Concentration Quenching Behavior of Thermally Activated Delayed

Article pubs.acs.org/JPCC

Concentration Quenching Behavior of Thermally Activated Delayed Fluorescence in a Solid Film Hyung Suk Kim, So-Ra Park, and Min Chul Suh* Department of Information Display, Kyung Hee University, Seoul 02447, Republic of Korea S Supporting Information *

ABSTRACT: Concentration-dependent photophysical properties were investigated using an approach for more rigorous interpretation through well-defined concentration quenching equations derived from an optical exciton model. These calculations verified that the solid-state selfquenching process of the 1,2,3,5-tetrakis(carbazol-9-yl)-4,6-dicyanobenzne (4CzIPN) emitter in a host matrix is controlled by the Dexter energy transfer model. By extension, we found that the reduction in the radiative singlet decay rate (krS) can be ascribed to the stabilization of excited states. This process may increase the efficiency of intersystem crossing as the doping concentration of 4CzIPN increases in the host material in a solid matrix. Furthermore, the nonradiative triplet decay process (knrT) could be an important consideration for estimating the exact concentration quenching rate constant value and the efficiency of reverse intersystem crossing corresponding to experimental photoluminescence behaviors with the various doping concentrations.

I. INTRODUCTION

It is well known that the concentration quenching mechanism of traditional fluorescence is deeply based on Förster resonance energy transfer due to the large cross-section between the absorption and emission spectra, which means that the deactivation process accounts for the long-range dipole−dipole interactions.10 Some common phosphorescent emitters in neat films also undergo an exciton quenching process based on Förster resonance energy transfer. Kawamura et al.11 elucidated that the deactivation process dampens radiative excitons via a multiple energy-transfer event. Recently, Lee et al.12 clarified the actual mechanism of the concentration quenching of TADF. They reported the triplet excitons are quenched based on electron exchange interactions, as described by a Dexter energytransfer model. Nevertheless, the commonly used TADF material, 4CzIPN, could be distinct from a specific TADF material (e.g., an orthogonal D−A molecular system of xanthone acceptor moieties coupled to different donor units).12 Thus it could reveal a quenching mechanism that involves a considerable emission spectra shift with an increase in doping concentration, indicating that the larger Stokes shift occurs due to the smaller spectral overlapping between the absorption and emission spectra for the lowest energy ICT. This could evince that a nonradiative pathway of a singlet exciton such as intersystem crossing (ISC) or a nonradiative decay process (knrS) is preferred over a radiative process (krS) because of the electronic

Exciton management in organic semiconductors has enabled the achievement of a high performance for organic optoelectronic devices. Of particular note are emissive dopants with thermally activated delayed fluorescence (TADF) utilized in organic lightemitting diodes (OLEDs), which show almost 100% internal quantum efficiency with the help of reverse intersystem crossing (RISC) with a small activation energy (EA).1,2 Intramolecular charge transfer (ICT) attributed to a donor−acceptor (D-A) molecular geometric configuration allows the suppression of spin-dependent, nonradiative decay pathways.3−5 However, excited triplet excitons with relatively long lifetimes in TADF molecules are likely to undergo the exciton quenching process before loss via the radiative pathway, which results in considerable energy loss from a nonradiative deactivation process.6 In an OLED with a TADF dopant, it is pivotal to modulate the behavior of triplet excitons generated with a 75% probability following electrical excitation (the so-called the exciton recombination of injected electrons and holes).7,8 To reduce the nonradiative decay between triplet excitons, a promising host−guest system could be introduced in which the dilution of the TADF dopant in the host material has a wide energy band gap in a solid matrix.9 Optimization of the host−guest is commonly approximated with the fabrication of OLEDs using an evaporation process. Accordingly, this work was motivated by the optimization of an adequate host−guest system through the concentration dependence of photoluminescence in condensed films. © 2017 American Chemical Society

Received: March 13, 2017 Revised: June 8, 2017 Published: June 9, 2017 13986

DOI: 10.1021/acs.jpcc.7b02369 J. Phys. Chem. C 2017, 121, 13986−13997

Article

The Journal of Physical Chemistry C

collected by a PerkinElmer PL spectrophotometer (LS 55 model).

