Photoluminescence Side Band Spectroscopy of Individual Single

Article pubs.acs.org/JPCC

Photoluminescence Side Band Spectroscopy of Individual SingleWalled Carbon Nanotubes Yara Kadria-Vili,† Sergei M. Bachilo,† Jeffrey L. Blackburn,‡ and R. Bruce Weisman*,†,§ †

Department of Chemistry and the Smalley-Curl Institute, Rice University, 6100 Main Street, Houston, Texas 77005, United States National Renewable Energy Laboratory, Golden, Colorado 80401, United States § Department of Materials Science and NanoEngineering, Rice University, 6100 Main Street, Houston, Texas 77005, United States ‡

S Supporting Information *

ABSTRACT: Photoluminescence spectra of single-walled carbon nanotubes (SWCNTs) have been recorded and analyzed for selected individual nanotubes and structurally sorted bulk samples to clarify the nature of secondary emission features. Room temperature spectra show, in addition to the main peak arising from the E11 bright exciton, three features at lower frequency, which are identified here (in descending order of energy difference from E11 emission) as G1, X1, and Y1. The weakest (G1) is interpreted as a vibrational satellite of E11 involving excitation of the ∼1600 cm−1 G mode. The X1 feature, although more intense than G1, has a peak amplitude only ∼3% of E11. X1 emission was found to be polarized parallel to E11 and to be separated from that peak by 1068 cm−1 in SWCNTs with natural isotopic abundance. The separation remained unchanged for several (n,m) species, different nanotube environments, and various levels of induced axial strain. In 13C SWCNTs, the spectral separation decreased to 1023 cm−1. The measured isotopic shift points to a phonon-assisted transition that excites the D vibration. This supports prior interpretations of the X1 band as emission from the dark K-momentum exciton, whose energy we find to be ∼230 cm−1 above E11. The remaining sideband, Y1, is red-shifted ∼300 cm−1 from E11 and varies in relative intensity among and within individual SWCNTs. We assign it as defect-induced emission, either from an extrinsic state or from a brightened triplet state. In contrast to single-nanotube spectra, bulk samples show asymmetric zero-phonon E11 peaks, with widths inversely related to SWCNT diameter. An empirical expression for this dependence is presented to aid the simulation of overlapped emission spectra during quantitative fluorimetric analysis of bulk SWCNT samples.

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INTRODUCTION Single-walled carbon nanotubes (SWCNTs) continue to be the focus of intense research activity aimed at exploring their unique physical characteristics and developing novel applications. One remarkable property is the emission of highly structured short-wave infrared (SWIR) photoluminescence from semiconducting SWCNTs.1 The main feature of this intrinsic emission is a single dominant peak (E11) at a wavelength reflecting the semiconducting optical band gap, which is determined by the nanotube’s specific diameter and roll-up angle.2,3 Those SWCNT geometrical parameters are in turn uniquely related to the (n,m) indices used to describe its structure,4 allowing photoluminescence spectroscopy to serve as a powerful tool for analyzing SWCNT samples and investigating their structure-dependent physical and chemical processes. Numerous prior studies have explored the dependence of the main E11 emission peak on nanotube structure, dielectric environment,5,6 axial deformation,7 oxygen doping,8,9 excitation intensity,10 and ultraviolet illumination.11 To obtain a deeper understanding of nanotube photophysics and improved capabilities for analytical spectroscopy, it is also necessary to © XXXX American Chemical Society

investigate the secondary features in SWCNT emission spectra. Such secondary emission features include defect-related emission and weak emission peaks involving states that may be formally forbidden by dipole or momentum selection rules. Such studies are quite challenging when using typical nanotube samples, which contain wide assortments of (n,m) structural species and show heavily overlapped spectral features. Measurements of single-species spectra therefore require either samples that have been carefully sorted for strong enrichment in one species,12−14 or else the study of individual nanotubes through microscopic spectroscopy.9,15,16 Furthermore, rigorous analysis of vibronic emission features, in which phonons are excited during exciton recombination, benefit from control of the SWCNT isotopic composition, because this isotopic variation gives predictable changes in phonon frequencies. We report here the results of an investigation using individual and bulk measurements with multiple (n,m) species and Received: August 30, 2016 Revised: September 27, 2016

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DOI: 10.1021/acs.jpcc.6b08768 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C controlled changes in isotopic composition, axial strain, and dielectric environment.

