The Triplet–Triplet Annihilation Efficiency of Some 9,10-Substituted Diphenyl Anthracene Variants—A Decisive Analysis from Kinetic Rate Constants

Abstract

Triplet–triplet transfer photochemical reactions are essential in many biological, chemical, and photonic applications. Here, the Pd-octaethylporphyrin sensitizer along with triplet–triplet annihilator (TTA) active 9,10-diphenylantracenes (DPA) and the related substituted variants in low concentrations were examined. A full experimental approach is presented for finding the necessary rate parameters with statistical standard deviation parameters. This was achieved by solving the pertinent non-analytical kinetic differential equation and fitting it to the experimental time-resolved photoluminescence of both slow fluorescence and sensitizer phosphorescence. The efficiency of the triplet–triplet energy transfer rate was found to be around 90% in THF but only around 75% in toluene. This appears to follow from the shorter lifetime of the sensitizer triplet in toluene. Moreover, the TTA transfer rate was on average more than 40% in THF toluene whereas a considerably lower value around 20–30% was found for toluene. This originated in an order of magnitude higher solvent quenching rate using toluene, based on the analysis of the delayed fluorescence decay traces. These are also higher than the statistically expected 1/9 TTA efficiency but in accordance with recent results in the literature, that attributed these high values to an inverse intersystem crossing process. In addition, quantum chemical calculations were carried out to reveal the pertinent excited triplet molecular orbitals of the lowest triplet excited state for a series of substituted DPAs, in comparison with the singlet ground state. Conclusively, these states distribute mainly in an anthracene ring in all compounds being in the range 1.64–1.65 eV above the ground state. The TTA efficiency was found to vary depending on the DPA annihilator substitution scheme and found to be smaller in THF. This is likely because the molecular framework over which the T1 excited molecular orbitals distribute is less sensitive for a longer lifetime of the annihilator triplet state.

1. Introduction

Photon upconversion (UC) via triplet–triplet annihilation (TTA) is a well-established phenomenon used in many applications ranging from photochemistry to modern photonics. Here, an excited sensitizer triplet state transfers its excess energy and excites a receiving triplet state of another molecular type, the annihilator. Concomitantly, two triplets of the latter kind undergo a recombination reaction ultimately rendering one of the annihilators into a ‘doubly excited’ singlet state, finally giving off an emitted photon of a substantially higher energy than those of the individual participating triplet states [1]. In this context, variants of anthracene are being used as an archetype molecular system because of their efficient singlet emission in combination with triplet states readily excited via bimolecular reactions. To facilitate solubility and fine-tune the molecular mechanisms behind the TTA process, a vast number of 9,10-disubstituted anthracene systems have been reported on, e.g., [2,3,4,5], notably also oligomers and dendrimers [6,7,8,9]. Applications of TTA in photochemical transformations and used as nanoparticles and clusters were recently reviewed [10,11]. Other applications involve organic light emitting devices. Although red and green devices are found to have high efficiencies, blue OLED perform poorly in comparison and require more research to improve [12,13]. In order to assess the TTA processes in various systems, many types of advanced spectroscopic methods are needed, from the excitation of suitable sensitizers and their triplet energy transfer to the annihilator, to the annihilation processes resulting in the upconverted excited state utilized for the application. The analyses of the photophysical processes are usually based on steady-state photoluminescence and transient absorption spectroscopy, or combinations thereof, e.g., [2,4,7,13,14,15].

Recently, we reported on a non-approximative approach to calculate the overall kinetics of the TTA UC process by independently and directly measuring the certain rate-depended kinetical steps of the complex chain of photophysical reactions leading to TTA [5]. Notably, the triplet energy transfer rate (k_TET) along with the natural quenching of the sensitizer together manifest the source term for the created annihilator triplets. From these auxiliary data, the TTA rate (k_TTA), along with the natural annihilator quenching rate, could be uniquely determined from a line-shape analysis of the delayed fluorescence, using an exponential decay function for the k_TET process as a source term. Taken together, this is a straight-forward technique to assess the efficiency/yield of different steps in the complicated bimolecular processes. By directly measuring the k_TET rate from the phosphorescence quenching upon annihilator titration, it is not necessary to perform the tedious spectral Stern–Volmer analysis with relatively high annihilator concentrations leading to parasitic aggregation and inner filter effects [14].

The experimental rate approach is here demonstrated and applied to compare some substituted variants of 9,10-DPA [16,17,18] (see Figure 1) in two solvents, toluene and THF, using Palladium(II)-2,3,7,8,12,13,17,18-octaethyl-21H,23H-porphyrin (PdOEP) as a sensitizer. We put special emphasis on also estimating errors of the fitted parameters to see how the measured parameters impact on the calculated overall slow fluorescence efficiency, including their uncertainties. The experimental data of the various substituted DPA variants were compared with the results of quantum chemical calculations of participating singlet and triplet states to shed further light on the basic molecular processes governing the TTA efficiency in substituted anthracene related systems. Our results are in good agreement with results recently outlined by Miyashita et al. [14] who reported on diphenylanthracene substituted in 9,10-, 1,5-, and 2,6-positions, shedding light on the role of the larger-than-expected spin-statistical factor via high-level reversed intersystem crossing.