reconfiguration of excited states with increasing doping concentration. This mechanism will be further delineated later in this article. Here, in this work, we tried to clarify the remaining unclear aspects of the concentration quenching process in the common TADF material. As a singlet exciton, the nonradiative triplet decay process (knrT) could be an important consideration for understanding the quenching mechanism in TADF materials. This could be understandable under the kinetic dynamics of the traditional TADF exciton model that depends on the time of the photophysical investigation. On the basis of the aforementioned fundamental equation, the difference between knrT and the concentration quenching rate constant (kCQ) in the equations could explain the exact effective tunneling distance (LET, 2β−1), as described by Dexter energy transfer.13,14

III. THEORY A simplified schematic state diagram of exciton behavior in a TADF material is shown in Figure 2. The system consisting of

II. EXPERIMENTAL SECTION The TADF material, 1,2,3,5-tetrakis(carbazol-9-yl)-4,6-dicyanobenzne (4CzIPN), was measured as a function of concentration of the wide energy gap host, 4,4′-bis(N-carbazolyl)-1,1′-biphenyl (CBP). Each material was purchased from Lumtec and Jilin OLED Material, respectively. The band diagram and molecular structures for the host (CBP) and dopant (4CzIPN) are shown in Figure 1. The selection of CBP as a host confines the 4CzIPN,

Figure 2. Schematic energy-state diagram for 4CzIPN. The rate constant terms between kCQ (concentration quenching process) and knrT (nonradiative triplet decay process) should be understood differently in the CBP-4CzIPN (host−guest) system with strong concentration dependence as R is smaller than LET.

singlet and triplet exciton behaviors can be described with the introduction of a traditional exciton model16−18 comprising time-dependent population rate equations under the assumption that the particles move independently,19 which can be expressed as follows dS1(t ) = −(k rS + k nrS + kISC)S1(t ) + kRISCT1(t ) + G dt

Figure 1. Energy band diagram and molecular structure for CBP and 4CzIPN.

(1)

dT1(t ) T = kISCS1(t ) − (k nr + kRISC)T1(t ) (2) dt where S1(t) and T1(t) are the singlet and triplet exciton densities, kSr , kSnr, and kTnr are the singlet radiative decay, nonradiative singlet decay, and triplet decay rate constants, respectively, kISC and kRISC are the rate constants of ISC and RISC, and G is the rate of singlet exciton generation resulting from photon absorption. In this equation, the optically generated triplet exciton is assumed to be negligible in eq 3. Meanwhile, the prompt PL efficiency (ΦPF) and delayed fluorescence PL efficiency (ΦDF), which are the experimental values, can be described as follows

which effectively transfers photogenerated excitons to 4CzIPN in the host−guest system. To investigate the doping concentration behavior of the TADF material, a series of 4CzIPN-doped CBP films were fabricated from 5 to 100 wt %. The quartz substrate was cleaned by sonication in acetone and isopropyl alcohol and was irradiated in an UV-ozone chamber to eliminate all of the remaining organic impurities during the previous process. Organic materials were deposited using a thermal vacuum evaporation technique under a pressure of ∼5 × 10−7 Torr at deposition rate of ∼0.5 Å/s without breaking vacuum. The film thickness for the photophysical investigation was 10 nm. The index of refraction (n) of the thin film was assumed to be 1.78. The transient photoluminescence (PL) decay characteristics were recorded with a time-correlated single photon counting (TCSPC) method using an LED at 340 nm and a QuantaurusTau fluorescence lifetime measurement system (C11367-03, Hamamatsu Photonics). The prompt and delayed photoluminescence quantum yield (PLQY) were extracted by weighting the total PLQY by the separately integrated prompt and delayed exponential decay component. Total PLQY was calculated using an absolute quantum yield technique.15 The UV−visible absorption spectra were obtained with a UV−visible spectrometer (V-570, JASCO). The absorption spectra in the solution state were obtained in toluene (conc. 1 ×10−5 M). The PL spectra of the solid-state deposited on a quartz substrate were

∞

ΦDF = ΦPF ∑ (ΦISCΦRISC)k

(3)

k=1

ΦPF =

k rS k rS + k nrS + kISC

(4) 2

After combining eqs 1−4 with a series of assumptions, the rate constants for prompt and delayed PL lifetimes, which are the reciprocal of the experimental values (i.e., τPF and τDF), could be estimated as follows2,12,20,21 1 kPF = k rS + k nrS + kISC = τPF (5) 13987


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The Journal of Physical Chemistry C T kDF = k nr + (1 − ΦISC)kRISC =