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EXPERIMENTAL METHODS This study used nanotubes grown in the Rice University HiPco reactor (batch 195.1) and at the National Renewable Energy Laboratory using normal (12C) and highly isotopically enriched (13C) feedstocks at reactor temperatures of 825 and 800 °C, respectively. SWCNT samples were structurally sorted either by density gradient ultracentrifugation (DGU)17 or by layer extraction using poly(9,9-dioctylfluorenyl-2,7-diyl) (PFO) or poly[9,9-dioctylfluorenyl-2,7-diyl)-alt-co-(6,6′-(2,2′-bipyridine))] (PFO-BPy) in toluene.18,19 Starting with HiPco batch 195.1, we used DGU followed by extraction with a custom-built precision fractionator20 to prepare an aqueous sodium cholate suspension highly enriched in (8,3) and (6,5) species. Separately, we prepared SWCNT samples enriched in neararmchair structures by dispersing the raw HiPco material into a solution of PFO in toluene. For the isotope study, the 12C and 13 C samples were dispersed into a solution of PFO-BPy in toluene to obtain enrichment in the (8,6), (11,3), (9,5), (10,5), and (10,6) species. (see Figure S1−2 for spectra of the bulk samples). We captured emission images and spectra from individual nanotubes using a customized SWIR fluorescence microscopy system.21 Dilute SWCNT samples in liquid suspension were drop-cast onto polycarbonate microscope slides, dried, and mounted onto the microscope stage. These specimens containing isolated and immobilized SWCNTs were excited with a tunable continuous wave Ti:sapphire laser beam whose linear polarization state was controlled with a Glan-Thompson calcite polarizer and a λ/2 retardation plate. Emission from the specimens was collected by a Nikon PlanApo 60x, NA 1.27 water immersion objective and passed through a 948 nm longpass dielectric filter to reject excitation light and short wavelength emission. The emission image was magnified by an additional factor of 1.5 and captured by a Roper OMA-V 2D InGaAs camera, on which each pixel’s width corresponded to 333 nm at the sample. By directing the microscope’s output mirror to another port, emission from a particular location in the specimen could be sent through an optical fiber to the entrance slit of small spectrograph with a 512-element cryogenically cooled InGaAs detector array. We limited integration times for PL spectral measurements to 50 s and controlled the excitation power density to avoid light-induced degradation of observed nanotubes.22 Only individual SWCNTs meeting specific criteria were selected for study. First, we required their emission intensities to be stable with time (see Figure S3). Second, we required their emission images to show uniform brightness along the nanotube axis (within our diffraction-limited resolution), indicating a low density of quenching defects. Figure 1 shows an example of an acceptably uniform emission image. Third, we required their emission spectra to show features of individual, disaggregated nanotubes. Specifically, the E11 peaks needed to have narrow and symmetric Voigt shapes (see Figures S4−5), and the ratio of emission intensities for excitation polarized parallel vs perpendicular to the nanotube axis needed to be at least ca. 30. These criteria ensured that the measured spectra represent, to the best degree possible, the intrinsic emissive properties of well isolated, low defect-density SWCNTs.

Figure 1. (Top) Emission spectrum of an (8,6) 12C nanotube acquired with 730 nm excitation and 50 s integration. The inset shows the nanotube’s spectrally integrated image. (Bottom) Spectral fit of the emission data showing three weaker features at frequencies below the main peak. Open circles are measured data points and colored curves are the four Voigt functions used to obtain the overall fit (black solid curve). The inset shows a magnified view of the lower frequency region.