2. Materials and Methods

9,10-Diphenylanthracene (DPA), manufactured by Tokyo Chemical Industry Co., Ltd. (Tokyo Japan), was purified by sublimation. 9-[4-(10-Phenyl-9-anthracenyl)phenyl]-9H-carbazole (CzPA), 7-[4-(10-phenyl-9-anthryl)phenyl]-7H-dibenzo[c,g]carbazole (cgDBCzPA), 7-(9,10-diphenyl-2-anthryl)benzo[a]anthracene (2aBAPA-02), and 9-(2-naphthyl)-10-[4-(2-naphthyl)phenyl]anthracene (αN-βNPA) were synthesized [16,17,18,19] and purified by sublimation. These compounds each had a purity higher than or equal to 99.9 % in high performance liquid chromatography (HPLC). Palladium(II)-2,3,7,8,12,13,17,18-octaethyl-21H,23H-porphyrin (PdOEP), manufactured by Sigma-Aldrich Co. LLC (St. Louis, MO, USA), was used.

Measurements were performed with 10 mm quartz cuvettes (Hellma Precision) with a Teflon cap allowing for gas purging using syringe needles. Toluene solutions and THF solutions of these five kinds of anthracene compounds and PdOEP were mixed to have predetermined concentrations, and then their absorption and emission spectra and emission lifetimes were measured. Oxygen was purged out from the sample with argon gas. See ref. [5] and Section 3.2.3 for more technical details of the experimental approaches and equipment used.

The anthracene compounds were investigated by employing quantum chemical calculations (Gaussian 16 Rev. C.02, Gaussian, Inc., Wallingford, CT, USA) based on the density functional theory (DFT) with the aim to find the most stable structures in the singlet ground state (S0) and the lowest triplet excited state (T1). The functional B3LYP was used with a 6-311G basis function applied to all atoms. In addition, to improve calculation accuracy, the p- and d-functions as polarization basis sets were added to hydrogen atoms and other atoms, respectively. A vibration analysis was carried out on each structure to obtain the zero-point vibration corrected energy difference from the most stable structures of the S0 and T1 states (0-0 bands). The excitation energies of 2aBAPA-02 from optimized S0 levels to T1 and T2 levels were calculated using time-dependent density-functional theory (TD-DFT, b3lyp/6-311g(d,p)).

Steady state absorption spectra were recorded using an UV-1601PC spectrophotometer (Shimadzu, Japan). Steady state photoluminescence measurements were carried out employing a PTI Quantamaster 8075-22 (Horiba Scientific, Grabels, France) equipped with Double Mono 300 spectrometer chambers for both excitation and emission. A Hamamatsu R928 PMT (Hamamatsu, Japan) was used for detection in the range 185–950 nm. A OB-75X (75W Xenon arc lamp, Horiba Scientific, France) was used as the light source. For the excitation scan of PdOEP in THF and toluene, a long-pass FGL590S filter (Thorlabs, Newton, NJ, USA) was used to block the 2nd order scatter of the gratings. The data acquisition and basic data-handling of steady state luminescence data were carried out with the Felix Data Analysis software (Felix GX 4.9.0.10216) and further processed and presented using Origin Pro (9.7.0.188).

Time-correlated single photon counting (TC SPC) decays were recorded using an IBH TCSPC spectrometer system with a 1–32 nm resolved emission monochromator (5000 M, Glasgow, UK). The system was equipped with an IBH TBX-04D picosecond photon detection module and the sample was excited using an IBH LED operating at 373 nm. The measured decay trace was analyzed using deconvolution fitting with the IBH Data Station v 2.1 software.

Transient Delayed Fluorescence Experiments were carried out using a tunable OPO laser, NT342A-SH-10WW (Ekspla, Vilnius, Lithuania), for excitation. Typically, pulses of energy 15–20 mJ with a 6 ns duration were used, hitting the center of a 1 cm path cuvette containing the sample. At right angles with respect to the laser beam, on opposite sides of the cuvette, two optical fibers were collecting the luminescence generated by the laser. The first fiber guided the signal to a Hamamatsu Photonic Multichannel analyzer (Model C10029-01, Hamamatsu, Japan), triggered by the laser. A Digital Delay generator Model DG 545 (Stanford Research Systems, Sunnyvale, CA, USA), also triggered by the laser, was used to set the delay and gate width and record a full spectrum in one laser flash. The output end of the second fiber was connected to the input port of a prism monochromator (M4 QIII, Carl Zeiss, Jena, Germany), used for monitoring the kinetics of the generated species at selected wavelengths, using a R928 PMT (Hamamatsu, Japan) at the exit port. The voltage signal developed by the current from the PMT over a 1K resistance was measured, averaged 128 times and stored by an Infinium 600 MHz oscilloscope (Agilent, Santa Clara, CA, USA), later used for fitting measured kinetics to model functions.

3. Results

The presentation of the results is divided into several subsections. Firstly, the molecular structures and basic photophysical properties of the DPA variants are presented. Then, we give an overview of the processes involved in delayed fluorescence phenomenon by employing time-gated/time-delayed spectra. Thereafter, it is presented how the various triplet-energy transfer processes were measured and fitted from time-resolved decay measurements of the different luminescence channels. For the details, the CzDPA annihilator molecule is chosen. The efficiency of the triplet transfer from the sensitizer along with the delayed fluorescence is determined from the measured rate constants. Finally, quantum chemical calculations were used to calculate the important T1 states for the various molecules for further discussions of the overall results.