1 τDF

(6)

kISC

ΦISC =

k rS

+ k nrS + kISC

(7)

kRISC

ΦRISC =

T k nr

+ kRISC

(8)

where ΦISC and ΦRISC are the efficiencies of ISC and RISC. Equations 5 and 6 only hold if the doping concentration is not associated with the self-quenching process. According to Lee et al.,12 the equation connoting the rate of concentration quenching (kCQ) (in eq 2) could be derived from the traditional optical exciton model. k CQ =

1 (kPF + kDF − 2kRISC 2 −

(kPF − kDF)2 − 4kISCkRISC )

(9) Figure 3. (a) Absorption and steady-state PL spectra of 4CzIPN in toluene solution measured at RT. (b) Normalized absorption (dashed line) and steady-state PL spectra (solid line) of 4CzIPN-doped CBP thin film (red) and 4CzIPN neat film (blue) measured at RT. The red solid line and cyan dashed line are the absorption spectra of 4CzIPN in toluene and the CBP neat film, respectively. The inset image shows the cross section between absorption and spectra in the case of 4CzIPN itself and the CBP:4CzIPN system.

12

To avoid a series of prerequisites needed to derive eq 9, the concentration quenching could also be simply expressed starting from the traditional equation20,21 as follows T k CQ = kDF − k nr − (1 − ΦISC)kRISC

(10)

where the efficiency of RISC (ΦRISC ′ ) could be re-established as Φ′RISC =

kRISC T k nr

+ kRISC + k CQ

spectral shift as the solvent polarity increases.21−23 The PL peak shift of 4CzIPN occurred from 507 to 551 nm when toluene was changed to a polar solvent, acetonitrile (conc. 2 × 10−5 M).21 In this experiment, the PL peak of the 4CzIPN diluted in toluene (conc. 1 × 10−5 M) at 514 nm is shown in Figure 3a. This phenomenon is also observed in the case of thin film deposited on a quartz substrate. The PL spectra of doped thin films with 5, 20, 40, 60, 80, and 100 wt % 4CzIPN are shown in Figure 5a. The PL peak shifted from 519 to 546 nm when the doping concentration of 4CzIPN in the host (CBP) solid matrix increased from 5 to 100 (neat) wt %. In the case of PL spectrum of 4CzIPN in a polar solvent, the excited singlet state (S1) could be stabilized by the polar solvent. Consequently, the large dipole moment (ΔμGE = μE − μG) between the ground state (S0) and S1 could be estimated at 17 D (Debye unit),21 which was obtained from the relationship between the Stokes shift values (ν̅A − ν̅F) and the orientation polarizability (Δf) (see eq 13). The large difference between μG and μE implies the existence of ICT between the carbazolyl (electron donating group) and dicyanobenzene (electron accepting group) moiety. These values were calculated using the following equation

(11)

This can be simply calculated by combining eq 3 with eqs 10 and 11, which also could be rearranged as kRISC =

kDFkPF ΦDF kISC ΦPF

(12)

This indicates that kRISC is mathematically unchanged with the addition of kCQ. The derivation of eq 12 is described in the Supporting Information.

IV. RESULTS AND DISCUSSION The absorption and steady-state PL spectra of the 4CzIPNdoped (5 wt %) and neat film, along with 4CzIPN in a toluene solution shown in Figure 3, were used to understand the behavior of the concentration quenching process. The difference between the absorption spectrum of the doped and neat film is mainly due to the existence of host (CBP), which efficiently transfers its energy to the dopant (4CzIPN). Indeed, the absorption spectrum of the doped film is almost similar to that of the neat host film (CBP). The observation of the intrinsic green PL spectrum in the doped thin film is also evidence of an efficient host−guest system. In the case of the neat thin film (4CzIPN), the absorption spectrum is roughly similar to that of 4CzIPN dissolved in toluene, as shown in Figure 3a. The observed absorption spectral shift (a slight red shift) did not occur even though the spectral difference between the doped and neat film was realized, as shown in Figure 3b. Those observed absorption and PL spectra show good agreement with those of a previous report20 dealing with the host (mCP)−guest (4CzIPN) system to elucidate the temperature dependence of PL properties in a TADF. The PL of the TADF molecule with electron donor−acceptor moiety (D-A unit or D-A-D unit) is typically influenced by the solvent polarity, which is well known to cause a significant red

hc(νA̅ − νF̅ ) =

2Δf a3

ΔμGE 2 + const

(13)

where h is Planck’s constant, a is the radius of the cavity where the 4CzIPN resides (i.e., the Onsager cavity radius), and νA̅ and ν̅F are absorption and PL of 4CzIPN in wavenumbers (cm−1). The Lippert equation (eq 13)24,25 provides a useful framework for consideration of the solvent-dependent spectral shift. The ε−1

n2 − 1

term (Δf = 2ε + 1 − 2n2 + 1 ) consists of two terms from the reorientation of the solvent dipoles and the redistribution of the electrons in the solvent molecules, as shown in Figure 4a. Here n is the refractive index and ε is the dielectric constant of the solvent. Strikingly, the structures of 4CzIPN at S0 and S1 did not 13988


