0 jqq 200 300 Fig. 7. Thermal conductivity of a

T(K) bulk sample of SWNTs [19]

above 200 W/mK [21], within an order of magnitude of the room-temperature thermal conductivity of highly crystalline graphite. Because even such an aligned sample contains many rope-rope junctions, it is likely that a single tube, or a rope of continuous tubes, will have significantly higher thermal conductivity than the bulk samples.

Simultaneous measurement of the electrical and thermal conductance of bulk SWNT samples yields a Lorenz ratio n/oT which is more than two orders of magnitude greater than the value for electrons at all temperatures. Thus the thermal conductivity is dominated by phonons, as expected.

Figure 8 highlights the low-T behavior of the thermal conductivity of SWNTs [19]. As discussed above, the linear T dependence of k(T) likely reflects the one-dimensional band-structure of individual SWNTs, with linear acoustic bands contributing to thermal transport at the lowest temperatures and optical subbands entering at higher temperatures. k(T) can be modeled using a simplified two-band model (shown in the inset to Fig. 8), considering a single acoustic band and one subband. In a simple zone-folding picture, the acoustic band has a dispersion w = vk and the first subband has dispersion ui2 = v2k2 + j1, where = v/R. The thermal conductivity from each band can then be estimated using (8) and assuming a constant scattering time t. Thus t provides an overall scaling factor, and v sets the energy scale of the splitting between the two bands.

Figure 8 shows the measured k(T) of SWNTs, compared to the results of the two-band model discussed above, with v chosen to be 20 km/s, which is between that of the 'twist' (v = 15km/s) and LA (v = 24km/s) modes. The top dashed line represents k(T) of the acoustic band: it is linear in T, as expected for a 1-D phonon band with linear dispersion and constant t. The lower dashed line represents the contribution from the optical subband;

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