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.

The chemical modification of semiconducting single-wall carbon nanotubes (SWCNTs) is a versatile tool to tune their properties for various applications such as quantum-light sources,[1−3] sensing, or bioimaging.[4−7] In particular, covalent functionalization of SWCNTs with luminescent sp3 defects (also referred to as organic color centers) creates red-shifted emissive states in the near-infrared (NIR).[8−12] These states exhibit deep optical trap potentials (100–250 meV), which are able to localize the highly mobile excitons[9] that would otherwise explore large nanotube segments to encounter quenching sites or decay radiatively by E11 emission (see Figure a).[13] By preventing excitons from reaching quenching sites and decaying nonradiatively, these sp3 defects can increase the total photoluminescence quantum yield (PLQY) of SWCNTs.[9,14] However, precise control of the degree of sp3 functionalization is crucial. The maximum ensemble PLQY is observed at fairly low levels of functionalization, which would be favorable for electrically pumped light-emitting devices.[15] In contrast, single-photon emission requires exactly one luminescent defect per SWCNT.[1] Hence, accurate control over the degree of functionalization and knowledge of the precise sp3 defect densities are highly desired for further optimization.

Figure 1

(a) Schematic illustration of a (6,5) SWCNT functionalized with luminescent sp3 defects. Mobile excitons can decay radiatively (E11 emission) or nonradiatively by quenching at nanotube ends and defect sites (Q). Localized sp3 defects result in red-shifted emission (E11* or E11*–). Normalized (to E11) PL spectra of polymer-sorted (6,5) SWCNTs functionalized (b) with 4-nitrobenzenediazonium tetrafluoroborate (E11* defects), (c) with 2-iodoaniline (E11*– defects), and (d) with both E11* and E11*– defects using a sequential reaction scheme. (e) Schematic of absolute PLQY measurements with an integrating sphere.

The emission wavelengths of functionalized SWCNTs are predominantly determined by the binding configuration of the defects, as two sp2 carbon atoms must be converted to sp3 carbons to form one defect state. In chiral SWCNTs there are six possible relative positions of the involved carbon atoms, all of which lead to different optical trap depths and photoluminescence (PL) peak wavelengths.[16,17] However, only two of them are commonly found in functionalized (6,5) SWCNTs and give rise to separate NIR emission peaks termed E11* and E11*–, the latter being more red-shifted and exhibiting a longer fluorescence lifetime than the former.[5,18]

Various synthetic methods have been developed in an attempt to control the degree and type of sp3 functionalization of nanotube dispersions in water or organic solvents.[14,18−20] However, comparing different reports on functionalized SWCNTs and their properties is difficult because of the use of indirect metrics for their quantification. For example, PL peak intensity ratios strongly depend on the specific experimental setup and excitation power. They only provide a relative but not an absolute defect density.[21] Currently, the most reliable technique to determine the number of luminescent defects on individual SWCNTs is to count distinct emission peaks at cryogenic temperatures.[5,22] However, this method requires substantial experimental effort and tedious statistical analysis.

For graphene, a simple approach to quantify lattice defect densities using Raman spectroscopy is already well-established.[23,24] The introduction of point-like defects into the planar sp2 carbon lattice leads to the activation of the Raman D mode. Its relative intensity compared to the G mode can be used as a direct metric for the areal defect density.[25] The corresponding equation has been applied as a means of quality control in graphene samples[26] and to monitor the degree of chemical functionalization.[27] It was recently modified and extended to include line defects in graphene.[28] Although the Raman D mode of SWCNTs also reflects the degree of structural disorder and number of defects,[29−32] no quantitative relation to the absolute density of defects, especially at low defect densities, has been reported so far.

Here, we present a robust empirical metric for the absolute quantification of sp3 defects in the most commonly used (6,5) SWCNTs. Our method is based on a cross-correlation of Raman spectra, PLQY data, and statistics of low-temperature single-nanotube PL measurements. The final protocol only requires resonant Raman spectroscopy of drop-cast SWCNT films. That way, we are able to extract the absolute sp3 defect density, independent of type, within an error of ±3 defects per micrometer.

