Charge Transfer from Photoexcited Semiconducting Single-Walled Carbon Nanotubes to Wide-Bandgap Wrapping Polymer

Abstract

As narrow optical bandgap materials, semiconducting single-walled carbon nanotubes (SWCNTs) are rarely regarded as charge donors in photoinduced charge-transfer (PCT) reactions. However, the unique band structure and unusual exciton dynamics of SWCNTs add more possibilities to the classical PCT mechanism. In this work, we demonstrate PCT from photoexcited semiconducting (6,5) SWCNTs to a wide-bandgap wrapping poly-[(9,9-dioctylfluorenyl-2,7-diyl)-alt-(6,6′)-(2,2′-bipyridine)] (PFO–BPy) via femtosecond transient absorption spectroscopy. By monitoring the spectral dynamics of the SWCNT polaron, we show that charge transfer from photoexcited SWCNTs to PFO–BPy can be driven not only by the energetically favorable E₃₃ transition but also by the energetically unfavorable E₂₂ excitation under high pump fluence. This unusual PCT from narrow-bandgap SWCNTs toward a wide-bandgap polymer originates from the up-converted high-energy excitonic state (E₃₃ or higher) that is promoted by the Auger recombination of excitons and charge carriers in SWCNTs. These insights provide new pathways for charge separation in SWCNT-based photodetectors and photovoltaic cells.

Introduction

The highly selective wrapping of semiconducting single-walled carbon nanotubes (SWCNTs) with conjugated polymers, e.g., polyfluorenes and polythiophenes, has enabled monochiral samples with high purity¹⁻³ to be available for a wide range of optoelectronic applications from field-effect transistors,⁴ light-emitting diodes,⁵ and electrochromic cells⁶ to photovoltaic cells^7,8 and photodiodes.⁹ The interaction of nanotubes with their immediate environment, i.e., the wrapping polymer or matrix, with regard to energy and charge transfer depending on the energy level alignment^10,11 is crucial for their functionality and not yet fully understood. The unique electronic structure and complex photophysics of SWCNTs¹² make this interaction highly interesting from a fundamental and application point of view. For photovoltaic cells based on carbon nanotubes, SWCNTs assume the role of donor in photoinduced charge transfer (PCT) only when a semiconductor with high electron affinity (e.g., fullerene derivatives) acts as an acceptor.¹³⁻¹⁵ When wrapped by typical semiconducting polymers, the narrow-bandgap nanotubes usually behave as acceptors for both charges and excitation.¹⁶⁻²¹

Various spectroscopic methods, including pump–probe transient absorption (TA) and transient fluorescence spectroscopy, have been applied to explore the excited-state interactions between SWCNTs and the conjugated wrapping polymer.^{11,16,22−25} Strong electronic interaction in SWCNT/polymer hybrids has been concluded by studying the modulation effect of the polymer frontier orbital levels on nanotube valence and conduction band energies, as well as newly formed hybridized electronic states between the two components.^22,23,25 The energy transfer observed in SWCNT/polymer composites also points to an electron-exchange mechanism.^11,16 However, only the first optical bandgap in semiconductors is usually taken into account in studies of the classical PCT mechanism. The electronic interplay between the complex band structure of SWCNTs and the wrapping polymer has not been clarified yet.^26,27

(6,5) SWCNTs are chosen for this study due to their availability as nearly monochiral samples in large amounts after selective dispersion with a polyfluorene–bipyridine copolymer (PFO–BPy).² The energy level alignment of (6,5) SWCNTs and PFO–BPy (Figure 1) indicates that the PFO–BPy-wrapped (6,5) SWCNT hybrid system (hereafter referred to as Hybrid) constitutes a Type-I heterojunction. When regarding the narrow-bandgap (6,5) SWCNT as a charge donor, the PCT from excited (6,5) SWCNT toward wide-bandgap acceptor PFO–BPy is energetically unfavorable, at least for the E₁₁ and E₂₂ transitions. However, the established exciton photophysics of SWCNTs suggests that low-energy photon excitation is able to promote populations of high-energy excitonic states via, e.g., Auger recombination of excitons.³⁰⁻³⁶ Under this mechanism, even in the presence of ultrafast intersubband relaxation, high-energy excitonic states still have a considerable decay time as that of the E₁₁ state, which may favor the PCT from excited SWCNTs to a wide-bandgap acceptor.³⁵ Here, we analyze this SWCNT-based Type-I heterojunction by femtosecond TA spectroscopy. A comparison with surfactant-dispersed (6,5) SWCNTs in water (hereafter referred to as SWCNT), which allows for observations of exciton dynamics without energy or charge transfer,³⁷⁻⁴⁰ is conducted throughout this work. The exciton dynamics of the Hybrid in tetrahydrofuran and SWCNT in water are investigated upon the E₁₁, E₂₂, and E₃₃ excitation with variable excitation fluences, and PCT products in the Hybrid are analyzed. We demonstrate that the PCT from photoexcited (6,5) SWCNT to PFO–BPy is driven by the energetically favorable E₃₃ excitation and may be also driven by the energetically unfavorable E₂₂ excitation. The latter process occurs via Auger recombination of excitons and charge carriers at high excitation fluences.

Figure 1.

