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For instance, at T= 0 K, eq 3 would lead to ∈ (△k, ℏw, l ∼ log, x, l)2, XE, y)2[(x, l) 2, XE, y)2, with x, q/2kF, XE, △k(Eext)/2kF, and y, mwlnq so that Kohn anomalies (x, 1) correspond, in the absence of field, to an infinite static response ∈ (0,0, 1→ ∞ and a null dynamic response ∈(0, ℏw, 1, 0 while, in the presence of field, ∈△k, 0, 1→ ∞
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F, and y = mwlnq so that Kohn anomalies (x = 1) correspond, in the absence of field, to an infinite static response ∈ (0,0) - 1→ ∞ and a null dynamic response ∈(0, ℏw) -1 = 0 while, in the presence of field, ∈(△k, 0) - 1→ ∞.
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Actually, the use of the Lindhard model relies on the adiabatic Born-Oppenheimer approximation which, as verified below, still holds in our SWNT thin films. In contrast, our adiabatic model will be inadequate in nonadiabatic systems e.g, graphene
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Actually, the use of the Lindhard model relies on the adiabatic Born-Oppenheimer approximation which, as verified below, still holds in our SWNT thin films. In contrast, our adiabatic model will be inadequate in nonadiabatic systems (e.g., graphene).
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Nevertheless, while the changes achieved including possible anharmonic effects in our model are low, the influence on the electron screening of the alternating electric fields used for Raman excitation might also be considerable. This would suggest that our model might also be useful in explaining the temperature dependence of the Raman peaks of SWNT thin films in the absence of a constant external field
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Zhou, Z.; et al. J. Phys. Chem. B 2006, 110, 1206. Nevertheless, while the changes achieved including possible anharmonic effects in our model are low, the influence on the electron screening of the alternating electric fields used for Raman excitation might also be considerable. This would suggest that our model might also be useful in explaining the temperature dependence of the Raman peaks of SWNT thin films in the absence of a constant external field.
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J. Phys. Chem. B
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The relaxation times determined within our model are of the order of magnitude available in literature (see ref 22, p 10, Furthermore, straightforward Drude analysis of the ellipsometry spectra of our samples (ref 2) also leads to τ ∼ 10-15 s. We suspect that especially intertube processes between one m-SWNT and one s-SWNT are important in lowering the relaxation times, since s-SWNTs may act as thermal sink ref 15, Thus, the higher the participation of s-SWNTs to electrical transport, the smaller TINTER. Impurities might also contribute in decreasing both intra- and intertube relaxation times
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-15 s. We suspect that especially intertube processes between one m-SWNT and one s-SWNT are important in lowering the relaxation times, since s-SWNTs may act as thermal sink (ref 15). Thus, the higher the participation of s-SWNTs to electrical transport, the smaller TINTER. Impurities might also contribute in decreasing both intra- and intertube relaxation times.
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u∥ and u∝ represent, in each SWNT, the modes polarization longitudinal and transversal to the electric field
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u∥ and u∝ represent, in each SWNT, the modes polarization longitudinal and transversal to the electric field.
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