Mechanism of the small radial-breathing-mode shifts of host tubes upon $\mathrm{C}_{60}$ encapsulation and assignment of the intermediate-frequency Raman modes of peapod-derived double-wall carbon nanotubes

When single-wall carbon nanotubes (SWNTs) are filled with one-dimensional chains of $\mathrm{C}_{60}$ molecules (peapods) and vacuum-annealed, concentric inner nanotubes form, yielding double-wall carbon nanotubes (DWNTs). The 2001 Raman study that established this transformation left three questions open: the physical origin of the small (2–5 $\mathrm{cm}^{-1}$) downshifts of the host-tube radial breathing mode (RBM) upon $\mathrm{C}_{60}$ filling (tentatively ascribed to small electron charge transfer and C–C bond softening); the detailed assignment of Raman peaks in the intermediate frequency region, including a broad band near 680 $\mathrm{cm}^{-1}$ in the 1200 °C-annealed material tentatively attributed to finite tube length and axial vibrations; and the need for multi-excitation-wavelength resonance Raman to sample the full diameter distribution. Later literature closed the multi-excitation thread and established a qualitative, diameter-dependent van der Waals origin for the RBM shifts. What remains open is a quantitative, diameter- and chirality-resolved decomposition of the small RBM shifts into their competing mechanisms (mass loading, steric van der Waals interaction, $\pi$-state charge redistribution, dielectric screening), and a definitive assignment of the intermediate-frequency modes of peapod-derived DWNTs, in particular whether the finite-length/defect-related components, including the ~680 $\mathrm{cm}^{-1}$ band, arise from finite-length-activated modes, intrinsic combination modes, or defect-induced scattering.

Background

A single-wall carbon nanotube (SWNT) is a graphene sheet rolled into a cylinder of nanometer diameter. Its low-frequency radial breathing mode (RBM), in which the tube circumference expands and contracts uniformly, has a frequency that scales approximately as the inverse tube diameter, so RBM Raman peaks act as a diameter fingerprint. Raman scattering from SWNTs is strongly resonant: the laser photon must match an allowed electronic transition between the tube's one-dimensional van Hove singularities (sharp peaks in the electronic density of states), and because these transition energies depend on diameter and chirality (the wrapping indices $(n,m)$ that specify how the graphene sheet is rolled up), a single laser line (such as the 514.5 nm line used in the source study) only enhances tubes in certain diameter windows — a relation usually summarized in the Kataura plot of transition energy versus tube diameter.

Fullerene molecules can be inserted into SWNTs, forming 'peapods', denoted $(\mathrm{C}_{60})_n$@SWNT: one-dimensional chains of $\mathrm{C}_{60}$ molecules spaced about 1 nm apart inside the tube. Bandow, Takizawa, Hirahara, Yudasaka and Iijima (Chem. Phys. Lett. 337 (2001) 48) showed that vacuum annealing of such peapods coalesces the $\mathrm{C}_{60}$ chains into a coherent inner nanotube, producing double-wall carbon nanotubes (DWNTs); in their HT1200 sample (annealed in vacuum at about 1200 °C) they observed new RBM bands near 256, 315 and 377 $\mathrm{cm}^{-1}$, assigned to inner tubes, with an inner-minus-outer diameter difference of about 0.71 nm confirmed by transmission electron microscopy.

The same study raised three questions. First, comparing peapods with empty SWNTs, the host-tube RBM peaks were downshifted by roughly 2–5 $\mathrm{cm}^{-1}$ upon $\mathrm{C}_{60}$ filling; the authors tentatively suggested small electron transfer from the tube to the molecules with resulting C–C bond softening, but did not establish this. Second, the Raman spectrum between the RBM region and the defect-induced D band (around 1300 $\mathrm{cm}^{-1}$) — the so-called intermediate-frequency modes (IFM), a weak structured set of bands roughly between 500 and 1200 $\mathrm{cm}^{-1}$ whose first-order origin is not obvious from graphene-derived selection rules — contained a new broad band near 680 $\mathrm{cm}^{-1}$ in HT1200, which the authors tentatively attributed to finite (tube-)length effects and axial vibrations, deferring detailed analysis. Third, because the 514.5 nm excitation left certain diameter ranges (near 1.1 nm and near 0.7–0.8 nm) essentially unobserved, the full tube diameter distribution could not be evaluated from a single laser line.