To produce nanotube samples with a controlled number of defects per nanotube length, polymer-sorted (6,5) SWCNTs were functionalized using two different procedures (see Methods, Supporting Information). E11* defects (emission at ∼1170 nm) were introduced by treatment with 4-nitrobenzenediazonium tetrafluoroborate (DzNO2) in a mixture of toluene/acetonitrile employing a phase-transfer agent.[14] More red-shifted E11*– defects (emission at ∼1250 nm) were created by reaction with 2-iodoaniline in the presence of the organic base potassium tert-butoxide (KOtBu).[18] The degree of sp3 functionalization was controlled by variation of the DzNO2 concentration or by adjusting the reaction time with 2-iodoaniline. Figure b,c shows the corresponding normalized PL spectra of selectively functionalized (6,5) SWCNT dispersions collected under pulsed excitation at the E22 transition (575 nm). Furthermore, we employed a sequential reaction scheme to create (6,5) SWCNTs with controlled concentrations of E11* and E11*– defects as shown in Figure d.

The increasing defect emission intensities in relation to the intrinsic E11 emission (∼1000 nm) reflect the rising number of defects, but this ratio strongly depends on excitation power[14,18] and cannot provide an absolute number. In contrast to that, absolute PLQY values of functionalized SWCNT dispersions can be used to calculate the density of luminescent sp3 defects within the framework of the diffusion-limited contact quenching (DLCQ) model. The DLCQ model assumes that excitonic E11 emission is governed by exciton diffusion and nonradiative decay at stationary quenching sites.[13] Within this model, luminescent sp3 defects represent an additional relaxation pathway competing for mobile excitons and resulting in a lower E11 PLQY of the functionalized SWCNTs (η*) compared to pristine SWCNTs (η) as introduced by Miyauchi et al.[10] The ratio (η/η*) can be used to calculate the density of luminescent defects nd [μm–1] according towhere D is the exciton diffusion constant and τrad is the radiative lifetime of the E11 exciton. The values for D and τrad were taken from previous experimental studies on (6,5) SWCNTs[13,33] (for details, see the Supporting Information). Absolute PLQY values of SWCNT dispersions can be obtained from the direct measurement of absorbed and emitted photons in an integrating sphere in comparison to a reference sample (cuvette with solvent, see Figure e and Supporting Information for experimental details) as described previously.[34] The spectral contributions of the intrinsic excitonic E11 emission and defect emission (E11*, E11*–) are separated, and the defect density is calculated using eq with only the E11 PLQY. Based on the uncertainties of the PLQY measurements and the error margins of the reported D and τrad values, a relative uncertainty of the defect density of about 15% can be estimated. Figure a shows the E11 and E11* contributions to the total PLQY versus the calculated defect densities for (6,5) SWCNTs functionalized with different concentrations of DzNO2. Pristine (6,5) SWCNTs exhibit a total PLQY of ∼2% in dispersion. Low levels of luminescent defects (up to ∼10 μm–1) increase the total PLQY by a factor of 2 followed by a strong reduction of the total PL yield at higher degrees of functionalization, in agreement with previous studies.[14,18]

Figure 2

(a) PLQY data with spectral contributions of the E11 (without sidebands) and E11* emission at different defect densities for (6,5) SWCNTs functionalized with DzNO2. Lines are guides to the eye. (b) Normalized Raman spectra of sp3-functionalized (6,5) SWCNTs with a zoom-in on the D mode region as an inset. (c) Correlation of the integrated Raman D/G+ ratio and defect density calculated from E11 PLQY with linear fit (red line, R2 = 0.98).

A major drawback of this approach is the necessity of an experimental setup with an integrating sphere for determining the PLQY in combination with precisely defined measurement conditions to prevent distortions due to photon reabsorption.[35] In contrast, determining the relative integrated D mode (ID, 1200–1400 cm–1) to G+ mode intensity (IG, 1560–1640 cm–1) from Raman spectra of the corresponding drop-cast nanotube films is straightforward and very reliable. As shown in Figure b, the D mode intensity increases with the degree of functionalization, being indicative of the number of sp3 carbon atoms. Figure c confirms a linear correlation of the integrated Raman signal ratio (ID/IG) with the calculated defect densities obtained from the E11 PLQY data in Figure a.