Schematic energy level alignment of (6,5) SWCNT and PFO–BPy. The density of states of (6,5) SWCNT with characteristic van Hove singularities of the valence (v₁, v₂, v₃) and conduction (c₁, c₂, c₃) band was based on ref (28) and shifted by the reported ionization potential.¹⁶ The HOMO and LUMO energies of PFO–BPy indicated by red horizontal lines were reported by Jang et al.²⁹ The gray arrows are simplified representations for observed excitonic absorption bands E₁₁, E₂₂, and E₃₃. The inset shows the molecular structure of PFO–BPy.

Experimental Section

Surfactant-Based Carbon Nanotube Dispersion and Chirality Enrichment

The preparation of aqueous (6,5) suspension is based on the pH-modulated aqueous two-phase extraction (ATPE) method.⁴¹ Simply, a 20 mg portion of CoMoCAT SG65i SWCNTs powder (SouthWest Nanotechnologies, lot no. SG65i-L58) was suspended in 20 mL of aqueous 1% (m/v) DOC (BioChemica) by tip sonication (Weber Ultrasonics, 35 kHz, 16 W in continuous mode) for 1 h while immersed in an ice bath. The resulting dispersion was centrifuged at 45 560g (Beckman Optima L-80 XP, SW 40 Ti rotor) for 1 h, and the supernatant collected for ATPE. ATPE then was performed at a concentration of 4% (m/m) dextran (Mw 70 000 Da, TCI), 8% (m/m) PEG (Mw 6000 Da, Alfa Aesar) with 0.5% m/v SDS (Sigma-Aldrich), and 0.05% m/v DOC (Sigma-Aldrich). First, 16 μL of HCl (0.5 M) was added to a 16 mL ATPE system (with 0.8 mL of SWCNT suspension) to remove the nanotubes with a diameter larger than the (6,5). Next, a fresh mimic top phase was added along with some new HCl (20 μL) to obtain (6,5) on the top phase. Finally, the (6,5) enriched top phase was added to a fresh mimic bottom phase with 40 μL of sodium hypochlorite (NaClO, Honeywell) and 20 μL of compensated HCl to separate the metallic tubes with similar diameters. After centrifugation, the purified single chirality (6,5) remained in the bottom phase while the metallic tubes (7,4) partitioned to the top phase.

Carbon Nanotube Dispersion by Polymer Wrapping

As described previously,² nearly monochiral polymer-wrapped (6,5) SWCNTs were obtained by shear force mixing (Silverson L2/Air, 10 230 rpm, 72 h) of CoMoCAT raw material (Chasm Advanced Materials, SG65i-L58, 0.38 g L^–1) and poly-[(9,9-dioctylfluorenyl-2,7-diyl)-alt-(6,6′)-(2,2′-bipyridine)] (PFO–BPy, American Dye Source, Mw 40 000 Da, 0.5 g L^–1) in toluene. Aggregates were removed by centrifugation at 60 000g (Beckman Coulter Avanti J26XP centrifuge) for 2 × 45 min with intermediate supernatant extraction and final filtration through a poly(tetrafluoroethylene) (PTFE) syringe filter (5 μm pore size). To remove unbound PFO–BPy, the dispersion was passed through a PTFE membrane filter (Merck Millipore, JVWP, 0.1 μm pore size) to collect the SWCNTs and separate the unbound polymer. The SWCNT-coated membrane was further washed by immersion in toluene at 80 °C for 10 min. Finally, the washed, PFO–BPy-wrapped (6,5) SWCNTs (Hybrid) were redispersed from the membrane by bath sonication in a small volume of tetrahydrofuran (THF) for 30 min.

Stationary and Transient Absorption Spectral Measurements

Stationary UV–visible–NIR absorption spectra were measured on a V-770 (JASCO) spectrophotometer. Femtosecond transient absorption (TA) spectral measurements were performed on a commercial TA spectrograph (Helios Fire, Ultrafast Systems). The pump spectra centered at 1000, 576, or 350 nm were generated with a commercial optical parametric amplifier (TOPAS-Prime, Light Conversion), which was pumped by a regeneratively amplified femtosecond Ti:sapphire laser (Astrella, Coherent) centered at 800 nm, with a 4 kHz repetition rate, 78 fs pulse durations, and 1.6 mJ pulse energy. The spectra of pump pulses are shown in Figure S1 in the Supporting Information (SI). The spot size of the focused pump beam was about 250 μm. Typically, pump fluences were 200 μJ·cm^–2 for pulse energies of 100 nJ. The supercontinuum probe beam was generated in a sapphire substrate for the NIR detection (800–1350 nm) or in a calcium fluoride substrate for the UV–vis detection (330–650 nm). The pump beam was linearly polarized at the magic angle (54.7°) relative to the probe beam. TA spectra were corrected for the group velocity dispersion of the broad-band probe beam before analysis. All measurements were performed under ambient conditions.

Spectroelectrochemical Measurement

The spectroelectrochemical measurement was carried out on a Lambda 750 (PerkinElmer) UV–visible spectrophotometer combined with a CHI 660D (CH Instruments) potentiostat. The working electrode was an ITO glass (<10 Ω/square). The counter electrode was a platinum coil. The reference electrode was Ag/AgCl. The electrolyte is 0.1 M nBu₄NPF₆. Experiments were carried out at ambient temperature under the protection of nitrogen.