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RESULTS AND DISCUSSION Figure 1 (top) shows the typical PL image and spectrum of a selected individual SWCNT. We identify it as an (8,6) structure based on its peak emission wavelength.2 As illustrated in Figure 1 (bottom), the measured emission spectrum could be well represented by a superposition of four components with Voigt line shapes: E11 (the main peak) plus three weaker, red-shifted side bands labeled Y1, X1, and G1. We similarly measured and analyzed emission spectra of more than 100 individual SWCNTs representing (9,5), (11,3), (8,6) and (8,3) species, spanning diameters from 0.772 to 1.036 nm (see Figure S5 for further examples). Within this set of data, the G1 feature was often not observable, but the Y1 and X1 sidebands were uniformly present. The X1 feature had a relatively consistent emission intensity relative to E11 of ∼6% in area and ∼3% in peak amplitude, whereas the Y1 magnitude showed larger variations, as will be discussed below. To clarify the nature of the X1 feature, we measured and analyzed emission spectra from more than 57 individual 12C nanotubes coated with sodium cholate (SC), PFO, or PFOBPy. Figure 2 shows each measured X1 peak frequency plotted as a function of the E11 peak frequency of the same nanotube. Although these values span a significant range within each (n,m) group because of environmental inhomogeneities, the B


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The Journal of Physical Chemistry C

Figure 2. X1 sideband versus E11 peak frequencies, as found by fitting emission spectra of 44 individual 13C nanotubes (red symbols) and 57 individual 12C nanotubes (blue symbols). The inset shows an expanded view of the spectral region for which 13C and 12C spectra were both available. Solid lines are linear least-squares fits to the 13C (red) and 12C (blue) data. They correspond to constant E11−X1 values of 1023 cm−1 for 13C and 1068 cm−1 for 12C. Figure 3. Jablonski diagram showing energy levels and transitions for a semiconducting SWCNT. States in the right and left manifolds have total (exciton−phonon) momenta differing by K (the separation between Brillouin zone K and K′ valleys, see the inset). Vibrationless excitonic levels are shown as heavy horizontal lines and marked with their symmetry labels; those with vibrational excitation are shown as thinner horizontal lines. Vertical green and red arrows represent optical excitation and emission transitions, respectively. Wavy arrows represent nonradiative electronic relaxation to the first bright exciton state. The dashed arrow denotes inelastic phonon scattering to populate the EK dark exciton state.

frequency shift between E11 and X1 peaks is much more constant: 1068 ± 1.7 cm−1 (standard error of the mean) with no systematic dependence on (n,m) or on coating agent. The structure-independence of this frequency shift agrees with the prior report of Matsunaga et al.15 Because the frequency interval of 1068 cm−1 does not match any Raman-active SWCNT vibrational mode, the X1 feature is not easily interpreted as a vibronic sideband of E11. In 2008, Kikkawa and co-workers interpreted the X1 emission feature as a vibronic satellite of a forbidden electronic transition to the ground state from a degenerate K-momentum excitonic state (termed EK) lying slightly above E11.12 In this view, excitation of the D mode vibration (observed near 1300 cm−1 in SWCNT Raman spectra) during radiative recombination of the EK exciton enables a momentum-conserving transition (X1) at a photon energy equal to EK minus the D mode energy. The Jablonski diagram of Figure 3 illustrates the relevant states and transitions. A subsequent bulk spectral study by Blackburn et al. compared 13C and 12C SWCNTs and confirmed that the X1 wavelength shifted with the mass-related change in D mode frequency, as predicted for emission from the K-momentum dark exciton.14 The X1 assignment can also be checked by isotopically labeled single-nanotube measurements on (8,6), (9,5) and (11,3) SWCNTs. We measured spectra from 44 individual 13C nanotubes and found E11−X1 shifts that were independent of (n,m) and had an average value of 1023 ± 2.7 cm−1 (standard error of the mean) (see Figure 2). If the assignment of Kikkawa and co-workers is correct, then the difference in shift values between 12C and 13C (1068 − 1023 = 45 cm−1) reveals the identity of the vibrational mode that makes the optical transition allowed through its momentum of K. To experimentally assess the isotopic shift in the D mode frequency, we examined bulk Raman spectra of 12C and 13C samples. As shown in Figure 4, we found that the G band is shifted by 60 cm−1, and the 2D mode is shifted by 95 cm−1. The latter value implies an isotopic shift in D mode frequency

