TRIUMF
Non UBC
DSpace
Optics 6 (1): 8 (2025)
Lindgren, Mikael
Bjelland, Victoria M.
Melø, Thor-Bernt
McCracken, Callum
Seo, Satoshi
Nakashima, Harue
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.
Academic Editor: Marco GandolfiReceived: 30 December 2024Revised: 4 March 2025Accepted: 7 March 2025Published: 12 March 2025Citation: Lindgren, M.; Bjelland,V.M.; Melø, T.-B.; McCracken, C.; Seo,S.; Nakashima, H. The Triplet–TripletAnnihilation Efficiency of Some9,10-Substituted Diphenyl AnthraceneVariants—A Decisive Analysis fromKinetic Rate Constants. Optics 2025, 6,8. https://doi.org/10.3390/opt6010008Copyright: © 2025 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license(https://creativecommons.org/licenses/by/4.0/).ArticleThe Triplet–Triplet Annihilation Efficiency of Some9,10-Substituted Diphenyl Anthracene Variants—A DecisiveAnalysis from Kinetic Rate ConstantsMikael Lindgren 1,* , Victoria M. Bjelland 1, Thor-Bernt Melø 1 , Callum McCracken 2 , Satoshi Seo 3and Harue Nakashima 31 Department of Physics, Faculty of Natural Sciences, Norwegian University of Science andTechnology (NTNU), Gløshaugen, Realfagbygget, NO-7491 Trondheim, Norway;victoria.m.bjelland@ntnu.no (V.M.B.)2 TRIUMF, The University of British Columbia, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada;cmccracken@triumf.ca3 Semiconductor Energy Laboratory Co., Ltd., 398 Hase, Atsugi-Shi 243-0036, Kanagawa, Japan;nakasima@sel.co.jp (H.N.)* Correspondence: mikael.lindgren@ntnu.no; Tel.: +47-41466510Abstract: Triplet–triplet transfer photochemical reactions are essential in many biological,chemical, and photonic applications. Here, the Pd-octaethylporphyrin sensitizer alongwith triplet–triplet annihilator (TTA) active 9,10-diphenylantracenes (DPA) and the relatedsubstituted variants in low concentrations were examined. A full experimental approachis presented for finding the necessary rate parameters with statistical standard deviationparameters. This was achieved by solving the pertinent non-analytical kinetic differentialequation and fitting it to the experimental time-resolved photoluminescence of both slowfluorescence and sensitizer phosphorescence. The efficiency of the triplet–triplet energytransfer rate was found to be around 90% in THF but only around 75% in toluene. Thisappears to follow from the shorter lifetime of the sensitizer triplet in toluene. Moreover, theTTA transfer rate was on average more than 40% in THF toluene whereas a considerablylower value around 20–30% was found for toluene. This originated in an order of mag-nitude higher solvent quenching rate using toluene, based on the analysis of the delayedfluorescence decay traces. These are also higher than the statistically expected 1/9 TTAefficiency but in accordance with recent results in the literature, that attributed these highvalues to an inverse intersystem crossing process. In addition, quantum chemical calcula-tions were carried out to reveal the pertinent excited triplet molecular orbitals of the lowesttriplet excited state for a series of substituted DPAs, in comparison with the singlet groundstate. Conclusively, these states distribute mainly in an anthracene ring in all compoundsbeing in the range 1.64–1.65 eV above the ground state. The TTA efficiency was found tovary depending on the DPA annihilator substitution scheme and found to be smaller inTHF. This is likely because the molecular framework over which the T1 excited molecularorbitals distribute is less sensitive for a longer lifetime of the annihilator triplet state.Keywords: triplet–triplet annihilation (TTA); TTA kinetics; TTA upconversion; tripletenergy transfer; blue OLED materials; 9,10-diphenylanthracene; triplet state calculations1. IntroductionPhoton upconversion (UC) via triplet–triplet annihilation (TTA) is a well-establishedphenomenon used in many applications ranging from photochemistry to modern photonics.Optics 2025, 6, 8 https://doi.org/10.3390/opt6010008Optics 2025, 6, 8 2 of 19Here, an excited sensitizer triplet state transfers its excess energy and excites a receivingtriplet state of another molecular type, the annihilator. Concomitantly, two triplets of thelatter kind undergo a recombination reaction ultimately rendering one of the annihilatorsinto a ‘doubly excited’ singlet state, finally giving off an emitted photon of a substantiallyhigher 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 theirefficient singlet emission in combination with triplet states readily excited via bimolecularreactions. To facilitate solubility and fine-tune the molecular mechanisms behind the TTAprocess, a vast number of 9,10-disubstituted anthracene systems have been reported on,e.g., [2–5], notably also oligomers and dendrimers [6–9]. Applications of TTA in photochem-ical transformations and used as nanoparticles and clusters were recently reviewed [10,11].Other applications involve organic light emitting devices. Although red and green devicesare found to have high efficiencies, blue OLED perform poorly in comparison and requiremore 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 suitablesensitizers and their triplet energy transfer to the annihilator, to the annihilation processesresulting in the upconverted excited state utilized for the application. The analyses of thephotophysical processes are usually based on steady-state photoluminescence and transientabsorption spectroscopy, or combinations thereof, e.g., [2,4,7,13–15].Recently, we reported on a non-approximative approach to calculate the overall ki-netics 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 (kTET) along with the natural quenching of thesensitizer together manifest the source term for the created annihilator triplets. From theseauxiliary data, the TTA rate (kTTA), along with the natural annihilator quenching rate, couldbe uniquely determined from a line-shape analysis of the delayed fluorescence, using anexponential decay function for the kTET process as a source term. Taken together, this is astraight-forward technique to assess the efficiency/yield of different steps in the compli-cated bimolecular processes. By directly measuring the kTET rate from the phosphorescencequenching upon annihilator titration, it is not necessary to perform the tedious spectralStern–Volmer analysis with relatively high annihilator concentrations leading to parasiticaggregation and inner filter effects [14].The experimental rate approach is here demonstrated and applied to compare somesubstituted variants of 9,10-DPA [16–18] (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 sensi-tizer. We put special emphasis on also estimating errors of the fitted parameters to seehow the measured parameters impact on the calculated overall slow fluorescence efficiency,including their uncertainties. The experimental data of the various substituted DPA vari-ants were compared with the results of quantum chemical calculations of participatingsinglet and triplet states to shed further light on the basic molecular processes governingthe TTA efficiency in substituted anthracene related systems. Our results are in goodagreement with results recently outlined by Miyashita et al. [14] who reported on dipheny-lanthracene substituted in 9,10-, 1,5-, and 2,6-positions, shedding light on the role of thelarger-than-expected spin-statistical factor via high-level reversed intersystem crossing.Optics 2025, 6, 8 3 of 19Optics 2025, 6, x FOR PEER REVIEW 3 of 19 Figure 1. 9,10-DPA and four other anthracene variants used in this study. 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 [16–19] 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-Al-drich 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 emis-sion 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 cal-culations (Gaussian 16 Rev. C.02, Gaussian, Inc., Wallingford, CT, USA) based on the den-sity 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 ac-curacy, 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 spectrophotom-eter (Shimadzu, Japan). Steady state photoluminescence measurements were carried out employing a PTI Quantamaster 8075-22 (Horiba Scientific, Grabels, France) equipped with Figure 1. 