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Figure 4. (a) Interactions of 4CzIPN with toluene solvent. This can be understood in terms of the dipole moment of ground (μG), and excited states excited (μE), and the reactive fields around those of dipole moments.35 Eground vertical and Evertical correspond to the energies for ground and nonequilibrium excited states unperturbed by toluene solvent. (b) Situations for ideal CBP-4CzIPN (host−guest) system (left) and the system as the concentration quenching occurs due to the interaction between 4CzIPN itself (right). Förster resonance energy transfer (FRET) from host to guest is only effective in an ideal doping system because RF for the 4CzIPN molecule was calculated to be 0.9 nm. Thus it is ineffective process (FRET (guest to guest)) compared with that of FRET (host to guest). In the concentration quenching process (i.e., the point that LET (2.46 nm) is larger than R), Dexter energy transfer (DET) between 4CzIPN occurs, which also contributes to the nonradiative decay process when the nonradiative triplet decay process (kTnr) is excluded.

efficient energy transfer as the doping concentration increased from 5 to 100 wt %. This was in fairly good agreement with the Förster radii (RF) of 4CzIPN (the critical intermolecular distance) estimated as 0.8 to 0.9 nm and the LET of 2.46 nm corresponding to the effective electron tunneling distance that quantifies the intermolecular electron-exchange interaction (a doping concentration of 10 wt % corresponds to an intermolecular distance of 2.51 nm; see Figure 5b). This could be why the stabilization of excited states (i.e., the spectral shift) and the reduction in the PL intensity occur simultaneously, as shown in Figure 5a. This will be explained with the rate constant in detail later. To calculate the average distance between two dopants (intermolecular distance, R), we used following equation:11 R = [(molecular density in film) × (mol % of the dopant in a film)]−1/3. As the doping concentration increased (i.e., from 5 wt % to a neat film (100 wt %) in the host−guest system), R decreased from 3.27 to 1.03 nm, as shown in Figure 5b. Figure 5c shows the resulting transient PL kinetics for representative concentrations of 4CzIPN diluted in CBP at 300 K (room temperature, RT). The prompt and delayed lifetimes are shown in Figure 5d, which correspond to the data fitted with the transient PL profiles. Interestingly, the prompt lifetime (τPF) was relatively insensitive to the doping concentration until 40 wt

depend on solvent polarity, as calculated from density functional theory (DFT) in a previous report,21 which could suggest that the spectral shift of 4CzIPN with strong ICT could be deeply based on the polarity of the surrounding solvent molecules. On the basis of the results in solution, the red shift of the PL spectrum in the neat film was attributed to the difference in the dipole moment of the surrounding molecules (i.e., the change of CBP to 4CzIPN itself). In this work, the utilization of CBP with a dipole moment of 0 D (cal.)26 as host surrounded by the guest (4CzIPN) with a large dipole moment in solid-state maintained the dipole moment of 4CzIPN in the host−guest system. However, the situation in the solid state is different from that in solution, as shown in Figure 4b. In the case of a film consisting of CBP and 4CzIPN, the stabilization of the excited states of 4CzIPN could be preferred through redistribution of electrons between 4CzIPN molecules (i.e., the interaction between each 4CzIPN molecule with a large dipole moment). This is confirmed by the agreement with the spectral shift shown in Figure 5a as the doping concentration increases from 5 to 100 wt %. In other words, the decrease in the nonpolar CBP composition from the neat film compared with the polar 4CzIPN caused the stabilization of the excited states from the addition of surrounding 4CzIPN. Furthermore, the occurrence of the self-quenching process was evidently larger than that of the 13989


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Figure 5. (a) Steady-state PL profiles with doping concentration. (b) Intermolecular distance (R) with doping concentration. (c) Transient PL decay characteristics of the 4CzIPN with strong concentration dependence. (d) Prompt (inset) and delayed lifetimes for 4CzIPN from film dilution in CBP to a pure film of 4CzIPN.

