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Phonon dispersion (as a function of ) for isolated (a) (3,3) and (b) (9,9) SWCNTs.
Thermal expansion of an isolated (9,9) SWCNT (a) calculated vs temperature ; solid line is based on Eq. (2), and dot-dashed line is its classical limit. (b) Gruneisen parameter vs phonon frequency , and mode-by-mode contribution (c) at and (d) at .
Temperature dependent specific heat of an isolated (9,9) SWCNT. Dotted line indicates the high temperature (classical) limit of . Inset shows the low temperature behavior of natural logarithm of , where . Solid circles are the calculated values and the dot-dashed line is a linear fit.
(Color online) Chirality dependence of thermal properties of SWCNTs: (a) Temperature dependence of for different ; dotted straight lines show high limit of . (b) Variation of constant (in , in ) with . (c) Variation of at room temperature with ; solid circles represent data points, whereas the line shows a fit with dependence. Error bars on are obtained from an overall error from (i) calculation of bulk modulus and (ii) -point convergence. (d) Variation of at room temperature with ; the inset shows ) vs for (red line), 6 (green line), 8 (blue line), 13 (magenta line).
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