9,10-DPA and four other anthracene variants used in this study.2. Materials and Methods9,10-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 [16–19] and purified by sub-limation. These compounds each had a purity higher than or equal to 99.9 % in highperformance 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) witha Teflon cap allowing for gas purging using syringe needles. Toluene solutions and THFsolutions of these five kinds of anthracene compounds and PdOEP were mixed to havepredetermined concentrations, and then their absorption and emission spectra and emissionlifetimes were measured. Oxygen was purged out from the sample with argon gas. Seeref. [5] and Section 3.2.3 for more technical details of the experimental approaches andequipment used.The anthracene compounds were investigated by employing quantum chemical calcu-lations (Gaussian 16 Rev. C.02, Gaussian, Inc., Wallingford, CT, USA) based on the densityfunctional theory (DFT) with the aim to find the most stable structures in the singlet groundstate (S0) and the lowest triplet excited state (T1). The functional B3LYP was used with a6-311G 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 otheratoms, respectively. A vibration analysis was carried out on each structure to obtain thezero-point vibration corrected energy difference from the most stable structures of the S0and T1 states (0-0 bands). The excitation energies of 2aBAPA-02 from optimized S0 levels toT1 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 spectrophotome-ter (Shimadzu, Japan). Steady state photoluminescence measurements were carried outemploying a PTI Quantamaster 8075-22 (Horiba Scientific, Grabels, France) equipped withOptics 2025, 6, 8 4 of 19Double Mono 300 spectrometer chambers for both excitation and emission. A HamamatsuR928 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 exci-tation 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 andbasic data-handling of steady state luminescence data were carried out with the Felix DataAnalysis software (Felix GX 4.9.0.10216) and further processed and presented using OriginPro (9.7.0.188).Time-correlated single photon counting (TC SPC) decays were recorded using an IBHTCSPC 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 de-tection module and the sample was excited using an IBH LED operating at 373 nm. Themeasured decay trace was analyzed using deconvolution fitting with the IBH Data Stationv 2.1 software.Transient Delayed Fluorescence Experiments were carried out using a tunable OPOlaser, NT342A-SH-10WW (Ekspla, Vilnius, Lithuania), for excitation. Typically, pulses ofenergy 15–20 mJ with a 6 ns duration were used, hitting the center of a 1 cm path cuvettecontaining the sample. At right angles with respect to the laser beam, on opposite sidesof 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 (ModelC10029-01, Hamamatsu, Japan), triggered by the laser. A Digital Delay generator ModelDG 545 (Stanford Research Systems, Sunnyvale, CA, USA), also triggered by the laser, wasused to set the delay and gate width and record a full spectrum in one laser flash. Theoutput 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 generatedspecies at selected wavelengths, using a R928 PMT (Hamamatsu, Japan) at the exit port. Thevoltage 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. ResultsThe presentation of the results is divided into several subsections. Firstly, the molecu-lar structures and basic photophysical properties of the DPA variants are presented. Then,we give an overview of the processes involved in delayed fluorescence phenomenon byemploying time-gated/time-delayed spectra. Thereafter, it is presented how the varioustriplet-energy transfer processes were measured and fitted from time-resolved decay mea-surements of the different luminescence channels. For the details, the CzDPA annihilatormolecule is chosen. The efficiency of the triplet transfer from the sensitizer along withthe delayed fluorescence is determined from the measured rate constants. Finally, quan-tum chemical calculations were used to calculate the important T1 states for the variousmolecules for further discussions of the overall results.3.1. Substituted DPA Structures and Basic Photophysical Characterization3.1.1. Molecular StructuresThe molecular structures of the annihilators are depicted in Figure 1. They all holdresemblance to the 9,10-DPA moiety through asymmetric substitutions of extended aromaticsystems in the 9- and/or 10-position of anthracene. CzPA and cgDBCzPA both are basedon a single carbazole skeleton unit attached via the nitrogen atom. The larger variant hasthe benzo groups replaced by more conjugated naphthalene units.Optics 2025, 6, 8 5 of 19In αN-βNPA, both the 9- and 10-positions are substituted with a naphthalene anda phenyl-naphthalene moiety. In 2aBAPA-02, the 7-position of benzo[a]anthracene issubstituted by the 2-position of anthracene. In view of understanding the details of the TTAresults, the triplet states of the various molecules were further investigated using quantumchemical calculations to be discussed in Section 3.3 after presenting the experimental results.3.1.2. Basic Absorption and Emission PropertiesThe basic absorption and emission spectra of the five studied annihilator molecules intoluene are shown in Figure 2.Optics 2025, 6, x FOR PEER REVIEW 5 of 19 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 sub-stituted 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 quan-tum 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. Figure 2. The absorption spectra (solid lines) and normalized emission spectra (dashed) of the in-vestigated molecules in toluene (10 μM). The absorption is given as the extinction coefficient whereas the emission spectra are normalized for an easy comparison of the line-shape and shifts. The integrated emission was plotted vs. the absorption at 370 nm to obtain the corre-sponding 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 vi-brational 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 Figure 2. The absorption spectra (solid lines) and normalized emission spectra (dashed) of theinvestigated molecules in toluene (10 µM). The absorption is given as the extinction coefficientwhereas the emission spectra ar normalized for n easy compar so of the line-shape and shifts.The integrated emission was plotted vs. the absorption at 370 nm to obtain the corre-sponding quantum efficiency following the procedure of Rurak et al. [20]; see Figure S1 forthe representative slope plots. As shown in Figure 2, the absorption spectrum of all com-pounds has a close resemblance to the 9,10-DPA molecule with its characteristic vibrationalsubstr cture. This also means that the π-conjugation into the substituents is small, as canalso be anticipated from the steric hindrance of the attached aromatic groups, keeping theplane of the planar aromatic structures at a substantial angle, to be presented more in detail inSection 3.3.In the absorption spectrum of DPA, the peaks around 360 nm, 380 nm, and 400 nm arecharacteristic to an anthracene ring. In the absorption spectrum of cgDBCzPA, the peaksaround 330 nm to 370 nm seem to be attributed not only to an anthracene ring but also to adibenzo[c,g]carbazole ring. The absorption spectrum of 2aBAPA-02 is slightly broader thanthose of the other anthracene compounds, and the peaks approximately from 330 nm to380 nm seem to be attributed not only to an anthracene ring but also to a benzo[a]anthracenering. For larger substituents, such as for 2aBAPA-02, there is actually a more extensive andelectron 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 similarfor the various structures dominated by the anthracene unit. The well-known absorptionspectra and phosphorescence emission of the PdOEP sensitizer [21] in the two solventsOptics 2025, 6, 8 6 of 19used, THF and toluene, are shown in Figure S2. The Q-band at 546 nm is used to activatethe 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 3and the fitted parameters are summarized in Table 1.Optics 2025, 6, x FOR PEER REVIEW 6 of 19 emission. However, the photoactivity of the ground state and lowest excited state are ex-pected 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 two solvents used, THF and oluene, are shown in Figure S2. The Q-band at 546 nm is used to activate th sensitizer triplets utilized in the TTA proces , to b discussed mor b low. Figure 3. TC SPC traces of the five DPA variants (Figure 1) in toluene. The samples were excited using a 373 nm LED and the emissions were collected in the range of 425 nm with a slit width of 16 nm. The sample concentration was in the range 2–3 μM. 