The Role of Electron–Hole Separation in Thermally Activated Delayed

Oct 29, 2015 - Harmon , N. J.; Flatté , M. E. Semiclassical Theory of Magnetoresistance in Positionally Disordered Organic Semiconductors Phys. Rev...
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The Role of Electron−Hole Separation in Thermally Activated Delayed Fluorescence in Donor−Acceptor Blends Eric Hontz,† Wendi Chang,‡ Daniel N. Congreve,‡ Vladimir Bulović,‡ Marc A. Baldo,‡ and Troy Van Voorhis*,† †

Department of Chemistry and ‡Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States S Supporting Information *

ABSTRACT: Thermally activated delayed fluorescence (TADF) is becoming an increasingly important OLED technology that extracts light from nonemissive triplet states via reverse intersystem crossing (RISC) to the bright singlet state. Here we present the rather surprising finding that in TADF materials that contain a mixture of donor and acceptor molecules the electron−hole separation fluctuates as a function of time. By performing time-resolved photoluminescence experiments, both with and without a magnetic field, we observe that at short times the TADF dynamics are insensitive to magnetic field, but a large magnetic field effect (MFE) occurs at longer times. We explain these observations by constructing a quantum mechanical rate model in which the electron and hole cycle between a near-neighbor exciplex state that shows no MFE and a separated polaron-pair state that is not emissive but does show magnetic field dependent dynamics. Interestingly, the model suggests that only a portion of TADF in these blends comes from direct RISC from triplet to singlet exciplex. A substantial contribution comes from an indirect path, where the electron and hole separate, undergo RISC from hyperfine interactions, and then recombine to form a bright singlet exciplex. These observations have a significant impact on the design rules for TADF materials, as they imply a separate set of electronic parameters that can influence efficiency.

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INTRODUCTION Organic light-emitting diodes (OLEDs) are a quickly evolving technology. The existing state of the art for these devices involves using phosphorescent organometallic complexes to extract light from otherwise dark triplet states that comprise the overwhelming majority of excitons formed in OLEDs.1−3 In addition to the high cost associated with the precious metals found in many of these phosphors, empirical evidence suggests there is a practical lower limit to the phosphorescence lifetime of commonly used phosphors, which has stagnated somewhere in the vicinity of 1 μs.4 This limit imposes a major roadblock to device design, because as the charge injection rate is increased to drive the OLED brighter, long-lived excitons result in substantial energy buildup in the device, which ultimately leads to lower efficiencya phenomenon often referred to as “rolloff.”5−7 To obtain high-efficiency, low-cost OLEDs, recent work has proposed thermally activated delayed fluorescence (TADF) as an alternative mechanism to phosphorescence for harvesting triplet excitons.8−10 TADF relies on efficient thermal upconversion from the triplet state to an emissive singlet state,11 a process termed reverse intersystem crossing (RISC) (see Figure 1a). Because TADF does not rely on phosphorescence, it offers a fresh set of electronic parameters to optimize that could lead to faster energy conversion and higher efficiencies than phosphorescent OLEDs (pOLEDs).12 In the quest to engineer organic systems with efficient RISC, the main focus has been placed on decreasing the energy gap ΔEST between the triplet (T1) and excited singlet (S1) states.13 © XXXX American Chemical Society

Figure 1. (a) Illustration of TADF in an OLED: 3/4 of the injected charges form nonemissive triplets, which can then undergo RISC and fluoresce from the singlet. (b) Chemical structures of the donor, mMTDATA, and acceptor, 3TPYMB, of the exciplex system studied.

Because ΔEST is the result of exchange interaction between the unpaired electrons of an exciton (i.e., the electron and hole), one way to shrink ΔEST is to spatially separate the electron (e) and hole (h), creating a charge transfer (CT) state. Increasing the separation results in a trade-off, however, because the oscillator strength that determines the fluorescence rate also decreases with e−h distance.14,15 In order to provide a more detailed perspective on how e−h separation influences device performance, here we study TADF in a blend of 4,4′,4″-tris[3-methylphenyl(phenyl)amino]triphenylamine (m-MTDATA) donors and tris-[3-(3-pyridyl)mesityl]borane (3TPYMB) acceptors (see Figure 1b).16,17 In Received: July 29, 2015 Revised: October 20, 2015

