Quantitative Analysis of Isolated Single-Wall Carbon Nanotubes with Their Molar Absorbance Coefficients

The molar absorbance coefficients of metallic, semiconducting, and (6,5) chirality enriched single-wall carbon nanotubes were evaluated by a spray technique combined with atomic force microscopy. Single-wall carbon nanotubes with isolated and a single predominant electronic type were obtained by using the density-gradient ultracentrifugation technique. In the visible region, all coefficients had similar values around 2–5× 10/mLmol cm, independent of their diameter distribution and the electronic types of single-wall carbon nanotubes, and the εS22/εM11 and εS11/εM11 were estimated to be 1.0 and 4.0, respectively.The coefficient strongly depends on the length of single-wall carbon nanotubes, independent of their electronic types and chirality.


Introduction
The absorption spectra of single-wall carbon nanotubes (SWCNTs) are one of the basic methods for determining the optical properties of SWCNTs and a very powerful tool for studying their electronic structure, purity, and quantity, known as purity assessment [1][2][3][4][5].All current methods for producing SWCNTs, however, give mixtures of metallic (M-) and semiconducting (S-) SWCNTs with a variety of lengths and chiralities.This structural diversity complicates the quantitative characterization or purity assessment of the electronic types, amount, and morphology of SWCNTs in the materials.
Recent progress in the sonication techniques [6] allows us to obtain well-dispersed SWCNT solutions, which show electronic absorption spectra with very sharp peaks related to individual SWCNT structures.These advanced sonication techniques have been applied to separation of SWCNTs, and the scalable technique of the density-gradient ultracentrifugation (DGU) and column chromatography easily provides bulk quantities of SWCNTs with an individual and a single predominant electronic type [7][8][9][10][11][12][13][14][15].By using these separated samples, the metal-to-semiconductor ratios [10,[16][17][18] were successfully evaluated.
In this study, a spray technique combined with atomic force microscopy (AFM) [5] was used to determine the molar absorbance coefficients of individual and single electronic types of SWCNT solutions which were prepared by DGU separation of SWCNTs [9,10,12].The length-diameter distribution was statistically evaluated with AFM, and each of the obtained coefficients was fairly compared.Then, the metalto-semiconductor ratios in unsorted dispersed solutions were evaluated by a weighted sum of the spectra of M-and S-SWCNTs in the visible region, which corresponds to S 11 , S 22 , S 33 , M 11 , and M 22 [10].The molar absorbance coefficient in UV region was also evaluated, and the length dependence on the coefficient of SWCNTs was discussed.
By using the protocol for DGU separation of SWCNTs reported by Arnold et al. [12], (6,5) chirality-enriched samples, M-and S-SWCNTs, were prepared.To improve the separation yield, the surfactant concentration was optimized to increase the distance between M-and S-SWCNTs enriched layers in the centrifugation tube [9,10,22].
Then, iodixanol, sodium cholate, and deoxycholate sodium salts were removed from obtained samples through dialysis [23] in 1% w/v aqueous SDS using a visking membrane (MW: ∼12,000, cellulose tube).Absorption spectra of the dispersions were measured, and the samples were sprayed onto SiO 2 substrates for AFM evaluation [5].Each sample was accurately diluted using 1% w/v SDS-H 2 O, and 2 mL solution was prepared.The sprayed samples were observed by AFM to determine the number of SWCNTs in dispersed solutions, and their absorbance coefficients were calculated as previously reported [5].All AFM measurements were carried out on Dimension 3100, Nanoscope IV (Veeco, Digital Instruments) in tapping mode with Si cantilevers at room temperature.
The (6,5) chirality-enriched sample was also characterized by the photoluminescence (PL) measurement using a Shimadzu NIR-PL system (CNT-RF) equipped with a liquid N 2 -cooled InGaAs detector array.A 10 nm slit width was used for both excitation and emission.Excitation light was generated by a xenon arc lamp with an exposure time of 5 sec.