Figure 6. (a) Prompt and delayed PL efficiency for 4CzIPN versus doping concentration. (b) Rate constant of ISC (kISC) with doping concentration. (c) Rate constant of RISC (kRISC) curves depending on the value of kISC. (d) Rate constant of kTnr(non) and concentration quenching (kCQ(1) and kCQ(2)) from eqs 6, 9, and 10.

prompt emission is deeply based on orbital overlap. The realization of the spatial separation of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) helped TADF to realize a small energy difference between S1 and the lowest triplet state (T1) (ΔEST or EA).27,28 Unfortunately, the small orbital overlap between the HOMO and LUMO prevented the achievement of a high rate constant for kSr according to Fermi’s golden rule (i.e., a trade-off relationship).29 In this context, the stabilization of excited states in the 4CzIPN molecule by the surrounding 4CzIPN molecules may reduce spatial separation between the HOMO−LUMO overlap (ΔEST of 4CzIPN itself) compared with its initial state (5 wt % doped film), which decreases the dipole moment. This

% but decreased with high doping concentration. In the case of the delayed lifetime (τDF), it decreased as the doping concentration increased (i.e., 4.32 to 1.30 μs corresponded to 5 and 100 wt %, respectively). Those inclinations are deeply associated with the transient PL decay characteristics and are distinct, which were the key factors to estimate the prompt (ΦPF) and delayed (ΦDF) PLQY. Figure 6a also shows the strong concentration dependence of the TADF emitter. The ΦPF decreased from 14.9% for a 5 wt % doped film at RT to 3.1% for a neat film at RT, which shows good agreement with previous research.19 Moreover, this photophysical investigation suggests an increase in ISC efficiency (ΦISC) due to a decrease in the radiative singlet decay constant (kSr ). Indeed, the behavior of 13990


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Figure 7. Equations for relevant rate constants to understand the behavior of TADF with concentration quenching effect. The three-level model was utilized to analyze such behavior. *The prerequisite for derivation of kISC(2) and kISC(3) is described in the Supporting Information.

Figure 8. (a) Concentration quenching efficiency for 4CzIPN versus doping concentration. (b) RISC efficiency for 4CzIPN depending on kTnr(non), kCQ (1), and kCQ (2). (c) Summary for the rate constant terms associated with concentration quenching. (d) Rate constants of kTnr(non) and concentration quenching (kCQ (1) and kCQ (2)) of 4CzIPN molecule as functions of average intermolecular distance.

could be explained by a decrease in oscillator strength (f) deeply related to the transition dipole moment.29,30 This electronic stabilization is almost saturated at 60 wt %, which leads to the observed slight change in spectral shift and intensity (see Figures 5a and 6a). The fact that the insertion of a phenyl ring between the electron-donating and electron-accepting units induced a large transition dipole moment30 could also support our aforementioned assertion. Meanwhile, the ΦDF decreases from 62.1% for 5 wt % 4CzIPN at RT to 4.0% for the neat film at RT. This result implies that the reduction in ΦDF with doping concentration is ascribed to the concentration quenching

between excited triplet excitons, which is also an important element to understand the PL profiles (Figure 6a). The kinetic dynamics described in Section III allows us to understand the strong concentration dependence of the TADF mechanism to extract rate constants related to the TADF process. However, there were no guidelines to investigate the photophysical characteristics of strongly interacting molecules with a concentration dependence. Thus we started from the traditional kinetic dynamics applicable to dopants in an efficient host−guest system and revised them as stated in Section III to explain the concentration quenching. All relevant rates for 13991


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Figure 9. Rate constants kTnr(non), kCQ(1), and kCQ(2) as a function of R corresponding to panels a−c, respectively. The dashed lines are fits of the plots using the Dexter model. The value of LET estimated from the fitting is inset in each Figure. Förster radius could be obtained when the value of the rate constant is equal to kRISC, as shown in panels d−f, respectively. The SE is defined as the standard error of the slope.

