pubs.acs.org/JPCL
Dependence of Exciton Mobility on Structure in Single-Walled Carbon Nanotubes Anni J. Siitonen,†,‡ Dmitri A. Tsyboulski,‡ Sergei M. Bachilo,‡ and R. Bruce Weisman*,‡ †
Nanoscience Center, Department of Chemistry, University of Jyv€ askyl€ a, P.O. Box 35, FIN-40014 Finland, and Department of Chemistry and Richard E. Smalley Institute for Nanoscale Science and Technology, Rice University, 6100 Main Street, Houston, Texas 77005
‡
ABSTRACT Optically generated excitons in semiconducting single-walled carbon nanotubes (SWCNTs) display substantial diffusional mobility. This property allows excitons to encounter ∼104 carbon atoms during their lifetime and accounts for their efficient deactivation by sparse quenching sites. We report here experimental determinations of the mobilities of optically generated excitons in 10 different (n,m) species of semiconducting SWCNTs. Exciton diffusional ranges were deduced from measurements of stepwise photoluminescence quenching in selected individual SWCNTs coated with sodium deoxycholate surfactant and immobilized in agarose gel. A refined data analysis method deduced mean exciton ranges from 190 to 370 nm. The results suggest that exciton range increases weakly with nanotube diameter over the 0.7-1.2 nm diameter range and that species with neararmchair roll-up angles have the smallest exciton ranges. No significant correlation was found between the exciton range and measured photoluminescence action cross section, which represents fluorimetric brightness. These findings highlight the importance of complementary photophysical studies to elucidate factors controlling SWCNT exciton mobility. SECTION Nanoparticles and Nanostructures
S
emiconducting single-walled carbon nanotubes (SWCNTs) display distinct optical transitions at wavelengths that depend systematically on nanotube structure.1 These transitions are associated with strongly bound excitons,2,3 whose sizes have been estimated from theory and experiment to be in the range of a few nanometers.4-7 One of the most important properties of the excitons is their mobility.6,8-12 Prior studies have demonstrated that one-dimensional exciton motion in room-temperature SWCNTs is diffusional in nature, with average displacements during the exciton lifetime deduced to be approximately 100-240 nm in nearly pristine samples.13-15 This mobility allows an exciton to visit ∼20 000 carbon atoms, a fact that explains the strong quenching of SWCNT photoluminescence by very low densities of quenching sites. Such quenching sites, which may arise from structural defects or chemical derivatization, reduce the exciton ranges below pristine values because they induce nonradiative decay of excitons that encounter them. Our recent study employing a refined analysis of stepwise photoluminescence quenching caused by single-molecule reactions revealed that SWCNT exciton displacements depend significantly on the surfactant environment coating the nanotube surface.13 An important related question is whether exciton mobility is also influenced by nanotube structure, that is, the diameter and roll-up angle that are uniquely specified by (n,m) indexes. In this Letter, we report results obtained using our refined single-particle stepwise quenching methods
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to compare exciton mobilities in 10 different SWCNT species. We find weak but intriguing correlations of exciton range with diameter and roll-up angle. However, the exciton range appears uncorrelated with the photoluminescence action cross section. The original and refined methods used to study stepwise photoluminescence quenching in individual SWCNTs have been described in detail.13,14 In brief, SWCNTs from the Rice University HiPco reactor (batches 188.4 and 166.12) were ultrasonically dispersed in 1% aqueous solutions of sodium deoxycholate (SDC) surfactant and then immobilized in agarose gels. We performed near-IR fluorescence microscopy and spectroscopy using a custom-built apparatus based on a commercial inverted microscope.16,17 Samples were excited with circularly polarized light from fixed wavelength (532, 659, 730, and 785 nm) cw lasers or from a tunable cw Ti-sapphire laser. To prevent interference from nonlinear effects such as exciton-exciton annihilation, we kept sample excitation intensities below ∼200 W/cm2. Wide-field images of near-IR SWCNT emission were captured by a cryogenically cooled two-dimensional InGaAs array (Princeton Instruments OMA-V 2D). We recorded near-IR image sequences with 50 ms
Received Date: June 2, 2010 Accepted Date: June 25, 2010 Published on Web Date: July 01, 2010
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DOI: 10.1021/jz100749c |J. Phys. Chem. Lett. 2010, 1, 2189–2192