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. 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). Figure 3. TC SPC traces of the five DPA variants (Figure 1) in toluene. The samples were excitedusing a 373 nm LED and the emissions were collected in the range of 425 nm with a slit width of16 nm. The sample concentration was in the range 2–3 µM.Table 1. A summary of the basic photophysical parameters of the five DPA variants in tolueneand THF.Compound 1 Decay Ti e (ns) 2 QY (Toluene) 2 QY (THF)DPA 6.62 ± 0.034 0.93 ± 0.054 0.94 ± 0.06CzPA 5.07 ± 0.026 0.89 ± 0.051 0.96 ± 0.13cgDBCzPA 4.77 ± 0.029 0.84 ± 0.059 0.83 ± 0.112aBAPA-02 6.92 ± 0.033 0.71 ± 0.042 0.78 ± 0.06αN-βNPA 3.67 ± 0.027 0.73 ± 0.043 0.75± 0.071 Excitation at 373 nm in toluene. 2 For the excitation at 370 nm, for QY plots, see Figure S1A,B.3.2. Delayed FluorescenceTo facilitate the discussion of the delayed fluorescence results, the essential kineticequations are briefly reviewed. The principle for the triplet–triplet annihilation process isoutlined in Scheme 1 and Equations (1) and (2).Optics 2025, 6, 8 7 of 19Optics 2025, 6, x FOR PEER REVIEW 7 of 19 Scheme 1. The principle for triplet–triplet annihilation where two excited triplet donor (sensitizer) molecules (red) transfer energy to acceptor molecules (blue). The process starts with the excitation of a sensitizer (here, PdOEP) that has a long-lived excited triplet state 𝑆𝑇∗ , with kinetics following Equation (1) below, as follows: 𝑑[𝑆𝑇∗ ]𝑑𝑡= −(𝑘3𝑆 + 𝑘𝑇𝐸𝑇[𝐴𝑆0] + 𝑘𝑆𝑂[𝑂2 ])[𝑆𝑇∗ ]. (1) Here, k3S is the natural solvent quenching rate in the absence of external quenchers, the term including kTET is the energy transfer rate (per mol annihilator in the solvent) of the triplets from the sensitizer to the annihilator singlet ground state 𝐴𝑆0, whereas the rate kSO 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 (𝐴𝑇∗ ) follows a 2nd order differential equation: 𝑑[𝐴𝑇∗ ]𝑑𝑡= 𝐾 ∙ 𝑘𝑇𝐸𝑇[𝐴𝑆0]𝑒−(𝑘3𝑆+𝑘𝑇𝐸𝑇[𝐴𝑆0])∙𝑡 − 𝑘3𝐴[𝐴𝑇∗ ] − 2𝑘𝑇𝑇𝐴[𝐴𝑇∗ ]2. (2) The left side is describing the change of the annihilator triplet concentration as gov-erned by a source term including 𝐴𝑆0 and kTET, having a positive sign, along with the losses in terms of natural solvent quenching rate (k3A) and the consumption via the TTA process (2·kTTA) 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 −𝑘𝑆𝑂[𝑂2 ][𝐴𝑇∗ ] has been omitted for simplicity. Equation (1) is readily solved analytically from the decay pro-file of the sensitizer phosphorescence and gives the important parameters kTET and k3S 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 de-tailed 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 biomedi-cal 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 Scheme 1. The principle for triplet–triplet annihilation where two excited triplet donor (sensitizer)molecules (red) transfer energy to acceptor molecules (blue).The process starts with the excitation of a sensitizer (here, PdOEP) that has a long-livedexcited tri let state S∗T , with kin tics following Equation (1) below, as follows:d[S∗T ]dt= −(k3S + kTET[A0S]+ kSO[O2])[S∗T ]. (1), k3St ter i cl i kTET i l ft t i l t f t iti r t t i il t r i l t t t A0S, s t tSO i t ffi , it is lly r e fro t e t f t, s s re i lt f t f t cite a i ilator tri let (AT ff i :d[A∗T ]dt= K·kTET[A0S]e−(k3S+kTET [A0S ])·t − k3A[A∗T ]− 2kTTA[A∗T ]2. (2)The left side is describing the ch ge of t e a nihilator triplet concentra ion as gov-erned by a source term including A0S and kTET, h ving a p sitive sign, along with the l ssein terms of atural solv nt quenching rat (k3A) and the consumpt on via the TTA p oces(2·kTTA) giving rise to the delayed fluorescence. The factor 2 arises since two excited tripletsare co sumed i each an ihilation event. Here, it has been assumed that no dissolvedoxygen is present that an quench the annihilator triplet, so the term −kSO[O2][A∗T ] hasbe n omitted for simplicity. Equation (1) is r adily solved analytically from the decayprofile of the sensitizer ph sphorescence and gives the important parameters kTET ndk3S of the source t rm in Equation (2), along with an apparatus constant K containinglaser power, detecti n sensitivity, etc. See ref [5] and Supplementary Materials S2 for moredetailed discussions of how to numerically solve Equation (2). It is also emphasized that asimilar approach (Equations (1) and (2)) can be applied for the analysis of singlet oxygenkinetics from the triplet–triplet energy transfer from chlorin photosensitizers in biomedicalapplications [22].3.2.1. Time-Gated Measurements of Delayed FluorescenceThe processes involved in the TTA and concomitant delayed fluorescence are nicelyvisualized, 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 withthe widely used PdOEP sensitizer. At the low annihilator loading (Figure 4A), one canobserve the distinct scatter from the ns excitation laser pulse operating at 546 nm (greenOptics 2025, 6, 8 8 of 19‘sc’) used to excite PdOEP in the dominating Q-band along with the phosphorescence of thesensitizer 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 enoughfor 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 reacha maximum in the range 20–40 µs and then it slowly decays out. Similarly, the exponentialdecay 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 interms of its phosphorescence, implying the triplet energy transfer of Equation (1).Optics 2025, 6, x FOR PEER REVIEW 8 of 19 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 fluo-rescence. As the time-gate is delayed, there is first a gradual increase of delayed fluores-cence 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). Figure 4. An overview of time-gated/time-delayed fluorescence measurements exemplified with CzPA and PdOEP in toluene. (A) At high annihilator loading. (B) At low annihilator loading. The sample compositions are also denoted in the insets. The excitation wavelength was 546 nm. Turning to Figure 4B, the very same settings are used but here the annihilator con-centration 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 flu-orescence has also increased approximately by a factor of four, as determined by the ki-netic relations in Equations (1) and (2) where the number of excited annihilator triplets Figure 4. An overview of time-gated/time-delayed fluorescence measurements exemplified withCzPA and PdOEP in toluene. (A) At high an ihilator loading. (B) At low an ihilator loading. Thesample compositions are also denoted in the insets. The excitation wavelength was 546 nm.Turning to Figure 4B, the very same settings are used but here the annihilator concen-tration of the sample has been increased by approximately four times, resulting in moredelayed fluorescence that builds up faster and peaks around 20 µs, together with a fasterdecay of the sensitizer triplet. It is noteworthy that the intensity of the delayed fluorescencehas also increased approximately by a factor of four, as determined