The linear correlation in Figure c should enable a direct evaluation of the number of sp3 defects based only on Raman spectra of functionalized (6,5) SWCNTs. However, this metric does not take into account the variations in initial quality of nanotubes before functionalization and thus the variability of the Raman D/G+ ratios of the pristine samples. As sp3 functionalization adds luminescent defects to a SWCNT lattice that already contains a certain number of defects depending on starting material and processing, the absolute Raman D/G+ ratios cannot be used to determine the number of introduced sp3 defects. Hence, we propose to use the difference between the integrated Raman D/G+ ratios of the pristine and functionalized sample, i.e., Δ(ID/IG), as a suitable metric for the quantification of defects introduced by functionalization. Note that we use the integrated Raman D/G+ ratio instead of just the peak intensity ratio because it provides more reliable and reproducible values, especially for small changes in defect density.

This differential integrated Raman D/G+ ratio enables comparison between different batches of nanotubes and different functionalization methods. Figure shows a summary of different batches of functionalized (6,5) SWCNTs (see Supporting Information, Figures S1–S3 for detailed PLQY data, PL and Raman spectra). The linear correlation of Δ(ID/IG) with the defect density extracted from the PLQY data holds for different defect densities, various SWCNT batches, E11* and E11*– defects as well as sequential functionalization to create both defects.

Figure 3

Differential integrated Raman D/G+ ratio versus calculated defect densities for different batches of polymer-wrapped (6,5) SWCNTs with E11*, E11*– and both defect configurations, including linear fit (black solid line, R2 = 0.98) and estimated error margin (±3 μm–1 shaded in gray). Arrow: defect densities for maximum PLQY (4–8 μm–1).

A linear fit to the compiled data yields the following simple expression for the density of introduced sp3 defects in (6,5) SWCNTs:

This equation is valid across a wide range of relevant defect densities (2–40 defects μm–1) and, in particular, covers the defect densities associated with maximum total PLQYs (i.e., 4–8 defects μm–1).

To exclude any potential influence of the laser excitation power on the integrated Raman D/G+ ratios and thus extracted defect densities, Raman spectra of functionalized (6,5) SWCNTs were recorded under identical conditions but at different excitation power densities (see Figure S4, Supporting Information). No significant changes of the integrated Raman D/G+ ratios were observed. Values obtained at typical laser power densities for Raman spectroscopy of (6,5) SWCNTs should also be comparable between different Raman spectrometers. Thus, this simple metric enables a quick and precise characterization of functionalized SWCNTs, and could be used for a reliable comparison of experiments in different laboratories using different experimental setups. It could also be applied to quickly identify a batch of functionalized nanotubes that is most likely to produce the strongest NIR emission upon excitation.

Note that other possible metrics were also tested, such as the integrated defect-to-E11 absorption and emission ratios. In general, absorption ratios are rather unreliable because of the very low absorbance values for E11* and E11*– transitions at low defect densities even for fairly concentrated dispersions (see Figure S5, Supporting Information). No clear correlation with the calculated defect densities could be identified across different SWCNT batches and defect configurations (see Figure S6, Supporting Information). The more commonly employed defect-to-E11 emission ratio, which can assess the relative degree of sp3 functionalization of SWCNTs,[20,36,37] is not applicable across different batches and functionalization methods because of the nonlinear and variable dependence of E11 and defect emission on excitation power (see Figure S7, Supporting Information).[18,38]

The demonstrated cross-correlation of integrated Raman D/G+ ratios and defect densities calculated from E11 PLQY data enables a simple evaluation of sp3 defect densities. However, even the DLCQ model only quantifies the number of defects indirectly and relies heavily on correct values for the exciton diffusion constant and radiative lifetime. In contrast, PL spectra of individual functionalized SWCNTs at cryogenic temperature (cryo-PL) allow for each luminescent defect to be counted as a separate emission peak,[22,39] assuming that each distinguishable peak within the E11* or E11*– spectral emission range corresponds to precisely one sp3 defect of the respective binding configuration. Different defect emission intensities only reflect the integrated probability for exciton relaxation in a given defect state (not multiple defects), as previously reported for the intrinsic E11 transition.[22]