3.1. Substituted DPA Structures and Basic Photophysical Characterization

3.1.1. Molecular Structures

The molecular structures of the annihilators are depicted in Figure 1. They all hold resemblance to the 9,10-DPA moiety through asymmetric substitutions of extended aromatic systems in the 9- and/or 10-position of anthracene. CzPA and cgDBCzPA both are based on a single carbazole skeleton unit attached via the nitrogen atom. The larger variant has the benzo groups replaced by more conjugated naphthalene units.

In αN-βNPA, both the 9- and 10-positions are substituted with a naphthalene and a phenyl-naphthalene moiety. In 2aBAPA-02, the 7-position of benzo[a]anthracene is substituted by the 2-position of anthracene. In view of understanding the details of the TTA results, the triplet states of the various molecules were further investigated using quantum chemical calculations to be discussed in Section 3.3 after presenting the experimental results.

3.1.2. Basic Absorption and Emission Properties

The basic absorption and emission spectra of the five studied annihilator molecules in toluene are shown in Figure 2.

The integrated emission was plotted vs. the absorption at 370 nm to obtain the corresponding quantum efficiency following the procedure of Rurak et al. [20]; see Figure S1 for the representative slope plots. As shown in Figure 2, the absorption spectrum of all compounds has a close resemblance to the 9,10-DPA molecule with its characteristic vibrational substructure. This also means that the π-conjugation into the substituents is small, as can also be anticipated from the steric hindrance of the attached aromatic groups, keeping the plane of the planar aromatic structures at a substantial angle, to be presented more in detail in Section 3.3.

In the absorption spectrum of DPA, the peaks around 360 nm, 380 nm, and 400 nm are characteristic to an anthracene ring. In the absorption spectrum of cgDBCzPA, the peaks around 330 nm to 370 nm seem to be attributed not only to an anthracene ring but also to a dibenzo[c,g]carbazole ring. The absorption spectrum of 2aBAPA-02 is slightly broader than those of the other anthracene compounds, and the peaks approximately from 330 nm to 380 nm seem to be attributed not only to an anthracene ring but also to a benzo[a]anthracene ring. For larger substituents, such as for 2aBAPA-02, there is actually a more extensive and electron rich aromatic moiety, showing up as a slight red shift of the emission. However, the photoactivity of the ground state and lowest excited state are expected to be similar for the various structures dominated by the anthracene unit. The well-known absorption spectra and phosphorescence emission of the PdOEP sensitizer [21] in the two solvents used, THF and toluene, are shown in Figure S2. The Q-band at 546 nm is used to activate the sensitizer triplets utilized in the TTA process, to be discussed more below.

The time-correlated single photon counting (TC SPC) traces representing the time-dependent fluorescence of the lowest singlet state of the DPA variants are shown in Figure 3 and the fitted parameters are summarized in

Table 1. A summary of the basic photophysical parameters of the five DPA variants in toluene and THF.

Compound	1 Decay Time (ns)	2 QY (Toluene)	2 QY (THF)
DPA	6.62 ± 0.034	0.93 ± 0.054	0.94 ± 0.06
CzPA	5.07 ± 0.026	0.89 ± 0.051	0.96 ± 0.13
cgDBCzPA	4.77 ± 0.029	0.84 ± 0.059	0.83 ± 0.11
2aBAPA-02	6.92 ± 0.033	0.71 ± 0.042	0.78 ± 0.06
αN-βNPA	3.67 ± 0.027	0.73 ± 0.043	0.75± 0.07

¹ Excitation at 373 nm in toluene. ² For the excitation at 370 nm, for QY plots, see Figure S1A,B.

.

3.2. Delayed Fluorescence

To facilitate the discussion of the delayed fluorescence results, the essential kinetic equations are briefly reviewed. The principle for the triplet–triplet annihilation process is outlined in Scheme 1 and Equations (1) and (2).

The process starts with the excitation of a sensitizer (here, PdOEP) that has a long-lived excited triplet state $S_T^{*}$, with kinetics following Equation (1) below, as follows:

$${\displaystyle \frac{d\left[S_T^{*}\right]}{dt}}=-\left(k_{3S}+k_{TET}\left[A_S^0\right]+k_{SO}\left[O_2\right]\right)\left[S_T^{*}\right].$$

(1)

Here, k_3S is the natural solvent quenching rate in the absence of external quenchers, the term including k_TET is the energy transfer rate (per mol annihilator in the solvent) of the triplets from the sensitizer to the annihilator singlet ground state $A_S^0$, whereas the rate k_SO is the quenching by oxygen (if present). As oxygen is an efficient triplet quencher, it is usually purged from the system of interest, so this can be set to zero. As shown previously, the fate of the excited annihilator triplet ($A_T^{*}$) follows a 2nd order differential equation:

$${\displaystyle \frac{d\left[A_T^{*}\right]}{dt}}={K·k}_{TET}\left[A_S^0\right]e^{-\left({k_{3S}+k}_{TET}\left[A_S^0\right]\right)·t}-k_{3A}\left[A_T^{*}\right]-2k_{TTA}{\left[A_T^{*}\right]}^2.$$

(2)

The left side is describing the change of the annihilator triplet concentration as governed by a source term including $A_S^0$ and k_TET, having a positive sign, along with the losses in terms of natural solvent quenching rate (k_3A) and the consumption via the TTA process (2·k_TTA) giving rise to the delayed fluorescence. The factor 2 arises since two excited triplets are consumed in each annihilation event. Here, it has been assumed that no dissolved oxygen is present that can quench the annihilator triplet, so the term $-k_{SO}\left[O_2\right]\left[A_T^{*}\right]$ has been omitted for simplicity. Equation (1) is readily solved analytically from the decay profile of the sensitizer phosphorescence and gives the important parameters k_TET and k_3S of the source term in Equation (2), along with an apparatus constant K containing laser power, detection sensitivity, etc. See ref [5] and Supplementary Materials S2 for more detailed discussions of how to numerically solve Equation (2). It is also emphasized that a similar approach (Equations (1) and (2)) can be applied for the analysis of singlet oxygen kinetics from the triplet–triplet energy transfer from chlorin photosensitizers in biomedical applications [22].

