Photoluminescence Dynamics of Aryl sp3 Defect States in Single

Aug 16, 2016 - (2, 13) It is important to broaden the defect types and paired SWCNT ... A typical example of a PL spectrum of Cl2-Dz-doped (5,4) SWCNT...
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Photoluminescence Dynamics of Aryl sp3 Defect States in Single-Walled Carbon Nanotubes Nicolai F. Hartmann,† Kirill A. Velizhanin,‡ Erik H. Haroz,† Mijin Kim,§ Xuedan Ma,† YuHuang Wang,§ Han Htoon,† and Stephen K. Doorn*,† †

Center for Integrated Nanotechnologies, Materials Physics and Applications Division and ‡Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States § Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, United States S Supporting Information *

ABSTRACT: Photoluminescent defect states introduced by sp3 functionalization of semiconducting carbon nanotubes are rapidly emerging as important routes for boosting emission quantum yields and introducing new functionality. Knowledge of the relaxation dynamics of these states is required for understanding how functionalizing agents (molecular dopants) may be designed to access specific behaviors. We measure photoluminescence (PL) decay dynamics of sp3 defect states introduced by aryl functionalization of the carbon nanotube surface. Results are given for five different nanotube chiralities, each doped with a range of aryl functionality. We find that the PL decays of these sp3 defect states are biexponential, with both components relaxing on time scales of ∼100 ps. Exciton trapping at defects is found to increases PL lifetimes by a factor of 5−10, in comparison to those for the free exciton. A significant chirality dependence is observed in the decay times, ranging from 77 ps for (7,5) nanotubes to >600 ps for (5,4) structures. The strong correlation of time constants with emission energy indicates relaxation occurs via multiphonon decay processes, with close agreement to theoretical expectations. Variation of the aryl dopant further modulates decay times by 10−15%. The aryl defects also affect PL lifetimes of the free E11 exciton. Shortening of the E11 bright state lifetime as defect density increases provides further confirmation that defects act as exciton traps. A similar shortening of the E11 dark exciton lifetime is found as defect density increases, providing strong experimental evidence that dark excitons are also trapped at such defect sites. KEYWORDS: carbon nanotubes, doping, exciton localization, photoluminescence, time-correlated single-photon counting, diazonium salts

T

photoluminescence (PL) quantum yields and for introduction of new functionality are reinvigorating SWCNTs as novel nearIR photon sources for photonics applications. The defect-state emission is providing a route to high-contrast imaging1 and new concepts in sensing,12 in which response can be enhanced by the localization of sensing functionality directly at the defect sites, which in turn optimizes interaction with optically generated excitons. New functionality is also emerging, including recent demonstrations of room-temperature singlephoton emission approaching telecom wavelengths,13 photon upconversion,14 and altered exciton−exciton annihilation

he introduction of defect states in low-dimensional semiconducting nanomaterials is emerging as a powerful route to generate new photonic functionality.1−10 In particular, new optical behaviors originating from controlled introduction of sp3 defect sites in single-walled carbon nanotubes (SWCNTs) are motivating an exciting new era of nanotube photophysics. Given that the sp3 defects introduce new isolated electronic states, covalent functionalization acts in a sense as a molecular dopant. Oxygen (ether and epoxide groups)1,2,11 and substituted aryl species3 introduced into the SWCNT structure at low levels create new photoluminescentemitting states (E11*) that are red-shifted by 100−300 meV (depending on specific covalent dopant and SWCNT chirality) from the typical lowest excitonic emission state (E11). The potential that these defects holds for dramatic gains in © 2016 American Chemical Society