To cross-check the calculated defect densities from PLQY measurements, two samples of (6,5) SWCNTs that were functionalized with low and medium densities of E11* defects (spectral region 1100–1220 nm) were produced and PL spectra at 4.6 K from a large number of individual nanotubes embedded in a polystyrene matrix were statistically analyzed (see Figure ). At low calculated defect densities of ∼4 μm–1, only few defect emission peaks were found in over 50 representative spectra (see Figures a and S8, Supporting Information). At medium defect densities (∼8 μm–1) significantly more defect PL peaks were identified on more than 40 single SWCNTs (see Figures b and S9, Supporting Information). Some E11*– defects (spectral region 1220–1360 nm) were found for these defect densities, which is consistent with literature reports for (6,5) SWCNTs functionalized with DzNO2.[16,17,40] As both defect configurations contribute equally to E11 quenching within the DLCQ model, and the developed quantification metric does not depend on the binding configuration, all defect peaks were included in the statistical analysis. The respective histograms for the number of defects per nanotube at low and medium sp3 defect densities are shown in Figure c,d. The defect densities calculated from PLQY data and the average defect densities obtained from histograms are in good agreement. However, while calculated defect densities are given per micrometer of SWCNT, cryo-PL spectra show defects on individual nanotubes with unknown length. Hence, the length distribution of sp3-functionalized SWCNTs needs to be considered for a thorough comparison. For this purpose, atomic force micrographs of nanotubes from the same dispersion of functionalized SWCNTs as those used in cryo-PL spectroscopy were recorded and statistically analyzed (see Figures S8 and S9, Supporting Information). Both pristine and functionalized (6,5) SWCNTs exhibited average lengths of ∼1.6 μm. This length distribution suggests that the number of defects per micrometer obtained via cryo-PL measurements is actually slightly lower than that extracted from PLQY measurements (possibly due to a selection bias toward less bright spots to avoid bundles and not all introduced defects being bright, see Supporting Information) but still within the margin of error (±3 μm–1) established in eq .

Figure 4

Low-temperature (4.6 K) single-SWCNT PL spectra of (6,5) SWCNTs in a polystyrene matrix functionalized with (a) low and (b) medium defect densities. Black triangles indicate individual defect emission peaks, spectral regions are highlighted for E11 (blue), E11* (red), and E11*– (orange) emission. Defect peak histograms of (c) 51 functionalized (6,5) SWCNTs with defect density 3.6 μm–1 and (d) 43 functionalized (6,5) SWCNTs with defect density 7.9 μm–1 as calculated from PLQY data.

Although eq was derived from measurements of long, polymer-wrapped (6,5) SWCNTs functionalized in organic solvents, the method is also applicable to short nanotubes and aqueous dispersions of SWCNTs. We used DzNO2 to functionalize polymer-sorted (6,5) SWCNTs that were intentionally shortened to average lengths of 0.46 μm by tip sonication (Supporting Information, Figures S10 and S11) and (6,5) SWCNTs sorted by aqueous two-phase extraction (ATPE), stabilized by surfactants in water (see Methods and Figure S12, Supporting Information). For both, a linear correlation between the differential Raman D/G+ ratios and calculated defect densities in agreement with eq was found (see Figure a). Moreover, nearly monochiral dispersions of polymer-sorted (7,5) SWCNTs were functionalized with DzNO2 (see Methods and Figure S13, Supporting Information) in a first attempt to expand our approach to other nanotube species. Because of the lower reactivity of (7,5) SWCNTs compared to (6,5) SWCNTs,[18] a maximum absolute defect density of ∼20 μm–1 was achieved. Nevertheless, the presented quantification method was also applicable to (7,5) SWCNTs (wrapped with polydioctylfluorene, PFO) as shown in Figure b, although with some deviations in the precise slope.

Figure 5

Differential integrated Raman D/G+ ratio versus calculated defect densities and linear fits for (a) aqueous dispersions of ATPE-sorted (6,5) SWCNTs and tip-sonicated, polymer-wrapped (6,5) SWCNTs and for (b) polymer-wrapped (7,5) SWCNTs. All functionalization steps were performed with DzNO2.