A

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HFI is typically negligible compared to SOC, with HFI energies as small as 10−4 meV. But for large electron−hole separations, HFI dominates because it is completely local. The electron or hole experiences a field due to the nuclei of its own molecule, and this field is independent of the distance between the electron and hole. Because of the relatively large electron−hole spacing required for TADF, HFIs are gaining attention in the OLED community.13,27−30 For intramolecular TADF (i.e., excited states with the electron and hole on the same molecule), the conclusion then is that ISC and RISC are driven by SOC between S and T states that are relatively widely separated in energy. This energetic separation is responsible for the observed thermally activated behavior.11,31 However, when the electron−hole separation is large (a so-called radical pair or polaron-pair (PP) state), the RISC mechanism is somewhat different.19,32−38 During the formation of a PP, the exponential decrease of J and ESOC eventually results in ESOC, ΔEST < EHFI, and HHFI becomes increasingly important. Most importantly, HHFI does not conserve spin (i.e., [HHFI, S2] ≠ 0). Thus, in the presence of HFI, an initially S or T state will evolve into an admixture of S, T+, T0, and T−. Therefore, when the PP state recombines, it may form an S, T+, T0, or T− exciplex, with the probability being proportional to the admixture of that state at the time of recombination. Magnetic Field Effects on Spin Transitions. Under application of an external magnetic field Bext of magnitude Bext, the T+ (T−) triplet substate increases (decreases) in energy by EZeeman = gμBBext/ℏ (see Figure 2a). Now, EZeeman is only

this case the luminescence comes from exciplex emission: the electron in the LUMO of the acceptor relaxes directly to the HOMO of the donor, so that the donor−acceptor spacing directly determines the electron−hole distance. By measuring magnetic field effects (MFEs) on the time-resolved photoluminescence, we discover rather complex dynamicsthe MFE is negligible at short times (5 μs). We are able to explain these observations using a quantum mechanical rate model in which the distance between the electron and hole f luctuates as a function of time. The photogenerated electron−hole pair begins on near neighbors and has a large exchange splitting that mutes the MFE. After some time, the electron and hole separate to a distance beyond the exchange radius, at which point ΔEST is on the order of the Zeeman energy of the applied field (∼50 μeV), and the MFE is large.18,19 The conclusion is that the bound electron−hole pairs in these blends are significantly more dynamic than previously appreciated, suggesting new avenues for controlling TADF efficiency. Background. Before presenting the results, we review the fundamental ideas that govern magnetic field effects in these systems. Energies of Spin States and Transitions between Them. In a simple molecular orbital picture, singlet (S) and triplet (T) excited states with the same orbital configuration are separated by the exchange energy (2J) where J=

∬ ϕn*(r1)ϕk(r1) |r −1 r | ϕn(r2)ϕk*(r2) d3r1 d3r2 1

2

(1)

with ϕn and ϕk corresponding to the electron and hole orbitals involved in the transition, respectively. Often ϕn is the LUMO and ϕk the HOMO. If the electron and hole orbitals are localized and spatially separated, J decays rapidly (typically exponentially) with electron−hole separation. J is therefore an extremely sensitive measure of the proximity of the electron and hole. For typical bright states, J can be as large as several hundred meV. For typical TADF single molecule emitters J is ≲100 meV. In the absence of magnetic fields and relativistic effects, spin is a good quantum number, and singlet and triplet states never interconvert. This approximation is generally good for organic molecules, where S−T interconversion times are typically long compared to fluorescence lifetimes.20 There are, however, two terms that can mix S and T states in organic systems. The first is spin−orbit coupling (SOC). SOC is a relativistic effect that arises from a coupling between the spin angular momentum of the electron and its orbital motion. It is the dominant mechanism for intersystem crossing in small molecules,20−22 with typical coupling values as large as a few meV. However, SOC decays rapidly with the electron−hole distance, making it insignificant for electron−hole pairs on non-neighboring molecules.23−26 At larger electron−hole distances, S−T transitions are driven by the hyperfine interaction (HFI). HFI arises from interactions between an electron’s spin S and the magnetic nuclei of its molecule, with a Hamiltonian of the form