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(d) Lorentzian emission profiles with widths below 150 cm-1 and comparable to those observed previously for unperturbed SWCNTs in aqueous SDBS.17 Figure 1 shows the near-IR PL image of a (8,7) nanotube and the time profile of its emission intensity following exposure to the diazonium salt solution. Each distinct step in the intensity versus time profile marks the reaction of a single diazonium ion with the nanotube sidewall.13,14,18 The intensity steps occur because excitons formed near the reaction site are nonradiatively recombined, or quenched, as they reach the site. The relative magnitudes of the intensity steps therefore reflect the fractions of excitons in the observed nanotube segment that are within diffusional range of the quenching site. In order to reliably determine the PL step magnitudes, we constructed differential image sequences and analyzed them using a custom Matlab program that implements the refined method recently described in detail.13 This refined method systematically identifies step events that have not been influenced by nearby prior reaction events on the nanotube and measures their magnitudes, Δ, through twodimensional Gaussian fitting of features in the differential images. From Δ and I0, the initial PL intensity, we deduce Λapp, the apparent effective length of the quenched region created by the reaction event, using the simple relation Λapp = L(Δ/I0). Here, L is the observed segment length and Λapp represents the product PQΛ, where PQ is the probability of quenching per encounter with the quenching site (commonly assumed to equal 1) and Λ is the true effective exciton range. For each of 10 different semiconducting (n,m) species, we made quenching measurements on 4-10 individual SWCNTs. The studied species spanned a diameter range of 0.75-1.10 nm. Figure 2 shows histograms of the measured Λapp values, and Table 1 lists structural parameters of the studied species along with their average Λapp values and absolute photoluminescence action cross sections (products of the absorption cross section σ22(λexc) per carbon atom at the E22 excitation
frame integration times while samples were exposed to aqueous solutions of 4-bromobenzenediazonium tetrafluoroborate (1-10 mg/mL) intended to quench PL emission by covalently functionalizing the SWCNT sidewalls. Before adding the diazonium reactant, we identified the (n,m) structure of individual SWCNTs by recording their nearIR emission spectra. We also measured PL action cross sections of all studied (n,m) species using the method described previously for SWCNTs coated with SDBS.17 Quenching observations were restricted to nanotubes that met the following criteria, which were intended to select those with minimal imperfections and, presumably, exciton mobilities approaching intrinsic values: (a) nanotube length greater than 2 μm to reduce the influence of end-related effects; (b) few or no defects visible as nonuniformities in the emission image; (c) emission spectral peaks within 3 nm of the peak position measured in bulk PL mapping of the same (n,m) species; and
Figure 1. (A) Near-infrared photoluminescence image of one (8,7) SWCNT and (B) its PL signal during chemical quenching, showing steps reflecting single-molecule reaction events. PL intensities are normalized to the average initial value.
Figure 2. Histograms of measured apparent quenching ranges, Λapp, for 9 (n,m) structures in SDC. Histogram bins are 20 nm wide. Dashed lines mark the mean values.
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Figure 4. Average apparent exciton range, Λapp, as a function of nanotube roll-up angle. Mod 1 and mod 2 species are marked with blue triangles and red circles, respectively. Error bars show one standard deviation of the data sets.
Figure 3. Average apparent exciton range, Λapp, as a function of nanotube diameter. Mod 1 and mod 2 species are marked with blue triangles and red circles, respectively. Error bars show one standard deviation of the data sets. The dashed line is a statistically weighted linear best fit to the data. Table 1. Structures, Apparent Exciton Ranges, and Relative Photoluminescence Action Cross Sections for Studied SWCNT (n,m) Species (n,m)
diameter (nm)
mod
Λapp (nm)
relative σ(λ22) 3 ΦFl in SDC and agarose gel
(6,5)
0.76
1
190 ( 50
0.52 ( 0.16
(8,3)
0.78
2
260 ( 45
0.79 ( 0.24
(7,5)
0.83
2
240 ( 50
0.73 ( 0.22
(10,2) (7,6)
0.88 0.90
2 1
270 ( 40 230 ( 40
1.0 ( 0.30 0.63 ( 0.19
(8,6)
0.97
2
320 ( 30
0.62 ( 0.19
(8,7)
1.03
1
240 ( 60
0.38 ( 0.11
(10,5)
1.05
2
300 ( 60
0.27 ( 0.08
(9,7)
1.10
2
260 ( 30
0.17 ( 0.05
(12,5)
1.20
1
370 ( 70
0.17 ( 0.05
Figure 5. Average apparent exciton range, Λapp, for different (n,m) species as a function of their relative PL brightness (PL action cross section). Blue triangles and red circles mark mod 1 and mod 2 species, respectively. The dashed line is a statistically weighted linear best fit to the data; its slope is not significantly different from 0.