curves may seem to be similar each other but result in significantly different estimates of LET and the curve for efficiency of concentration quenching (denoted as CQ), as shown in Figure 8a. This implication suggests that the host−guest system with strong concentration dependence could be comprehended in terms of efficiency rather than comparison of rate constant values. In that sense, Figure 8a,b shows appropriate examples for dealing with the former perspective. The establishment of each efficiency follows the following relationships for knrT(non), kCQ(1), and kCQ(2), respectively

process to investigate our assertion are summarized, as shown in Figure 7. As mentioned above, kISC increases with high doping concentration. kISC for 5 wt % doped film was 3.53 × 107 s−1, which matched quite well with previous research,1,19 but the values for over 40 wt % deviated from the initial value, as shown in Figure 6b. Typically, the kISC has been regarded as a fixed rate constant to determine kRISC, which is a key factor to estimate ΔEST from the Arrhenius relationship.31 To investigate the correlation between kISC and kRISC as the doping concentration changes, we first introduced two types of kISC: an unchanged rate constant (at 5 wt %) and kPF(1 − ΦPF), which correspond to kISC(1) and kISC(2), respectively. The value of kISC(2) reflects the fluctuation from the doping concentration dependence. Strikingly, using eq 12, the deviation of kRISC(2) is smaller than kRISC(1) with the criteria of unchanged kRISC(1.13 × 106 s−1). This suggests that considering changes in kISC fusing eq 12 facilitates estimating kRISC, which is insensitive to the dopant concentration, as shown in Figure 6c. In other words, we experimentally found that the assumption that kRISC is impervious to dopant concentration for calculating kCQ is reasonable. Reflecting on the experimental results, the rate constant of concentration quenching (kCQ) was obtained through the introduction of equations such as knrT(non), kCQ(1), and kCQ(2) corresponding to eqs 6, 9, and 10, respectively. Solving for knrT(non) from the traditional optical exciton model suggests the understanding the behavior of the undetermined value equal to kCQ because of the mathematical form of eq 6 is intrinsically similar to eq 10. The utilization of kCQ(1) based on an unchanged kRISC (1.55 × 106 s−1 estimated from kPFkDF at 5 wt %

ΦX =

kX T k nr(non) +

ΦY =

kY kRISC + k CQ

ΦZ =

kRISC

kZ T kRISC + k nr + k CQ

Here X, Y, and Z, and the rate constant is part of the denominator. The different definitions for efficiency are based on the assumptions needed to estimate each rate constant, which shows why the analysis within the framework of efficiency is needed. As explained above, the difference in the efficiency for CQ among a series of rate constant such as knrT(non), kCQ(1), and kCQ(2) is more explicit in Figure 8a, although the dependences of the rate constants on doping concentration in Figure 6d are hard to differentiate each other. An increase in efficiency with high doping concentration (Figure 8a) supports the fact that the concentration quenching is occurring as the intermolecular distance (R) decreases. Specifically, ΦTnr(non), ΦCQ(1), and ΦCQ(2) increased from 16.3, 9.0, and 10.6% for a 20 wt % 4CzIPN doped film to 42.0, 33.4, and 38.4% for the neat film, respectively. Understandably, the decrease in RISC efficiency for knrT(non), kCQ(1), and kCQ(2) while the doping concentration increases was also observed, as shown in Figure 8b

kPF − kISC

corresponding to no concentration quenching)2,12 induced a slight overestimation of kCQ(1) compared with knrT(non) starting at 60 wt %, as shown in Figure 6d (kCQ(1) = 5.88 × 105 s−1, knrT(non) = 5.47 × 105 s−1). As expected, the difference between kCQ(2) and knrT not only showed similar curves to others but also did not overestimate knrT(non). Indeed, those 13992


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Figure 10. (a) ISC (kISC) efficiencies for 4CzIPN with doping concentration. (b) Rate constants of kSr and kSnr for 4CzIPN versus doping concentration. (c) kCQ−R plot as the efficiency of ISC was fixed. The value of LET (inset) fitted from the kCQ(3)−R plot deviated from that of kCQ(2).

kCQ(1), the utilization of kRISC (1.55 × 106 s−1 estimated from kPFkDF at 5 wt %) results in a different RF (0.61 nm), as shown in

(ΦRISC for knrT(non), kCQ(1), and kCQ(2) decreases from 94.8, 96.7, and 94.8% at 5 wt % to 58.1, 66.6, and 58.1% for a neat film). Actually, the overlay of curves between knrT(non) and kCQ(2) is ascribed to its mathematical form (i.e., the term kTnr(non) corresponds to kTnr + kCQ) to elucidate the relationship between concentration quenching and nonradiative triplet decay. The deviation of kCQ(1) compared with knrT(non) and kCQ(2) curves also could be explained with the introduction of RISC efficiency based on different definitions applicable to each system (i.e., ΦX, ΦY, and ΦZ). Strikingly, the rate constant of RISC did not depend on the doping concentration but showed different behavior when the TADF system with concentration dependence was analyzed in terms of efficiency. To summarize, rate constant terms associated with the concentration quenching are shown in Figure 8c. As mentioned above, kRISC might not depend on doping concentration, but its efficiency does. Furthermore, the separation of knrT(non) into knrT and kCQ(2) satisfies the initial condition that kCQ should not exceed the value of knrT(non). The knrT (6.26 × 104 s−1) is constant and unchanged in this exciton model. Figures 8d and 9 strongly support our assertion that knrT(non) should be separated as two components. As depicted, the term kCQ has an exponential dependence on R (see Figure 5b), which is the evidence that the concentration quenching process is based on Dexter energy transfer. The equation could be expressed as follows13,14 k CQ (R ) = kRISCe−2/ LET(R − R 0)