Figure 2. (a) Zeeman effect of an external magnetic field of strength Bext on the energies of the spin states of a PP. At zero field, all four states are degenerate and can be mixed by HFI; at high field, only S and T0 are mixed. (b) Spin-vector representation of singlet−triplet mixing in a PP. The electron e− and hole h+ spins (black vectors) precess about different total magnetic field vectors and at different Larmor frequencies, resulting in oscillations between various linear combinations of the mutual orientations corresponding to S, T+, T0, and T− depicted in (c).

approximately 4.5 × 10−3 kBT in a relatively strong magnetic field of 1 T, so the Zeeman effect will not appreciably affect the thermodynamic singlet/triplet equilibrium ratio or the RISC activation energy. However, the Zeeman splitting will influence the unitary evolution of states that are coupled by an interaction on the order of EZeeman by changing the oscillation frequencies and amplitudes. In the case of PPs, all four of the S, T+, T0, and T− spin states will be mixed by HHFI at zero field. As the external field increases, the mixing of T+ and T− with S and T0 is decreased at a rate roughly proportional to Bext−2, resulting

nuclei

HHFI = S·[ ∑ aN IN ] N

(2)

where aN is the hyperfine coupling constant of the Nth magnetic nucleus with nuclear spin IN. For small molecules, B

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Figure 3. (a) Experimental and fitted model t-PLMFE of the a 1:1 blend film of m-MTDATA:3TPYMB at zero and high field (0.35 T). Inset: rapid short time decay of ∼60% of PL signal (see discussion in text). (b) ΔPL/PL0 (eq 3) based on the experimental and fitted model transient decays.

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EXPERIMENTAL RESULTS The transient PL MFE (t-PLMFE) for a 1:1 blend film of mMTDATA:3TPYMB is shown in Figure 3a. To better visualize the magnetic field effect over the PL decay, we have also plotted the normalized magnetic field induced change in the transient PL in Figure 3b, which is defined as

in a monotonic decrease in the overall rate of S−T transitions within the PP state. To model HFI from the relatively large number of magnetic nuclei, we employ the model of Schulten and Wolynes.39 Within this semiclassical approximation, the sum over nuclear spins ∑aNIN of eq 2 is replaced with a static, classical “hyperfine field” BHF representing the effective magnetic field experienced by the electron due to HFI with its molecule’s magnetic nuclei. Because it is the sum of a large number of independent nuclear fields, BHF can be reasonably approximated by a Gaussian distribution with a standard deviation, σHF, on the order of 1 mT for most organics.40 The total effective field of the ith polaron spin of the ensemble is then Btot,i = Bext + BHF,i. Observables are calculated by averaging over random samples of BHF fields. The interplay of BHF and Bext can be visualized using the vector representation of spin angular momentum. Each spin precesses at the Larmor frequency (ωi = gμB|Btot,i|/ℏ) about a cone oriented along the total field vector it experiences, as shown in Figure 2b. Within the standard spin-vector model, the pure spin states of S, T+, T0, and T− are represented as drawn in Figure 2c. To remain in one of these mutual orientations, the two spins must precess about the same axis at the same frequency. At zero field, the hyperfine fields experienced by each polaron of a pair are randomly oriented and have different magnitudes. Therefore, the electron and hole precess about different axes and at different frequencies, resulting in timedependent mutual orientations that are (in general) linear combinations of those corresponding to S, T+, T0, and T− (see Figure 2b). At high field (Bext ≫ σHF), Btot,e− and Btot,h+ are effectively parallel, precluding mixing of S, T+, and T−. Only the difference in precession frequencydue to components of BHF,e− and BHF,h+ along Bextcauses oscillations between S and T0. Therefore, pure spin states are more long-lived at high field.