Received: May 5, 2016 Accepted: August 16, 2016 Published: August 16, 2016 8355

DOI: 10.1021/acsnano.6b02986 ACS Nano 2016, 10, 8355−8365

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suggested by Miyauchi et al.2 We find a significant lifetime dependence on both nanotube structure and aryl functionality of the dopant. Lifetimes can vary from 77 ps for (7,5) SWCNTs and increase to >600 ps for small-diameter (5,4) structures. The E11* energy dependence of the lifetimes indicates a multiphonon decay mechanism. Changes in dopant functionality can further alter lifetimes by ∼10−15% as a consequence of modulating E11* energies and possibly by altering low-efficiency detrapping processes associated with variation in trapping potential depths. E11 lifetimes are also obtained for all samples studied and are found to change significantly with dopant density. Such a result provides a direct demonstration of diffusive quenching as the dominant nonradiative decay mechanism for E11 excitons and further confirms diffusive transport to trap sites as the primary population mechanism of the defect states. Dark E11 excitons are also found to be transported diffusively to trap sites, providing evidence for a first step in conversion of dark E11 excitons into the photoluminescent defect state.3

processes that may create opportunity for stimulated emission and lasing.11,15 Through the range of aryl species already demonstrated as effective dopants,3 significant synthetic control over defect-state emission properties can be obtained, thus placing this new class of functionalized SWCNTs as model systems for understanding and developing similar defect behavior in other low-dimensional materials, including 2D systems such as transition-metal dichalcogenides4−7 and boron nitride.8 This potential for new SWCNT functionality has motivated a number of experimental11,13,15,16 and theoretical efforts3,11,17−19 toward understanding the origins of the defect-state optical behaviors. These new behaviors ultimately originate from the defects acting as trap sites for localization of excitons. The traps are populated by diffusive transport of excitons to the sites, where they take on the electronic structure defined by the specific defect, thus giving rise to new PL emission properties.11,16 Localization is directly responsible for the observed single photon emission at room-T and altered nonlinear behavior. Since localization is expected to reduce diffusive quenching of excitons, as the principle mechanism for nonradiative decay in these systems,20−24 PL lifetimes are expected to increase significantly. In fact, lifetimes have been reported to increase from ∼10s of picoseconds in undoped tubes to decay times on the order of 100−200 ps.2,13 Despite the significant potential for synthetically altering the photophysics of SWCNT defect states, PL lifetimes reported to date have only been for oxygen-doped (6,5) SWCNTs.2,13 It is important to broaden the defect types and paired SWCNT chiralities for which PL lifetimes are measured to fully capture the range of possible behaviors. Excited-state lifetimes are expected to have significant energy dependence,25 and a range of transition energies may be obtained by accessing different nanotube chiralities.26 Furthermore, with trap depths being strongly dependent on dopant functionality,3 dopants have the potential to further influence contributions to decay mechanisms such as detrapping processes, which can affect PL emission stability and photon upconversion. With significant interest in designing new dopants as routes to improving quantum yields, emission stability, and pushing PL to longer wavelengths, it is necessary to understand the potential impacts dopant design may have on relaxation mechanisms and dynamics. Since PL response also is ultimately determined by which specific nanotube structure is paired with a given dopant,3 it is important to also understand how excited state defect dynamics change with SWCNT structure. A comprehensive knowledge of the dopant and SWCNT (n,m) dependence of relaxation rates can therefore provide critical information for strategies in dopant design and for pairing of specific dopants with a particular chirality for optimizing desired behaviors. Toward this goal, we present here solution-phase PL lifetime data (thus free of intertube and solid-state matrix or substrate interactions) obtained at room temperature for five different SWCNT chiralites (with diameters varying from 0.62 to 0.83 nm), each functionalized with six different aryldiazonium dopants. PL decays of the E11* defect emission show two different decay components, with both decaying on time scales of ∼100 ps. The two-component decays are reminiscent of similar behavior (albeit over different time scales) for E11 emission arising from splitting of exciton states into bright and dark components. The results thus provide additional evidence for bright/dark splitting of defect states, as initially