wavelength and fluorescence quantum yield ΦFl). The average Λapp values were found to lie between 190 and 370 nm. To examine possible systematic variations of exciton range with nanotube structure, we plot Λapp as a function of tube diameter in Figure 3 and as a function of roll-up angle in Figure 4. In these plots, we use different symbols to distinguish species belonging to the two subsets of semiconducting SWCNTs, blue triangles for “mod 1”, for which mod(n-m,3)=1 and red circles for “mod 2”, for which mod(n-m,3) = 2. The linear best fit drawn in Figure 3 shows a weak positive correlation between nanotube diameter and exciton range, although experimental uncertainties prevent a precise determination of the slope. Our original study of SWCNT stepwise quenching reported smaller exciton ranges with no diameter dependence. We attribute the difference to refinements in the sample preparation and data analysis methods that reduce the influence of prior quenching sites. Figure 4 suggests that the average exciton range may decrease as the roll-up angle approaches the armchair limit. The systematic variations in Figures 3 and 4 are only slightly larger than the variations
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among replicate measurements on the same (n,m) species. These mild structure dependencies are comparable in size to the exciton range variations found recently for a specific (n,m) species in different surfactant coatings.13 One could expect correlations between the exciton range and exciton lifetime and also between the exciton lifetime and PL action cross section (the product of the σ22 absorption cross section per carbon atom and the quantum yield for E11 emission). It is therefore of interest to examine the variation of exciton range with PL action cross section. This is plotted in Figure 5 for the 10 studied species. The linear best fit shows no significant trend as the cross sections per atom span a factor of 6. This finding is not specific to the SDC surfactant, as we observed a similar result for SWCNTs coated with SDBS. The PL action cross section is known to vary significantly with (n,m) structure.17 A plausible view is that these variations mainly reflect structure-dependent exciton lifetimes, τ, which
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are dominated by nonradiative recombination processes. Then, because the exciton range is Λ = 2(Dτ)1/2,13 where D is the exciton diffusion coefficient, one would expect the exciton range to show a strong positive correlation with the PL action cross section (presuming that D values vary less than lifetimes). However, Figure 5 shows no such correlation. One possibility is that D and τ have opposing variations with structure such that their product remains nearly constant. A more likely explanation is that differences in PL action cross sections are dominated not by τ but instead by σ22 or the efficiency of nonradiative relaxation from the initial (E22) to the emitting (E11) excitonic state. Future measurements of (n,m)-resolved absorption cross sections should help to identify the specific photophysical parameters affecting SWCNT exciton mobility. In summary, we have measured the stepwise quenching of SWCNT photoluminescence caused by single-molecule sidewall reactions and deduced exciton ranges for 10 different (n,m) species. Our study employed a refined data analysis method and careful selection of individual nanotubes to minimize the influence of defects or prior derivatization. The results show a mild increase of exciton range with increasing nanotube diameter and reduced exciton ranges in nanotubes with near-armchair roll-up angles. In addition, no correlation was found between the exciton range and photoluminescence action cross section. Interpretations of these findings should be aided by future measurements of additional photophysical properties in individual single-walled carbon nanotubes.
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AUTHOR INFORMATION
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Corresponding Author: *To whom correspondence should be addressed. E-mail: weisman@ rice.edu.
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ACKNOWLEDGMENT This research has been supported by the
National Science Foundation (Grant CHE-09098097) and the Welch Foundation (Grant C-0807). A.J.S. is grateful to the Finnish National Graduate School in Nanoscience (NGS-NANO) and the Jenny and Antti Wihuri Foundation for fellowship support.
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