kPF − kISC

Figure 9e. Meanwhile, Förster radius RF also can be calculated by an introduction of Förster theory.32 RF =

6

9ΦPFκ 2 128π 5n 4

JF

(15)

where κ is the dipole orientation factor(κ = 0.845 2/3 corresponds to an amorphous film with randomly oriented, rigid dipoles)33 and JF is the spectral overlap integral between donor PL, f D(υ), and the acceptor absorption, εA(υ), when the value of ∫ f D(υ) dυ is 1.11 From eq 15, RF = 0.89 nm for a neat film is in strikingly good agreement with RF estimated in kCQ−R plots, as shown in Figure 9d−f. Finally, the correlation between kISC and ΔEST should be discussed. The value of ΔEST for a 5 ± 1 wt % doped 4CzIPN in CBP host decreased from 83 to 33 meV (neat film).1,19 This is ascribed to the stabilization of the excited states deeply associated with ΔEST. The large change in the dipole moment of 4CzIPN is due to the change in the surrounding molecules from CBP to 4CzIPN itself. Therefore, the decrease in ΔEST with the doping concentration suggests that the inclination of kISC could be reasonable, which can be expressed as follows34 kISC ∝

(14)

⟨T1|/̂ SOC|S1⟩2 ΔEST 2

(16)

where /̂ SOC corresponds to the spin−orbit coupling (SOC) typically enhanced by singlet−triplet mixing via the heavy atom effect such as phosphorescence. Meanwhile, TADF is based on another concept that ISC is enhanced by an introduction of small ΔEST. Thus eq 16 strongly supports this phenomenon, as mentioned above. To investigate our assertion, we intentionally fixed the ISC efficiency at 85.1% obtained from 5 wt % 4CzIPN doped film system (kISC(1)). Then, kISC(2) was calculated from the experimental data in each host−guest system, as shown in Figure 10a. (The value of ΦISC(2) from 5 wt % to neat film increases from 85.1 to 96.9%, respectively.) The deviation efficiency between those two types of ISC upon changing the concentration quenching results in knrS, as shown in Figure 10b. A turnover point starting with 50 wt % is observed where knrS overrides krS with similar behavior to ΦPF in Figure 6a. Considering all changes in the rate constants in the TADF mechanism to fix the efficiency of ISC, we recalculated variations in LET fitted from kCQ−R plot (Figure 10c, kCQ(3)). As depicted, the value of LET (2.74 nm) slightly deviated from that of kCQ(2) based on kISC(2), which suggests that the increased efficiency of

where R0 is the intermolecular distance and corresponds to RF as aforementioned. Utilizing eq 14, the optimized fit of kCQ−R plots for 4CzIPN films with different terms (i.e., knrT(non), kCQ(1), and kCQ(2)) corresponds to Figure 9a−c, respectively, which show LET values of 3.03, 2.63, and 2.46 nm. According to Menke et al.,19 triplet exciton diffusion based on a Dexter energy-transfer model in a thin film of 4CzIPN has an attenuation coefficient β of 0.08 Å−1, which yields a value of LET of 2.50 nm. Strikingly, the calculation of LET (2.46 nm) fitted from kCQ−R plot [kCQ(2)] agrees with the value of 2β−1. In addition, LET (2.63 nm) obtained from kCQ(1) supported the proper range of LET for 4CzIPN. As expected, the LET (3.03 nm) for knrT(non) shows significant deviation from others, even though it agrees with the Dexter energy-transfer model. In conclusion, knrT (6.26 × 104 s−1) is small value compared with kCQ(2) (1.16 × 105 for 20 wt % to 6.75 × 105 s−1 for neat) but can estimate the effective electron tunneling distance (LET). Under the condition that the CQ and RISC occurred with the same probability, RF can be estimated by following the steps shown in Figure 9d−f. Roughly, the RF is within 0.8 to 0.9 nm with small fluctuations in kRISC. In the case of 13993