Results and Discussion
The photographs of the centrifuge tubes and optical absorbance spectra after DGU are shown in Figure 1.By comparing the diameter distribution of the samples with the calculated energies between mirror-image spikes in the density of states, each absorbance was assigned as S 22 and M 11 as denoted in the spectra [24].The absorption spectra of M-SWCNTs showed the strong suppression of optical transitions associated with S-SWCNT species and vice versa.In the DGU separation of CoMoCAT, a (6,5) chirality-enriched layer, the purple-colored layer, appeared between the M-and S-SWCNT layers (Figure 1(a)) [11,12].
The relative magnitude of the absorbance of M-CoMoCAT and S-CoMoCAT varied with the concentration of cosurfactants in the sample layers.At a total amount of 3.5% w/v surfactant, the strong suppression of the absorption of S-CoMoCAT was observed, while M-HiPco was well separated at a total amount of 2.0 w/v surfactant.This indicates that a high concentration of surfactants was needed to separate SWCNTs with small diameters, CoMoCAT, by their electronic types.It is suggested that the coordination and the mass per volume of a wrapped and hydrated SWCNT are important for separation by DGU during the first step of diameter separation and that the interaction of surfactants within gradients and coordinated around SWCNTs is more effective for separations when the gradients are slowly sedimented towards the bottom of the centrifuge tube.The SWCNTs with small diameters have less  interactions and fewer differences in mass per volume of a wrapped and hydrated nanotube rather than SWCNTs with larger diameter due to the difference in sidewall curvature and surfactant coordination around SWCNTs.As a consequence, in order to use the interaction for sorting with the electronic type of SWCNTs, it is suggested that a high concentration of surfactant in the gradient is required.
The absorption spectrum from the (6,5) chiralityenriched sample (Figure 1(c)) showed strong absorption signals at a wavelength of 570 nm and 987 nm.A spectrum of unsorted supernatant from the starting material is also shown in Figure 1(c) for comparison.The absorption peak at 570 nm and 987 nm was assigned as S 22 and S 11 in the (6,5) tube, respectively.The other partially overlapped absorption around a wavelength of 960 nm is associated with S 22 in the (8,3) tubes.The PL mapping of the (6,5) chirality-enriched layer (Figure 1(d)) also indicated that PL from the (6,5) chirality was significantly enhanced, and the low intensity of PL from (8,3) chirality was observed too.
The number of SWCNTs in the separated samples and their absorbance coefficients were determined as previously reported [5].Briefly, monolayer SDS membranes were formed by spraying dispersed SWCNTs onto SiO 2 substrates, and the area of the formed membranes was evaluated by AFM observation (Figure 2(f)).Then, the SDS molecules alone were washed out with rinsing in water, and SWCNTs were observed by AFM (Figure 2(g)).Finally, by comparing the number of SDS molecules and SWCNTs in the formed membranes, the molarity of SWCNTs in 1% w/v SDS dispersion was accurately determined, and the molar absorbance coefficient was evaluated.
In the case of the (6,5) chirality-enriched sample (diameter,  = 0.76 nm), the average number of SWC-NTs in a bundle and the mean length was estimated to be 1.1 nm and 350 nm from the height and length distribution (Figure 2(c)).The absorbance coefficient of the (6,5) chirality-enriched SWCNTs was evaluated to be 6.9 × 10 −15 /mL SWCNT −1 cm −1 at a wavelength of 570 nm and 1.9 × 10 −14 /mL SWCNT −1 cm −1 at a wavelength of 987 nm, respectively.Moreover, a SWCNT with the diameter of 0.76 nm and the length of 350 nm was regarded as an individual molecule, and the molar absorbance coefficients of the (6,5) chirality-enriched SWCNT were estimated to be 4.2 × 10 9 /mL mol −1 cm −1 at a wavelength of 570 nm and 1.1 × 10 10 /mL mol −1 cm −1 at 987 nm.
We also obtained the molar absorbance coefficients of each SWCNT dispersed solutions separated by their electronic types.Figure 3 presents the optical absorption spectra of each sample normalized by their determined absorbance coefficients.In the visible region, all coefficients had almost the same value of 2-5 × 10 9 /mL mol −1 cm −1 independent of their diameter distributions and electronic types of SWCNT, and  S22 / M11 was estimated to be ∼1.0, while  S11 / M11 was estimated to be ∼4.0.It is indicated that the obtained absorption coefficients enable us to estimate the relative concentration of SWCNTs species with their electronic types or chiralities.
To evaluate the metal-to-semiconductor ratio in the starting materials, the spectra of the unsorted dispersed solutions were reproduced by the sum spectra of the M-and S-SWCNTs [10].As shown in Figure 4(a), the sum spectrum of the M-HiPco multiplied by 0.3 and the S-HiPco spectrum multiplied by 0.7 reproduced the unsorted spectrum.It is understood that the starting materials of HiPco contained 30% metal and 70% semiconductor.It is well known that the concentration of M-SWCNTs would be 33% when all chiralities grow at the same rate.The value is very close to our evaluation as mentioned above.
In the case of CoMoCAT samples, the sum of the spectra of the M-, S-, and the (6,5) chirality-enriched SWCNTs was required to reproduce the unsorted dispersed solution since a (6,5) chirality-enriched layer existed between the layers of M-and S-SWCNTs during the sorting of CoMoCAT samples.The sum spectrum of the M-CoMoCAT multiplied by 0.2, the S-CoMoCAT multiplied by 0.5, and the (6,5) chiralityenriched layer multiplied by 0.3 reproduced the spectrum of the unsorted solution as shown in Figure 4(b).
The molar absorbance coefficient of SWCNTs in the UV absorption region, known as the collective excitation of the electron system polarized along the nanotube axis, was previously reported and found to be ca.1.9 × 10 7 /L mol −1 cm −1 at 280 nm with an average length of around 660 nm [5]. Figure 5 presents the optical absorption spectra in the UV region of the HiPco samples in this study normalized by the determined absorbance coefficients.The value of the unsorted HiPco was obtained by the sum spectrum of the M-HiPco multiplied by 0.3 and the S-HiPco multiplied by 0.7.The average length was around 180 nm, and the molar absorbance coefficient was evaluated as 3.6 × 10 6 /L mol −1 cm −1 at 280 nm in this work.The value of the coefficient was about five times smaller than the one previously reported due to the shorter length of SWCNTs.It is understood that the molar absorbance coefficient is proportional to the average length of SWCNTs in the dispersed solutions and that the coefficient depends on the number of carbons in a SWCNT.The obtained molar absorbance coefficient normalized by their average length in this work, however, was a little smaller than the previously reported one.It is suggested that damage on the sidewall of SWCNTs generated by long-time and high power sonication process broke the crystalline of SWCNTs, which decreased the absorbance coefficient of short-length SWCNTs.