RESULTS AND DISCUSSION Studying the effect of SWCNT chirality and dopant functionality on the PL lifetimes of SWCNTs requires nanotube samples with a high degree of chirality enrichment in order to achieve isolated emission features. These enable an accurate lifetime measurement without contribution from E11 emission of other chiralities, specifically in the region of the defect-state E11* emission. Isolating the individual chiralities was achieved either by the recently published two-step aqueous two-phase (ATP) separation route27,28 for (6,4), (7,3), (6,5), and (7,5) or an iterative ATP separation route29,30 in the case of (5,4). (PL excitation maps of all separated SWCNT samples are shown in Figure S1.) At the end of each separation step the separation media were exchanged to a 1% sodium dodecyl sulfate (SDS) environment, which as a surfactant leaves enough SWCNT surface exposed to enable access by the reactive diazonium dopant species. The doping process itself follows ref 16 and was performed for this study with benzenediazonium (H-Dz), 4-methoxybenzendiazonium (MeO-Dz), 4-carboxybenzendiazonium (COOH-Dz), 4-bromobenzenediazonium (Br-Dz), 3,5-dichlorobenzenediazonium (Cl2-Dz), and 4-nitrobenzenediazonium (NO2-Dz). During the doping reaction the appearance of the additional E11* PL feature in the spectrum can be observed; thus, the progress can be monitored and the reaction halted at a desired doping level via exchange of the surfactant environment into 1% sodium deoxycholate (DOC).16 After this step, the samples are in a stable environment preventing any further reaction. Samples of all five chiralities, each functionalized with each of six dopant species, and an additional series of Cl2-Dz-doped (6,5) SWCNTs with increasing doping concentration were prepared. A typical example of a PL spectrum of Cl2-Dz-doped (5,4) SWCNTs is shown in Figure 1a, which features E11 emission at 832 nm and the E11* defect-state emission at 1014 nm. Representative of lower bandgap chiralities, another example PL spectrum is shown in Figure 1b for MeO-Dz-doped (7,5) SWCNTs, with E11 emission at 1035 nm and the E11* emission peaking at 1190 nm. ΔE Dependence on Chirality and Nature of Dopant. On comparing the PL spectra shown in Figure 1 for the (5,4) and (7,5) chiralities, it is apparent that the difference in emission energy (ΔE) between E11 and E11* changes for the two chiralities, thus demonstrating a ΔE dependence on 8356

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SWCNT chiral indices (n,m). Consistent with previous findings, ΔE is found to increase as the SWCNT diameter decreases or as E11 increases (see Figure 2a).3 In Figure 2a, we also group together the observed ΔE values for the range of dopants used in our covalent functionalization of all chiralities. The various dopants are seen to also modulate ΔE values. This effect is seen more clearly in Figure 2b−f, where, for each of our chiralities, ΔE is plotted as a function of the Hammett substituent constant σ (a measure of the electron-withdrawing nature of the different functional groups attached to the benzene ring in the diazonium dopants).31 Consistent with previous results,3 ΔE increases with σ across all chiralities. We note that in the case of the (7,3) structure (Figure 2d) the trend in ΔE is not as consistent, due to convolution of the E11 emission peak for this chirality with the dopant emission from (6,4) species in this more mixed-chirality sample. These results demonstrate an ability to vary the defect-state emission properties via changes in SWCNT (n,m) and nature of the attached dopant and form an extensive basis for evaluating potential structural and electronic effects on defect-state PL lifetimes. Photoluminescence Lifetime Evaluation. For all prepared samples we measured the PL decays of the E11 and E11* emission through time-correlated single photon counting (TCSPC) at room temperature in solution. In the case of (5,4) for E11 and E11*, and of (6,4), (7,3) and (6,5) for E11, a silicon-based avalanche photodiode (APD) with the appro-

Figure 1. Representative PL spectra for (a) Cl2-Dz-doped (5,4) and (b) MeO-Dz-doped (7,5) samples featuring the E11 emission peak (green trace) and the E11* luminescence peak caused by aryl diazonium doping (red trace). Both spectra showcase highest (a) and lowest (b) extremes in terms of E11−E11* energy separation (ΔE) within the investigated sample series.