by the kinetic relationsin Equations (1) and (2) where the number of excited annihilator triplets are proportionalOptics 2025, 6, 8 9 of 19to [A0S] in the source term. This holds as long as the system is not depleted of annihilatorsand sensitizers.3.2.2. Quantifying the Triplet Energy Transfer Rate, kTETThe processes involved in the TTA and the delayed fluorescence are described byEquation (2). The delayed fluorescence emitted is proportional to the term [A∗T ]2, scaledby the quantum efficiency of the annihilator singlet state. Thus, the time profiles of thedelayed blue fluorescence in Figure 4 contains four kinetic rate constants k3S, kTET, k3A,and kTTA; however, it is difficult to fit all these unambiguously from the correspondingslow fluorescence line-shape. On the other hand, the rate constant kTET along with k3Sare also decisive for the time profile of the phosphorescence decay (red label ‘ph’ inFigure 4A). Thus, it is mathematically more stable to first determine the kTET and k3S ratesfrom the phosphorescence (Equation (1)) and then use these as fixed parameters in thefitting 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, thephosphorescence was collected into a light guide and directed through a spectrometerbefore detection using a rapid conventional PMT.Optics 2025, 6, x FOR PEER REVIEW 9 of 19 are proportional to [𝐴𝑆0] in the source term. This holds as long as the system is not depleted of annihilators and s nsitizers. 3.2.2. Quantifying the Triplet Energy Transfer Rate, kTET The processes involved in the TTA and the delayed fluorescence are described by Equation (2). The delayed fluorescence emitted is proportional to the term [𝐴𝑇∗ ]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 k3S, kTET, k3A, and kTTA; however, it is difficult to fit all these unambiguously from the corresponding slow fluorescence line-shape. On the other hand, the rate constant kTET along with 𝑘3𝑆 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 kTET and 𝑘3𝑆 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 phos-phorescence time-profiles are shown in Figure 5A for CzPA/PdOEP. Here, the phospho-rescence was collected into a light guide and directed through a spectrometer before de-tection using a rapid conventional PMT. Figure 5. (A) Phosphorescence decay traces recorded at 663 nm upon excitation at 546 nm. (B) The corresponding Stern–Volmer plots based on analyzed exponential decays. (n.b., For clarity, only three decays are shown in panel (A). Toluene was used as the solvent. 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 plot-ted 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: 𝜏0𝜏= 1 + 𝑘𝑄𝜏0[𝑄], (3) where 𝜏0 here is the phosphorescence lifetime in the absence of the quencher, 𝜏 is the lifetime with the quencher and [𝑄] is the quencher concentration. In our case, the annihi-lator is the quencher (Equation (1)) and substituting 𝜏 = 1/𝑘𝑚𝑒𝑎𝑠 for the measured decay rate constants and similarly for the other rates gives the following: 𝑘𝑚𝑒𝑎𝑠 = 𝑘0 + 𝑘𝑇𝐸𝑇[𝐴𝑆0], (4) where 𝑘0 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 kTET is obtained directly along with the quenching rate for the case with no annihilator present (𝑘3𝑆). Representative plots are shown in Figure 6 us-ing THF as the solvent. Here, we have included also DPA in toluene to compare the Figure 5. (A) Phosphorescence decay traces recorded at 663 nm upon excitation at 546 nm. (B) Thecorresponding Stern–Volmer plots based on analyzed exponential decays. (n.b., For clarity, only threedecays are shown in panel (A). Toluene was used as the solvent.Such decays are readily fitted to a single exponential decay giving the apparent rateconstant for each concentration of the annihilator. The apparent rate constant is then plottedagainst the annihilator concentration giving the plot shown in Figure 5B. We note that thisgives a straight line which is in accordance with the general Stern–Volmer relation:τ0τ= 1+ kQτ0[Q], (3)where τ ere is the phosphorescence lifetime in the absence of the quencher, τ is the lifetimewith the quencher a d [Q] is the quencher co entration. In our case, the annihilator is thequencher (Equation (1)) and substituting τ = 1/kmeas for the measured decay rate constantsnd similarly for the other rates gives the following:kmeas = k0 + kTET[A0S], (4)where k0 is the quenching rate in th absence of the annihilator (and ther externalquenchers such as oxygen) in accordance with Equations (1) and (2). Thus, from fittingthe straight line i Figure 5B, th kTET is obtained directly along with the quenching ratefor the c se with no annihilator present (k3S). Repre entative plots are sh wn in Figure 6Optics 2025, 6, 8 10 of 19using THF as the solvent. Here, we have included also DPA in toluene to compare thedifference between THF and toluene. For the substituted variants it can be seen that thereis a significant difference with less steep slopes i.e., the kTET rate is slightly lower in thepertinent compounds. The fits of the additional DPA variants in toluene are shown in Fig-ure S3. Quenching rates for all the DPA variants using two solvents, toluene and THF, aresummarized in Tables 2 and 3, respectively, and used further as inputs to fit the parameterset for the delayed fluorescence time-profile described further below.Optics 2025, 6, x FOR PEER REVIEW 10 of 19 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 kTET 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 Tables 2 and 3, respectively, and used further as inputs to fit the pa-rameter set for the delayed fluorescence time-profile described further below. Figure 6. Stern–Volmer plots to fit the kTET rate of PdOEP for all DPA variants in THF. Included is also DPA with toluene to compare the solvents. Table 2. A summary of the fitted triplet energy transfer rate kTET for the DPA variants along with fitted parameters for the delayed fluorescence: k3A and K·kTTA. 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 k3S 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. Table 3. A summary of the fitted triplet energy transfer rate kTET for the DPA variants along with fitted parameters for the delayed fluorescence: k3A and K·kTTA. 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 Figure 6. Stern–Vol er plots to fit the k ET rate of PdOEP for all DPA variants in THF. Included isalso DPA with toluene to compare the solvents.Table 2. A summary of the fitted triplet energy transfer rate kTET for the DPA variants along withfitted parameters for the delayed fluorescence: k3A and K·kTTA. Toluene was used as the solvent with10 µM PdOEP as the sensitizer.Compound 1 kTET (109 s−1M−1) k3A (s−1) 2 K·kTTA (s−1)DP 1.53 ± 0.016 16,000 ± 3100 12,000 ± 1900CzPA 1.28 ± 0.060 16,400 ± 1000 13,200 ± 2500cgDBCzPA 1.44 ± 0.047 26,300 ± 2800 11,900 ± 39002aBAPA-02 1.47 ± 0.060 12,400 ± 1000 12,400 ± 1500αN-βNPA 1.39 ± 0.095 17,100 ± 3500 6110 ± 8401 Excitation 546 nm, data collected at 663 nm. The average of the natural solvent quenching k3S was found tobe 35,400 ± 4700 s−1. For fits of Stern–Volmer plots, s e Figure S3. 2. The ve ge and s.d. of parameters from3–4 fittings of different concentrations of annihilators in the range 20–80 µM.Table 3. A summary of the fitted triplet energy transfer rate kTET for the DPA variants along withfitted parameters for the delayed fluorescence: k3A and K·kTTA. THF was used as the solvent with10 µM PdOEP as the sensitizer.Compound 1 kTET (109 s−1M−1) k3A (s−1) 2 K·kTTA (s−1)DPA .64 ± 0.043 1240 ± 330 6110 ± 170CzPA 1.52 ± 0.087 1450 ± 2.8 3320 ± 470cgDBCzPA 1.36 ± 0.043 1380 ± 290 4250 ±4102aBAPA-02 1.51 ± 0.045 1730 ± 130 3720 ± 420αN-βNPA 1.34 ± 0.051 1590 ± 520 3400 ± 3101 Excitation 546 nm, data collected at 663 nm. The average of the natural solvent quenching k3S was found to be15,300± 1300 s−1. 