3.2.1. Time-Gated Measurements of Delayed Fluorescence

The processes involved in the TTA and concomitant delayed fluorescence are nicely visualized, making a time-gated emission recording, where the time-gate can be delayed. Such spectral responses are plotted in Figure 4 where the CzPA annihilator was used with the widely used PdOEP sensitizer. At the low annihilator loading (Figure 4A), one can observe the distinct scatter from the ns excitation laser pulse operating at 546 nm (green ‘sc’) used to excite PdOEP in the dominating Q-band along with the phosphorescence of the sensitizer around 670 nm (red ‘ph’) and some weak delayed fluorescence around 440 nm (blue ‘df’). The occurrence of the latter two is due to the gate width of 10 μs, long enough for the triplet exchange mechanisms to start operating, generating delayed fluorescence. As the time-gate is delayed, there is first a gradual increase of delayed fluorescence to reach a maximum in the range 20–40 μs and then it slowly decays out. Similarly, the exponential decay of the sensitizer triplet phosphorescence can also be discerned at the first time points. Clearly, the increase in delayed fluorescence follows the decay of the sensitizer triplets in terms of its phosphorescence, implying the triplet energy transfer of Equation (1).

Turning to Figure 4B, the very same settings are used but here the annihilator concentration of the sample has been increased by approximately four times, resulting in more delayed fluorescence that builds up faster and peaks around 20 μs, together with a faster decay of the sensitizer triplet. It is noteworthy that the intensity of the delayed fluorescence has also increased approximately by a factor of four, as determined by the kinetic relations in Equations (1) and (2) where the number of excited annihilator triplets are proportional to [$A_S^0$] in the source term. This holds as long as the system is not depleted of annihilators and sensitizers.

3.2.2. Quantifying the Triplet Energy Transfer Rate, k_TET

The processes involved in the TTA and the delayed fluorescence are described by Equation (2). The delayed fluorescence emitted is proportional to the term ${\left[A_T^{*}\right]}^2$, scaled by the quantum efficiency of the annihilator singlet state. Thus, the time profiles of the delayed blue fluorescence in Figure 4 contains four kinetic rate constants k_3S, k_TET, k_3A, and k_TTA; however, it is difficult to fit all these unambiguously from the corresponding slow fluorescence line-shape. On the other hand, the rate constant k_TET along with $k_{3S}$ are also decisive for the time profile of the phosphorescence decay (red label ‘ph’ in Figure 4A). Thus, it is mathematically more stable to first determine the k_TET and $k_{3S}$ rates from the phosphorescence (Equation (1)) and then use these as fixed parameters in the fitting of the other parameters of the delayed fluorescence in Equation (2), as seen in ref. [5]. Such phosphorescence time-profiles are shown in Figure 5A for CzPA/PdOEP. Here, the phosphorescence was collected into a light guide and directed through a spectrometer before detection using a rapid conventional PMT.

Such decays are readily fitted to a single exponential decay giving the apparent rate constant for each concentration of the annihilator. The apparent rate constant is then plotted against the annihilator concentration giving the plot shown in Figure 5B. We note that this gives a straight line which is in accordance with the general Stern–Volmer relation:

$${\displaystyle \frac{{\tau }_0}{\tau }}=1+k_Q{\tau }_0\left[Q\right],$$

(3)

where ${\tau }_0$ here is the phosphorescence lifetime in the absence of the quencher, $\tau$ is the lifetime with the quencher and $\left[Q\right]$ is the quencher concentration. In our case, the annihilator is the quencher (Equation (1)) and substituting $\tau =1/k_{meas}$ for the measured decay rate constants and similarly for the other rates gives the following:

$$k_{meas}=k_0+k_{TET}\left[A_S^0\right],$$

(4)

where $k_0$ is the quenching rate in the absence of the annihilator (and other external quenchers such as oxygen) in accordance with Equations (1) and (2). Thus, from fitting the straight line in Figure 5B, the k_TET is obtained directly along with the quenching rate for the case with no annihilator present ($k_{3S}$). Representative plots are shown in Figure 6 using THF as the solvent. Here, we have included also DPA in toluene to compare the difference between THF and toluene. For the substituted variants it can be seen that there is a significant difference with less steep slopes i.e., the k_TET rate is slightly lower in the pertinent compounds. The fits of the additional DPA variants in toluene are shown in Figure S3. Quenching rates for all the DPA variants using two solvents, toluene and THF, are summarized in

Table 2. A summary of the fitted triplet energy transfer rate k_TET for the DPA variants along with fitted parameters for the delayed fluorescence: k_3A and K·k_TTA. Toluene was used as the solvent with 10 μM PdOEP as the sensitizer.

