Letter pubs.acs.org/NanoLett
Evidence for Long-lived, Optically Generated Quenchers of Excitons in Single-Walled Carbon Nanotubes Anni J. Siitonen,†,‡,§ Sergei M. Bachilo,† Dmitri A. Tsyboulski,† and R. Bruce Weisman*,† †
Department of Chemistry and Richard E. Smalley Institute for Nanoscale Science and Technology, Rice University, 6100 Main Street, Houston, Texas 77005, United States ‡ Nanoscience Center, Department of Chemistry, University of Jyväskylä, P.O. Box 35, FIN-40014 Finland S Supporting Information *
ABSTRACT: The nonlinear dependence of near-infrared photoluminescence (PL) emission on excitation intensity has been measured for individual nanotubes representing six different (n,m) species. Significant deviations from linearity are observed for intensities as low as ∼100 W/cm2, and an approximate inverse correlation is found between nonlinearity and PL action cross section (brightness). A model in which all PL nonlinearity arises from exciton−exciton annihilation is insufficient to account for the experimental data using realistic parameters. It is proposed that additional nonlinear quenching arises from photoinduced quenching states or species with longer lifetimes than emissive excitons. Evidence is also found for metastable photogenerated PL quenchers with lifetimes up to 20 s. KEYWORDS: SWCNT photophysics, exciton quenching, photoluminescence nonlinearity, metastable quenchers, single nanotube photobleaching, emission instabilities
P
Methods. Samples containing dispersed SWCNTs several micrometers in length were prepared by mild sonication of raw HiPco material in a 1% aqueous solution of sodium deoxycholate (SDC).22 Nanotubes were immobilized by mixing the dispersion with 5% low-melting agarose gel.25 The gel pH was adjusted to ∼8 by adding a small amount of NaOH solution. A drop of melted gel containing nanotubes was then spread between a microscope slide and a coverslip and allowed to solidify. The edges between the coverslip and the slide were sealed with vacuum grease to prevent liquid evaporation. Near-IR (NIR) fluorescence imaging and spectroscopy were performed with a Nikon TE-2000U microscope equipped with a Nikon PlanApo VC 60×/1.4 NA oil-immersion objective and auxiliary 1.5× magnification. One output port of the microscope was equipped with a InGaAs NIR imager (OMA-V 2D, Roper Scientific), and another port was coupled via optical fiber to the entrance slit of a spectrograph (J-Y C140) with a 512element InGaAs detector array (OMA-V, Roper Scientific)4 to record emission spectra of spatially selected regions. We excited samples with linearly polarized, circularized 730 or 785 nm diode laser beams that were focused to a spot diameter of ∼8 μm. Spatial profiles and powers of the excitation beams were measured at the sample position for each experimental session. A set of neutral density filters was used to vary excitation intensities between ∼0.02 and 100 kW/cm2. We used a λ/2
hotoluminescence (PL) of semiconducting single-walled carbon nanotubes (SWCNTs) is an important structuredependent property that has numerous applications ranging from bulk compositional analysis, through single-molecule reaction detection, to imaging in biological systems.1−9 It has been demonstrated that SWCNT PL arises from a bound excitonic state with strong electron−hole interaction.10−12 Intriguing photophysical phenomena in SWCNTs include very efficient PL quenching by nanotube imperfections and strongly nonlinear variations of PL intensity with excitation intensity. Recent experiments that measured stepwise PL quenching of individual nanotubes revealed high diffusional mobility of the excitons along the nanotube axis,13−15 thereby accounting for the sensitivity of PL to quenching by sparse defect sites. Exciton mobility should also lead to Auger-type exciton−exciton annihilation (EEA), which has been considered the source of PL nonlinearity.16−18 However, definitive photophysical studies on bulk SWCNT samples are hampered by heterogeneity in (n,m) structure, length, aggregation state, defect density, and microenvironment, all of which may influence photophysical behavior.10,19,20 Experiments on selected individual nanotubes may avoid many heterogeneous complications and provide additional insights into SWCNT photophysics.21−24 We report here experimental measurements of PL nonlinearities in individual semiconducting SWCNTs of a number of (n,m) types. By analyzing the results within the framework of an exciton diffusion model, we deduce that a major source of PL nonlinearity is relatively long-lived transient quenchers that are formed at moderate excitation intensities. © 2011 American Chemical Society
Received: August 15, 2011 Revised: November 23, 2011 Published: December 5, 2011 33