2. The average and s.d. of the parameters from fittings of 40 and 80 µM annihilator concentrations.Optics 2025, 6, 8 11 of 193.2.3. Quantifying the TTA Rate and the Natural Quenching of the AnnihilatorKnowing all the parameters of the source term in Equation (1) from the fitting of thewell-defined kTET and k3S of the Stern–Volmer expression (Equation (4)) and the annihilatorconcentration of the sample, the recording of the delayed fluorescence time-profiles suchas in Figure 4 are readily analyzed [5]. Also here, the emitted fluorescence at the emissionmaximum was guided into a lightguide through a spectrometer to a fast PMT, recordedby a transient digital oscilloscope. Such time-profile traces are shown in Figure 7 for theCzPA/PdOEP system with five different annihilator concentrations using identical settingsfor the excitation source and the PMT amplification, time constants of the detector, etc. It isnoteworthy that at high loadings there is a large spectral overlap between the absorptionspectrum of the annihilator and the emission spectrum of the delayed fluorescence due tothe small Stokes’ shift, as seen in Figure S4. Thus, by monitoring the time-dependent slowfluorescence at 425–430 nm at moderate annihilator loadings, these effects are minimizedcompared to attempting to analyze the full spectral emission for the TTA yield as discussedwith some detail by Miyashita et al. [14]. In addition, the inner filter effects the highconcentration of the annihilator and also deteriorates the fluorescence quantum yield andmust be compensated for [14].Optics 2025, 6, x FOR PEER REVIEW 11 of 19 1 Excitation 546 nm, data collected at 663 nm. The average of the natural solvent quenching k3S 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. 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 kTET and k3S 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 set-tings 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 fluores-cence 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]. Figure 7. Line-shapes of time-delayed fluorescence measurements with the annihilator CzPA at dif-ferent concentrations. The solvent was toluene and 10 μM PdOEP was used as the sensitizer. The sample composition is denoted in the insets. The excitation wavelength was 546 nm and the emis-sion at 425 ± 8 nm was collected. Oxygen has been purged out from the sample with Argon gas. The plots in Figure 7 are shown together with fits of K, k3A, and kTTA from the temporal line-shape, fixing the remaining parameters of the source term from the Stern–Volmer analysis (k3S and kTET in Tables 2 and 3) along with the known annihilator concentration of the sample [𝐴0𝑆]. Note that the product K·kTTA 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 Figure 7. Line-shapes of time-delayed fluorescence measurements with the annihilator CzPA atdifferent concentrations. The solvent was toluene and 10 µM PdOEP was used as the sensitizer. Thesample composition is denoted in the insets. The excitation wavelength was 546 nm and the emissionat 425 ± 8 nm was collected. Oxygen has been purged out from the sample with Argon gas.The plots in Figure 7 are shown together with fits of K, k3A, and kTTA from the temporalline-shape, fixing the remaining parameters of the source term from the Stern–Volmeranalysis (k3S and kTET in Tables 2 and 3) along with the known annihilator concentration ofthe sample[AS0]. Note that the product K·kTTA gives the apparent TTA rate as discussed inref. [5] as the pre-factor K has the dimension [mol]. In Table 2, K is set to unity to obtain theresulting physical TTA rate per mol annihilator triplet compared to the natural quenchingrate of the annihilator. The error analysis of k3A and kTTA is based on the average andpertinent s.d. of measurements of the delayed fluorescence at various concentrations ofthe annihilator. The relative values of the natural solvent quenching (k3A) and delayedOptics 2025, 6, 8 12 of 19fluorescence decay (kTTA) rates are essential for determining the TTA efficiency of theannihilator, to be more discussed below.Following a similar procedure as outlined above using toluene as the solvent, all soluteswere examined using THF, but we limited the analysis to two concentrations, 40 and 80 µM ofannihilator loading. Representative data for 80 µM are shown in Figure 8 (parameters such aslaser power, time constant, PMT gain, etc. were held the same for each sample) and the fittedparameters are collected in Table 3, in a similar way as for toluene in Table 2. Another set ofdata was obtained using a 40 µM loading of the annihilators (Figure S5).Optics 2025, 6, x FOR PEER REVIEW 12 of 19 the resulting physical TTA rate per mol annihilator triplet compared to the natural quenching rate of the annihilator. The error analysis of k3A and kTTA 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 (k3A) and delayed fluorescence decay (kTTA) rates are essential for determining the TTA efficiency of the an-nihilator, to be more discussed below. Following a similar procedure as outlined above using toluene as the solvent, all so-lutes 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 (pa-rameters 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). 0.0 0.1 0.2 0.3 0.401234 80 uM DPA CzPA 2aBAPA-02 cgDBCzA aN-bNPATTA Signal (mV)Time (ms) Figure 8. Line-shapes of the time-delayed fluorescence measurements with the 9,10-DPA and the four DPA variants at 80 μM annihilator loading. The solvent was THF and 10 μM PdOEP was used as the sensitizer. The sample composition is denoted in the insets. The excitation wavelength was 546 nm. The emission at 430 (±8) nm was collected. Oxygen has been purged out from the sample with Argon. 3.2.4. The Overall Efficiency of the TET and TTA Processes The efficiency of the overall upconversion process (Φ𝑈𝐶) is usually described by the collective impact of the various processes, summarized as follows: Φ𝑈𝐶 = Φ𝐼𝑆𝐶Φ𝑇𝐸𝑇Φ𝑇𝑇𝐴Φ𝐹𝐿, (5) where Φ𝐼𝑆𝐶 is the intersystem crossing efficiency of the sensitizer, Φ𝑇𝐸𝑇 is the efficiency of the triplet energy transfer from the sensitizer to the annihilator, Φ𝑇𝑇𝐴 is the efficiency of the recombination process between excited annihilator triplets, and finally Φ𝐹𝐿 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 Φ𝑇𝑇𝐴, 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 Figure 8. Line-shapes of the time-delayed fluorescence measurements with the 9,10-DPA and thefour DPA variants at 80 µM annihilator loading. The solvent was THF and 10 µM PdOEP was usedas the sensitizer. The sample composition is denoted in the insets. The excitation wavelength was546 nm. The emission at 430 (±8) nm was collected. Oxygen has been purged out from the samplewith Argon.3.2.4. The Overall Efficiency of the TET and TTA ProcessesThe efficiency of the overall upconversion process (ΦUC) is usually described by thecollective impact of the various processes, summariz d as follows:ΦUC = ΦISCΦTETΦTTAΦFL, (5)r ISC is t e i t r t r i ffi i f t iti r, TET i t ffi if t tri l t r tr sf r fr t s siti r t t i il t r, TTA is t ffi if t r c i ti r c ss t cit i il t r tri l ts, fi ll FL is tt ffici c f t i il t r fr its r c i cit si l t st t . tt ese, t ere is als a s i statistical fact r c tai e i TTA, li iti t e ssi le erf excite a i ilat r si lets fr t e c i e a i ilat r excite tri lets. trictl , t isis 1 9 f r a ‘fr ze ’ s i s ste , t it is ell t e excee e i a s ste so erati g at roo temperature and in diffusion-controlled liquid systems [5,14,15], tobe discussed more below. Here, it is focused on the comparison of the efficie cy of t evarious annihilators. Hereby, we omit the ΦISC contribution by using the very same PdOEPsensitizer at a fixed (and low) concentration and by keeping the laser power at a constantvalue in all measurements.Optics 2025, 6, 8 13 of 19As outlined in our previous study, the detailed kinetic theory was outlined [5] andit was shown how the ΦTET fractional efficiency of Equation (5) could be quantified fromthe following:ΦTET =kTET[A0S]k3S + kTET[A0S] (6)Notably, as kTET is a 2nd order rate