Illustration of the system of interest to us with some of the quantities required in the derivation of dispersion interaction.
Arrangement of cylinders and specification of distances used to construct the dielectric response of the left half space.
(Color online) vdW interaction for a (6,5) carbon nanotube above a half space made of (6,5) carbon nanotubes as a function of distance for (panel a) and (panel b). The values of dispersion interaction with retardation included are indicated by (red) pluses. The nonretarded values are indicated by (green) ×’s. The power-law behaviors and are denoted by dotted and dashed lines, respectively.
(Color online) Dielectric responses (along imaginary axis) of the (6,5) SWCNT. The (red) pluses and (green) ×’s show the longitudinal and transverse responses, respectively. On the -axis is the (shifted) Matsubara frequency index.
(Color online) Retarded dispersion interaction between (6,5) SWCNT and a half space made of (6,5) SWCNTs as a function of the angle between the longitudinal axes of the two subsystems. The distance between the two subsystems is .
(Color online) Illustration of the cutoff effect of retardation for a (6,5) carbon nanotube interacting with the gold half space in vacuum—the partial sums are shown for several different separations between the SWCNT and the half space, as indicated. The -axis is the order of the summation, see Eq. (15).
(Color online) Retarded (crosses) and nonretarded (circles) vdW interactions between a (6,5) CNT and golden half space as a function of distance. The parameters of the medium are , , and . The inset shows how the retarded vdW interaction depends on for and .
(Color online) Dielectric responses [gold, SWCNT (6,5), and medium] used in the calculations displayed in Fig. 7. Two different models of the medium, differing only in parameter , are denoted.
(Color online) Dielectric responses [polystyrene, SWCNT (6,5), and medium] used in the calculation of the retarded dispersion interaction displayed in the inset of the figure.
(Color online) Contributions of different parts of the spectra to the total vdW interaction. A function defined by Eq. (15) is shown on the -axis for four different separations between CNT (6,5) and polystyrene: 3.03 nm (a), 3.48 nm (b), 4.59 nm (c), and 8.0 nm (d). The dielectric response of the medium in these calculations is shown in Fig. 9. A thin horizontal line denotes the value of [i.e., the limit ]. Two thin vertical lines denote the positions where the medium dielectric response crosses the longitudinal CNT (6,5) response (see Fig. 9). Note that the vdW interaction is repulsive for (a) and attractive for (b)–(d).
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