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retardation plate to align the excitation beam polarization plane for maximum emission from each studied nanotube. Nanotubes of (10,2), (9,4), (8,6), (8,7), (10,5), and (9,7) types were selected for this study because their E22 resonances nearly matched the available excitation wavelengths. The following criteria were used to select nanotubes: length greater than 2 μm to minimize influence of end-related quenching effects; absence of defects seen as nonuniformities in the SWNCT PL image; and an emission peak within 3 nm of the standard E11 emission peak found in bulk samples. A central method of our study was measuring long sequences of PL images from single nanotubes to determine average emission levels and to uncover any intensity abnormalities, such as photobleaching or photoinduced PL instabilities. In these measurements, SWCNT images were acquired continuously with a 50 ms integration interval for ∼10 s at a fixed excitation intensity. Emission was captured from a 1 μm2 region (3 × 3 pixels) centered at the position of maximum intensity. Then the SWCNT was displaced from the excitation beam, and the measurement sequence was repeated to record the emission background under nearly identical experimental conditions. The average background was subtracted from the sample sequence values. These background corrections represented less than 10% of SWCNT PL signals. Results and Discussion. An example of the measured PL time profile for a (10,5) nanotube is shown in Figure 1. Here,
Figure 2. Linear and log−log plots of the average PL intensity in each bar of Figure 1 versus excitation intensity. The sample was a single (10,5) SWCNT. Closed circles indicate measurements taken at increasing excitation intensity, and open circles show values for decreasing intensity. Good reversibility is apparent here. The smooth red curves show a fit to the data using eq 1 in the text, and the dashed vertical lines mark the excitation intensity for 50% emission nonlinearity.
Figure 1. PL intensity measurements on an individual (10,5) SWCNT. Each bar shows repeated 50 ms intensity measurements at a single excitation level that is adjusted from bar to bar. Vertical lines are artifacts corresponding to excitation filter changes. For this (typical) nanotube, the PL intensity is stable during the ∼10 s measurement bars.
(n,m) species. In 53% of measured SWCNTs, PL values measured with decreasing excitation intensity after reaching the highest excitation levels (open symbols) accurately matched those measured with increasing intensity (filled symbols). This reversibility indicates the absence of permanent photoinduced changes in emissive behavior for those SWCNTs. We observed that emission spectral shapes did not change over the range of excitation levels explored here. For each (n,m) structure, we recorded PL intensity dependencies of 8−12 individual nanotubes that showed reversible behavior. I50 denotes the excitation intensity at which a nanotube’s PL signal is one-half of the value predicted by the initial linear slope. To determine the I50 value for each measurement, experimental data were fit with the threeparameter function:
each time segment shows the PL signal for a fixed excitation intensity, and vertical drop lines mark the excitation steps as attenuation filters were repositioned. After the maximum excitation intensity had been reached, nanotube PL emission was remeasured at four lower excitation levels. The average background-corrected nanotube PL signals from Figure 1 are plotted as a function of excitation intensity in Figure 2. To assist comparisons among different nanotube species, we have scaled the experimental excitation intensity down by a factor of σ(λexc)/σ(λ22), where σ(λexc) and σ(λ22) are absorption cross sections at the experimental excitation wavelength and the E22 resonance peak, respectively. These ratios were deduced from photoluminescence excitation maps of bulk SWCNT suspensions.2,22 We find that SWCNT PL increases linearly with excitation at the low end of our intensity scale. When extrapolated to the maximum excitation intensities used here, that linear slope predicts PL values that are greater than observed by factors of approximately 2−7, depending on the
f (x ) =
ax 1 + b x + cx
(1)
which was selected because it represents experimental results and simulations well (see solid lines in Figure 2). It is of interest to correlate I50 values (for which the denominator equals 2) 34
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time interval Δt as ⟨Δx2⟩ = 2DΔt. A general kinetics equation describing the linear density of excitons, N, at a given photon irradiance Iexc is
with excited state lifetimes among the (n,m) species. Unfortunately, reliable lifetimes for this set of specific SWCNTs are not yet available. In Figure 3 we instead show the
dN = σ(λ 22)Iexc − k1N − k 2N2 (2) dt where k1 is the first-order rate coefficient for intrinsic exciton decay (dominated by nonradiative channels) and k2 represents a rate coefficient for the EEA process. Note that k2 is not a conventional second-order rate coefficient because of recurrent motions in one-dimensional diffusion.33,34 Its value depends not only on the density of excitons in the nanotube but also on their instantaneous spatial distribution. As a result, a useful analytic solution of eq 2 describing EEA over a wide range of excitation intensities is not available. Instead, we use a relatively simple but versatile numerical simulation to model onedimensional diffusion of excitons and find the nonlinear dependence of PL on excitation intensity. In this model, the exciton is considered to have a finite small length, δx. Excitons are created at random positions and times at