Figure 2. Energy difference ΔE between the E11 peak and the E11* peak, plotted as a function of E11 emission energy for (5,4) (black squares), (6,4) (red circles), (7,3) (green triangles), (6,5) (blue diamonds), and (7,5) (orange hexagons) SWCNTs in (a). All data points for all dopant functionalities are plotted, showing a linear dependence. (b−f) Energy difference for each individual chirality plotted against the Hammett substituent constant σ representing the different dopants (MeO-Dz: σ = −0.27; H-Dz and COOH-Dz: σ = 0.0, Br-Dz: σ = 0.23; Cl2-Dz σ = 0.74; NO2-Dz σ = 0.78). Uncertainty in the plotted energy values is ±1 meV. 8357

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Figure 3. (a) PL decays of the (5,4) Cl2-Dz sample (Figure 1a) after pulsed excitation at the second excitonic resonance (E22 = 490 nm), filtered for the E11 transition (green solid line) and the E11* transition (red solid line). The black solid and blue solid curves are fits for the E11 and E11* decay, respectively, using a biexponential model including a reconvolution method taking the IRF (gray solid line) into account. Lower middle panel: weighted residual from fitting the E11 decay. Bottom panel: weighted residual from fitting the E11* decay. The same data are plotted in (b) for (7,5) MeO-Dz SWCNTs (spectrum in Figure 1b) after pulsed excitation at 640 nm, close to E22. Again with the E11 decay (green solid line), E11* decay (red solid line), and their fits (E11: black solid line, E11*:blue solid line), together with the IRF (gray solid line). The differences in IRF correspond to use of a Si APD detector in (a) and the superconducting nanowire detector in (b) (see the Methods).

priate optical filters (see Methods) was used as the detector. Since the PL emission for all the other chiralities and emission features occurs at wavelengths outside the typical detection window of silicon-based detectors, a superconducting nanowire detector was used in those cases. Representative PL decays for the same (5,4) Cl2-Dz and (7,5) MeO-Dz samples, for which spectra are shown in Figure 1, are depicted in parts a and b, respectively, of Figure 3. The solid green curve represents the rapid E11 decay, together with the significantly longer E11* decay represented by the solid red curve, measured after pulsed excitation at or close to the second excitonic level E22 (490 nm/ 640 nm). All transients were fitted with a biexponential decay model also considering the instrument response function (IRF, gray solid line) in a reconvolution approach. The resulting fits are shown superimposed on the experimental decay curves for E11 (black dashed curve) and E11* (blue dotted curve) together with the corresponding residuals (Figure 3a,b, middle and lower panel of each subfigure) as a measure of the fit quality. In the case of the Cl2-Dz-doped (5,4) SWCNTs, the time constants of the short (s) and long (l) lifetime components of the E11 emission are τs = 29 ± 1 ps and τl = 217 ± 11 ps. For the E11* emission, they are τ*s = 215 ± 14 ps and τ*l = 608 ± 5 ps. Additionally, the MeO-Dz-doped (7,5) exhibits an E11 lifetime of τs < 5 ps (limited by the instrument resolution) and τl = 57 ± 3 ps, together with τs* = 24 ± 3 ps and τl* = 82 ± 3 ps for the E11* emission. A summary of all fit results of lifetimes for the different chiralities and dopants can be found in the Supporting Information (see Tables T1 and T2). Comparing only these two chiralities already indicates a clear impact of the SWCNT chirality on the dynamics of the optical processes in the pristine parts of the nanotubes and also of the locally confined defect sites. Five-State Model for Covalently Doped SWCNTs. We discuss the experimental observations in terms of the simplified five-state model shown in Figure 4. The electronic ground state, G(5), is the energetically lowest state, where the numeral indexes the continuous numbering of the relevant electronic states, starting at the highest energy. If the concentration of dopants is not too high, i.e., the characteristic distance between dopants is large compared to the typical exciton size (electron−