Results

Stationary Spectral Characterizations

The stationary absorption spectra (Figure 2) of SWCNT/PFO–BPy Hybrid and surfactant-dispersed SWCNT show the typical excitonic transitions, i.e., E₀₀ → E₁₁, E₀₀ → E₂₂, and E₀₀ → E₃₃ (E₀₀ denotes the ground state in the exciton picture, as shown in Figure S1 in the Supporting Information), peaking around 1000, 576, and 350 nm, respectively. The absorption of PFO–BPy in the Hybrid system is observed as a shoulder on the red side of the E₀₀ → E₃₃ absorption band (see Supporting Information, Figure S2 for details). The visibility of the E₀₀ → E₃₃ absorption is due to the carefully reduced PFO–BPy concentration. Moreover, the chirality distributions of the SWCNT and Hybrid samples have been characterized by absorption spectroscopy (see Supporting Information, section B).⁴²

Figure 2.

Stationary absorption spectra of surfactant-dispersed (6,5) SWCNT in water, PFO–BPy-wrapped (6,5) SWCNT Hybrid in THF, and PFO–BPy in THF. The positions of absorption peaks are marked with corresponding colors.

Transient Absorption Spectra of the SWCNT

Figure 3 displays selected near-infrared (NIR) TA spectra of SWCNT upon the E₁₁, E₂₂, and E₃₃ resonant excitations. Due to the purity of the sorted (6,5) SWCNT, several known absorption features are clearly observed in the TA spectra. Upon E₁₁ excitation (Figure 3a) the dominant negative signal centered at ∼1000 nm arises from the E₀₀ → E₁₁ bleach, as reported previously.⁴³ The photoinduced absorption (PA) band centered at ∼1110 nm (∼1.12 eV) on the red side of the E₀₀ → E₁₁ bleach builds up within the instrumental response time and decays subsequently. This PA band has been assigned to the transition from exciton to biexciton (E₁₁ → E_11,BX).^39,44 Another PA band peaking at ∼1143 nm (∼1.08 eV) is evident after ∼10 ps and dominating the long-time scale spectra up to the limit of the measurement time window. Previous studies attributed this band to the triplet exciton absorption (³E₁₁ → ³E_nn).⁴⁵ Additionally, a broad PA band over 1200–1350 nm decays rapidly within the initial ∼1 ps. This spectral feature is commonly observed for the optical excitation into the E₁₁ excitonic band at high pump fluence and has been discussed to be related to multiple E₁₁ exciton interactions.^38,39,46,47 The PA band on the blue side of the E₀₀ → E₁₁ bleach is attributed to a transition from a dark E₁₁ state to the unbound two-exciton manifold.⁴⁸

Figure 3.

Selected TA spectra of SWCNT in water upon the (a) E₁₁, (b) E₂₂, and (c) E₃₃ excitations. Experimental conditions: (a) λ_ex = 1000 nm, (b) λ_ex = 576 nm, and (c) λ_ex = 350 nm; pump energy: 100 nJ·pulse^–1. Dotted lines highlight major transition manifolds.

Resonant excitation into the E₂₂ or E₃₃ excitonic band of SWCNT results basically in the same spectral features (Figure 3b, c): the E₁₁ → E_11,BX and ³E₁₁ → ³E_nn transitions are still evident and show spectral line shapes and positions in agreement with those upon the E₁₁ excitation (vide supra). For excitons created by higher band transitions, such as E₂₂, the intersubband relaxation to the E₁₁ state has been shown to take place within 100 fs.^30,40,48,49 Upon E₂₂ or E₃₃ excitation, the E₀₀ → E₁₁ bleach with a large negative amplitude becomes broader and slightly blue-shifted, which results in larger overlap with the blue-side PA band. Similar spectral dynamics of SWCNT are observed in our results upon the excitation of either the E₁₁, E₂₂, or E₃₃ excitonic band.⁴⁴

Transient Absorption Spectra of the SWCNT/PFO–BPy Hybrid

In the previous section, the intrinsic exciton dynamics of (6,5) SWCNTs upon different excitonic–transition excitations have been shown. Our focus now turns to the excited-state dynamics of the (6,5) SWCNT/PFO–BPy formed heterojunction to find evidence for PCT. Selected NIR TA spectra of the Hybrid upon the E₁₁, E₂₂, and E₃₃ excitations are shown in Figure 4. Besides the known E₁₁ → E_11,BX (∼1100 nm, ∼1.13 eV) and ³E₁₁ → ³E_nn (∼1160 nm, ∼1.07 eV) transitions, an additional broad PA band emerges on the red side of the E₀₀ → E₁₁ bleach in the Hybrid upon E₂₂ and E₃₃ excitation (highlighted by shaded areas in Figure 4b, c). It covers the spectral range of ∼1050–1200 nm that overlaps with the absorption of E₁₁ → E_11,BX and ³E₁₁ → ³E_nn transitions and lasts for tens of picoseconds. Furthermore, on this time scale, we note that the E₀₀ → E₁₁ bleach in the TA spectra of the Hybrid upon the E₃₃ excitation manifests a dynamic blue-shift of up to ∼5 nm. We summarize the peak dynamics in Figure 5. The time-dependent peak-shifting of the E₀₀ → E₁₁ bleach was extracted from the TA spectra by Gaussian-peak fitting in the energy domain within the spectral region of the dominant bleach band centered at ∼1000 nm. Considering that the exciton density is strongly dependent on the excitation fluence (section I), we investigated this peak shift for the SWCNT and Hybrid with various excitation fluences (see Supporting Information, section C for fluence-dependent TA spectra).