a rate σ(λ22)·Iexc and are allowed to make random elementary steps along the nanotube axis in every short time interval, δt. For simplicity, the step size is assumed equal to the exciton size, δx. This parameter and δt, the time interval between steps, together determine the diffusion coefficient D = (1/2)δx2/δt. The EEA process was included in our simulation through the condition that when two excitons overlap, one of them disappears. The model can also be extended to account for fixed quenching sites, which terminate an exciton with a specified probability when it reaches a position adjacent to the site. This allows for inclusion of end-quenching effects. For reliable simulations, in the absence of EEA or fixed site quenching, an exciton should decay with probability k1δt ≪ 1 during each simulation interval δt. We typically chose this interval to give a decay probability near 10−3. For convenience, we used the following fixed parameters: step size δt = 5 nm, SWCNT absorption cross section = 10−12 cm2/μm, and nanotube length = 30 μm (to minimize end effects). The simulation was run for a time period of ∼4k1−1 after the start of excitation to achieve steady-state conditions before computing the average exciton population density, which is proportional to the measured SWCNT PL signal. We found simulated curves, N(I), that were qualitatively similar to the experimental findings. Examples are shown in Figure 4. We used such simulations to fit hysteresis-free experimental data such, as shown in Figure 2. First, a simulation was computed with parameters k1 and D selected such that 2(D/ k1)1/2 = Λ, where Λ is the SWCNT exciton diffusion range deduced from an independent method. Since the differences in diffusion ranges are relatively minor among the SWCNT species studied here, we used an average Λ value of 280 nm. The initial simulation parameters were: δx = 5 nm, δt = 5 fs, k1−1 = 8 ps, and D = 2500 nm2/ps (25 cm2/s). Then the simulation was represented by the three-parameter function (eq 1, see Figure 4) to obtain an analytical form of the simulation results. After this, we fit the parametrized simulation function to the experimental data by scaling the x- and y-coordinates without changing the Λ value. The resulting x-axis scaling factor was multiplied by k1 and D to give the deduced values kexp and Dexp, respectively. This fitting procedure appears robust for experimental traces with large nonlinearities but becomes imprecise when the nonlinearity is relatively small. We note that if the y-axis scaling coefficient can be quantitatively
Figure 3. I50 values (excitation intensities at which one-half of PL emission is nonlinearly quenched) for six different nanotube structures as a function of their relative PL intensities. Samples were suspended in DOC and immobilized in agarose gel, except for one set of (10,2) SWCNTs (red triangle) in a SDBS/agarose environment.
correlation of I50 with PL action cross sections (products of PL quantum yield, Φfl, and absorption cross section per carbon atom, σ(λ22)), measured under the present experimental conditions.15,22 It is seen that “dimmer” nanotubes have generally higher I50 nonlinearity parameters. We performed similar measurements on a set of seven gel-immobilized (10,2) nanotubes suspended in 1% sodium dodecylbenzenesulfonate (SDBS) rather than SDC. As compared to the same species in aqueous SDBS suspension, the substitution of SDBS for SDC in gel samples significantly reduced the PL intensities of the gel samples and broadened the emission peaks, suggesting shorter exciton lifetimes.24,26 The PL nonlinearity parameter was significantly higher for these gel/SDBS nanotubes, in agreement with the general trend seen in Figure 3. Nonlinear effects in SWCNT emission have previously been reported for relatively high excitation intensities and attributed to EEA.16−18 However, our results and a recent ultrafast spectroscopy study27 indicate that SWCNT PL nonlinearity occurs in a lower intensity regime not easily explained by EEA. For example, we observed that in (10,2) SWCNTs, 50% of excitons are quenched by a nonlinear process at an excitation intensity of ∼0.3 kW/cm2. Although there are clearly some uncertainties in SWCNT absorption cross sections and exciton lifetimes, we can reasonably estimate these as ∼10−12 cm2/μm for the absorption cross section σ(λ22) with linearly polarized light22,23,27−30 and ∼100 ps or less for the exciton lifetime at low intensities.10,20,23,24,31,32 From these values one predicts that fewer than 0.2 excitons are created, on average, during 100 ps in a 1 μm nanotube excited at 0.3 kW/cm2. Because their mobility ranges are less than ∼300 nm,13−15 the excitons formed at this intensity will only rarely encounter another exciton during their lifetime and therefore will not undergo significant EEA. Instead, another nonlinear quenching mechanism must be active. Below we describe the model used to more rigorously reach this conclusion. In a defect-free nanotube in a homogeneous environment, exciton motion is expected to be a one-dimensional random walk described by a diffusion coefficient D, which is related to the mean square displacement ⟨Δx2⟩ of the exciton during a 35