Compound	1 kTET (109 s−1M−1)	k3A (s−1)	2 K·kTTA (s−1)
DPA	1.53 ± 0.016	16,000 ± 3100	12,000 ± 1900
CzPA	1.28 ± 0.060	16,400 ± 1000	13,200 ± 2500
cgDBCzPA	1.44 ± 0.047	26,300 ± 2800	11,900 ± 3900
2aBAPA-02	1.47 ± 0.060	12,400 ± 1000	12,400 ± 1500
αN-βNPA	1.39 ± 0.095	17,100 ± 3500	6110 ± 840

¹ Excitation 546 nm, data collected at 663 nm. The average of the natural solvent quenching k_3S was found to be 35,400 ± 4700 s⁻¹. For fits of Stern–Volmer plots, see Figure S3. ^2. The average and s.d. of parameters from 3–4 fittings of different concentrations of annihilators in the range 20–80 μM.

and

Table 3. A summary of the fitted triplet energy transfer rate k_TET for the DPA variants along with fitted parameters for the delayed fluorescence: k_3A and K·k_TTA. THF was used as the solvent with 10 μM PdOEP as the sensitizer.

Compound	1 kTET (109 s−1M−1)	k3A (s−1)	2 K·kTTA (s−1)
DPA	1.64 ± 0.043	1240 ± 330	6110 ± 170
CzPA	1.52 ± 0.087	1450 ± 2.8	3320 ± 470
cgDBCzPA	1.36 ± 0.043	1380 ± 290	4250 ±410
2aBAPA-02	1.51 ± 0.045	1730 ± 130	3720 ± 420
αN-βNPA	1.34 ± 0.051	1590 ± 520	3400 ± 310

¹ Excitation 546 nm, data collected at 663 nm. The average of the natural solvent quenching k_3S was found to be 15,300 ± 1300 s⁻¹. ^2. The average and s.d. of the parameters from fittings of 40 and 80 μM annihilator concentrations.

, respectively, and used further as inputs to fit the parameter set for the delayed fluorescence time-profile described further below.

3.2.3. Quantifying the TTA Rate and the Natural Quenching of the Annihilator

Knowing all the parameters of the source term in Equation (1) from the fitting of the well-defined k_TET and k_3S of the Stern–Volmer expression (Equation (4)) and the annihilator concentration of the sample, the recording of the delayed fluorescence time-profiles such as in Figure 4 are readily analyzed [5]. Also here, the emitted fluorescence at the emission maximum was guided into a lightguide through a spectrometer to a fast PMT, recorded by a transient digital oscilloscope. Such time-profile traces are shown in Figure 7 for the CzPA/PdOEP system with five different annihilator concentrations using identical settings for the excitation source and the PMT amplification, time constants of the detector, etc. It is noteworthy that at high loadings there is a large spectral overlap between the absorption spectrum of the annihilator and the emission spectrum of the delayed fluorescence due to the small Stokes’ shift, as seen in Figure S4. Thus, by monitoring the time-dependent slow fluorescence at 425–430 nm at moderate annihilator loadings, these effects are minimized compared to attempting to analyze the full spectral emission for the TTA yield as discussed with some detail by Miyashita et al. [14]. In addition, the inner filter effects the high concentration of the annihilator and also deteriorates the fluorescence quantum yield and must be compensated for [14].

The plots in Figure 7 are shown together with fits of K, k_3A, and k_TTA from the temporal line-shape, fixing the remaining parameters of the source term from the Stern–Volmer analysis (k_3S and k_TET in Table 2 and Table 3) along with the known annihilator concentration of the sample $\left[A_0^S\right]$. Note that the product K·k_TTA gives the apparent TTA rate as discussed in ref. [5] as the pre-factor K has the dimension [mol]. In Table 2, K is set to unity to obtain the resulting physical TTA rate per mol annihilator triplet compared to the natural quenching rate of the annihilator. The error analysis of k_3A and k_TTA is based on the average and pertinent s.d. of measurements of the delayed fluorescence at various concentrations of the annihilator. The relative values of the natural solvent quenching (k_3A) and delayed fluorescence decay (k_TTA) rates are essential for determining the TTA efficiency of the annihilator, to be more discussed below.

Following a similar procedure as outlined above using toluene as the solvent, all solutes were examined using THF, but we limited the analysis to two concentrations, 40 and 80 μM of annihilator loading. Representative data for 80 μM are shown in Figure 8 (parameters such as laser power, time constant, PMT gain, etc. were held the same for each sample) and the fitted parameters are collected in Table 3, in a similar way as for toluene in Table 2. Another set of data was obtained using a 40 μM loading of the annihilators (Figure S5).

3.2.4. The Overall Efficiency of the TET and TTA Processes

The efficiency of the overall upconversion process (${\mathsf{\Phi }}_{UC}$) is usually described by the collective impact of the various processes, summarized as follows:

$${\mathsf{\Phi }}_{UC}={\mathsf{\Phi }}_{ISC}{\mathsf{\Phi }}_{TET}{\mathsf{\Phi }}_{TTA}{\mathsf{\Phi }}_{FL},$$

(5)

where ${\mathsf{\Phi }}_{ISC}$ is the intersystem crossing efficiency of the sensitizer, ${\mathsf{\Phi }}_{TET}$ is the efficiency of the triplet energy transfer from the sensitizer to the annihilator, ${\mathsf{\Phi }}_{TTA}$ is the efficiency of the recombination process between excited annihilator triplets, and finally ${\mathsf{\Phi }}_{FL}$ is the quantum efficiency of the annihilator from its recombined excited singlet state. Added to these, there is also a spin statistical factor contained in ${\mathsf{\Phi }}_{TTA}$, limiting the possible number of excited annihilator singlets from the combined annihilator excited triplets. Strictly, this is 1/9 for a ‘frozen’ spin system, but it is well known to be exceeded in many systems operating at room temperature and in diffusion-controlled liquid systems [5,14,15], to be discussed more below. Here, it is focused on the comparison of the efficiency of the various annihilators. Hereby, we omit the ${\mathsf{\Phi }}_{ISC}$ contribution by using the very same PdOEP sensitizer at a fixed (and low) concentration and by keeping the laser power at a constant value in all measurements.