Figure 4. Five-state model applied for aryl sp3 defect-tailored SWCNTs including the E11 exciton manifold (bright B(1) and dark D(2) states) and the defect site E11* manifold (bright B*(4) and dark D*(3) states). Some representative exciton pathways are indicated by black arrows with their corresponding rate constant kmn, and two emission pathways marked with a green arrow for E11 and a red arrow for E11* down to the ground state G(5).

hole distance), the manifold of electronically excited (excitonic) states of a doped SWCNT can be considered as a simple superposition of excitonic states of the undoped SWCNT and the localized (trapped) excitonic states residing on the covalently introduced defect sites. This assumption is validated by the observed near-independence of the UV/vis absorption spectrum of the doped SWCNTs on the dopant concentration (see Figure S2).32 The lowest E11 exciton states of the undoped SWCNT are the previously well-established bright, B(1), and dark, D(2), states.33−37 Temperature-dependent PL studies2 and quantum chemistry calculations32 for ozone-generated ether-d defect sites suggest the existence of a similar bright/dark splitting of the defect-trapped exciton states, with the dark defect state also being lower in energy than the bright state.2,32,36 For aryl defects, however, theory suggests the reverse ordering, with the 8358

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Figure 5. (a) PL spectra of a sample series of Cl2-Dz-doped (6,5) SWCNTs with increasing dopant concentration. All spectra are normalized with respect to their E11 intensity, and the first trace in the front represents the spectrum for the undoped sample. (b) Corresponding E11 lifetimes with τs (black squares) and τl (red circles) as a function of relative dopant (or Trap) concentration [Tr] as represented by the ratio of integrated E11* and E11 PL intensities ([Tr] increasing with increasing E11*/E11 peak area ratio). (c) Amplitude A(τl) of the long E11 lifetime component vs increasing τs. The red dashed line and the blue dashed dotted line represent linear and quadratic fits, respectively, both with a fixed origin at (0/0).

bright defect state being energetically lowest.32 Such a finding is also in agreement with the finding that aryl defects are generally significantly brighter emitters than those produced by oxygen functionalization.3 Definitive ordering of the aryl bright and dark excitons will require more extensive experimental study. For the sake of our discussion, however, we remain consistent with our theory findings and depict the bright-dark ordering in Figure 4 with the bright state B*(4) being energetically lower than the dark state D*(3). We find below, however, that the actual energy ordering does not impact interpretation of the defect-state relaxation behavior. The five-state model of Figure 4 is the minimal model required to explain the transitions between low energy excitonic states and the ground state in SWCNTs with relatively low defect densities. Transitions between these states following the initial photoexcitation can be described within a five-state kinetic model where the rate constant for the transition from state n to state m is denoted as kmn in Figure 4. For example, k41 is the rate constant for the process of trapping of the free bright exciton B(1) to the bright dopant-localized state B*(4). Accordingly, time-resolved populations of the considered excitonic states can be found by solving the following rate equation dpn (t ) dt