of 47.5 cm−1, which agrees within experimental uncertainty with our 45 ± 3 cm−1 isotopic difference in E11 − X1 values. Another estimate uses the relation that the ratio of 13C /12C vibrational frequencies equals 12/13 = 0.961, so the isotopic vibrational shift should be 3.9% of the parent frequency. We observed a weak D mode Raman feature for 12C SWCNTs at 1298 cm−1 using incident light at 671 nm (1.85 eV). However, the D-mode Raman transition is known to be dispersive, increasing by approximately 50 cm−1 per eV of excitation frequency.23 Adjusting for this dispersion, we estimate the Dmode vibrational frequency corresponding to Raman scattering with the X1 photon to be ∼1250 cm−1, which predicts a value of 49 cm−1 for the isotopic difference in E11−X1 peak separations. This is again consistent with our fluorescence measurements, supporting the assignment of the X1 band as a vibronic transition that combines de-excitation of the K-momentum exciton with excitation of the vibrational D mode, as diagrammed in Figure 3. Given this assignment, one can find EK, the energy of the Kmomentum dark exciton, and ΔK, the energy splitting between EK and the bright E11 exciton (see Figure 3). ΔK can be expressed as D − (E11 − X1), where D is the vibrational frequency discussed above. Although it has been suggested that this D mode frequency depends on nanotube structure,24−26 its variation over our range of SWCNT diameters (0.78 to 1.01 nm) is apparently less than 5 cm−1, and we therefore consider it C


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Figure 4. Resonance Raman spectra of bulk 12C and 13C SWCNT samples suspended in PFO-BPy/toluene and excited at 671 nm. Frames (A) and (B) show the G and 2D (G′) vibrational features, respectively.

constant for this analysis. In addition, Figures 2 and S15, which include measurements on 14 individual (8,3) 12C nanotubes coated with sodium cholate, show that E 11 − X1 is experimentally constant for our diameter range. Therefore, within the precision of our measurements, the value of ΔK is apparently independent of nanotube diameter and equal to 230 ± 25 cm−1 (29 ± 3 meV). This is close to the ΔK values previously reported from theory27 and experiments.12,14−16,28 However, we cannot confirm the structure dependencies predicted by theory and deduced experimentally by Vora et al.13 using X2 as well as X1 data from sorted SWCNT bulk samples. We performed further experiments to monitor changes in the X1 optical transition when the nanotube is externally perturbed. Various studies have demonstrated spectral shifts in SWCNT main (E11) transitions with changing dielectric environments.6,29 Here we compared emission spectra from individual (7,5) nanotubes in contact with solvents with different dielectric constant (ε) and refractive index (n) values. The nanotubes were originally suspended with PFO, dried on a plastic slide, covered with a drop of hexane (ε = 1.9, n = 1.375) or methylnaphthalene (ε = 2.7, n = 1.61), and sealed with a plastic coverslip. We then recorded emission spectra from single nanotubes excited at 800 nm. Analysis of the measured PL profiles showed an average red-shift from the hexane to the methylnaphthalene surroundings of 73 ± 4 cm−1 for the E11 peak and 65 ± 6 cm−1 for the X1 peak (see Figure S8). We consider these shift values to be essentially equal, suggesting very similar polarizability for the Γ-momentum bright exciton and the K-momentum dark exciton.30 Further measurements were made to study the effects of axial stretching on the EX1 state. Here, HiPco SWCNTs were dispersed in a toluene solution of the polymers PFO and poly(methyl methacrylate) (PMMA). The dilute dispersion was applied to a plastic slide and dried to form a solid film. The sample slide was then clamped into a mechanism to apply stress along one axis while mounted on the microscope stage. We positioned the stage to observe an isolated (8,6) long nanotube (2 to 4 μm) that was aligned nearly parallel to the stretching axis and then measured its emission spectrum before and after the substrate slide was stretched. This process was repeated for 13 (8,6) nanotubes with various induced strains. The resulting spectral shifts in X1 and E11 peak positions are shown as a correlation plot in Figure 5. A linear fit to the data gives a slope of 1.08, indicating that the strain-induced spectral shifts in X1 emission peaks matched those of E11 in direction and

