Reconstructing the radial breathing mode resonance Raman spectra for HiPco single-wall carbon nanotubes

The radial breathing mode (RBM) region of the resonance Raman spectra of HiPco single-wall carbon nanotubes (SWNTs) was investigated as a function of aggregation and presence of environmental contaminants. This was modeled using an energetic deviation term $\left(\Delta E\right)$, imparted to the optical transitions $\left[E_{ii}(n,m)\right]$ by the change in SWNT physicochemical environment. Three sets of $E_{ii}(n,m)$ values were used to reconstruct these RBM profiles, based on (i) photoluminescence (PL) measurements, (ii) a simple tight-binding (TB) model, and (iii) a set of modified (TB-based) $E_{ii}(n,m)$ values to account for the underestimation of the influence of chiral angle for SWNTs with diameters below $1\mathrm{nm}$. The simulation revealed that the PL-determined $E_{ii}(n,m)$ set provided a good fit in terms of peak position as opposed to TB-calculated values. Moderate improvement was attained using the third set of $E_{ii}(n,m)$ values, indicative of the importance of both curvature and chirality effects. Providing an accurate set of $E_{ii}(n,m)$ values becomes available, the RBM profile reconstruction methodology discussed herein could greatly enhance our ability to model a range of physicochemical changes to the immediate environment of SWNTs.

Figure 1

RBM band of HiPco SWNTs for $E_{\text{laser}}=1.579\mathrm{eV}$ obtained experimentally for (I) acid-purified and DI-water-washed SWNTs; (II) vacuum-annealed and sealed SWNTs; (III) ${\mathrm{D}}_2\mathrm{O}$ suspension of SDS-assisted dispersed SWNTs. The $\sim 303{\mathrm{cm}}^{-1}$ feature has a contribution from the Si substrate. No baseline correction was performed.

Figure 2

(a) Concentration distribution of HiPco SWNTs, and (b) optical transition energies $E_{ii}(n,m)$ as a function of nanotube diameter (Kataura plot). Circles and crosses are for met-SWNTs and sem-SWNTs, respectively, obtained from simple tight-binding model (Refs. 31, 32, 33) Solid trigonals depict $E_{ii}(n,m)$ observed by photoluminescence measurements (Ref. 13). The horizontal solid line indicates the excitation laser energy and the dotted line represents the imaginary laser energy equivalent to a downshift of $E_{ii}(n,m)$ by $200\mathrm{meV}$.

Figure 3

Calculated Raman cross section as a function of TB-determined $E_{22}^S(n,m)$, for 0 (crosses) and 200 (rectangles) meV $\Delta E$ values under $1.579\mathrm{eV}$ laser excitation. Solid and dotted vertical lines refer to the notation used in Fig. 2.

Figure 4

Chirality map for HiPco SWNT. Shaded cells indicate the sem-SWNTs observed by photoluminescence measurements. Deep and light shaded cells represent strong and weak resonance, respectively, under $785\mathrm{nm}$ $\left(1.579\mathrm{eV}\right)$ laser excitation. The hatched triangular section depicts the sem-SWNTs with tight-binding model calculated $E_{ii}(n,m)$ values having considerable error, due to small diameter and high chiral angle.

Figure 5

Experimental (open circles) and simulated (solid lines) RBM spectra arranged vertically for samples III, II, and I and horizontally for various sets of $E_{ii}(n,m)$ values (see text for details). Marked peaks refer to simulated spectra.