As outlined in our previous study, the detailed kinetic theory was outlined [5] and it was shown how the ${\mathsf{\Phi }}_{TET}$ fractional efficiency of Equation (5) could be quantified from the following:

$${\mathsf{\Phi }}_{TET}={\displaystyle \frac{k_{TET}\left[A_S^0\right]}{k_{3S}+k_{TET}\left[A_S^0\right]}}$$

(6)

Notably, as k_TET is a 2nd order rate constant (unit s⁻¹M⁻¹), this efficiency is dependent on the concentration of available annihilator singlets in the ground state, $A_S^0$ (and experimentally also on the power of the excitation source and sensitizer concentration via Equation (2)). Similarly, the efficiency of the TTA process can be calculated from a similar expression [5]:

$${\mathsf{\Phi }}_{TTA}={\displaystyle \frac{K·k_{TTA}}{k_{3A}+2K·k_{TTA}}}$$

(7)

where K, k_TTA, and k_3A are obtained from the fitted time trace of the slow fluorescence (see e.g., Figure 6 and Figure 7). Setting the concentration fixed to 80 μM, representative of the high concentration used, the efficiencies summarized in

Table 4. The efficiency of the triplet energy transfer and triplet–triplet annihilation of the five DPA variants in toluene for the 80 μM concentration of the annihilator.

Compound	ΦTET	ΦTTA	ΦTET·ΦTTA
DPA	0.776 ± 0.023	0.300 ± 0.025	0.233 ± 0.021
CzPA	0.743 ± 0.025	0.308 ± 0.013	0.229 ± 0.013
cgDBCzPA	0.765 ± 0.009	0.238 ± 0.024	0.182 ± 0.020
2aBAPA-02	0.769 ± 0.024	0.333 ± 0.011	0.256± 0.012
αN-βNPA	0.759 ± 0.009	0.208 ± 0.026	0.158± 0.021

and

Table 5. The efficiency of the triplet energy transfer and triplet–triplet annihilation of the five DPA variants in THF for the 80 μM concentration of the annihilator.

Compound	ΦTET	ΦTTA	ΦTET·ΦTTA
DPA	0.896 ± 0.008	0.454 ± 0.011	0.407 ± 0.011
CzPA	0.888 ± 0.008	0.410 ± 0.005	0.364 ± 0.006
cgDBCzPA	0.877 ± 0.009	0.430 ± 0.013	0.377 ± 0.012
2aBAPA-02	0.888 ± 0.008	0.406 ± 0.007	0.360± 0.007
αN-βNPA	0.875 ± 0.009	0.405 ± 0.025	0.354± 0.022

can be calculated from the experimental values summarized in Table 2 and Table 3, for respective solvents.

3.3. Quantum Chemical Calculations of the Triplet Levels and Molecular Orbitals

Density functional theory (DFT) was used to calculate the S0 and T1 optimized structures of DPAs. The vibrations of the structures were analyzed and used to calculate the T1 levels from the S0-T1 zero-point energy gaps. The calculations revealed that the lowest T1 levels of 9,10-DPA, CzPA, cgDBCzPA, and αN-βNPA are each 1.65 eV and the T1 level of 2aBAPA-02 is 1.64 eV; that is, all the values calculated here are very similar. 2aBAPA-02, which has an anthracene ring with three substituents, is a special case because it can have two stable triplet structures (T1 and T2) with different triplet spin distributions. The situation is depicted in Figure 9 along with spin density distributions for the two cases. One such state was found to have a T2 level at the benzo[a]anthracene ring (1.90 eV) relatively close to the state localized to the anthracene ring (1.64 eV). In addition, we calculated the excitation energy of 2aBAPA-02 from the S0 optimized structure to T1 and T2 by TD-DFT. The calculated values and T1 and T2 spin density distributions are shown in Supplementary Figure S6. T1 and T2 spins are mainly distributed in the area similar to that in Figure 9. ΔE was 0.29 eV, which was slightly widened but is still of a similar small magnitude as that in Figure 9. This also indicates that the triplet level of the benzo[a]anthracene ring is close to that of the anthracene ring. Thus, not only the anthracene ring but also the benzo[a]anthracene ring may be capable of participating in the triplet-exchange processes.

In addition, when the T1 level of 2aBAPA-02 is close to 1.76 eV, its T2 level is estimated to be higher than the T1 level by approximately 0.26 eV. This suggests that the T1 level of PdOEP (1.87 eV [23]) is lower than the T2 level of 2aBAPA-02, and in this case, the energy transfer from PdOEP to 2aBAPA-02 is considered to be energetically unfavored. However, in the previous research [23], even when the T1 level of a sensitizer is lower than the T1 level of the annihilator, TTA is observed while the TTA probability is lowered. The previous research suggests that the interaction between the sensitizer and the annihilator may be involved in the TTA mechanism.