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Figure 11. Schematic energy diagrams of the three-level model and four-level model.37 The dissection of energy level between S1 and T1 could shine on the triplet to singlet up conversion mechanism.

locally excited triplet state (3LE or Tn state)37,39−44 including the similar energy level lying T1 has been dealt with.43 Within the Condon approximation (e.g., Fermi’s golden rule expression, first-order perturbation theory), the kRISC with the consideration of direct SOC (i.e., 3CT to 1CT) could also be written as follows42,45−47

ISC with high doping concentration might be a rational approach rather than an increase in knrS. This also could be supported by the fact that knrS is less insensitive to overlap density between the electronic wave functions of the ground state (S0) and the lowest excited singlet state (S1) than krS.27,28 Actually, there is an arbitrariness in the physical constants denoted here because those constants are obtained experimentally from the PL decay measurement. Nevertheless, we would like to emphasize our conclusions that the physical constants are consistent with those of precedent reports.1,19 The scenario we have discussed here may raise a question regarding the existence of different state between S1 (1CT) and T1 (3CT), and some readers may wonder such level is associated with the behavior of TADF with concentration dependence. The three-level model36,37 has been regarded as an adequate system to understand photophysical characteristics of TADF (see Figure 11). Thus the basics of exciton dynamics in TADF emitter could be realized by introduction of three terms (e.g., S0, S1, and T1). This simple model seems to be sufficiently explicable in terms of the lowest energy state according to Kasha’s rule.38 The kinetic dynamics in our paper to understand the behavior of TADF emitter with concentration dependence is also based on these three-level models. Unfortunately, the systematic problem of three-level model could not include the influence on existence of different state energy level in between S1 and T1. The fundamental equation for kRISC in the three-level model depends on the Boltzmann distribution, which could be expressed as follows1,2,20,21,37 kRISC = kISCe−ΔEST / kBT

kRISC =

2π ⌈⟨Ψfinal|/̂ SOC|Ψinitial⟩⌉q2 0 ℏ

∑ ∑ e−E /k T ⌈⟨νfinal, k|νinitial, j⟩⌉2 δ(Einitial,j − Efinal, k) j

j

B

k

(18)

⟨Ψfinal|/̂ SOC|Ψinitial⟩ is the SOC matrix between the initial and final adiabatic electronic states. Reference point (q0) corresponds to the equilibrium geometry of initial state or the crossing point of the two potential energy surfaces. j and k denominate the vibrational state. Z = Σje−βEj is a canonical partition function for vibrational motion in the initial electronic state, which means that the introduction of the Boltzmann factor known as the exponential factor (e−βEj) where thermodynamic β is defined as 1 . ⟨vfinal,k|vinitial,j⟩ denotes the overlap between the vibrational kBT

wave functions (i.e., Franck−Condon integral). Ej (Ek) is the energy level for vibrational level in the initial (final) electronic state. The introduction of delta (δ) function ensures the molecular energy conversation for the nonradiative transition. Actually, this quantum dynamic implies that the state transition between ones with different spin multiplicity is mediated by the SOC component. Thus eq 18 is commonly utilized in phosphorescent materials (see eq 16). However, this type of approximation is insufficient to explain a fast equilibration of the singlet and triplet population (i.e., nonadiabatic) because the electronic SOC matrix elements between 1CT and 3CT are very small.40,42 Thus the proposed mechanism is spin-vibronic coupling between 3CT and 3LE. The role of 3LE (or Tn) in TADF is the mediator to reach the equilibrium between the two lowest triplet states (3CT and 3LE).40,41,43 In the case of 4CzIPN

(17)

where kB is the Boltzmann constant and T is the temperature. Equation 17 was the key for adopting appropriate ΔEST, which was the rational approach to explain the lowest excited singlet and triplet states. However, such approach provides the wrong estimation of ΔEST due to the existence of an additional state lying between S1 and T1.37 Very recently, the importance of the 13994


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The Journal of Physical Chemistry C molecule, the ISC pathway (CTTn → 1CT) coupled by hyperfine coupling (HFC) suggested by Ogiwara et al.44 might be included, as shown in Figure 11. The HFC-induced ISC from the 1CT should require the Tn state with CT character (CTTn), where the energy gap between 1CT and CTTn is

Concentration Quenching Behavior of Thermally Activated Delayed

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