Figure 4.

Selected TA spectra for the Hybrid in THF upon the (a) E₁₁, (b) E₂₂, and (c) E₃₃ excitations. Experimental conditions: (a) λ_ex = 1000 nm, (b) λ_ex = 576 nm, and (c) λ_ex = 350 nm; pump energy: 100 nJ·pulse^–1. Dotted lines highlight major transition manifolds. The shaded shapes indicate the absorption signature of the suspected SWCNT polaron. The asterisks (*) denote the wavelength of 1050 nm.

Figure 5.

Pump-energy-dependent peak-shifting dynamics of the E₀₀ → E₁₁ bleaching in TA spectra of the SWCNT (a, b, c) and the Hybrid (d, e, f) in the time window of 0.1–500 ps. Excitation wavelength and corresponding pump energy per pulse are given in legends. Due to dispersion instability under high pump fluences, TA spectra of SWCNT are unavailable at higher fluences in b and c.

As shown in Figure 5a, the peak position of the E₀₀ → E₁₁ bleach for the SWCNT upon the E₁₁ excitation remains stable across the investigated time window. For the SWCNT upon E₂₂ or E₃₃ excitation (Figure 5b and 5c, respectively), the bleach peak shows a slight and smooth red-shift through the entire time window. This trend is widely observed when tracking the dynamics of excitonic band bleach recovery in SWCNTs, and it can be explained by intersubband and intrasubband relaxation.^39,50 Upon exciting the Hybrid with different pump wavelengths, the initial peak position at ∼0.1 ps shifts slightly, which matches well with the trend observed in the SWCNT. However, the peak-shifting dynamics are significantly different for the Hybrid. Besides the smooth red-shift through the entire time window, a dynamic blue-shift of the E₀₀ → E₁₁ bleach is particularly evident within the time delay from 1 to 50 ps when the Hybrid is pumped at E₃₃ (Figure 5f). Notably, the extent of the dynamic blue-shift progressively becomes larger with increasing excitation fluence. When the peak-shifting curves of the Hybrid upon E₂₂ excitation (Figure 5e) are examined, although these curves do not show an obvious blue-shift as E₃₃ excitation, the peak position plateaus on the same time scale at the highest excitation energy. For the Hybrid upon E₁₁ excitation, we hardly observe this trend (Figure 5d), and it behaves almost the same as the SWCNT upon E₁₁ excitation. The additional peak dynamics of the E₀₀ → E₁₁ bleach in the Hybrid upon E₃₃ (and less pronounced upon E₂₂) excitation indicate an additional quasiparticle with a blue-shifted E₀₀ → E₁₁ bleach and an observable buildup time, which may be the PCT product. One point to note is that the dynamic blue-shift in tens of picoseconds does not directly reflect real population dynamics. It only suggests that the share of this new species is increasing among all quasiparticles, and the population of each transient species may be decaying individually on that time scale.

Absorption Features of Charge Transfer Products

To identify the PCT in the Hybrid, we examine the spectroscopic features of potential PCT transient products.^22,51 Charged transient products in SWCNTs have been demonstrated to be two kinds of quasiparticles: (a) the polaron, which describes a conduction electron (or hole) strongly coupled with the lattice ions,⁵² or (b) the trion, which is a three-body charge-exciton bound state.^38,47,53,54

The (6,5) SWCNT polaron can be created in steady state by two methods, namely redox-chemical doping^{22,25,55−57} and electrochemical doping.^6,58,59 We carried out the redox-chemical hole-doping of the Hybrid dispersion with NOBF₄ (+1.00 V vs Fc/Fc⁺ in CH₂Cl₂)⁶⁰ as a one-electron oxidant.⁶¹ As shown in Figure 6a, along with the increasing doping level, the stationary absorption of the E₀₀ → E₁₁ transition (∼1000 nm) decreases dramatically and exhibits a blue-shift in wavelength. On the red side of the dominant E₀₀ → E₁₁ transition, stationary spectra of the doped Hybrid feature a broad absorptive band extending from 1030 to 1200 nm, including a peak around ∼1150 nm. The weak absorption at 1150 nm before the oxidative titration ([NOBF₄] = 0 μM) results from the slight p-doping of SWCNTs in the air.⁶² We expect that the polymer in the Hybrid remains unoxidized during the titration, since the HOMO energy of PFO–BPy is stabilized by 1.4 eV with respect to the first valence band of (6,5) SWCNT. The previously reported electrochemical doping for the Hybrid in films shows a very similar trend to the redox doping.⁶ Note that for very high doping levels, the entire NIR absorption of the Hybrid is strongly bleached. We conclude that the above spectral features describe the (6,5) SWCNT hole-polaron absorption transition, denoted as E⁺₀₀ → E⁺₁₁.

Figure 6.