ΔPL/PL0 =

PL(t ; Bext = 0.35 T) − PL(t ; 0) PL(t ; 0)

(3)

Based on the ΔPL/PL0 data, the t-PLMFE of this system can be divided into three time periods: (I) For t ≲ 100 ns, there is little to no MFE. (II) For 100 ns ≲ t ≲ 1 μs the MFE rises and becomes significantly positive. (III) For 5 μs ≲ t ≲ 30 μs the MFE becomes significantly negative. Based on the discussion of S−T transitions in the previous sections, the following explanation suggests itself: (i) During period I, most of the electron−hole pairs remain on near neighbors within the exchange radius. At these close separations, the magnetic field is insufficient to influence the rate of S−T transitions, and there is little or no MFE. (ii) During period II, a large fraction of the surviving electron−hole pairs separate beyond the exchange radius, forming PPs that are initially spin singlet. At these distances, the MFE is significant and suppresses hyperfineinduced mixing with the T+ and T− PP spin states. The decreased mixing in the PP manifold increases the number of PPs that recombine with singlet spin, resulting in increased PL. (iii) During period III, the luminescence comes almost entirely from TADF of long-lived triplet states. In the presence of the field, the number of surviving triplets is reduced (because fewer triplets were formed during the recombination events in period II), resulting in a negative MFE. Some of the PL dynamics can be explained by the classic picture of SOC-induced ISC and RISC within the exciplex states. However, the important point is that the presence of an MFE requires a significant amount of indirect ISC and RISC, where the electron and hole must separate beyond the exchange radius (forming a PP) and geminately recombine on the time scale of the PL. Thus, the electron−hole separation is dynamic. This qualitative picture is further supported by examining the PL decay itself. At times t > 40 ns the PL decay is fit well by a biexponential function, Ipe−t/τp + Ide−t/τd, with two time scales: a “prompt” signal with τp ∼ 1 μs and a “delayed” signal with τd ∼ 20 μs. It is natural to associate the prompt signal with TADF from singlets that never underwent ISC to form triplets (and thus relax to the ground state more quickly), while the delayed signal originates from singlets that underwent ISC to form triplets, followed by RISC to the singlet manifold. The delayed

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EXPERIMENTAL METHODS Optical characterization was performed through the substrate using an inverted microscope (Nikon Ecllipse Ti). The film samples were excited using a 405 nm pulsed 31.25 kHz laser (PicoQuant LDH) focused to 10 mm spot size. Sample emission was collected through the objective and filtered using a 405 nm dichroic and a 450 nm long-pass filter. Time-resolved PL measurements were taken using an avalanche photodiode single-photon detector (PicoQuant PDM). A pair of rare earth magnets were placed around the sample on the microscope setup to achieve magnetic field of ∼0.35 T for high field measurements. C

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Figure 4. Jablonski-type diagram depiction of our theoretical model. The electron and hole are on neighboring donor and acceptor molecules (illustrated as circles) in the exciplex (EXP) configuration and on non-neighboring molecules (separated beyond the exchange radius) in the polaron pair (PP) configuration. The spin-vector representations of Figure 2c are used to depict the spins states within the EXP and PP configurations. The stochastic transitions are indicated by straight arrows and are labeled with the corresponding phenomenological rate constant (fit parameter), while the HFI-induced coherent evolution within the PP configuration is indicated as a cycling.

spatial degrees of freedom are course-grained into the two discrete EXP and PP configurations, the electronic spins of the pair are treated explicitly and evolve according to interactions relevant to the spatial configuration they occupy. To treat both the coherent spin evolution in the PP configuration and the incoherent transitions throughout the model, we used the Lindblad quantum master equation44−46 to solve for the time dependent density matrix ρ of our system:

states then have longer lifetimes because the triplets relax slower and are longer lived, resulting in the larger τd. In the presence of the magnetic field, the prompt PL signal increases in intensity (Ip = 0.40 → Ip,B = 0.43), which suggests that with the field on there are more singlets that relax without ever undergoing ISC to triplets. At the same time, the magnetic field also increases the lifetime (τp = 1.15 μs → τp,B = 1.22 μs), which is also to be expected, as the reduced ISC rate will increase the lifetime of singlet CT states. Meanwhile, the delayed signal has a lower intensity with the field on (Id = 0.019 → Id,B = 0.016), which is again consistent with fewer singlets undergoing ISC to form triplets that would contribute to the delayed signal. The field slows down the delayed signal as well (τd = 21 μs → τd,B = 22 μs), consistent with the reduced RISC rate in the presence of field. We should note that there is a significant drop in the PL signal for t < 10 ns, during which time ∼60% of the initial signal decays away (see inset of Figure 2b). This decay is not magnetic field dependent, and it is not entirely clear what leads to this drop. It also appears to be absent from another transient PL measurement in the literature [see Supplementary Figures 1b, 1c, and 3 of ref 16]. Possible sources include (1) radiative decay of the initial population of exciplexes, which never underwent charge separation and, therefore, never formed a magnetic field sensitive PP; (2) PL decay of overlapping 3TPYMB exciton emission in the range of 450−650 nm [see Figure 6 of ref 16]; and (3) limitations of the instrumental response function.41,42 Because of the uncertainty about this initial signal, we focus our attention on explaining the dynamics for t > 40 ns. The picture above seems qualitatively plausible but lacks any qualitative or predictive power. In the next section, we construct a theoretical model that allows us to quantitatively test this picture and make predictions about the underlying microscopic rates.

