Absolute Quantification of sp3 Defects in Semiconducting Single-Wall Carbon Nanotubes by Raman Spectroscopy

The functionalization of semiconducting single-wall carbon nanotubes (SWCNTs) with luminescent sp3 defects creates red-shifted emission features in the near-infrared and boosts their photoluminescence quantum yields (PLQYs). While multiple synthetic routes for the selective introduction of sp3 defects have been developed, a convenient metric to precisely quantify the number of defects on a SWCNT lattice is not available. Here, we present a direct and simple quantification protocol based on a linear correlation of the integrated Raman D/G+ signal ratios and defect densities as extracted from PLQY measurements. Corroborated by a statistical analysis of single-nanotube emission spectra at cryogenic temperature, this method enables the quantitative evaluation of sp3 defect densities in (6,5) SWCNTs with an error of ±3 defects per micrometer and the determination of oscillator strengths for different defect types. The developed protocol requires only standard Raman spectroscopy and is independent of the defect configuration, dispersion solvent, and nanotube length.

After removal of unexfoliated material by centrifugation (Beckman Coulter Avanti J26SXP centrifuge) at 60000 × g for 1 h, the collected supernatant was passed through a poly(tetrafluoroethylene) (PFTE) syringe filter (pore size 5 µm). Excess polymer was removed by vacuum filtration through PTFE membrane filters (pore size 0.1 µm) and washing of the filter cakes with toluene at 80 °C, followed by redispersion in fresh toluene using bath sonication.

Tip Sonication of (6,5) SWCNTs
Toluene dispersions of SFM (6,5) SWCNTs were tip-sonicated (Sonics, Vibracell VXC-500) with a tapered microtip at 35 % amplitude with 8 seconds on and 2 seconds off pulses at 5 °C for 48 h. The resulting dispersions were centrifuged at 60000 × g for 45 min, and the collected supernatant was used for characterization and further processing.

Atomic Force Micrographs
Atomic force micrographs were recorded using a Bruker Dimension Icon atomic force microscope (AFM) in ScanAsyst TM mode under ambient conditions. SWCNTs were spincoated (2000 rpm, 60 s) from toluene dispersions with an optical density (OD) of 0.15 cm -1 at S-4 the E11 transition onto cleaned native silicon wafers. The wrapping polymer was removed by rinsing with tetrahydrofuran (THF) and isopropanol. Length distributions were analyzed using Gwyddion 2.6.

Raman Spectroscopy of SWCNTs
Raman spectra of pristine and sp 3 -functionalized SWCNTs were collected with a Renishaw inVia Reflex confocal Raman microscope in backscattering configuration equipped with a 50× long working distance objective (N.A. 0.5). Dispersions of SWCNTs were drop-cast on glass substrates (Schott AF32eco) and rinsed with THF and isopropanol (toluene-based dispersions) or ultrapure water (aqueous dispersions). Near-resonant excitation of the samples was performed with 532 nm and 633 nm lasers for (6,5) and (7,5) SWCNTs, respectively. For each sample >3600 spectra were averaged and baseline-corrected.

PL Quantum Yield Measurements
The PL quantum yields (PLQYs) of pristine and sp 3 -functionalized SWCNTs in dispersion were determined using an absolute method as reported previously. 1 SWCNT dispersions were diluted to an OD of 0.2 cm -1 at the E11 transition to minimize re-absorption. For all measurements, 1 mL of the analyte was filled into a cuvette (Hellma Analytics, QX type), which was placed in an integrating sphere (LabSphere, Spectralon coating). SWCNTs were excited resonantly at the E22 transition by the wavelength-filtered output of a picosecond-pulsed supercontinuum laser source (Fianium WhiteLase SC400). The light exiting the integrating sphere was coupled into an Acton SpectraPro SP2358 spectrometer using an optical fiber. Spectra were acquired using a liquid nitrogen-cooled InGaAs line camera (Princeton Instruments OMA V:1024).
PLQYs were calculated as the number ratio of emitted (Nem) to absorbed photons (Nabs) according to: For SWCNT dispersions, a value proportional to Nabs is obtained by integration of the laser signal intensity relative to that of a solvent reference sample (note, the product of intensity and wavelength is used for the integral to be proportional to the number of photons). Equally, integration of recorded PL spectra relative to the PL signal of the solvent provides a value proportional to Nem, allowing for the calculation of the PLQY. 4 Detector efficiency and absorption characteristics of optical components were accounted for by acquisition of calibration spectra employing a broadband light source (Thorlabs SLS201/M). NIR absorption of the solvent was corrected for by measuring the lamp spectrum while a cuvette filled with the respective solvent was placed inside the integrating sphere. Correction measurements for absorption spectra in the spectral region of the E22 absorption were performed without the cuvette in the integrating sphere. Prior to integration, every spectrum was divided by the correction function calculated from the ratio of the recorded and theoretical lamp spectrum.
The error of the PLQY determination primarily results from uncertainties for the laser absorption measurements and is estimated to be 10%.