Figure 5. Correlation plot of strain-induced spectral shifts in the E11 and X1 peaks as measured from individual SWCNTs. The red line is a zero-intercept least-squares fit to the data. Its slope is 1.08 ± 0.05.

magnitude, within the precision of our measurements. Apart from the modulation of SWCNT band gaps by strain, it is necessary to consider whether vibrational effects contribute to the observed X1 shifts, because axial strain is known to affect SWCNT mode frequencies. For example, a (17,0) nanotube shows a ∼ 7 cm−1 decrease in its 2D Raman frequency under 0.5% strain.31 This would correspond to only a 3.5 cm−1 change in the D fundamental frequency at a strain for which the predicted E11 shift is 350 cm−1.32 We therefore neglect vibrational contributions to the observed X1 spectral shifts and conclude that the EK and E11 energies change to an equivalent degree under axial deformation of the nanotube. This result plus the similar shifts observed from changes in surface coatings or solvent environment imply that the electronic states giving EK and E11 emission have very similar orbital structures. Additional information on the character of the EK state was obtained from emission polarization measurements on single nanotubes and on an enriched bulk sample. The transition dipole moment is aligned parallel to the nanotube axis for strongly allowed SWCNT transitions such as E11 and E22. In single nanotube measurements, we fixed the excitation beam polarization parallel to the nanotube axis, while an emission polarizer was set parallel or perpendicular to that axis. For both the E11 and X1 emission peaks of an individual (6,5) SWCNT, we measured maximum intensities for parallel alignment and minimum emission (ca. 25× weaker) for perpendicular D