This is particularly interesting as resonant Raman measurements of (7,5) SWCNTs are performed at a different excitation wavelength (633 nm) compared to (6,5) SWCNTs (532 nm). For point-like defects in graphene, Cançado et al. reported a strong dependence of the Raman D/G intensity ratio on excitation laser wavelength, which was included in the expression for the average defect distance. However, for large defect distances, the influence of the excitation wavelength on the absolute Raman D/G intensity ratio becomes negligible.[23] The mean defect distances in sp3-functionalized SWCNTs relevant for most applications and investigated here (20–300 nm, see Figure S14, Supporting Information) are much larger than those considered in studies of defective graphene (5–30 nm).[25] Nevertheless, it remains to be tested what impact the Raman laser excitation wavelength has on SWCNTs with larger diameters.

One direct application of the presented quantification method is the experimental determination of the oscillator strengths of E11* and E11*– defects. Integration of the defect peak areas in the NIR absorption spectra of functionalized SWCNTs with different defect densities yielded the integrated molar absorptivities and absorption cross sections of the E11* and E11*– states (see Table and Figure S15, Supporting Information). The oscillator strength of an optical transition was calculated usingwhere ε0 denotes the vacuum permittivity, c is the speed of light, me is the electron mass, NA is Avogadro’s number, e is the elementary charge, εD is the molar extinction coefficient of the E11* or E11*– transition, and υ̃ is the wavenumber.[41]

Table 1

Integrated Absorptivity, Integrated Absorption Cross Section, and Oscillator Strength per Defect for E11* and E11*– Defect Configurations, Obtained from NIR Absorption Data of sp3-Functionalized (6,5) SWCNTs

defect configuration	integrated absorptivity ∫εDdλ [cm–1nm L mol–1]	integrated absorption cross section ∫σdυ̃ [cm]	oscillator strength f
E11*	(7.8 ± 1.4)·107	(3.1 ± 0.5)·10–12	3.5 ± 0.6
E11*–	(2.5 ± 0.4)·107	(1.0 ± 0.3)·10–12	1.1 ± 0.3

For E11* and E11*– defects, oscillator strengths of (3.5 ± 0.6) and (1.1 ± 0.3) per defect were obtained, respectively. The error margins for the oscillator strengths of E11* and E11*– are mainly due to the low total absorbances of the sp3 defects and the corresponding uncertainties of the integrated defect absorption (see Figure S5, Supporting Information). While density functional theory calculations predicted larger oscillator strengths (by a factor of 3–5),[16,17] they also suggested a reduction of the oscillator strength with a greater red-shift of the defect emission, which is in agreement with our findings. It is important to note that the discussed spectroscopic metrics provided here are given per defect site and are not directly comparable to literature data on the E11 oscillator strengths of (6,5) SWCNTs (∼0.01 per carbon atom).[42] As electron–hole correlation lengths are still on the order of 1 nm despite localization at defect sites,[43] ∼100 carbon atoms are presumed to contribute to the sp3 defect oscillator strength. Although the acquired data is not accurate enough to corroborate an increase of oscillator strength by a factor of 2 upon exciton trapping as proposed by Miyauchi et al.,[10] our findings suggest that the oscillator strengths of sp3 defects are at least on the same order of magnitude as those for the E11 transition.

In conclusion, we have developed a straightforward and reliable method to quantify the number of sp3 defects in (6,5) SWCNTs using resonant Raman spectroscopy. By establishing a linear correlation between the differential integrated Raman D/G+ ratio and sp3 defect densities calculated from PLQYs, the number of added defects per micrometer nanotube can be obtained within an error margin of ±3 defects μm–1. This method is suitable for SWCNTs functionalized with E11*, E11*–, or both defect configurations, independent of the type of dispersion (polymer-wrapped in organic solvent or surfactant-stabilized in water) and nanotube length of the starting material. A statistical analysis based on PL spectra of individual (6,5) SWCNTs at cryogenic temperature provided direct access to the number of defects per nanotube, which roughly matched the densities calculated from Raman spectra. From these data, the oscillator strengths of the E11* and E11*– defects were determined experimentally, confirming the predicted decrease in oscillator strength with optical trap depth of the defects. The applicability of the presented quantification method also extends to other nanotube species as demonstrated for (7,5) SWCNTs. However, additional resonant Raman and PLQY data of functionalized SWCNTs with different diameters will be required to obtain a universal expression similar to that for defects in graphene.