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simulations fit experimental traces very well, the deduced exciton lifetimes are on the order of several nanoseconds. These values substantially exceed the major PL lifetime components (generally below 100 ps) reported from timeresolved studies on selected individual nanotubes.23 This discrepancy confirms that EEA alone cannot account for the experimentally observed nonlinearity. Instead, the additional nonlinearity must be attributed to other quenchers that live longer than the excitons. To explore this explanation, we have modified the EEA model to describe a system in which a metastable quenching species, X, is irreversibly formed from the exciton population through a minor first-order channel. Equation 2 will then be extended to
⎧ k ⎫ dN = σ(λ 22)Iexc − k1N − ⎨k 2 + k 2′ X ⎬N2 dt k1X ⎭ ⎩
Figure 4. Points show the nonlinear dependence of PL emission on excitation as found from the numerical simulations described in the text. Here the first-order exciton decay rate coefficient k1−1 was assumed to be 1, 8, and 30 ps in the three traces, while other simulation parameters were held fixed at δx = 5 nm, δt = 5 fs, and D = 2500 nm2/ps. Solid curves are fits to the numerical simulations using eq 1 in the text. Experimental data were analyzed by scaling the threeparameter function based on an 8 ps k1−1 value (red curve).
(3)
Here, kX is the first-order rate coefficient for exciton conversion to metastable species X, k2′ is the second-order rate coefficient describing exciton quenching in each encounter with X, k1X is the first-order rate coefficient representing decay of species X, and the steady-state population of X is equal to the exciton population times kX/k1X. This model, which neglects processes involving two or more X quenchers, fits the experimental data as well as that of eq 2 without requiring unrealistically long exciton lifetimes. Instead, it points to a long-lived quenching species that is generated through a process that is linear in exciton population. Even if species X is formed with a very small quantum yield, it can still accumulate to concentrations sufficient to act as the dominant exciton quencher if it has a −1 . This model can qualitatively account for the long lifetime, k1X inverse correlation of PL nonlinearity and PL brightness, as longer first-order exciton lifetimes give larger PL action cross sections and also increase the probability of quenching by encounters with species X. X may represent one or several dark species, such as triplet excitons (which should have nonzero formation yields and relatively long lifetimes) or separated charge carriers formed by exciton dissociation.35−37 Unfortunately, little is currently known about formation yields of these species in SWCNTs. To explore the lifetimes of metastable exciton quenchers, we modulated the excitation light at frequencies up to 1 kHz and compared PL nonlinearities to those recorded for the same nanotube without excitation modulation. Decreased nonlinearity would be expected when the modulation period becomes shorter than the metastable lifetime, but we found no differences up to our maximum modulation frequency, implying that the quencher lifetimes are below ∼1 ms. Berciaud et al. have suggested that SWCNT PL nonlinearity could be caused by reduced ground-state absorption as population accumulates in long-lived dark states under steady-state excitation.23 However, ground-state bleaching large enough to account for observed nonlinearities has not been reported in prior pump−probe studies of SWCNT samples. Our observation of unshifted emission spectra under nonlinear PL conditions also seems inconsistent with charged excitons.38 Evidence for even longer-lived exciton quenchers can be found in a subset of our PL data. Figure 6 shows emission measured from two segments of an individual (7,6) nanotube over a period of several minutes while the excitation intensity was switched between ∼30 and 300 W/cm2. These values fell within the linear and nonlinear regimes, respectively, so the
calibrated using the SWCNT action cross-section and the experimental detection efficiency, our fitting method can determine Λ in addition to k1 and D. Figure 5 displays (n,m)-dependent results deduced for exciton lifetimes (kexp−1) and diffusion coefficients within the model that attributes all nonlinearity to EEA. Although the
Figure 5. Deduced exciton lifetimes (a) and exciton diffusion coefficients (b) obtained by fitting experimental data with a model in which nonlinearity arises only from EEA. Open squares show average values of the individual single-nanotube measurements marked by small solid circles. Labels next to squares indicate the (n,m) species. The large values of deduced exciton lifetimes suggest that a quenching process other than EEA is present. 36
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Figure 6. PL intensities from segments of an individual (7,6) nanotube measured over 50 ms intervals, with excitation intensities that were switched between ∼30 and 300 W/cm2. The red and blue traces (A and B) were recorded from the regions labeled in the NIR PL image. Trace A (red) is vertically offset by 12 units for clarity. Occasional stepwise changes of SWCNT PL are apparent only at the higher excitation intensity.