The most stable structures and spin density distributions of all remaining compounds in the T1 state are similar to the spin density of 2a-BAPA-02 with T1 located in the anthracene unit (Figure 9) and are all shown in Figure S7. It was also noted that there is no difference in the zero-point corrected energy of 9,10-DPA between differently twisted substituents: the phenyl groups bonded at the 9- and 10-positions of an anthracene can be twisted symmetrically or asymmetrically (the latter seemingly to be crossed when seen from the long-axis direction). Accordingly, both structures are assumed to exist with the same probability. The same is probably applied to the substituents at the 9- and 10-positions of the other anthracene compounds.

4. Discussions

Our study introduced some new concepts in the analysis of TTA processes in the use of experimentally derived rate constants for the master Equation (1) describing the TTA phenomenon at the limit of a relatively low concentration of both sensitizer and annihilator molecules. This makes it stable for certain experimental artefacts such as inner filter effects and the aggregation of the solutes. It can be noticed that our values of the quenching rates agree well with the literature values, e.g., Miyashta et al. [14] and Gray et al. [2] reported k_TET rates of 1.21 × 10⁹ and 1.88 × 10⁹ M⁻¹s⁻¹, respectively, for PtOEP in toluene, to be compared with our value around 1.5 × 10⁹ for PdOEP in both THF and toluene. It is emphasized that our k_TET values, herein and in ref. [5] are obtained directly from the rate version of the Stern–Volmer plot Equation (4) whereas the reported values [2,14] usually were based on Equation (3) and assumptions of the sensitizer lifetimes without an annihilator for the particular solvent. It is also noteworthy that the solvent quenching in the absence of external quenchers ($k_{3S}$) is quite different for the two solvents, i.e., around 15 × 10³ s⁻¹ for THF and approximately 35 × 10³ s⁻¹ for toluene. In our approach, we explicitly contain the annihilator concentration in the source term, which gives a large flexibility in varying its concentration and also determines the statistical s.d. errors deduced from the plots and linear fittings to estimate the overall error of both the TET and TTA efficiencies. The Φ_TET efficiencies that we see are indeed the same within the experimental error for all compounds in each solvent set. Thus, for toluene, it is 0.76 and for THF, 0.88. This is due to the difference in the natural quenching rates presented in Section 3.2.2, with essentially larger rates found for toluene. As the annihilator concentration increases, the natural quenching factor contributes less, as stated by the Stern–Volmer relation, as we also can see by comparing Table 2 and Table 3. The studies of Gray and Miyashita et al. [2,14] used similar sensitizers and stated values close to unity, but here considerably higher annihilator concentrations were used (typically 1 mM or more) pushing the efficiency towards unity considering Equation (6).

For the k_TTA rate, the widely used approach involves all the parameters to deduce the efficiency and is tedious and complicated as it relies on the non-linear behavior of a kinetic process, along with concentration dependencies of the annihilator and the combined effect of the sensitizer and annihilator concentration. Here also, the used excitation power is critical. At high annihilator concentrations (above approx. 50 μM), the inner filter effects much be taken into account (as exemplified in Figure S3) for an accurate spectral analysis, as, e.g., quantum efficiencies can be concentration dependent [14]. Here, the relevant quenching rates were determined using fixed values of the source term (Equation (2)) determined in the very same experiment but in another wavelength channel. When it comes to the measured TTA rates, we found a similar efficiency for all annihilators. This can be expected since this process relies mostly on the sensitizing triplet and its formation, meaning that the triplet–triplet energy transfer from sensitizer to annihilator is quite insensitive to the detailed substitution scheme (Figure 1). This is also since the ground state configurations of the various substituted DPA units, and possibly their lowest triplet states, are similar having the same basic 9,10-DPA electronic structure of the aromatic rings. The latter arises since aromatic substituents attached to DPA are not in a planar configuration due to steric hindrance. Other substitution schemes, notably 2,6-DPA, was found to have a considerably lower efficiency (0.1) also at the 1 mM annihilator concentration [14], possibly since the triplet ground state here is much different from the one in 9,10-DPA.

To conclude, the most stable T1 structures of the five anthracene compounds were estimated to have almost the same T1 energy levels, with the T1 spin density distributed over the planes of an anthracene ring in each compound. This is probably because the substituents are bonded to the anthracene ring while being considerably twisted, diminishing the possible hyperconjugation between the larger planar π-electron moieties as pointed out above. It is generally believed that intermolecular energy transfers such as TTA, or Dexter triplet energy transfer (TET) from a triplet sensitizer to an annihilator during molecular collisions in solution phase, require an overlap between orbitals relating to the excited states. Thus, the overlap causes an interaction between the anthracene compounds in the excited T1 states (TTA) and an interaction between another compound (sensitizer) in the excited T1 state and the anthracene compound in the S0 ground state (TET).　 In all of the investigated compounds, the substituents are bonded at the 9- and 10-positions of the anthracene ring while being twisted, so that the other molecule paired with the anthracene molecule (a triplet sensitizer or an annihilator molecule) are not likely to approach around the substitution sites. In each of the 9,10-DPA, CzPA, and cgDBCzPA variants, only phenyl groups are directly attached to the 9- and 10-positions of the anthracene ring, with the anthracene ring of 9,10-DPA being as bulky as those of CzPA and cgDBCzPA. Thus, the excited orbitals of the other molecule paired with the anthracene molecule need to overlap with the plane phase at any of the 1-, 2-, 3-, and 4-positions and the 5-, 6-, 7-, and 8-positions of the anthracene ring. However, the carbazole units of both the CzPA and cgDBCzPA are considerably longer than the phenyls of 9,10-DPA. On the other hand, in αN-βNPA, an α-naphtyl group, bulkier than the phenyl group, it is bonded at the 9-position of the anthracene ring while being twisted vertically. The angle here is 90° in both the S0 and T1 states, whereas the angle is 90° in the S0 state and is 68° to 74° in the T1 state in the case of a phenyl group. This suggests that another molecule paired up beside the αN-βNPA molecule for triplet exchange is less likely to approach around the substitution sites of αN-βNPA, compared with the case of 9,10-DPA, CzPA, and cgDBCzPA molecules. Similarly, in 2aBAPA-02, a large benzanthracene is bonded to the 2-position of an anthracene ring, suggesting that another molecule approaching the 2aBAPA-02 molecule is less likely to approach around not only the 9- and 10-positions but the 2-position as well. Here also, the proximity of a T1 state localized into the carbazole unit can have some influence.