(a) NIR stationary absorption spectra monitor the oxidative titration of the Hybrid with NOBF₄ in toluene:CH₂Cl₂ (ratio 1:1) mixed solution. Experimental conditions: [(6,5) SWCNT] ∼ 2.74 nM; SWCNT length ∼1000 nm; optical path length = 10 mm. (b) Selected TA spectra for a heavily hole-doped ([NOBF₄] ∼ 128 μM) Hybrid in toluene:CH₂Cl₂ (ratio 1:1) mixed solution. Experimental conditions: λ_ex = 1000 nm, i.e., in resonance with E₁₁; pump energy = 50 nJ·pulse^–1. Scaled steady-state absorption spectrum (inverted shaded shape) is shown for comparison.

In order to examine the spectral signature of trions, we conducted the TA measurement on the heavily hole-doped ([NOBF₄] ∼ 128 μM) Hybrid under E₁₁ excitation.⁴⁷ As shown in Figure 6b, the initial TA spectra show the E₀₀ → E₁₁ bleach at ∼1000 nm and E⁺₀₀ → E⁺₁₁ bleach at ∼1150 nm. The E⁺₀₀ → E⁺₁₁ bleach decreases within ∼1 ps, and meanwhile a new absorptive species centered at ∼1190 nm (∼1.04 eV) is formed. This band has been assigned to a positive trion (Tr⁺₁₁ → Tr⁺_nn) absorption of (6,5) SWCNTs.^38,47 The spectral signature of trions in the Hybrid is consistent with that observed in (6,5) SWCNT superstructures reported by Therien et al.^38,47

Discussion

Observation of Charge Transfer in SWCNT/PFO–BPy Hybrid

Combining the results of redox-chemical and electrochemical doping (vide supra), we can summarize the spectroscopic features of the (6,5) SWCNT hole-polaron (E⁺₀₀ → E⁺₁₁) in comparison with the excitonic absorption spectrum of neutral (6,5) SWCNTs. The (6,5) SWCNTs hole-polaron features a bleached and blue-shifted E₀₀ → E₁₁ transition and an additional absorption band covering 1030–1200 nm, the line shape of which strongly depends on the charge carrier level.^{25,55,57−59,63} The electronic absorption transitions of oxidized nanotubes are explained by the electron depletion of the top of the valence band, which results in an increase in the E₀₀ → E₁₁ transition energy and leads to additional electronic transitions.^25,59 It is noteworthy that studies by electron paramagnetic resonance (EPR) spectroscopy reveal that the unpaired electrons in lightly reduced SWCNTs are relatively free and fast-relaxing.²⁰ This is certainly valid for metallic SWCNTs but has been corroborated as well for semiconducting SWCNTs.⁶⁴ Thus, the “polaron” in SWCNTs is relatively delocalized, which may prolong the lifetime of the charge-separation state.

As shown in Figure 5, TA spectra of the Hybrid feature a dynamic blue-shift of the E₀₀ → E₁₁ bleach in picoseconds following the E₂₂ and E₃₃ excitations, which strongly suggests the formation of the SWCNT polaron (E^±₀₀ → E^±₁₁). Although the triplet absorption also contributes to the absorption around 1160 nm where an absorption peak of E^±₀₀ → E^±₁₁ is located, the TA spectra of SWCNT indicate that the formation of triplet excitons is independent of the excitation energy and fluence. According to the reported time constant of intersystem crossing of ∼20 ps in (6,5) SWCNTs,⁴⁵ the broad absorption band at 1030–1200 nm and the peak around 1160 nm formed in the first few picoseconds in the Hybrid upon high-energy excitation should be attributed to the E^±₀₀ → E^±₁₁ transition. However, the spectral overlap between E^±₀₀ → E^±₁₁, E₁₁ → E_11,BX, and ³E₁₁ → ³E_nn transitions (compare Figure 4 with Figure 6a) impedes a spectral disentanglement of the SWCNT polaron dynamics via global analysis of the TA dynamics of the Hybrid. Thus, we select the TA kinetics at 1050 nm, where an isosbestic point with almost zero ΔA is located in the TA spectra of the SWCNT, to further investigate the formation of the SWCNT polaron in the Hybrid. As shown in Figure 7a–c, the normalized kinetic traces for the Hybrid pumped at very low pump energy (5 or 20 nJ·pulse^–1) show a smooth decay which is generally the same for the E₁₁, E₂₂, and E₃₃ excitations. This decay component arises from the absorption edge of E₁₁ → E_11,BX (centered at 1100 nm) transition. When the pump energy is increased from 50 to 400 nJ·pulse^–1, the dynamics of the SWCNT polaron emerge. It becomes progressively evident in the Hybrid upon E₂₂ and E₃₃ excitation (Figure 7b, c) and overlaps with the E₁₁ → E_11,BX absorption. The absorption amplitude reaches its maximum at ∼3 ps and slowly decays over a few hundred picoseconds. The spectroscopic features of SWCNT polaron absorption over 1050–1200 nm can be observed in the normalized TA spectra of the Hybrid at the probe delay of 3 ps (Figure 7e, f), matching well with the absorptive feature of the SWCNT hole-polaron (E⁺₀₀ → E⁺₁₁, shown in blue lines) obtained by chemical doping (vide supra). In the TA spectra of the Hybrid upon E₁₁ excitation, the signature of the SWCNT polaron is hardly observed in the respective kinetics and spectra (Figure 7a, d). In addition, using the spectroelectrochemical method, the PFO–BPy polaron was prepared and observed in the steady-state spectrum. As one would expect, the formation of the PFO–BPy polaron is also observed in the UV region of the Hybrid TA spectra around 380 nm (see Supporting Information, sections E and F). Hence, we conclude that a PCT reaction takes place in the SWCNT/PFO–BPy Hybrid system, forming an interfacial charge-separated state.²²

Figure 7.

