Fig. 1: Platform and observations for the temperature-dependent Radial Breathing Mode (RBM) shift for isolated and suspended Double Walled Carbon Nanotubes (DWNTs).

a Schematic of isolated DWNT consisting of as-grown and free-standing entities. b Scanning electron microscopy (SEM) image of free-standing DWNTs. c Local CNT temperature calibration using stage temperature (\({T}_{{{{{{\rm{stage}}}}}}}\)) and the Raman G (\({\omega }_{{{{{{\rm{G}}}}}}}\)) responses with the linear fit (dash line). \({R}^{2}=0.96\). d Example Raman spectra of the as-grown, free-standing (19,3)@(22,11) DWNT as a function of local temperature heated by the excitation spot at 633 nm using a vacuum stage at \(7.4\times {10}^{-7}\) bar. The Raman G-band was separately calibrated and used as a local thermometer of the CNT. Lorentzian fits (shaded curves) served to extract Raman mode frequencies. e Low frequency RBM (\({\omega }_{{{{{{\rm{L}}}}}}}\)) corresponding to the outer shell of the (19,3)@(22,11) DWNT (CNT F), demonstrating the characteristic trajectory observed for a subset of CNTs studied in this work. All trajectories consist of a concave down curve towards a cusp at a limiting temperature \({T}_{\max }\), (red arrow) followed by an invariant RBM frequency for all \(T\, > \,{T}_{\max }\). Scan (i) is the initial heating curve at \(1.2\times {10}^{-6}\) bar towards 916.5 K, showing a \({T}_{\max }\) = 565.4 K. Subsequent scans on the same spot then show \({T}_{\max }\) values consistently lower and repeatable. Scan (ii) heating at the same ___location towards 628.2 K with a \({T}_{\max }\) = 355.8 K and (iii) heating towards 621.5 K with \({T}_{\max }\) at 352.8 K, both measured at \(2.5\times {10}^{-3}\) bar. The red line is an analytical fit using Eq. (6), and the fitting parameters are provided in Supplementary Table 12-2. f Transmission electron microscopy (TEM) images of (i) a (15,6)@(20,12) DWNT with a 20 nm scale bar, (ii) sharper contrast at a 10 nm scale bar showing the specific structure. The graphitic impurities are found on every CNT imaged. A (21,6)@(24,14) DWNT (iii) with a 50 nm scale bar, (iv) with a 10 nm scale bar, showing similar graphitic and ribbon-like impurities. (v) A cropped TEM image from (iii) to show distinct (21,6)@(24,14) DWNT (Supplementary Movie 1). (vi) Segments that are labeled in red indicate the presence of graphitic carbon decoration at about 60% coverage per linear distance of the DWNT. The blue shaded lines are empty regions in Fig. 1f(v). Source data are provided as a Source Data File.