dρ i = − [H , ρ] + ℏ dt

⎛

∑ ⎝ΓnρΓ†n − ⎜

n

⎞ 1 1 † {ΓnΓn, ρ}⎟ − {Λ, ρ} ⎠ 2 2 (4)

where {A,B} = AB + BA is the anticommutator. The density matrix ρ of our system is composed of the eight states labeled next to their spin-vector representation in Figure 3 and is given by ρ=

∑ pλEXP |λ EXP⟩⟨λ EXP| + ∑ pλPP |λ PP⟩⟨λ PP| λ

λ

(5)

where λ represents a member of the set of four spin substates {S, T−, T0, T+}. The first term on the right-hand side of eq 4 describes the unitary evolution under the influence of the system Hamiltonian H = HEXP + HPP. Within our model, we assume the relatively large exchange interaction prevents unitary evolution in the EXP manifold; the |λEXP⟩ states are eigenfunctions of the exchange Hamiltonian. Therefore, we can simply take HEXP = 0. The Hamiltonian for HFIs was discussed above within the semiclassical approximation, so the PP states experience a Hamiltonian: gμ HPP = B (Btot,e− ·SePP− + Btot,h+ ·SPP h+ ) (6) ℏ The second term of eq 4 describes the stochastic, incoherent transitions between the states of ρ. For each of the vertical transitions indicated between the states of Figure 4, there is a corresponding Γ operator of the form Γb←a = (kb←a)1/2|b⟩⟨a|. For example, the Γ operator corresponding to the charge separation of SEXP is ΓSPP←SEXP = (kCS)1/2|SPP⟩⟨SEXP|. The final term on the right-hand side of eq 4 describes population decay. In our case, this occurs (mainly) via photon emission from SEXP and nonradiative decay from TEXP. Thus

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THEORETICAL METHODS To lend credence to our proposed set of dynamical processes underlying these three distinct time periods of the t-PLMFE, we developed a simplified model (drawing inspiration from Frankevich and co-workers32,36 and from Kersten and coworkers43) in which an excited electron−hole pair can exist in one of two “spatial” configurations: an exciplex (EXP) configuration or a PP configuration (see Figure 4). While the

Λ = k S|SEXP⟩⟨SEXP| + k T|TEXP⟩⟨TEXP| D

(7)

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• kT = 27 ms−1 [τT = 37 μs]. While we were unable to find a literature estimate for this parameter, this value appears too high to be entirely due to triplet nonradiative recombination, which is spin-forbidden. It is possible that this parameter is artificially high due to compensation for a lack of processes omitted from the model, such as charge or exciplex trap states, for instance. Another possibility is triplet quenching by oxygen contaminants. It as also possible an unexplored set of parameters could yield a similar fit with a smaller kT (and a necessarily higher value for kRISC). • kCS = 720 ms−1 [τCS = 1.4 μs] and kCR = 530 μs−1 [τCR = 1.9 ns]. These values are physically reasonable when considering the energy required for detailed-balance between charge separation and recombination:

The rate constants in this model (kCS, kT, kS, ...) are treated as parameters and used to reproduce the experimental data. To solve eq 4, we write it as a superoperator equation d |ρ) = 4|ρ) dt

(8)

where here ρ is treated as a super vector |ρ) (with 8 × 8 = 64 elements) and 4 is a superoperator (a 64 × 64 matrix). Equation 8 is then solved as |ρ(t )) = e4t |ρ(0))

