Département de physique et Regroupement Québécois sur les Matériaux de Pointe, Université de Montréal, C. P. 6128 Succursale Centre-ville, Montréal, QC, Canada.
Nanotechnology. 2013 Sep 20;24(37):375702. doi: 10.1088/0957-4484/24/37/375702. Epub 2013 Aug 23.
We study the thermodynamics of bromophenyl functionalization of carbon nanotubes with respect to diameter and metallic/insulating character using density-functional theory (DFT). On the one hand, we show that the functionalization of metallic nanotubes is thermodynamically favoured over that of semiconducting ones, in agreement with what binding energy calculations previously suggested. On the other hand, we show that the activation energy for the grafting of a bromophenyl molecule onto a semiconducting zigzag nanotube ranges from 0.72 to 0.75 eV without any clear diameter dependence within numerical accuracy. This implies that this functionalization is not selective with respect to diameter at room temperature, which explains the contradictory experimental selectivities reported in the literature. This contrasts with what is suggested by the clear diameter dependence of the binding energy of a single bromophenyl molecule, which ranges from 1.52 eV for an (8, 0) zigzag nanotube to 0.83 eV for a (20, 0) zigzag nanotube. Also, attaching a single bromophenyl to a nanotube creates states in the gap close to the functionalization site. It therefore becomes energetically favourable for a second bromophenyl to attach close to the first one on semiconducting nanotubes. The para configuration is found to be favoured for resulting bromophenyl pairs and their binding energy is found to decrease with increasing diameter, ranging from 4.35 eV for a (7, 0) nanotube to 2.26 eV for a (29, 0) nanotube. An analytic form for this radius dependence is derived using a tight binding Hamiltonian and first order perturbation theory. The 1/R(2) dependence obtained (where R is the nanotube radius) is verified by our DFT results within numerical accuracy. Finally, bromophenyl pairs are shown to be favoured by only 50 meV with respect to separate moieties on (9, 0) metallic nanotubes, which suggests that pair formation is not significantly favoured on some metallic nanotubes. This result explains the observation of stable isolated moieties at room temperature in nanotube samples containing random nanotube chiralities.
我们使用密度泛函理论（DFT）研究了溴苯基官能团对碳纳米管直径和金属/半导体性质的热力学影响。一方面，我们表明，金属纳米管的官能团化在热力学上优于半导体纳米管，这与先前的结合能计算结果一致。另一方面，我们表明，在室温下，将一个溴苯基分子接枝到半导体锯齿形纳米管上的激活能在数值精度范围内没有明显的直径依赖性，范围在 0.72 到 0.75eV 之间。这意味着这种官能团化在室温下对直径没有选择性，这解释了文献中报道的相互矛盾的实验选择性。这与单个溴苯基分子结合能的明显直径依赖性形成对比，其范围从 1.52eV（8,0）锯齿形纳米管到 0.83eV（20,0）锯齿形纳米管。此外，将单个溴苯基附着到纳米管上会在靠近官能团化位置的能带隙中产生状态。因此，对于半导体纳米管，第二个溴苯基靠近第一个溴苯基附着变得在能量上有利。发现对位构型有利于形成溴苯基对，并且它们的结合能随着直径的增加而减小，范围从 7,0 纳米管的 4.35eV 到 29,0 纳米管的 2.26eV。使用紧束缚哈密顿量和一阶微扰理论导出了这种半径依赖性的解析形式。在数值精度内，通过我们的 DFT 结果验证了获得的 1/R(2)依赖性（其中 R 是纳米管的半径）。最后，对于（9,0）金属纳米管，溴苯基对相对于单独的部分仅具有 50meV 的优势，这表明在一些金属纳米管上，对形成对的形成没有明显的优势。这一结果解释了在含有随机纳米管手性的纳米管样品中，在室温下观察到稳定的孤立部分的现象。