Subsequent work transformed this landscape. Multi-wavelength resonance Raman on the same class of samples (Bandow et al. 2002; Li et al. 2003; Bandow et al. 2004) resolved many inner-tube RBM peaks and assigned them chiralities, discharging the single-wavelength limitation. On the RBM shifts, density-functional calculations (Okada 2007) found upshifts for tightly packed $\mathrm{C}_{60}$ and small downshifts for larger tubes caused by hybridization between tube $\pi$ states (the delocalized states of the carbon out-of-plane bond network) and the nearly-free-electron (NFE) states of the encapsulated chain — low-lying electronic states of electrons delocalized in the annular space between the $\mathrm{C}_{60}$ chain and the tube wall. Experiments (Ryabenko et al. 2007; Joung et al. 2009, 2010; Anis et al. 2016) found diameter-dependent shifts of either sign with unchanged G-mode (tangential C–C stretching) frequencies, variously attributed to mass loading, van der Waals interaction varying with the $\mathrm{C}_{60}$-to-wall inter-spacing, small charge redistribution, and dielectric screening. On the IFM region, Kalbac et al. (2006) showed that in ex-peapod DWNTs the SWNT intermediate-frequency bands split into components attributable to inner and outer tubes, found them diameter-dependent, assigned the ~1050 $\mathrm{cm}^{-1}$ feature to a longitudinal-acoustic-phonon overtone, and noted that inner tubes — which must be short segments for carbon-budget reasons — plausibly enhance defect- and finite-length-activated IFM intensity, without however settling the microscopic origin of the dispersive components; continuum-phonon calculations for finite-length DWNTs (Sbai et al. 2008) predict additional length-dependent modes. For isolated SWNTs the IFM interpretation continued to be revised, with assignments as combination modes of optical and acoustic branches, defect-activated scattering, and, most recently, phonons derived from the out-of-plane acoustic (ZA) branch (Luo et al. 2007; Vierck et al. 2017). No later work has specifically re-examined the broad ~680 $\mathrm{cm}^{-1}$ band reported for the HT1200 material.

Problem Statement

For the Raman spectrum of $\mathrm{C}_{60}$-derived double-wall carbon nanotubes (and of their $\mathrm{C}_{60}$-filled precursors), establish a physically grounded, quantitative interpretation of the small frequency shifts and of the intermediate-frequency region, in two linked parts (the multi-excitation-wavelength part of the original 2001 question has been discharged by later work and is not part of the target):

1. Determine the physical origin of the small (about 1–5 $\mathrm{cm}^{-1}$) shifts of the radial breathing mode of a host single-wall carbon nanotube upon encapsulation of a $\mathrm{C}_{60}$ chain, as a function of tube diameter and chirality (and, after heat conversion, of the inner tube), by quantitatively decomposing the competing mechanisms proposed in the literature — mass loading by the encapsulated chain, steric/van der Waals interaction varying with the $\mathrm{C}_{60}$-to-wall inter-spacing, hybridization-induced $\pi$-state charge redistribution, and dielectric screening — and reconciling them with the measured diameter-dependent sign change (downshift for $d_t \ge 1.32$ nm, upshift below) and with the observed absence of G-mode shifts.

2. Determine, chirality- and diameter-resolved, the origin of the finite-length- and defect-related intermediate-frequency Raman modes (roughly 500–1200 $\mathrm{cm}^{-1}$) of peapod-derived double-wall carbon nanotubes, in particular the broad band near 680 $\mathrm{cm}^{-1}$ reported for the 1200 °C-annealed (HT1200) material that was tentatively attributed to finite (tube-)length effects and axial vibrations: distinguish finite-length-activated and defect-induced one-phonon scattering from intrinsic combination modes (optical-plus-acoustic or ZA-derived phonons), resolving the dependence of these components on inner-tube length, defect content and resonance conditions, and their assignment to the specific inner and outer tube species present.

The common objective is a closed, quantitative link between the observed Raman frequencies of the peapod/DWNT system and its structure (tube diameters and chiralities, $\mathrm{C}_{60}$-to-wall spacing, inner-tube segment length, defect content), so that RBM shifts and intermediate-frequency bands become reliable, mechanism-understood probes of the encapsulated-molecule interaction and of inner-tube geometry.

References

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