5

=

5

∑ knmpm (t ) − ∑ kmnpn (t ) m≠n

i.e., population transfer from defect-site trap states back to the E11 manifold, is low. While detrapping has been demonstrated to occur via T-dependent PL studies,1,32 and as the underlying basis for photon upconversion,14 we demonstrate below that this is an inefficient process (as also consistent with the relatively low upconversion efficiencies reported in ref 14). As a zeroth-order approximation, detrapping rate constants (k13, k24, etc.) are therefore neglected and set to zero. This assumption allows the full 5-state problem to be reduced instead to consideration as two independent excited state manifolds (E11 and E11*). Population of E11* via diffusive transport of E11 excitons to trap sites can be treated simply as an additional component contributing to E11 diffusive quenching, which is the primary E11 nonradiative decay mechanism,20−24 as discussed below. The observation of a two-component decay in the E11 PL lifetime traces (Figure 3 and Table T1) on time scales of 10s of ps (short component, τs) and 100s of ps (long component, τl), respectively, is consistent with previous PL lifetime studies on undoped SWCNTs.33−35,39 In accord with these studies, the short time component is assigned as occurring from decay of the bright E11 exciton. The long decay component has been assigned as the lifetime of the dark E11 exciton.33−35,39 Our observation of two decay components for E11* parallels the behavior of the E11 manifold and suggests a similar internal structure for E11*. As noted above, quantum chemical models of the aryl defect states also support the expectation of energetically close bright and dark states, but with reverse energy ordering; thus, our designation of the bright B*(4) and dark D*(3) states associated with E11* in Figure 4. We have considered the possibility that one of the two decay components may instead arise from the occurrence of a second emitting state. As can be seen in Figure 1, the E11* emission feature is not entirely symmetric and usually exhibits a broader shoulder toward longer wavelengths; possible evidence of such a state. We rule this out as a possible contributor, however, by making lifetime measurements while selecting (via a bandpass filter) specific spectral areas of the E11* emission feature. The temporal response at the shoulder did not result in significantly

m≠n

(1)

The initial populations, p0n = pn (t = 0), encode the effect of the photoexcitation. Specifically, we consider initial population of the system as occurring through photoexcitation of the second (E22) transition, which decays rapidly (∼40 fs) to populate only the E11 manifold,38 i.e., p01, p02 ≠ 0. The linearity of the rate equation with respect to excitonic population stems from the assumption of low fluence (see the Methods) where excitons do not interact with each other, and therefore, no second-order processes (e.g., Auger recombination) occur. In general, eq 1 can only be solved numerically. However, for the specific case of doped SWCNTs studied here, the problem can be simplified significantly by considering the following point: It will be demonstrated below that the rate of detrapping, 8359

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ACS Nano different decay times than those found for E11* peak emission (see Figure S3). In the following sections, we begin with a demonstration of how dopant influence on exciton decay provides insight into both E11 relaxation processes and E11* populating mechanisms. Effects of SWCNT chirality and dopant variation on E11* PL lifetimes further provide additional understanding of the photophysics of localized excitons. Influence of Dopant Concentration on E11 Lifetime Components. The primary mechanism for nonradiative relaxation of the bright E11 state in undoped SWCNTs has been shown to be efficient diffusive transport of the exciton to PL quenching sites (Q).20−24 Rate constants for such diffusive contact quenching (i.e., k51 and k52) are time-dependent.20 Hertel et al., however, demonstrate that the diffusive quenching can be described by a single effective decay time for each of the E11 states (B(1) and D(2)).20 The result is a biexponential fit that also models our data well and is consistent with other previous descriptions as well.33,35,40 Thus, in the following discussion, we do not include an explicit time dependence in the E11 decay constants. In doped tubes, trapping of E11 excitons at the covalently introduced defect (or trap) sites (Tr) has been demonstrated to also be a diffusive process.16 Such trapping thus introduces an alternative diffusive pathway for rapid loss of E11 population from the initial bright state B(1). Given this additional relaxation channel, the rapid initial decay of the B(1) population, τs, is expected to be sensitive to the concentration of defect trap sites along the SWCNT axis. We tested this expectation by measuring the E11 lifetimes of Cl2-Dz-doped (6,5) SWCNTs within a wide range of dopant concentrations. Figure 5a shows the PL spectra of the prepared samples, normalized to their E11 peak intensity. From these spectra, it is clear that a ratio of E11*/E11 peak areas can serve as a semiquantitative measure of the trap-site concentration [Tr]. For this we integrated the spectra numerically from 900 to 1070 nm (E11) and from 1070 to 1400 nm (E11*). We use the ratio of these integrated intensities as a relative measure of [Tr], which serves as the x-axis when plotting the lifetime results of the two E11 components as shown in Figure 5b. As expected, with increasing dopant concentration the short component τs (black squares, Figure 5b) becomes significantly shorter as the mean free path of the exciton is reduced upon introduction of additional defect trap sites. Such behavior may be considered also in relation to the effective length of nanotube experienced by an exciton, with shorter lengths corresponding to faster quenching rates, as demonstrated by Hertel et al.20 and Miyauchi et al.24 Introduction of dopant sites along the SWCNTs effectively creates shorter SWCNT subunits. The results of Figure 5b thus demonstrate that the time constant, τs, is strongly dependent on the concentration of covalently introduced trap sites. In the limit of vanishing dopant concentration, τs ≈ 26 ps. That at the highest dopant concentrations the time constant becomes smaller by almost a factor of 3 signifies that at such concentrations the shorter time constant is determined almost exclusively by defect-site trapping and highlights the potential that covalent doping has for increasing PL quantum yields. These results further support exciton diffusion to covalently introduced defect trap sites as the primary population mechanism for the E11* emitting states. Similar to the behavior of the bright exciton decay, we find that the lifetime of the longer lived, dark E11 exciton component τl, plotted in red circles in Figure 5b, also decreases as dopant concentration increases. While the dark exciton