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The Journal of Physical Chemistry C alignment (see Figure S10A,B). Consistent with this finding, spectra measured from a (6,5)-enriched bulk sample clearly show that E11 and X1 bands have the same relative intensities in both VV and VH polarization configurations (see Figure S10C,D). The X1 transition therefore has a transition dipole aligned parallel to the SWCNT axis. The Jablonski diagram of Figure 3 illustrates the apparent source of X1 emission. In this diagram, the right and left columns represent states with total (exciton−phonon) momenta differing by K. Optical transitions between those two manifolds are forbidden. Normal optical excitation above the E11 level is followed by nonradiative relaxation to give the Γ-momentum bright E11(A2) exciton, which can emit at the dominant PL origin (zero-phonon) peak or at the weak vibronic satellite marked G1. Alternatively, the bright E11(A2) exciton can relax to a lower-lying dark exciton state (not shown) or be converted into the K-momentum dark exciton, E11(E), at slightly higher energy through inelastic intervalley scattering by a phonon that transfers momentum K. Simple radiative recombination of this exciton is forbidden by momentum conservation, so no origin emission band (zerophonon line) is observed from it. However, the dark exciton can undergo phonon-assisted emission if a K-momentum phonon is excited during the transition. This gives the X1 emission feature, which creates an in-plane transverse optical (iTO) phonon at the K point, corresponding to the D mode vibration in the Raman spectrum. Imperfections in the SWCNT periodicity, such as ends, covalently functionalized sidewall sites, or lattice defects, may relax the momentum selection rule and induce emission at the dark EX1 origin. To examine whether imperfections influence emission from EX1, samples containing SWCNTs ∼2 μm long were suspended with PFO and dried on a plastic microscope slide. Emission spectra from (7,5) and (8,6) nanotubes were measured from different regions along their axes. Although the E11 emission intensities varied from point to point, the normalized E11 spectral profiles matched very well on the high energy edge, where the emergence of EX1 origin emission would be observed, even at the ends of the nanotube (see Figure S11). Thus, we did not obtain any evidence for defectinduced emission directly from EK, although the sensitivity of this analysis was low because of the relatively large diffractionlimited region over which our spectra were averaged. The Y1 and G1 emission features in our individual nanotube spectra are less distinct than X1. Analysis of Y1 for 14 (8,3) nanotubes showed a red-shift from E11 of approximately 300 cm−1, closely matching the radial breathing mode (RBM) frequency and suggesting that Y1 may be the RBM vibronic sideband of E11.33 However, several factors point to a different assignment. First, the study of Metzger et al.34 found that the separation of this band from E11 changed with temperature while the RBM frequency remained constant, and it also showed decay kinetics different from E11. This implies that it is emission from a different excitonic state. Only three other intrinsic singlet excitonic states exist near the E11 bright state:35 a dark Γ-momentum state experimentally located only a few millielectronvolts (less than 50 cm−1) below E11;36,37 and EK, the doubly degenerate dark K-momentum state above E11 that gives the X1 transition. By process of elimination, Y1 would then have to be either from an extrinsic state or a triplet exciton whose emission is induced by chemical perturbation.38 We observe that the intensity of the Y1 feature relative to E11 varies among nanotubes of the same (n,m) structure and even for

different positions within a single nanotube (see Figure S11). This supports the tentative assignment of Y1 emission to a SWCNT triplet exciton or to an extrinsic state that is induced by local imperfections. The emission band labeled G1 was challenging to study in individual nanotube spectra because its integrated area was only ∼2% relative to E11. However, it is more pronounced in enriched bulk samples (see Figure S7). Its position ∼1600 cm−1 below E11 suggests assignment as the vibronic (phonon) sideband of E11 that generates the G mode vibration. A detailed study of isotope-enriched, (6,5)-enriched bulk samples by Blackburn and co-workers has confirmed this G mode involvement on the basis of a measured 67 cm−1 isotopic shift that was close to the expected 62.5 cm−1 shift for that vibration.14 The low intensity of the G1 band is consistent with the weak exciton−phonon coupling in SWCNTs that has been deduced from analysis of Raman excitation profiles.39,40 The “X2” absorption feature approximately 1600 cm−1 above E11, which would appear to be a G-mode vibronic sideband of E11,41 is more prominent than its emissive counterpart G1 despite the expectation that it should reflect similarly weak exciton− phonon coupling. This anomaly is resolved by the interpretation of Kikkawa and co-workers, who assigned the X2 feature as the phonon-assisted absorptive transition to the EK + D state (with zero net momentum), as illustrated in Figure 3. The role of K-momentum phonons in allowing optical excitation of the dark exciton was previously proposed from computations by Perebeinos et al.42 We observe a significant difference in E11 emission line shapes between bulk and single nanotube spectra. The E11 emission components from individual SWCNTs are symmetric enough to be well fit by Voigt functions, whereas those from bulk samples are broadened on the low frequency side and must be represented by an asymmetric function such as Pearson IV (see Figures S12−S13). We attribute the enhanced low frequency intensity in bulk samples to a subpopulation of nanotubes containing local regions with environments that slightly lower the exciton energy and generate red-shifted emission. Those SWCNTs are likely excluded from our single particle spectral measurements by the selection criteria described in the Experimental Methods section. From careful fits of emission spectra from both bulk and single nanotube samples, we find that the line width of the zerophonon E11 component has a clear inverse dependence on SWCNT diameter. Figure 6 shows a plot of our deduced full widths at half-maximum versus diameter for bulk samples, along with an empirical curve and an expression representing the trend. Our data suggest that line widths in bulk samples asymptotically approach ∼135 cm−1 for large nanotube diameters. Additional results showing the Gaussian and Lorentzian line width components for single nanotubes as well as enriched bulk samples are plotted in Figure S14. We note that observations of an inverse dependence of line width on diameter were previously reported by Inoue et al.43 and Murukami et al.16 Although observed widths will depend somewhat on sample preparation and nanotube coating, our empirical expression for the structure-dependent bulk line widths will be very valuable for quantitative fluorimetric analysis of SWCNT samples with congested emission spectra.44,45