Normalized pump-energy-dependent TA traces at 1050 nm for the Hybrid in THF upon (a) E₁₁, (b) E₂₂, and (c) E₃₃ excitation. Note that traces were normalized by the ΔA amplitude at 0.1–0.2 ps considering the instrumental response. Normalized pump-energy-dependent TA spectra for the Hybrid in THF at a time delay of ∼3 ps upon the (d) E₁₁, (e) E₂₂, and (f) E₃₃ excitations. Note that spectra were normalized at the E₀₀ → E₁₁ bleaching maximum. The blue lines represent the stationary absorption feature of the (6,5) SWCNT hole-polaron obtained by redox-chemical doping ([NOBF₄] ∼ 128.4 μM, shown in Figure 6a).

It is worth adding that we have not observed any spectral evidence of trion formation, as previously identified from the hole-doped Hybrid solution (Figure 6b), in the TA spectra of undoped SWCNT or Hybrid.

In the Hybrid, the direction of PCT can be deduced by analyzing the excitation distribution between the two components. In the case of E₁₁ or E₂₂ excitation of the Hybrid, the pump pulse centered at 1000 or 576 nm is far away from the UV resonant absorption of PFO–BPy. Thus, the PCT in both cases purely originates from the excited (6,5) SWCNT to the PFO–BPy. In the case of E₃₃ excitation, the pump spectrum centered at 350 nm is resonant with (6,5) SWCNT as well as with PFO–BPy. Since PCT from excited PFO–BPy to the (6,5) SWCNTs is also energetically favorable in this case, one needs to evaluate the excitation contribution from (6,5) SWCNT and PFO–BPy in the Hybrid by comparing the initial UV–vis TA spectra of the Hybrid, SWCNT, and PFO–BPy excited at 350 nm. As shown in Figure 8, the TA spectrum of PFO–BPy at 0.2 ps clearly manifests a negative bleach peak (∼365 nm) and a negative stimulated emission peak (∼390 nm) (see Supporting Information, section D for the TA spectral analysis of PFO–BPy). However, the above TA spectral features from excited PFO–BPy are hardly observed in the TA spectrum of the Hybrid at the same time delay (see Supporting Information, section E for a comparison of the full dynamics). The Hybrid TA spectrum only retains the excitation features of the SWCNT, especially for the region of 350–450 nm, and the excitation contribution of PFO–BPy is minimal in comparison to the excitation of (6,5) SWCNTs in the Hybrid. Thus, we conclude that although the PCT from excited PFO–BPy to (6,5) SWCNT cannot be completely ruled out, the current analysis shows that, in the case of E₃₃ (350 nm) excitation of the Hybrid, the PCT from excited (6,5) SWCNT to PFO–BPy is absolutely dominant.

Figure 8.

UV–vis TA spectra for the Hybrid in THF, SWCNT in water, and PFO–BPy in THF at a time delay of 0.2 ps. Excitation wavelength: 350 nm. Pump energy: 100 nJ·pulse^–1.

An additional point to address is whether an electron or hole transfer takes place. Since the electron and hole in SWCNT have a similar effective mass, electron- and hole-polaron will show very similar absorptive signatures at the same doping level.⁶⁵ However, the energy level alignment in the Hybrid (Figure 1) implies that the electron transfer from the third conduction subband (c₃) of (6,5) SWCNT to the LUMO of PFO–BPy has a larger driving force than the hole transfer from the third valence subband (v₃) to the HOMO. Therefore, photoinduced electron transfer from (6,5) SWCNT to PFO–BPy is more likely to take place than hole transfer.

Charge Transfer Assisted by Auger Recombination

As discussed above, when the wide-bandgap PFO–BPy acts as a charge acceptor in the Hybrid, the PCT from the E₁₁/E₂₂-excited (6,5) SWCNT to PFO–BPy is energetically unfavorable (Figure 1). However, when multiple excitons are present on a SWCNT in a high-excitation-density regime, strong exciton–exciton interactions lead to Auger recombination of excitons, also known as exciton–exciton annihilation (EEA), in which one exciton recombines to the ground state and the other is promoted to a higher excitonic state or dissociates into free charge carriers.^34,35,39,66 Hence, Auger recombination of excitons can be regarded as a potential energy up-conversion process that forms one high-energy exciton through absorbing two low-energy photons. Under this assumption, the occurrence of PCT driven by E₂₂ (576 nm, 2.15 eV) excitation in the Hybrid indicates that E₃₃ (350 nm, 3.54 eV) or higher-energy excitons are generated via Auger recombination of excitons, thus making the reaction energetically favorable. For the Hybrid upon E₁₁ (1000 nm, 1.24 eV) excitation, however, the annihilation of two E₁₁ excitons is energetically insufficient to directly promote an E₃₃ exciton (350 nm, 3.54 eV). Consequently, the PCT from the E₁₁-excited (6,5) SWCNT to PFO–BPy is quite inefficient as observed in Figure 7. According to previous reports on fluence-dependent dynamics in SWCNTs,⁶⁷ we conclude from the estimated exciton density (see Supporting Information, section I) that the exciton–exciton Auger process is unlikely to occur under E₂₂ excitation with less than 20 nJ·pulse^–1. As shown in Figure 7, the PCT characteristics are hardly observable under these conditions.

