RESEARCH ARTICLE www.advopticalmat.de Enhancing the Efficiency of Polariton OLEDs in and Beyond the Single-Excitation Subspace Olli Siltanen,* Kimmo Luoma, Andrew J. Musser, and Konstantinos S. Daskalakis* Organic light-emitting diodes (OLEDs) have redefined lighting with their environment-friendliness and flexibility. However, only 25% of the electronic states of organic molecules can emit light upon electrical excitation, limiting the overall efficiency of OLEDs. Strong light–matter coupling, achieved by confining light within OLEDs using mirrors, creates hybrid light-matter states known as polaritons, which could “activate” the remaining 75% electronic triplet states. Here, triplet-to-polariton transition is studied and rates for both reverse inter-system crossing and triplet-triplet annihilation are derived. In addition, how the harmful singlet-singlet annihilation could be reduced with strong coupling is explored. 1. Introduction Organic light-emitting diodes (OLEDs) offer several advantages over traditional lighting alternatives. One key aspect is their versatility in design and form; OLEDs are incredibly thin, lightweight, and flexible, allowing for innovative lighting solu- tions and high-definition displays.[1] However, due to spin statis- tics, electrical injection in molecular materials results in 25% of the excitations to populate singlet electronic states, the remain- ing 75% populating triplets. Typically, singlets are favored due to their ability to undergo fluorescence, which is substantially faster compared to phosphorescence, thus reducing the likelihood of losses from exciton-exciton and exciton-polaron collisions.[2,3] O. Siltanen, K. S. Daskalakis Department of Mechanical and Materials Engineering University of Turku Turun yliopisto FI-20014, Finland E-mail: olmisi@utu.fi; konstantinos.daskalakis@utu.fi K. Luoma Department of Physics andAstronomy University of Turku Turun yliopisto FI-20014, Finland A. J.Musser Department of Chemistry andChemical Biology Cornell University Ithaca,NY14853,USA The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adom.202403046 © 2025 The Author(s). Advanced Optical Materials published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. DOI: 10.1002/adom.202403046 While optical excitation is experimentally simpler and allows to create more sin- glets, electrical excitation—despite the problematic triplets—remains practical in real-world applications. The performance of such devices can be enhanced by con- verting the triplets into singlets or rapidly and radiatively depopulating them.[4–6] Emitters displaying thermally activated delayed fluorescence (TADF) have recently emerged as a class of OLED emitters with high internal quantum efficiency (IQE). In TADF emitters, triplet excitations are efficiently converted into singlets by re- verse inter-system crossing (RISC).[7] Gen- erally, high RISC rates can be achieved by tuning orbital overlaps or incorporating charge-transfer char- acter into the wave functions of the lowest electronic states.[8] However, suchmolecular design techniques are very demanding, and they can simultaneously reduce the oscillator strength of the singlet-to-ground state transition, weakening fluorescence. Thus, alternative strategies to achieve high RISC rates without compro- mising the emitters’ ability to emit photons are needed. Microcavity polaritons have been recently introduced as a sys- tem that can resolve the RISC-IQE trade-off. Polaritons, eigen- states emerging from the strong coupling of singlet excitons and cavity photons, can act as artificially “Stokes-shifted” singlet states.[9–11] In the context of OLEDs and beyond, this means that by utilizing straightforward cavity designs,[12–14] the emitters in- side a cavity can exhibit high RISC rates and high IQE, result- ing in optoelectronic devices combining simple architectures and superior performance. While preliminary experimental results have been reported,[15–20] the theoretical models are quite rudi- mentary, limiting our understanding on how polaritons interact with these molecular processes. This is a critical bottleneck that hinders efficient triplet harvesting in actual OLED devices. In this work we introduce a theoretical model for polaritonic OLED processes not restricted to the single-excitation subspace, allowing us, for the first time, to explore RISC together with triplet-triplet and singlet-singlet annihilation (TTA and SSA). In particular, we derive rates for both polaritonic RISC and TTA, an intermolecular mechanism of triplet-to-singlet transition, by us- ing the Marcus theory of electron transfer and Fermi’s golden rule. The system is illustrated in Figure 1a. By scanning the pa- rameter space of our model, we construct “enhancement maps” for both RISC and TTA; Figure 1b and c gives the singlet and triplet energies andminimum coupling strengths required to en- hance RISC and TTA, respectively. In addition, we analyze the effect of the number of molecules and study how SSA could be Adv. Optical Mater. 