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CONCLUSIONS SWCNT emission spectra near the E11 peak have been studied at room temperature for individual SWCNTs selected for E


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Additional sample spectra, stability plot of emission spectrum from individual nanotube, statistical plots of data from spectral analyses, further examples of analyzed emission spectra, plots of emission line width components vs nanotube diameter for spectra analyzed with Voigt line shapes, and tables summarizing data collected from more than 100 individual SWCNTs. (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: 713-348-3709. Fax: 713-3485155. Notes

The authors declare no competing financial interest.

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Figure 6. Full width at half-maximum line widths of the E11 emission band, as deduced from analysis of bulk and individual nanotube PL spectra. Triangles show data measured in aqueous sodium cholate (SC) surfactant; circles show data measured in PFO/toluene; stars show data measured from dried individual nanotubes coated with SC, PFO, or PFO-BPy (bars mark standard deviations). The red curve is a fit for the widths from bulk samples, corresponding to the boxed expression in which dt is nanotube diameter in nanometers.

ACKNOWLEDGMENTS This research was sponsored at Rice University by the National Science Foundation (grant CHE-1409698) and the Welch Foundation (grant C-0807). J.L.B. was supported by the Solar Photochemistry Program of the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences, under Contract No. DE-AC36-08GO28308 to NREL.

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relatively low defect densities. One weak, lower frequency spectral feature, the G1 peak, is assigned as a G mode vibrational satellite. We assign Y1, a second weak sideband located closer to E11, to perturbation-induced emission from an extrinsic state or triplet exciton. The remaining sideband, X1, was previously assigned as phonon-coupled emission from a dark K-momentum excitonic state. We investigated X1 in detail for several standard (99% 12C) and isotopically labeled (100% 13 C) (n,m) species to clarify its nature. Although significantly more intense than G1, the X1 feature is still much weaker than the main E11 feature: ∼3% of its peak amplitude and 6% of its area. Within the limited spatial resolution of our observations, these relative X1 intensities appeared unchanged near the ends of individual SWCNTs. We found the average spectral shift between E11 and X1 to be 1068 cm−1 for 12C nanotubes, with no clear dependence on (n,m) or coating. The shift decreased to 1023 cm−1 for 13C nanotubes, as is consistent with a phonon-assisted transition that excites one quantum of the D vibration. This finding supports the assignment of X1 to emission from the dark K-momentum exciton at energy EK. We estimate that EK lies approximately 230 cm−1 above E11. We also found that the X1 emission is polarized parallel to the nanotube axis (like E11). Furthermore, the X1 and E11 peaks shift by nearly the same amount when nanotubes are perturbed by a change in environment or by axial stretching. The EK and E11 excitonic states therefore display very similar electronic characters. Analysis of emission spectra from bulk samples shows that the E11 zero-phonon peaks are asymmetric (unlike single nanotube spectra), with widths that vary inversely with nanotube diameter. These findings should permit more reliable spectral interpretation and quantitative fluorimetric analyses of SWCNTs.

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REFERENCES

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Photoluminescence Side Band Spectroscopy of Individual Single

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