(9)

using the eigendecomposition of 4 . Finally, to obtain the normalized photoluminescence at time t, we start with the t = 0 density matrix corresponding to a unit population of SEXP states after a pulse: ρ(0) = |S

EXP

⟩⟨S

EXP

|

⎛ E(PP) − E(EXP) ⎞ k CS = exp⎜ − ⎟ ⇒ E(PP) − E(EXP) = 170 meV k CR kBT ⎝ ⎠

(10)

which is comparable to the literature estimate of the same energy gap for poly(1,4-phenylene-1,2-dimethoxyphenylvinylene) (150 meV).36 We note that technically kCS and kCR should have different values for singlets and triplets, but we ignored this fact in order to minimize the number of adjustable parameters. • kISC = 140 ms−1 [τISC = 7.1 μs] and kRISC = 36 ms−1 [τRISC = 28 μs]. These values also yield a physically reasonable energy gap E(SEXP) − E(TEXP) 35 meV, which is comparable to the Poole−Frankel model estimate of 51 meV.48 The results from our theoretical model are shown in in Figure 3. As can be seen from the data, the rate model quantitatively reproduces the experimental results. The model reproduces the distinct behavior of the ΔPL/PL0, yielding an initial latency period followed by a positive MFE and then a negative MFE. The magnitude of the MFE is also well reproduced because the fast kCR rate results in incomplete spin mixing within the PP manifold43 and because some of the ISC and RISC occurs through the field-insensitive, SOC-induced mechanism.

We then evolve the density matrix using eq 9 and evaluate the expectation value for the population of SEXP states, which gives the normalized PL signal: PL(t ) = Tr[|SEXP⟩⟨SEXP|ρ(t )]

(11)

Equation 11 is then averaged over 1000 random pairs of the hyperfine fields, Btot,e− and BHF,h+, sampled from a 3-dimensional Gaussian distribution with σHF = 1 mT, per the above discussion (σHF was not treated as an adjustable parameter). To calculate the PL under the external magnetic field and the ΔPL/PL0 (eq 3), the external field was taken to be oriented along the z-axis (an arbitrary choice, due the randomly oriented hyperfine fields) by setting Bext = 0.35 T ẑ in eq 6. (Note: a more detailed explanation of our model can be found in the Supporting Information.)

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THEORETICAL RESULTS In order to obtain the model parameters, we performed a bruteforce optimization search using a root-mean-square deviation metric, with the calculated ⟨SEXP⟩ scaled by 0.42 to match the experimental PL magnitude at t = 10 ns (i.e., after the ambiguous initial drop discussed above). There are six parameters: (kS, kT, kCS, kCR, kISC, and kRISC). In fitting the data, we found the follow effects of the parameters: kS was very important to fitting the overall decay magnitude without overshooting the prompt and delayed decay rates. kCS and kCR were important for fitting the onset of the MFE because an MFE will only be present once a population of PPs begins to influence the SEXP population. kISC was important for fitting the transition from the prompt and delayed components and the transition from positive to negative MFE. Both kCR and kRISC were important for fitting the magnitude of the MFE, with larger values of kCR decreasing both the positive and negative MFE components and larger values of kRISC decreasing the negative MFE in the vicinity of τRISC = 1/kRISC. kT was important for fitting the delayed lifetime. The final rate constants we arrived at are as follows: • kS = 320 ms−1 [τS = 3.1 μs]. This is a physically reasonable value when compared to the range of fluorescence and radiationless decay rates (∼1−10 μs−1) measured and calculated for various tetracyanobenzene singlet exciplex complexes in PMMA ridged solutions.47 Also, in combination with the values of kCS and kISC, the prompt PL quantum yield Φp = kS/(kS + kCS + kISC) = 27% corresponds well with the literature PL quantum yield of 26%.16