Due to the effect of exciton dissociation in SWCNTs, the elementary excitation specifically involved in the Auger recombination may not be limited to excitons but can also involve unbound charge carriers, i.e., electrons and holes (e, h). The up-converted product in the Auger recombination of charge carriers is a high-energy carrier (electron or hole), while the product in the Auger recombination of excitons is a high-energy exciton (schematically shown in Figure 9a). It has been shown that these two mechanisms can be distinguished by their distinct population kinetics.³⁴ Auger recombination of charge carriers, as a three-particle process, can be described by a rate equation as

1

where n_e,h(t) is the population of charge carriers, and γ_A is the rate constant of the Auger recombination of charge carriers. The solution of eq 1, [n_e,h(0)/n_e,h(t)]² – 1 = 2/3γ_An_e,h²(0)t, where n_e,h(0) denotes the initial population of charge carriers, predicts a linear dependence between the reciprocal of the charge carrier population squared and the delay time. Auger recombination of excitons, as a two-particle process, can be described as

2

where n_ex(t) is the population of excitons, and γ_EEA is the rate constant of the Auger recombination of excitons. The solution of eq 2, [n_ex(0)/n_ex(t)] – 1 = 1/2γ_EEAn_ex(0)t, where n_ex(0) denotes the initial population of excitons, predicts a linear dependence between the reciprocal of the exciton population and the delay time.

Figure 9.

(a) Schematic description of the Auger recombination of charge carriers (left) and excitons (right). ET denotes energy transfer. (b) Kinetics of the integral E₀₀ → E₁₁ bleaching in the TA spectra of the Hybrid in THF upon the E₁₁, E₂₂, and E₃₃ excitations, plotted as {[ΔA(0)/ΔA(t)]² – 1} (red dots, left axis) and {[ΔA(0)/ΔA(t)] – 1} (blue squares, right axis). Traces are shifted by different offset on the vertical axis for a better comparison. Solid black lines represent the results of the linear fitting. Adjusted R-squared (Adj. R²) and fitting residuals are shown with corresponding colors. Note that the fitting of the E₁₁-excited TA trace started from 1 ps to exclude the nondiffusion-controlled rapid annihilation.³⁵ Pump energy: 100 nJ·pulse^–1.

To analyze the time dependence of the bleach signal in the initial 10 ps of Hybrid upon E₁₁, E₂₂, and E₃₃ excitations, the E₀₀ → E₁₁ bleaching band in the TA signal is integrated, and its kinetics are plotted as shown in Figure 9b (pump energies of 100 nJ·pulse^–1) and section G (pump energies of 2–400 nJ·pulse^–1) in the Supporting Information. The linear fitting of [ΔA(0)/ΔA(t)] and [ΔA(0)/ΔA(t)]² shows, however, comparable adjusted R-squared and fitting residuals for all excitation photon energies and excitation fluences. This result suggests that Auger recombination in the Hybrid in the initial 10 ps is not purely excitonic, but the Auger recombination of charge carriers coexists as well.

It is worth noting that when the pump photon energy increases from 1.24 eV (1000 nm, E₁₁ excitation) to 2.15 eV (576 nm, E₂₂ excitation) and 3.54 eV (350 nm, E₃₃ excitation), the charge carrier nature does not obviously replace the excitonic nature as dominant in the elementary excitations of the Hybrid in THF. Besides, the trion, as an indication of efficient free carrier generation (FCG), is absent as well in the TA spectra of the undoped Hybrid as discussed above. All these results indicate that the FCG of the Hybrid in THF is relatively inefficient. The exciton binding energy in carbon nanotubes increases with decreasing solvent dielectric permittivity,⁶⁸ which entails that FCG is highly sensitive to the electrostatic environment. Efficient FCG in pristine SWCNTs is usually observed in high dielectric permittivity microenvironments, such as polar solvents, ionic surfactants, or ionic semiconducting polymers.^33,38,69,70 Therien et al. pointed out the adverse effect of the low dielectric environment on FCG in SWCNTs by quantitatively analyzing the FCG efficiency in mixtures of D₂O (ε = 78.5) and MeOH (ε = 32.6).³⁸ Therefore, we deduce that the FCG in the Hybrid may be suppressed by the low dielectric solvent, THF (ε = 7.5). The wrapping PFO–BPy, as a weakly polar polymer, also provides a low dielectric microenvironment for SWCNTs, which is unfavorable to efficient FCG as well. The influence of environmental effects on all-optical FCG in polymer-wrapped SWCNTs still needs further study.

