Table 3. Length (Lx) Dependence (in Å) of the Conductivity
σx along the Length of the GNR in
Units of
(in Bold), and LUMO–HOMO Gaps in
eV, for Various Constant Width (Ly) Armchair GNRs Consisting of n (n = 3, 4, 6, 8, 10, 13, 18, 20, 24)× Armchair Rings along the x-axis (Perpendicular to the Zigzag Edges) and m (m = 3, 4, 5) Rings along Their Width, with Widths
about 9.2 Å (3 Rings, 3×), 11.7 Å (4 Rings, 4×),
and 14.1 Å (5 Rings, 5×), Respectively.
3× | 4× | 6× | 8× | 10× | 13× | 18× | 20× | 24× | ||
---|---|---|---|---|---|---|---|---|---|---|
GNR width (Ly)/Å | properties | Lx/Å | Lx/Å | Lx/Å | Lx/Å | Lx/Å | Lx/Å | Lx/Å | Lx/Å | Lx/Å |
13.6 | 17.9 | 26.5 | 34.9 | 43.6 | 56.5 | 77.8 | 86.5 | 103.6 | ||
3× Ly = 9.2 | ![]() |
0.03 | 0.08 | 0.37 | 1.04 | 2.31 | 5.88 | 18.53 | 26.66 | 53.20 |
L–H(eV) | 1.239 | 0.729 | 0.263 | 0.144 | 0.102 | 0.074 | 0.051 | 0.046 | 2.68a 0.037 | |
4× Ly = 11.7 | ![]() |
0.04 | 0.11 | 0.38 | 1.01 | 2.15 | 5.27 | 16.04 | 22.94 | 45.16 |
L–H (eV) | 0.589 | 0.320 | 0.169 | 0.119 | 0.093 | 0.070 | 0.049 | 0.044 | 1.75a 0.037 | |
5× Ly = 14.1 | ![]() |
0.04 | 0.11 | 0.39 | 1.11 | 2.19 | 5.28 | 16.62 | 24.54 | 48.93 |
H–L (eV) | 0.386 | 0.254 | 0.156 | 0.114 | 0.090 | 0.068 | 0.049 | 0.044 | 0.45a 0.037 |
The underlined numbers in the last column correspond to the gap-defining (“effective”) LUMO–HOMO gaps (i.e., the gaps between HOMO–1 and LUMO+1 in the present case, see text).