constant (unit s−1M−1), this efficiency is depen-dent on the concentration of available annihilator singlets in the ground state, A0S (andexperimentally also on the power of the excitation source and sensitizer concentration viaEquation (2)). Similarly, the efficiency of the TTA process can be calculated from a similarexpression [5]:ΦTTA =K·kTTAk3A + 2K·kTTA (7)where K, kTTA, and k3A are obtained from the fitted time trace of the slow fluorescence (seee.g., Figures 6 and 7). Setting the concentration fixed to 80 µM, representative of the highconcentration used, the efficiencies summarized in Tables 4 and 5 can be calculated fromthe experimental values summarized in Tables 2 and 3, for respective solvents.Table 4. The efficiency of the triplet energy transfer and triplet–triplet annihilation of the five DPAvariants in toluene for the 80 µM concentration of the annihilator.Compound ΦTET ΦTTA ΦTET·ΦTTADPA 0.776 ± 0.023 0.300 ± 0.025 0.233 ± 0.021CzPA 0.743 ± 0.025 0.308 ± 0.013 0.229 ± 0.013cgDBCzPA 0.765 ± 0.009 0.238 ± 0.024 0.182 ± 0.0202aBAPA-02 0.769 ± 0.024 0.333 ± 0.011 0.256± 0.012αN-βNPA 0.759 ± 0.009 0.208 ± 0.026 0.158± 0.021Table 5. The efficiency of the triplet energy transfer and triplet–triplet annihilation of the five DPAvariants in THF for the 80 µM concentration of the annihilator.Compound ΦTET ΦTTA ΦTET·ΦTTADPA 0.896 ± 0.008 0.454 ± 0.011 0.407 ± 0.011CzPA 0.888 ± 0.008 0.410 ± 0.005 0.364 ± 0.006cgDBCzPA 0.877 ± 0.009 0.430 ± 0.013 0.377 ± 0.0122aBAPA-02 0.888 ± 0.008 0.406 ± 0.007 0.360± 0.007αN-βNPA 0.875 ± 0.009 0.405 ± 0.025 0.354± 0.0223.3. Quantum Chemical Calculations of the Triplet Levels and Molecular OrbitalsDensity functional theory (DFT) was used to calculate the S0 and T1 optimized struc-tures of DPAs. The vibrations of the structures were analyzed and used to calculate the T1levels from the S0-T1 zero-point energy gaps. The calculations revealed that the lowest T1levels of 9,10-DPA, CzPA, cgDBCzPA, and αN-βNPA are each 1.65 eV and the T1 level of2aBAPA-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 havetwo stable triplet structures (T1 and T2) with different triplet spin distributions. The situa-tion is depicted in Figure 9 along with spin density distributions for the two cases. Onesuch state was found to have a T2 level at the benzo[a]anthracene ring (1.90 eV) relativelyclose to the state localized to the anthracene ring (1.64 eV). In addition, we calculated theexcitation 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 SupplementaryFigure S6. T1 and T2 spins are mainly distributed in the area similar to that in Figure 9.∆E was 0.29 eV, which was slightly widened but is still of a similar small magnitude asOptics 2025, 6, 8 14 of 19that in Figure 9. This also indicates that the triplet level of the benzo[a]anthracene ringis close to that of the anthracene ring. Thus, not only the anthracene ring but also thebenzo[a]anthracene ring may be capable of participating in the triplet-exchange processes.Optics 2025, 6, x FOR PEER REVIEW 14 of 19 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]an-thracene 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 esti-mated 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 annihi-lator may be involved in the TTA mechanism. Figure 9. Conformational structures along with the spin density distribution for two possible triplet states (T1 and T2) of 2aBAPA-02 and their triplet energies (0-0 gaps). To the left, the T1 spin is on the anthracene ring whereas to the right, the T2 spin is on the benzo[a]anthracene ring. The S0, T1, and T2 structures were optimized, and the vibrations of the structures were analyzed (b3lyp/6-311g(d,p)). The iso value of the T1 and T2 spin density distribution is 0.03 [e·bohr−3]. See text for details. The most stable structures and spin density distributions of all remaining com-pounds 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-posi-tions of the other anthracene compounds. Figure 9. Conformational structures along with the spin density distribution for two possible tripletstates (T1 and T2) of 2aBAPA-02 and their triplet energies (0-0 gaps). To the left, the T1 spin is on theanthracene ring whereas to the right, the T2 spin is on the benzo[a]anthracene ring. The S0, T1, andT2 structur s were optimized, and the vibrations of the structures were analyzed (b3lyp/6-311g(d,p)).The iso value of the T1 and T2 spin densi y distribution is 0.03 [e·bohr−3]. S e text for details.In addition, when the T1 level of 2aBAPA-02 is close to 1.76 eV, its T2 level is estimatedto be higher than the T1 level by approximately 0.26 eV. This suggests that the T1 level ofPdOEP (1.87 eV [23]) is lower than the T2 level of 2aBAPA-02, and in this case, the energytransfer 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 T1level of the annihilator, TTA is observed while the TTA probability is lowered. The previousresearch suggests that the interaction between the sensitizer and the annihilator may beinvolved in the TTA mechanism.The most stable structures and spin density distributions of all remaining compoundsin the T1 state are similar to the spin density of 2a-BAPA-02 with T1 located in the an-thracene unit (Figure 9) and are all shown in Figure S7. It was also noted that there isno difference in the zero-point corrected energy of 9,10-DPA between differently twistedsubstituents: the phenyl groups bonded at the 9- and 10-positions of an anthracene can betwisted symmetrically or asymmetrically (the latter seemingly to be crossed when seenfrom the long-axis direction). Accordingly, both structures are assumed to exist with thesame probability. The same is probably applied to the substituents at the 9- and 10-positionsof the other anthracene compounds.4. DiscussionsOur study introduced some new concepts in the analysis of TTA processes in the useof experimentally derived rate constants for the master Equation (1) describing the TTAphenomenon at the limit of a relatively low concentration of both sensitizer and annihilatormolecules. This makes it stable for certain experimental artefacts such as inner filter effectsand the aggregation of the solutes. It can be noticed that our values of the quenchingOptics 2025, 6, 8 15 of 19rates agree well with the literature values, e.g., Miyashta et al. [14] and Gray et al. [2]reported kTET 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 kTET values, herein and in ref. [5] are obtained directly fromthe 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 anannihilator for the particular solvent. It is also noteworthy that the solvent quenching inthe absence of external quenchers (k3S) is quite different for the two solvents, i.e., around15 × 103 s−1 for THF and approximately 35 × 103 s−1 for toluene. In our approach, weexplicitly contain the annihilator concentration in the source term, which gives a largeflexibility in varying its concentration and also determines the statistical s.d. errors deducedfrom the plots and linear fittings to estimate the overall error of both the TET and TTAefficiencies. The ΦTET efficiencies that we see are indeed the same within the experimentalerror 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, withessentially larger rates found for toluene. As the annihilator concentration increases, thenatural quenching factor contributes less, as stated by the Stern–Volmer relation, as we alsocan see by comparing Tables 2 and 3. The studies of Gray and Miyashita et al. [2,14] usedsimilar sensitizers and stated values close to unity, but here considerably higher annihilatorconcentrations were used (typically 1 mM or more) pushing the efficiency towards unityconsidering Equation (6).For the kTTA rate, the widely used approach involves all the parameters to deduce theefficiency and is tedious and complicated as it relies on the non-linear behavior of a kineticprocess, along with concentration dependencies of the annihilator and the combined effectof the sensitizer and annihilator concentration. Here also, the used excitation power iscritical. At high annihilator concentrations (above approx. 