diffusion constant is expected to be significantly lower than for the bright state (estimated to be a factor of ∼3 smaller40,41), a dependence of lifetime on dopant density would still appear for such a diffusive mechanism. The τl behavior is a strong indication that the dark E11 exciton also undergoes diffusive trapping at defect sites. A key question regarding the increased quantum yield apparent in E11* emission (compared to that for E11) is what contribution arises from E11 dark state conversion to the E11* emitting state. A prerequisite for such conversion is exactly the trapping of the dark exciton that the data of Figure 5b indicates. While these results alone are not sufficient to claim subsequent conversion to the emitting state, they show that the primary dark exciton trapping event is likely. These results also suggest that the difference in decay times for the E11 bright and dark excitons is directly related to the difference in their diffusion rates. Based on determination of the dark exciton mass being ∼15 times greater than that for the bright exciton, it has been expected that the dark exciton diffusion constant will be three to four times smaller than for the bright state.40,41 Our results are a direct experimental confirmation of this expectation. We find the τs and τl behaviors to be independent of dopant. A similar dependence of τs and τl on dopant concentration is found for the NO2-aryl diazonium species as well (see Figure S4). We also note that the amplitudes of the E11 exciton decay components show a dependence on dopant density and can provide information on the relative populations initially formed in the bright and dark E11 states. The amplitude corresponding to the longer time component can be written as (see the SI) A(τl) ≈ k12p20 τs + k12[k12p10 + k 2p20 ]τs2

(2)

where p01 and p02 are the initial populations of the B(1) and D(2) states, respectively. All of the decay channels for the D(2) population, other than the D(2)-to-B(1) transition, are encoded by k2 = k32 + k42 + k52. The weak dependence of the rate constant k2 on the dopant concentration (see Figure 5b and also Figure S4) is neglected here. Then, the only dopant concentration-dependent quantity in the rhs of eq 2 is τs. Comparison of this expression with the experimentally observed dependence, Figure 5c, allows one to place constraints on values of the initial populations of B(1) and D(2). Qualitatively, one sees that if p02 is very small, then A(τl) would depend quadratically on τs. This is, however, not the case since a linear fit (rather than the quadratic) results in a much better agreement with the experimental data in Figure 5c. This implies that the first rhs term in eq 2 dominates over the second rhs term, which in turn means that p02 cannot be very small. More quantitatively, it is possible to show (see SI) that p02 must be significantly larger than ∼0.2 to satisfy the observed linearity in Figure 5c. This is in qualitative agreement with earlier results of Crochet et al.,40 who show ∼90% of the initially photoexcited population likely resides in the dark state. Finally, while the defect concentration [Tr] has a clear impact on E11 relaxation dynamics, the [Tr] dependence of E11* dynamics is more complex. At relatively low [Tr] (i.e., intensity ratios