brightness (PL action cross section). If EEA is assumed to be the only source of nonlinearity, accurate simulation of the measured data requires exciton lifetimes that are unrealistically long. However, the nonlinear data can be successfully simulated with plausible exciton lifetimes if the dominant quencher is a longer-lived nonemissive species produced through an exciton first-order decay channel. In some nanotubes at modest excitation intensities, and in most at high intensities, our data also reveal PL intensity instabilities that appear to be caused by photogenerated species with even longer lifetimes (up to 20 s). It seems possible that important quenchers may include triplet excitons and free charges that have a wide range of stabilities reflecting inhomogeneities in local nanotube environments. Further experimental studies will be needed to directly detect and characterize metastable quenching species in optically excited SWCNTs.
ratio of average emission intensities was much less than 10 because of PL nonlinearity. At the lower excitation level, essentially no distinct fluctuations in SWCNT PL were observed. However, under 300 W/cm2 excitation there were many distinct reversible steps persisting for approximately 0.1− 20 s. These qualitatively resembled the PL steps reported previously from protonation and deprotonation reactions.13 The increased occurrence of such steps at higher excitation intensities indicates that they involve photoinduced quenchers. Also, the lack of correlation in emission steps from the two segments indicates that the quenching is local. These quenchers might be individual charges formed through EEA, exciton dissociation, or photoassisted protonation and then trapped in specific locations by irregularities in the nanotube coating. Because a covalent reaction would give irreversible PL quenching,39 we rule out such processes. We conclude that metastable localized quenchers can be formed in SWCNTs by moderate optical irradiation. However, these quenchers seem not to account for the “smooth” nonlinearity observed in most nanotubes at intensities below 10 kW/cm2 (see Figure 1), which is instead attributed to species with lifetimes shorter than 1 ms but greater than lifetimes of emissive excitons. We also observed that nearly half of the measured nanotubes did not show stable PL at excitation intensities below 10 kW/ cm2. Instead, 19% displayed abrupt steps in emission during periods of constant excitation intensity, as shown in Figure S1, Supporting Information. In these cases the measurements with decreasing intensity (open circles in Figure S1b, Supporting Information) revealed hysteresis indicating persistent photobleaching. A larger fraction, approximately 28% of the measured nanotubes, showed changes in PL emission at a fixed excitation intensity that appeared to be smooth rather than abrupt (on our 50 ms time scale). This effect is illustrated in Figure S1c, Supporting Information. In these cases, the SWCNT PL signal often returned to its original level during hysteresis checks, as seen in Figure S1d, Supporting Information, for intensities below 2 kW/cm2. At still higher excitation levels up to 100 kW/ cm2, we observed PL emission with strong instabilities, significant photobleaching, and average emission levels that saturate or decline at the highest intensities (see Figure S2, Supporting Information). Such behavior presumably arose from the light-induced formation of stable and metastable quenchers. Conclusions. We have measured the nonlinear dependence of PL emission on excitation intensity for individual nanotubes representing six different (n,m) species. We find that nonlinearity in SWCNT PL seems inversely correlated with
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ASSOCIATED CONTENT S Supporting Information * Supporting Information showing additional data for nonlinear PL in individual SWCNTs. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION Corresponding Author *E-mail:
[email protected]. Present Address § Department of Chemistry, University of Rochester, Rochester, New York, United States.
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ACKNOWLEDGMENTS This research has been supported by the National Science Foundation (grants CHE-09098097 and CHE-1112374) and the Welch Foundation (grant C-0807). A.J.S. is grateful to the Finnish National Graduate School in Nanoscience (NGSNANO) and the Jenny and Antti Wihuri Foundation for fellowship support.
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