Comparing the solvents toluene and THF, the Φ_TTA efficiencies are much more disperse for the former case. In the TTA process, two annihilator triplets collide and the steric hindrance of a bulky substituent must have a more decisive impact on the annihilation rate. Moreover, the substituents can more or less shield the triplet state from quenching.

It can be noted that in toluene 9,10-DPA, CzPA, and 2a-BAPA-02, they have the highest TTA efficiencies and the smallest substituents in the 9,10-position. Although the TTA rates are similar for all three within experimental uncertainty, 2a-BAPA-02 has a slightly higher efficiency owing to its significantly smaller solvent quenching. This also shows the benefit of deducing both parameters in the same experiment. TTA efficiencies of αN-βNPA and cgDBCzPA are low. The low TTA efficiency of αN-βNPA attributes to the low K·k_TTA (see Table 2). The excited orbitals of the two molecules have been highly likely inhibited considerably from overlapping with each other when the α-naphtyl group is bonded at the 9-position of an anthracene ring whose T1 spin density is the highest. (If orbitals overlap with each other around the 1-, 2-, 3-, and 4-positions and 5-, 6-, 7-, and 8-positions having no substituent, energy can probably be transferred; there might be other factors that contribute to the low TTA efficiency.) The low TTA efficiency of cgDBCzPA is attributed to the high $k_{3A}$ in toluene, and might require further investigation. Further investigation is required also on the high Φ_TTA of 2a-BAPA-02 whose anthracene rings each have three substituents. For example, the T2 level of a benzo[a]anthracene ring having a spin (2.04 eV) is close to that of an anthracene ring (ΔE = 0.29 eV), and thus not only the anthracene ring but also the benzo[a]anthracene ring may be capable of receiving energy.

In THF, the natural solvent quenching is one order of magnitude lower which is the main reason for the higher efficiencies even though the TTA rates are also smaller (but not to the same extent). This goes well with our previous conclusions on solvent effects comparing DMSO, toluene, and THF for 9,10-DPA [5]. Conclusively, with small solvent quenching rates, there is more time for the diffusion-controlled TTA process to occur, diminishing the effects of bulky substituents. We note that all TTA efficiencies are higher than expected from the spin-statistical rule. Miyashita et al. [14] recently used time-dependent DFT calculations along with experimental data to suggest that some of the recombined higher spin multiplets can give rise to an inverse intersystem crossing, thus increasing the efficiency of emitting annihilator singlet states beyond the 1/9 limit. Concerning the TTA efficiency, we deduced 0.30 for 9,10-DPA using the luminescence-based rate-efficiency approach whereas Miyashta et al. [14] got the value 0.29 based on luminescence intensity measurements. Since all our DPA variants have a similar substitution scheme in the 9,10-position, this mechanism is likely to also explain our results.

5. Conclusions

In conclusion, this work demonstrates further investigation into triplet–triplet annihilation having PdOEP as a sensitizer and exploring with DPA and four other substitutions. We also demonstrate how different solutions will affect the decay times of the process by testing in both toluene and THF. We also avoid too-high concentrations, to not quench the process. Typically, the upconversion efficiency is found using non-measured quenching values. However, we demonstrate a fully experimental measurement of all the necessary parameters to simulate and find the TTA kinetic parameters. We also note the high quantum efficiencies found, due to the increased efficiency of the emitting annihilator singlet states beyond the 1/9th limit. A high TTA efficiency of more than 40% was estimated for the solutions containing a blue-fluorescent material. If such high TTA efficiencies could be utilized in high-concentration states, such as found in a thin film state, it would create high efficiency, blue-fluorescent OLEDs. If the outcoupling efficiency is estimated to be 30%, future OLEDs would have an internal quantum efficiency of 55% and an external quantum efficiency of 16%. They would outperform and replace existing OLEDs. The presented approach of deducing the key parameters for TTA from relatively simple time-resolved measurements can also be important in facilitating the screening of cheap, light-weight organic materials in future applications of solar energy conversion based on TTA upconversion [24].

In addition, an available link is made to our Python code to solve the TTA kinematic equations in Supplementary Materials S2 in Supplementary Information (SI). The details are outlined and discussed in SI, including a guide on how to operate the program.