2025, 2403046 2403046 (1 of 9) © 2025 The Author(s). Advanced Optical Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.advopticalmat.de Figure 1. Overview of the study and enhancement maps. a) Schematic picture of polaritons in the 1- and 2-excitation subspaces (1E and 2E), RISC, and TTA. The different surfaces are the new eigenenergies as functions of in-plane momentum, while the spheres represent localized triplet excitons. b) Singlet and triplet energies of enhanced RISC under strong coupling. c) Singlet and triplet energies of enhanced TTA under strong coupling. In b (c), the heat map gives the coupling strength gN at which the polaritonic RISC (TTA) rate equals the bare-film rate. In the white areas, polaritonic RISC and TTA cannot be enhanced with any gN. The inset in c is a magnification of the highlighted area. The parameters in b and c are N = 1010, neff = 2, m = 1, Lc = 100 nm, k‖ = 0, T = 293 K, 𝜆s = 0.10 eV, and 𝜆± = 0.79 eV. reduced with strong coupling. Finally, we apply our model to six molecules previously studied under strong coupling.[15–20] 2. Results 2.1. The System We consider a system of N identical organic molecules carrying 0–2 excitations in total, all coupled to a single cavity mode. The system can be described by the Tavis–CummingsHamiltonian[13] H = N∑ n=1 Es|Sn⟩⟨Sn| + N∑ n=1 Et|Tn⟩⟨Tn| + Ecâ†â + N∑ n=1 g1 (|Sn⟩⟨Gn|â + |Gn⟩⟨Sn|â†) (1) where we have used the rotating-wave approximation, Sn, Tn, and Gn denote a singlet, triplet, and ground-state exciton at themolec- ular site n, respectively, Es(t) is the singlet (triplet) energy—for simplicity, we have set the ground-state energy to zero—↠is the creation operator of a photon with the energy Ec, and â is the cor- responding annihilation operator. g1 = 𝜇 √ Ec∕(2𝜖0V) is the light– matter coupling strength, with 𝜇, ϵ0, and V being the transition dipole moment (TDM), vacuum permittivity, and mode volume, respectively. Finally, the energy of the cavity mode satisfies Ec = ℏc neff √ m2𝜋2 L2c + k2‖ (2) where ℏ is the reduced Planck’s constant, c is the speed of light in vacuum, neff is the refractive index of the medium, m ∈ ℕ, Lc is the length of the cavity, and k‖ is the in-plane momentum. Notably, we have assumed the dominance of singlet-cavity mode coupling over all other couplings in Equation (1); Triplets, despite sometimes having non-negligible emission TDM, do not have high enough absorption TDM to strongly couple with the cavity mode.[13] Even quite efficient heavy-metal triplet emitters have phosphorescence lifetimes in the microsecond timescale. This suggests that the triplet extinction coefficient is roughly 1000 times weaker than that of singlet states with nanosecond ra- diative lifetimes,[21] making it reasonable to neglect triplet-cavity mode coupling. Phonon-couplings (and phonons altogether) can be neglected due to polaritons being able to decouple electronic and vibrational degrees of freedom.[22] Finally, the S-T couplings gst can be omitted if |Es − Et| ≫ gst, i.e., if the energy required to transition between these states is so high that the perturbation provided by the coupling is insufficient to cause significant mix- ing. This ensures that the S-T coupling terms oscillate rapidly and average out, allowing the singlets and triplets to be treated as effectively decoupled for the purposes of solving the system’s eigenstates (polaritons). 2.2. Single-Excitation Subspace Diagonalizing the Hamiltonian (1), we arrive at the N trivial eigenstates |Tn〉 in the triplet manifold and the following N + 1 eigenstates in the singlet-cavity mode manifold with one excitation, |P+⟩ = 𝛼(1)√ N N∑ n=1 |Sn⟩⊗ |0⟩ + 𝛽 (1)|⟩⊗ |1⟩ (3) |P−⟩ = 𝛽 (1)√ N N∑ n=1 |Sn⟩⊗ |0⟩ − 𝛼(1)|⟩⊗ |1⟩ (4) Adv. Optical Mater. 2025, 2403046 2403046 (2 of 9) © 2025 The Author(s). Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 0, D ow nloaded from https://advanced.onlinelibrary.w iley.com /doi/10.1002/adom .202403046 by D uodecim M edical Publications Ltd, W iley O nline Library on [11/03/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on W iley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.advopticalmat.de |Dk⟩ = 1√ N N∑ n=1 ei2𝜋nk∕N|Sn⟩⊗ |0⟩, k ∈ [1, N − 1] (5) |P+〉 is the upper polariton (UP) and |P−〉 the lower polariton (LP), whereas {|Dk〉} constitutes the non-emitting exciton reservoir. In the above expressions, the states not explicitly shown are in their electronic ground states and |⟩ denotes the global (electronic) ground state. The matching eigenvalues are E± = Es + Ec 2 ± √ g2N + (Es − Ec)2 4 (6) for the polaritons (+ for UP and − for LP) and Es for the dark states. Here, gN = √ Ng1. Finally, it is straightforward to show that the parameters 𝛼(1) and 𝛽 (1) satisfy |𝛼(1)|2 = 1 2 ⎛⎜⎜⎜⎝1 + Es − Ec√ (Es − Ec)2 + 4g2N ⎞⎟⎟⎟⎠ (7) |𝛽 (1)|2 = 1 2 ⎛⎜⎜⎜⎝1 − Es − Ec√ (Es − Ec)2 + 4g2N ⎞⎟⎟⎟⎠ (8) the squares being known as the Hopfield coefficients.[23] 2.3. Two-Excitation Subspace In realistic systems, there can be many excitations present at the same time. Diagonalizing the Hamiltonian (1) in the presence of two excitations, we arrive at the N(N − 1)/2 trivial eigenstates |TmTn〉 (m < n) in the triplet manifold. In the polariton manifold, we use the ansatz |𝜓 (2)l ⟩ =𝛼(2)l √ 2N(N − 1) ∑m 𝜆s because polaritons are partially in the electronic ground state, which is further away from the triplet states than the excited singlet states. Figure S2 (Supporting In- formation) shows that the greater the difference between 𝜆− and 𝜆s, the higher the coupling strength required to enhance RISC. Adv. Optical Mater. 2025, 2403046 2403046 (4 of 9) © 2025 The Author(s). Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 0, D ow nloaded from https://advanced.onlinelibrary.w iley.com /doi/10.1002/adom .202403046 by D uodecim M edical Publications Ltd, W iley O nline Library on [11/03/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on W iley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.advopticalmat.de Almost equivalently [see Equation (21)], one could scan tempera- ture and keep the reorganization energies fixed. With our param- eter choices, the intervals in Figure S2 (Supporting Information) would roughly translate into the temperature range of 100–500 K. Therefore, as OLEDs typically operate across 253–323 K, tem- perature changes within this range do not significantly alter the enhancement map in Figure 1b. A few more remarks are in order. While the rate k−RISC is appli- cable in the presence of any number of triplets, here we implic- itly assumed that there are no excitations in the polariton mani- fold before RISC—or that the single-excitation polaritons depop- ulate fast enough before the consecutive RISC processes; Typi- cal fluorescence rates of organic molecules are of the order of 108 s−1, while high-performance materials have displayed RISC rates of 104–106 s−1.[21] If this is not the case, we go from the single-excitation subspace to the two-excitation subspace, where the closest state in energy is |𝜓 (2)− ⟩. However, since |𝜓 (2)− ⟩ is non- degenerate in energy and there are N(N + 1)/2 other states, the reciprocal scaling of RISC can be expected to become even worse. Hence, the ratio k−RISC∕k s RISC should actually be interpreted as the upper bound of relative RISC enhancement, in terms of excita- tion number. When bringing LP closer to the first-order triplet state, we inevitably enhance inter-system crossing (ISC) as well. This is against our goal: to convert the slow triplets to fast singlets (or po- laritons). Yet, while RISC is weighted by the long-lived triplet pop- ulation, ISC is weighted by themuch smaller LP population. This is an important point we want to highlight, since high RISC/ISC ratio can be achieved if the triplets have long enough lifetimes and the LP empties quickly enough. Finally, even though we have focused on LP, we might be able to harvest higher-order triplets with UP and “hot RISC” as well.[26] 2.5. Enhancing TTA Because there are three triplet states, under the simplest scheme two of them can combine in nine different ways when colliding. 1/9 of the encounter complexes are of the singlet character— denoted here by S—that can relax to the singlet branch, while 3/9 and 5/9 are of the triplet and quintet character T and Q, respectively.