50 µM), the inner filter effectsmuch 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 relevantquenching rates were determined using fixed values of the source term (Equation (2))determined in the very same experiment but in another wavelength channel. When itcomes to the measured TTA rates, we found a similar efficiency for all annihilators. Thiscan 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 quiteinsensitive to the detailed substitution scheme (Figure 1). This is also since the ground stateconfigurations 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. Thelatter arises since aromatic substituents attached to DPA are not in a planar configurationdue to steric hindrance. Other substitution schemes, notably 2,6-DPA, was found to have aconsiderably lower efficiency (0.1) also at the 1 mM annihilator concentration [14], possiblysince 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 wereestimated to have almost the same T1 energy levels, with the T1 spin density distributedover the planes of an anthracene ring in each compound. This is probably because the sub-stituents are bonded to the anthracene ring while being considerably twisted, diminishingthe possible hyperconjugation between the larger planar π-electron moieties as pointed outabove. It is generally believed that intermolecular energy transfers such as TTA, or Dextertriplet energy transfer (TET) from a triplet sensitizer to an annihilator during molecularcollisions in solution phase, require an overlap between orbitals relating to the excitedstates. Thus, the overlap causes an interaction between the anthracene compounds in theexcited T1 states (TTA) and an interaction between another compound (sensitizer) in theOptics 2025, 6, 8 16 of 19excited T1 state and the anthracene compound in the S0 ground state (TET). In all ofthe investigated compounds, the substituents are bonded at the 9- and 10-positions of theanthracene ring while being twisted, so that the other molecule paired with the anthracenemolecule (a triplet sensitizer or an annihilator molecule) are not likely to approach aroundthe substitution sites. In each of the 9,10-DPA, CzPA, and cgDBCzPA variants, only phenylgroups are directly attached to the 9- and 10-positions of the anthracene ring, with theanthracene ring of 9,10-DPA being as bulky as those of CzPA and cgDBCzPA. Thus, theexcited orbitals of the other molecule paired with the anthracene molecule need to overlapwith the plane phase at any of the 1-, 2-, 3-, and 4-positions and the 5-, 6-, 7-, and 8-positionsof the anthracene ring. However, the carbazole units of both the CzPA and cgDBCzPAare 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 theanthracene ring while being twisted vertically. The angle here is 90◦ in both the S0 and T1states, whereas the angle is 90◦ in the S0 state and is 68◦ to 74◦ in the T1 state in the caseof a phenyl group. This suggests that another molecule paired up beside the αN-βNPAmolecule 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 toapproach around not only the 9- and 10-positions but the 2-position as well. Here also, theproximity of a T1 state localized into the carbazole unit can have some influence.Comparing the solvents toluene and THF, theΦTTA efficiencies are much more dispersefor the former case. In the TTA process, two annihilator triplets collide and the sterichindrance 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 highestTTA efficiencies and the smallest substituents in the 9,10-position. Although the TTA ratesare similar for all three within experimental uncertainty, 2a-BAPA-02 has a slightly higherefficiency owing to its significantly smaller solvent quenching. This also shows the benefitof deducing both parameters in the same experiment. TTA efficiencies of αN-βNPA andcgDBCzPA are low. The low TTA efficiency of αN-βNPA attributes to the low K·kTTA(see Table 2). The excited orbitals of the two molecules have been highly likely inhibitedconsiderably from overlapping with each other when the α-naphtyl group is bonded at the9-position of an anthracene ring whose T1 spin density is the highest. (If orbitals overlapwith each other around the 1-, 2-, 3-, and 4-positions and 5-, 6-, 7-, and 8-positions having nosubstituent, energy can probably be transferred; there might be other factors that contributeto the low TTA efficiency.) The low TTA efficiency of cgDBCzPA is attributed to the highk3A in toluene, and might require further investigation. Further investigation is requiredalso on the high ΦTTA 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 tothat of an anthracene ring (∆E = 0.29 eV), and thus not only the anthracene ring but alsothe benzo[a]anthracene ring may be capable of receiving energy.In THF, the natural solvent quenching is one order of magnitude lower which is themain reason for the higher efficiencies even though the TTA rates are also smaller (but not tothe same extent). This goes well with our previous conclusions on solvent effects comparingDMSO, toluene, and THF for 9,10-DPA [5]. Conclusively, with small solvent quenchingrates, there is more time for the diffusion-controlled TTA process to occur, diminishing theeffects of bulky substituents. We note that all TTA efficiencies are higher than expected fromthe spin-statistical rule. Miyashita et al. [14] recently used time-dependent DFT calculationsalong with experimental data to suggest that some of the recombined higher spin multipletsOptics 2025, 6, 8 17 of 19can give rise to an inverse intersystem crossing, thus increasing the efficiency of emittingannihilator singlet states beyond the 1/9 limit. Concerning the TTA efficiency, we deduced0.30 for 9,10-DPA using the luminescence-based rate-efficiency approach whereas Miyashtaet al. [14] got the value 0.29 based on luminescence intensity measurements. Since all ourDPA variants have a similar substitution scheme in the 9,10-position, this mechanism islikely to also explain our results.5. ConclusionsIn conclusion, this work demonstrates further investigation into triplet–triplet annihi-lation 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 bytesting in both toluene and THF. We also avoid too-high concentrations, to not quench theprocess. Typically, the upconversion efficiency is found using non-measured quenchingvalues. However, we demonstrate a fully experimental measurement of all the necessaryparameters to simulate and find the TTA kinetic parameters. We also note the high quantumefficiencies found, due to the increased efficiency of the emitting annihilator singlet statesbeyond the 1/9th limit. A high TTA efficiency of more than 40% was estimated for thesolutions containing a blue-fluorescent material. If such high TTA efficiencies could beutilized in high-concentration states, such as found in a thin film state, it would create highefficiency, 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 quantumefficiency of 16%. They would outperform and replace existing OLEDs. The presentedapproach of deducing the key parameters for TTA from relatively simple time-resolved mea-surements can also be important in facilitating the screening of cheap, light-weight organicmaterials 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 kinematicequations in Supplementary Materials S2 in Supplementary Information (SI). The detailsare outlined and discussed in SI, including a guide on how to operate the program.Supplementary Materials: The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/opt6010008/s1; Supplementary Materials S1—Additional spectra, photophysi-cal data, and results from quantum chemical calculations; Supplementary Materials S2—Insights to theTTA master equation and tests of the numeric equation solver. This file contains more detailed informationabout the numerical solution of Equation (2) and instructions on how to operate the Python code for thepurpose of simulating or fitting data. In addition, an available link is made to our Python code to solve theTTA kinematic equations in Supplementary Materials S2, Supplementary Information (SI). The details areoutlined and discussed in SI, including a guide on how to operate the program.Author Contributions: Conceptualization, M.L. and T.