Radial-Tangential Mode of Single-Wall Carbon Nanotubes Manifested by Landau Regulation: Reinterpretation of Low- and Intermediate-Frequency Raman Signals
Bibliographic record
Abstract
Abstract The low-frequency Raman signals of single-wall carbon nanotubes (SWNTs), appearing in the range of 100-300 cm-1, have been interpreted as radial-breathing mode (RBM) comprising pure radial Eigenvectors. Here, we report that the majority of the low-frequency, as well as the intermediate-frequency signals of SWNTs are radial-tangential modes (RTMs) coexisting radial and tangential Eigenvectors, while only the first peak at the low-frequency side is the RBM. Density functional theory simulation for a SWNT of ~2 nm in diameter shows that dozens of RTMs exhibit following the RBM (~150 cm-1) up to G-mode (~1592 cm-1) in order with Landau regulation. We specify the RBM and the RTM on Raman spectra obtained from SWNTs, where both appear as a prominent peak between 149 cm-1 and 170 cm-1 and as ripple-like peaks between 166 cm-1 and 1440 cm-1, respectively. We report that the RTMs have been regarded as RBM (~300 cm-1) and ambiguously named as intermediate-frequency mode (300-1300 cm-1) without assignment. The RTMs gradually interlink the RBM and the G-mode resulting in the symmetric Raman spectra in intensity. We reveal high-resolution transmission microscope evidence for a helical structure of SWNTs informing the typical diameter of commercial SWNTs to be 1.4-2 nm.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".