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DISCUSSION These findings have a significant impact on our understanding of how charge recombination occurs in OLEDs. In the simplest picture, charge recombination occurs when two charges diffuse onto near-neighbor molecules, at which point they become bound by Coulomb attraction and cannot escape one another. From this trapped CT state, they either emit (if the spin is a singlet) or recombine nonradiatively (if the spin is triplet). Our results show that this simple model is incorrect. Instead, even while the electron and hole are on near neighbors immediately after photoexcitation, the distance between them continues to thermally fluctuate.49 The separation must routinely exceed the exchange radius of ∼1 nm to generate the observed MFE. But the electron and hole must remain bound, because only geminate recombination is sensitive to the magnetic field. Thus, the separation cannot exceed ∼10 nm; an e−h pair separated by ≥10 nm in a dielectric medium with ε ∼ 2.8 (typical for organic semiconductors) are unbound at room temperature. This picture of dynamically fluctuating bound electron−hole pairs in OLED materials is both physically reasonable and strongly supported by the experimental data and theoretical modeling presented above. It is also possible to use the model fitting results to estimate the amount of RISC that takes place through the PP-mediated E

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The Journal of Physical Chemistry C mechanism (3EXP → 3PP→ 1PP→ 1EXP). The effective rate constant kRISC(PP) for the overall process of going from 3EXP to 1 EXP through the intermediate PP manifold can be obtained from the 3EXP decay rate in a variation of the model used above, in which kS = kT = kISC = kRISC = 0 and the process of charge separation from 1EXP is turned off. Using the fit values of kCS and kCR above, the indirect RISC takes place at a rate of 10 ms−1, yielding a branching ratio of kRISC(PP)/kRISC ∼ 30%. Therefore, a substantial amount of the RISC takes place through the PP-mediated mechanism. This picture has a significant impact on the design principles for OLEDs. First, we note that in these TADF blends the electron−hole pairs look much more like excitons in a traditional inorganic semiconductor. In those materials, the electron−hole pair binding energy is very small (only slightly more than kBT), and the average distance between the electron and hole is very large. Thus, many of the design principles used in creating inorganic LEDs could potentially be translated to the design of TADF-based OLEDs. In addition, it is interesting to speculate whether the same dynamics might be present in intramolecular TADF materials or even traditional OLED systems. A recent transient EPR study indicates that HFIs contribute to ISC/RISC in particular, high-efficiency TADF molecules.29 The authors hypothesized that these molecules possess higher-energy triplet states with large CT character that are nearly degenerate (ΔE < 25 μeV) with the emissive singlet CT and serve as intermediates in the ISC/RISC process. Therefore, it seems plausible that in certain TADF systems intramolecular CT states play a similar roll to the PP states of this study. To maximize energy efficiency, devices are moving more and more toward chromophores with small binding energies.50,51 The work here suggests that as that occurs, one may also see the beneficial effect that more weakly bound excitons will be in equilibrium with PP-like states where singlet−triplet interconversion is facile. The fluctuations in the bound CT distance will thus provide a second, TADF-like mechanism for harvesting energy from bound triplet excitons in which T1 → 3 PP → 1PP → S1.

In the future, it will be interesting to study the morphology dependence of these characteristics. Do these observations persist in a host−guest architecture? In particular, spectroscopic probes of the spatial dynamics, coupled with microscopic models of charge hopping, could give us a much more finegrained picture of how disorder in these materials affects the time scale for recombination.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b07340. Detailed explanation of the theoretical model used in this study (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected], Ph (617) 253-1488 (T.V.V.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by a grant from the US Department of Energy, Basic Energy Sciences (BES ER46474). REFERENCES

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CONCLUSIONS In this work we demonstrate that the electron−hole pair separation in a 1:1 blend film of m-MTDATA:3TPYMB is a dynamic variable, fluctuating on the 1 μs time scale and leading to complex time- and magnetic-field-dependent dynamics in the photoluminescence spectrum. Through careful theoretical modeling of the underlying dynamics, we are able to conclude that approximately 30% of the delayed photoluminescence is due to an indirect mechanism in which the electron and hole of a triplet exciplex separate beyond the exchange radius (∼1 nm) before eventually rejoining one another and emitting light. The implications for this discovery are twofold. First, in designing OLEDs, our results suggest that thinking about CT states as static objects is not appropriate. Rather, they should be seen as dynamically evolving states in which the electron and hole can move between multiple molecules before recombining. Second, the fact that the bond between electron and hole is apparently much weaker in this TADF system than previously assumed suggests that many of the design principles for inorganic LEDs could be useful in generating the next generation of OLED materials. F

DOI: 10.1021/acs.jpcc.5b07340 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.5b07340 J. Phys. Chem. C XXXX, XXX, XXX−XXX