-B.M.; methodology, M.L.; software, V.M.B.,C.M. and M.L.; investigation, M.L., V.M.B. and C.M.; writing—original draft preparation, M.L.;writing—review and editing, T.-B.M., V.M.B., C.M., S.S. and H.N.; visualization, M.L.; supervision,M.L.; Analysis and considerations through computational chemistry approach, S.S. and H.N. Allauthors have read and agreed to the published version of the manuscript.Funding: This research received no external funding.Data Availability Statement: Supplementary Information S1 gives additional data. Computer codefor analysis can be retrieved on demand (Supplementary Information S2).Conflicts of Interest: Authors Satoshi Seo and Harue Nakashima were employed by the companySemiconductor Energy Laboratory Co., Ltd. The remaining authors declare that the research wasconducted in the absence of any commercial or financial relationships that could be construed as apotential conflict of interest.Optics 2025, 6, 8 18 of 19References1. Parker, C.A.; Hatchard, C.G. Delayed Fluorescence from Solutions of Anthracene and Phenantracene. Proc. R. Soc. Lond. Ser. A1962, 269, 574–584.2. Gray, V.; Dreos, A.; Erhart, P.; Albinsson, B.; Moth-Poulsen, K.; Abrahamsson, M. Loss channels in triplet-triplet annihilationphoton upconversion: Importance of annihilator single and triplet surface shapes. Phys. Chem. Chem. Phys. 2017, 19, 10931–10939.[CrossRef] [PubMed]3. Nishimura, N.; Gray, V.; Allardice, J.R.; Zhang, Z.; Pershin, A.; Beljonne, D.; Rao, A. Photon Upconversion from Near-Infrared toBlue Light with TIPS-Anthracene as an Efficient Triplet-Triplet Annihilator. ACS Mater. Lett. 2019, 1, 660–664. [CrossRef]4. Olesund, A.; Gray, V.; Mårtensson, J.; Albinsson, B. Diphenylanthracene Dimers for Triplet-Triplet Annihilation Photon Upconver-sion: Mechanistic Insights for Intramolecular Pathways and the Importance of Molecular Geometry. J. Am. Chem. Soc. 2021, 143,5745–5754. [CrossRef]5. Bjelland, M.V.; Nakashima, H.; Hashimoto, N.; Seo, S.; Melø, T.B.; Lindgren, M. Non-approximative Kinetics of Triplet-TripletAnnihilation at Room Temperature: Solvent Effects on Delayed Fluorescence. ChemPhotoChem 2023, 7, e202300064. [CrossRef]6. Gray, V.; Moth-Poulsen, K.; Albinsson, B.; Abrahamsson, M. Towards efficient solit-state triplet-triplet annihilation based photonupconversion: Supramolecular, macromolecular and self-assembled systems. Coord. Chem. Rev. 2019, 123, 20181–20187.7. Gao, G.; Prasad, S.K.K.; Zhang, B.; Dvorak, M.; Tayebjee, M.J.Y.; McCamey, D.R.; Schmidt, T.W.; Smith, T.; Wong, W.W.H.Intramolecular versus Intermolecular Triplet Fusion in Multichromophoric Photochemical Upconversion. J. Phys. Chem. C 2019,123, 20181–20187. [CrossRef]8. Dzebo, D.; Börjesson, K.; Gray, V.; Moth-Poulsen, K.; Albinsson, B. Intramolecular Triplet-Triplet Annihilation Upconversion in9,10-Diphenylanthracene Oligomers and Dendrimers. J. Phys. Chem. C 2016, 120, 23397–23406. [CrossRef]9. He, G.; Churchill, E.M.; Parenti, K.R.; Zhang, J.; Narayanan, P.; Namata, F.; Malkoch, M.; Congreve, D.N.; Cacciuto, A.; Sfeir, M.Y.;et al. Promoting multiexciton interactions in singlet fission and triplet fusion upconversion dendrimers. Nat. Commun. 2023,14, 6080. [CrossRef] [PubMed]10. Niihori, N.; Kosaka, T.; Negishi, Y. Triplet-triplet annihilation-based photon upconversion using nanoparticles and nanoclusters.Mater. Horiz. 2024, 11, 2304. [CrossRef] [PubMed]11. Jin, J.; Yu, T.; Chen, J.; Hu, R.; Yang, G.; Zeng, Y.; Li, Y. Recent advances of triplet-triplet annihilation upconversion in photochemicaltransformations. Curr. Opin. Green Sustain. Chem. 2023, 43, 100841. [CrossRef]12. Fukagawa, H.; Shimizu, T.; Ohbe, N.; Tokito, S.; Tokumaru, K.; Fujikake, H. Anthracene derivatives as efficient emitting hosts forblue organic light-emitting diodes utilizing triplet–triplet annihilation. Org. Electron. 2012, 13, 1197–1203. [CrossRef]13. Zhang, Y.; Lee, J.; Forreste, S.R. Tenfold increase in the lifetime of blue phosphorescent organic light-emitting diodes. Nat.Commun. 2014, 5, 5008. [CrossRef] [PubMed]14. Miyashita, T.; Jaimes, P.; Mardini, A.; Fumanal, M.; Lee Tang, M. High-Level Reverse Intersystem Crossing and MolecularRigidity Improve Spin Statistics for Triplet-Triplet Annihilation Upconversion. J. Phys. Chem. Lett. 2023, 14, 6119–6126. [CrossRef][PubMed]15. Zhou, Q.; Zhou, M.; Wie, Y.; Zhou, X.; Liu, S.; Zhang, S.; Zhang, B. Solvent effects on the triplet-triplet annihilation upconversionof diiodo-Bodipy and perylene. Phys. Chem. Chem. Phys. 2017, 19, 1516–1525. [CrossRef]16. Kawakami, S.; Nakashima, H.; Kojima, K.; Nomura, R.; Ohsawa, N.; Inventors; Semiconductor Energy Laboratory Co., Ltd.Anthracene Derivative, Material or Light Emitting Element, Light Emitting Element, Light Emitting Device, and ElectronicAppliance. US Patent US 7,879,464, 1 February 2011.17. Suzuki, H.; Seo, S.; Kawakami, S.; Suzuki, S.; Inventors; Semiconductor Energy Laboratory Co., Ltd. Dibenzo[c,g]carbazoleCompound, Light-Emitting Element, Light-Emitting Device, Display Device, Lighting Device and Electronic Device. US PatentUS 8,986,857, 24 March 2015.18. Kadoma, H.; Seo, S.; Suzuki, H.; Hashimoto, N.; Suzuki, T.; Inventors; Semiconductor Energy Laboratory Co., Ltd. OrganicCompound, Light-Emitting Device, Light-Emitting Apparatus, Electronic Apparatus, and Lighting Apparatus. US PatentApplication Publication US 2021/0119133, 22 April 2021.19. Gao, W.; Herron, N.; Inventors; LG Chem, Ltd., Assignee. Electroactive Materials. US Patent US 11,114,621, 7 September 2021.20. Rurack, K.; Spieles, M. Fluorescence Quantum Yields of a Series of Red and Near-Infrared Dyes Emitting at 600–1000 nm. Anal.Chem. 2011, 83, 1232–1242. [CrossRef] [PubMed]21. Marta, P.; Fausto, O.; Fausto, E.; Pier, L.G. New molecular pairs for low power non-coherent triplet–triplet annihilation basedupconversion: Dependence on the triplet energies of sensitizer and emitter. J. Lumin. 2013, 135, 265–270. [CrossRef]22. Hageberg, I.U.; Arja, K.; Vindstad, B.E.; Bergvoll, J.K.; Gederaas, O.A.; Melø, T.-B.; Nilsson, K.P.R.; Lindgren, M. Photophysicsof Glycosylated Ring-Fused Chlorin Complexes and Their Photosensitizing Effects on Cancer Cells. ChemPhotoChem 2023, 7,e202300028. Available online: https://chemistry-europe.onlinelibrary.wiley.com/doi/full/10.1002/cptc.202300028 (accessed on6 March 2025). [CrossRef]Optics 2025, 6, 8 19 of 1923. Cheng, Y.Y.; Khoury, T.; Clady, R.G.C.R.; Tayebjee, M.J.Y.; Ekins-Daukes, N.J.; Crossley, M.J.; Schmidt, T.W. On the efficiency limitof triplet–triplet annihilation for photochemical upconversion. Phys. Chem. Chem. Phys. 2010, 12, 66–71. [CrossRef]24. Schultze, T.F.; Schmidt, T.W. Photochemical upconversion: Present status and prospects for its application to solar energyconversion. Energy Environ. Sci. 2015, 8, 103–125. [CrossRef]Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individualauthor(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury topeople or property resulting from any ideas, methods, instructions or products referred to in the content.
Article
eng
Reviewed
Vancouver : University of British Columbia Library
Multidisciplinary Digital Publishing Institute
CC BY 4.0
Faculty
Researcher
triplet–triplet annihilation (TTA)
TTA kinetics
TTA upconversion
triplet energy transfer
blue OLED materials
9,10-diphenylanthracene
triplet state calculations
The Triplet–Triplet Annihilation Efficiency of Some 9,10-Substituted Diphenyl Anthracene Variants : A Decisive Analysis from Kinetic Rate Constants
Text