Conclusion
The molar absorbance coefficients of M-and S-SWCNTs, which were separated by using the DGU method, have been successfully evaluated by the spray technique we developed.In the visible region, all coefficients had similar values of 2-5 × 10 9 /mL mol −1 cm −1 , independent of their diameter distribution and the electronic type of SWCNTs, and  M11 / S22 was estimated to be ∼1.0.The (6,5) enriched samples had the same value.As a consequence, the absorbance coefficient of SWCNTs was independent of their electronic types and chiralities but was proportional to their length.It is suggested that we can assess the number of SWCNTs in dispersions when the length distributions of the dispersions are evaluated.

Figure 1 :
Figure 1: Photographs of the ultracentrifuge tubes of (a) CoMoCAT, (b) HiPco, and (c) (6,5) chirality-enriched samples after DGU.Each layer was collected from gradients at the points labeled by black lines and characterized by using optical absorbance.The dashed gray lines indicate unsorted materials.(d) A photoluminescence map for the (6,5) chirality-enriched sample in (c).The red stripe of high intensity is due to Rayleigh scattered excitation light.

)Figure 3 :
Figure 3: The optical absorption spectra of (a) CoMoCAT and (b) HiPco normalized by the determined molar absorbance coefficients.

Figure 4 :
Figure 4: Optical absorption spectra of (a) HiPco and (b) CoMoCAT with the sum spectrum of the M-and S-SWCNTs.