aspect ratio of the carbon nanotube. For a carbon nanotube array with definite aspect ratio, there would be its optimum density correspondingly. For instance, an array of namotubes in length of 6 μm and in diameter of 5 nm, 13 nm, and 20 nm, respectively, would have its optimum densities as 3. 05 × 10^11 cm^-2 , 4.83×10^10 cm^-2 , and 2. 12 × 10^10 cm^-2, respectively. The field enhancement factor of the hexagonal carbon nanotube array was higher than that of square carbon nanotubes array with identical density. The distribu- tion of tip electric potential of the hexagonal carbon nanotube array was obtained by means of calculation.