Low-Temperature Single-SWCNT PL Spectroscopy
Low-temperature PL spectroscopy of individual SWCNTs was performed at 4.6 K using a closed-cycle liquid helium-cooled optical cryostat (Montana Instruments, Cryostation s50).
Dispersions of SWCNTs were diluted with a solution of polystyrene (Polymer Source Inc., MW = 230 kg•mol -1 ) in toluene (20 g•L -1 ) to an OD of 0.005 cm -1 at the E11 absorption peak.
30 µL of the obtained mixture were spin-coated (2000 rpm, 60 s) onto a glass substrate coated with 150 nm of gold.
The output of a continuous wave laser diode (Coherent, Inc., OBIS 640 nm, 1 mW) was focused onto the sample using a NIR-optimized 50× long-working distance objective (Mitutoyo, N.A. 0.42). Scattered laser light was blocked by appropriate long-pass filters. Low-temperature PL spectra were recorded with a thermoelectrically cooled two-dimensional InGaAs camera array (Princeton Instruments, NIRvana 640ST) coupled to a grating spectrograph (Princeton Instruments, IsoPlane SCT-320) using a grating with 85 grooves•mm -1 and 1200 nm blaze.
Very bright or asymmetrical emission spots were disregarded for PL measurements as they likely originate from SWCNT bundles instead of individual nanotubes. Only those peaks were included in the statistical analysis that could be unambiguously identified as single-defect emission based on the sharp, asymmetric peak shape typically observed for polymer-wrapped S-6 SWCNTs at cryogenic temperatures. For any analyzed spectrum the precise number of defects might be underestimated by 1-2 at most.

Tetrafluoroborate
Dispersions of (6,5) SWCNTs wrapped with PFO-BPy were functionalized with 4nitrobenzenediazonium tetrafluoroborate (DzNO2, Sigma-Aldrich) according to a protocol by Berger et al. 5 The reaction was carried out in a mixture of toluene and acetonitrile, using 18crown-6 (Sigma-Aldrich) as phase-transfer agent. Variations of the defect density were achieved by adjustment of the diazonium salt concentration. As the first step of the functionalization procedure, a solution of 18-crown-6 in toluene was prepared so that its final concentration in the reaction mixture after addition of all remaining reactants amounted to 7.6 mmol·L -1 . Subsequently, an appropriate volume of (6,5) SWCNT dispersion in toluene was

Sequential Functionalization of Polymer-Wrapped SWCNTs
The sequential functionalization procedure of (6,5) SWCNTs employed both protocols presented before. In the first step, SWCNTs were functionalized with DzNO2 in different concentrations ranging from 20 mg·L -1 to 1000 mg·L -1 . The obtained dispersions were then subjected to an additional functionalization step using 2-iodoaniline and a fixed reaction time of 40 min.

Calculation of sp 3 Defect Densities and Concentrations
The For a sp 3 defect density of nd, the E11 PLQY of functionalized SWCNTs η* can be written as: The combination of eqs (2) and (3) yields an expression for the density of luminescent sp 3 defects: The uncertainty of the defect density was estimated to be about 15% as a result of the error margins of the PLQY measurements and the values for D and τrad.
The defect concentration cd [nmol•L -1 ] can be obtained from the defect density by = • 11 88 nm −1 • 11 (5) where the geometrical factor of 88 nm -1 is the number of carbon atoms per nanometer of (6,5) SWCNT, A11 is the decadic absorbance at the E11 transition, and ε11 is the molar absorption coefficient of the E11 transition. For the latter, a value of 6700 L•mol -1 •cm -1 was used as