Beside Auger recombination, high-energy and high-fluence excitations may also lead to other nonlinear effects in SWCNTs. The multiple-exciton generation (MEG), as the opposite process of the Auger recombination, forms two excitons by absorbing one photon with energy higher than twice the bandgap.³⁶ MEG is, however, an intrinsic feature of SWCNTs and should thus be observable in both surfactant-dispersed and polymer-wrapped SWCNTs. The lack of any obvious changes in the line shape of the spectra caused by MEG upon E₃₃ excitation at high pump fluence for pure SWCNTs shows that MEG is not present. Furthermore, MEG as an energy down-conversion process should not contribute to the PCT from excited SWCNTs to wide-bandgap PFO–BPy. Finally, while two-photon absorption (TPA) is an energy up-conversion process which may favor the PCT, TPA coefficients in pristine semiconducting SWCNTs have been reported to be very low.⁷¹

Charge Separation and Recombination Dynamics

Finally, reaction time constants for photoexcited interfacial charge separation (τ_CS) and thermal charge recombination (τ_CR) in the SWCNT/PFO–BPy Hybrid were estimated by fitting the fluence-dependent kinetic traces (see Supporting Informaton, section H). The buildup of the SWCNT polaron signature takes place in τ_CS ≈ 0.9 ps, which is consistent with the time scale of reported electron transfer in perylenediimide-based polymer-wrapped carbon nanotube superstructures (τ_CS ≈ 0.4 ps).²² The decay of the SWCNT polaron manifests in a multiphase process, which was reproduced by three-exponential kinetics (τ_CR ≈ 3, 50, and 1000 ps). However, the UV–vis TA spectra of the Hybrid corroborate that the decay of the PFO–BPy polaron is on a time scale of a few picoseconds and does not feature a nanosecond-lived component (see Supporting Information, section E). The charge recombination path should not be limited to the direct recombination between the SWCNT hole polaron and PFO–BPy electron polaron. The Type-I heterojunction can efficiently funnel the electron on the LUMO of PFO–BPy into the conduction band of the SWCNT, which is independent of whether the SWCNT is charged or neutral. Consequently, the PFO–BPy polaron features a significantly shorter decay time compared with that of the SWCNT polaron. When electrons back-transfer to neutral SWCNTs, SWCNT electron polarons will be formed and coexist with the hole polarons because of the high migration rate and large delocalization length of the SWCNT polaron.^25,72 Therefore, we deduce that the fast decay of the SWCNT polaron on a time scale of ∼3 ps might originate from the direct charge recombination between the closely associated SWCNT electron polaron and PFO–BPy hole polaron. The delocalized SWCNT electron and hole polarons, which migrate along the nanotubes backbone, prolong the final charge recombination to the subnanosecond time scale.^22,73−75

Through comparison of the spectra of the SWCNT polaron produced by chemical oxidation and the maximal E₀₀ → E₁₁ blue-shift in the TA spectra (see Supporting Information, section J), we estimate that PCT induces a doping level higher than the equivalent of ∼8 μM NOBF₄ in the SWCNTs. However, because of the spectral overlap in the TA spectra, especially at the delay time when the population of the SWCNT polaron reaches its maximum at around 1–3 ps, we could not extract the pure E₀₀ → E₁₁ bleach of the SWCNT polaron. Thus, the degree of charge transfer in the PCT reaction cannot be quantified precisely in this work. The question could be addressed in the future through TA spectroscopy on polymer-SWCNTs in thin-film electrochromic devices.⁶

Conclusion

In summary, we have investigated the charge transfer from photoexcited semiconducting (6,5) SWCNTs to a wide-bandgap wrapping polymer PFO–BPy via femtosecond TA spectroscopy. By spectral and dynamic analysis of the PCT products, we show that the PCT from excited SWCNTs to PFO–BPy can be driven not only by the energetically favorable E₃₃ excitation but also by the energetically unfavorable E₂₂ excitation under high excitation fluences. The energetically unfavorable PCT originates from the Auger recombination of excitons and charge carriers in the SWCNT, which promotes higher energy excitonic states (E₃₃ or higher) and thus makes the charge transfer from the photoexcited narrow-bandgap SWCNT toward the wide-bandgap polymer possible. The spectral dynamics of the SWCNT polaron indicate a time constant of ∼0.9 ps for the interfacial charge separation reaction between the SWCNT and PFO–BPy. The charge recombination may manifest in multiple paths. It includes the direct recombination between the closely associated SWCNT electron polaron and PFO–BPy hole polaron on a time scale of ∼3 ps, while the delocalized SWCNT electron and hole polarons prolong the final charge recombination to the subnanosecond time scale. These findings expand our understanding of the PCT mechanism in Type-I heterojunctions with SWCNTs. When an energy up-conversion process, such as Auger recombination of excitons, takes place in a hybrid system, the energetically unfavorable PCT from a narrow-bandgap nanotube donor to a wide-bandgap polymer acceptor can be driven as well. Such processes might need to be considered for optoelectronic devices that rely on charge separation between nanotubes and semiconducting polymers (e.g., solar cells or photodiodes), in particular in systems where the polymer bandgap is much smaller than that of PFO–BPy.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.0c10171.

• Excitonic transitions in the exciton picture, stationary absorption spectra, pump pulse spectra, fluence-dependent NIR transient absorption spectra of SWCNT and SWCNT/PFO–BPy hybrid, transient absorption spectra of PFO–BPy, PFO–BPy polaron in UV–vis transient absorption spectra of the SWCNT/PFO–BPy hybrid and spectroelectrochemistry, elementary excitation analysis of the Auger process, analysis of charge-transfer dynamics, exciton density estimate, and comparison between all-optical doping and chemical doping (PDF)

Author Present Address

^⊥ Institut für Experimentelle Physik, Freie Universität Berlin, Arnimallee 14, Berlin 14195, Germany.

The authors declare no competing financial interest.