[19] Due to spin symmetry, the triplets and quintets cannot efficiently reach the polaritons. And because the individ- ual triplet excitons are effectively uncoupled from the cavity, their collision rate can be expected to remain constant. For these rea- sons, we focus on the relaxation of singlet encounter complexes and whether it can be enhanced with polaritons. The exact dynamics of encounter complexes is a subject of ac- tive research, including whether and how the Q states impact the spin-statistics of TTA[27–29] and the optical accessibility of the encounter complex itself.[30,31] In systems where twice the triplet energy is close to the bright singlet, configuration inter- actions can substantially complicate the wavefunctions and shift the energies of the triplet pairs relative to two triplets.[32] More- over, in solid systems, it can be essential to factor in the role of longer-range encounter complexes where weaker exchange coupling between triplets results in spin mixing between S and Q states that enrich the simple picture laid out above.[33] The detailed evolution of these pair states is strongly material- dependent and poorly understood,[34] but aside from specially de- signed systems,[17,19,30,31,33] these encounter complexes should be fleetingly short-lived. In particular, in typical OLEDmaterials, the very large energy gap between singlet and triplet pair shouldmin- imize the impact of these complications. Thus, it is sufficient for our purposes here to use, similarly to RISC, non-zero coupling strength of singlets and encounter complexes gsc that does not change within the cavity. We take the interaction Hamiltonian of the S states and sin- glets to be of the form Hint = gsc∑m < n[(|Sm〉 + |Sn〉)〈Sm, n| + |Sm, n〉(〈Sm|+ 〈Sn|)] (cf. ref. [35]). Again, we apply both theMarcus theory and Fermi’s golden rule. Assuming reorganization and free energies twice as high as those with RISC, we obtain ksTTA = k(2𝜆s, Es − 2Et) (26) in the bare-film case and k+TTA = 4|𝛼(1)|2 N k(2𝜆+, E+ − 2Et) (27) k−TTA = 4|𝛽 (1)|2 N k(2𝜆−, E− − 2Et) (28) in the polariton cases. The factor of 4 in the numerators of k±TTA is explained by both possible singlet states contributing to the same polariton, effectively doubling its probability amplitude. Still, be- cause polaritons are collective states and TTA an intermolecular process, one might have anticipated even more prominent en- hancement. In fact, the situation might be different with non- negligible triplet TDM. Consider sparsely excited triplets, i.e., triplets outside their capture radii and therefore not promoting TTA. As the triplet polaritons would consist of all the possible permutations of triplet-occupied molecular sites, some of them might be within the capture radii and contribute to TTA. On the other hand, we would also have the competing process of strong coupling “separating” triplets. This idea is discussed later inmore detail with singlet-singlet annihilation (SSA). Equations (26–28) might imply the stability of encounter com- plexes: the bigger the free-energy difference, the slower they re- lax to singlets. There are, however, competing channels that ef- fectively reduce TTA to the singlet branch. In fact, we suspect that the doubled reorganization energies pose a severe penalty against TTA in the presence of these other channels. In partic- ular, triplet encounter complexes can relax back to free triplets and decay non-radiatively.[36] Nevertheless, since both can be as- sumed ubiquitous and unaffected by the cavity, they do not affect the bare-film/cavity comparison and can therefore be omitted. Figure 1c shows the singlet and triplet energies at which S- to-UP TTA can be enhanced with strong coupling. Again, we have k+TTA = k s TTA in the colored region and k + TTA < k s TTA in the white region, i.e., the region of already efficient TTA (see, e.g., ref. [37]). LP-TTA has been considered in the Supporting In- formation, where we have plotted the ratios k±TTA∕k s TTA and per- formed a more detailed scan of reorganization energies (Figures S3 and S4, Supporting Information). Comparing Figure 1b,c, one can see that the boundary between enhancement and no en- hancement is twice as steep with TTA as with RISC, which can Adv. Optical Mater. 2025, 2403046 2403046 (5 of 9) © 2025 The Author(s). Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 0, D ow nloaded from https://advanced.onlinelibrary.w iley.com /doi/10.1002/adom .202403046 by D uodecim M edical Publications Ltd, W iley O nline Library on [11/03/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on W iley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.advopticalmat.de Figure 3. N-dependent rates of 3DPA3CN. The rates are shown in units of g2st (RISC) or g 2 sc (TTA). The parameters are Es = 2.92 eV, Et = 2.41 eV, Ec = 2.56 eV, 𝜆s = 0.10 eV, 𝜆± = 0.79 eV, and T = 293 K. be explained by the doubled triplet energies. It is also very in- teresting and important to notice that either RISC or TTA—or both—can always be enhanced, at least relatively. 2.6. Effects of N The number ofmolecules playsmany roles in polaritonic OLEDs. In particular, there are two competing effects of N with single- excitation polaritons. On one hand, we can move the polariton states and close the free-energy gaps ΔE in the Marcus rates by increasing gN which, in a fixed mode volume V and molecular TDM, means increasing N. On the other hand, the factor of 1/N strongly dilutes the polaritonic rates as shown in the previous two sections. The number (or density) of molecules also affects TTA, SSA, and other annihilation processes, but with a triplet-triplet collision rate there should be no connection to strong coupling due to negligible TDM.N-dependent SSA, on the other hand, will be discussed shortly. To highlight the differences between the actual rates and the rates obtained by naïvely lowering the singlet energies—and forgetting the collective nature of polaritons—we have plotted the polaritonic rates of 1,3,5-tris(4-(diphenylamino)phenyl)-2,4,6- tricyanobenzene (3DPA3CN) in Figure 3, both with and without the inverse scaling factor 1/N. With the parameters reported in ref. [16], the coupling strength can be expressed as gN = √ N × 112.5 × 10−6 eV. Comparing the solid (correct rates) and dashed (no inverse scaling) curves of the same color, we can clearly see how 1/N hinders, and in the case of UP-TTA, even weakens the rates. The critical value of N is the most prominent with RISC; The rates increase in a Gaussian fashion just beforeN≈ 108, after which E− surpasses Et − 𝜆− and the rates quickly die. Finally, al- though the rates of UP-TTA and LP-TTA are orders of magnitude larger than LP-RISC, one should keep in mind that the triplet ex- citons should first collide, and the values of N in Figure 3 are relatively small in planar microcavities. In fact, no enhancement of TTA was reported in ref. [16], where the number of coupled molecules was estimated to be only 4 × 106. 2.7. Reducing SSA When two singlet excitons interact, they are promoted to a higher- order excited singlet which then either relaxes back to the first- order singlets or ground state—releasing heat at the same time— or breaks into free charge carriers.[38] This may lead to efficiency roll-off and device degradation.[39] However, with strong coupling it should be possible to “separate” such close singlet excitons, as the formed polaritons also consist of distant singlets. Let us clarify this idea by deriving a naïve estimate for the “no SSA” probability. Consider the initial state |SmSn〉⊗|0〉, where the two singlets are close to each other and about to annihilate. Fo- cusing solely on the unitary dynamics induced by U(t) = exp (− iHt/ℏ), the probability of finding the singlets at the same sites at time t is Pm, n(t) = |〈SmSn|U(t)|SmSn〉|2 which, after some algebra, can be written as Pm,n(t) = ||||| 2N(N − 1) (|𝛼(2)+ |2e−i 2E+ tℏ + |𝛼(2)0 |2e−i (Es+Ec )tℏ +|𝛼(2)− |2e−i 2E− tℏ ) + 2N (|𝛽 (1)|2e−i (Es+E+ )tℏ +|𝛼(1)|2e−i (Es+E− )tℏ ) + N − 3 N − 1 e−i 2Est ℏ ||||| 2 (29) Note that this equation only holds for very short times, until inco- herent effects take place. If we further assume a cubic-centered lattice of molecular sites and the annihilation of nearest neigh- bors only, the probability to have further-apart singlets becomes Pr(t) = N 2 − 9N N2 − N − 2 [ 1 − Pm,n(t) ] (30) Figure 4a shows the “no SSA” probability (30) as a function of both gN and t. In the Tavis–Cummings model, emitters in- teract collectively with the cavity mode. The initial state |SmSn〉 is not a symmetric state under permutation of emitters. Sym- metric states, such as Dicke states, are typically more efficient in exchanging excitations with the cavity mode. Since |SmSn〉 is not symmetric, the coupling to the cavity mode is less efficient, which explains the low probabilities. Note also that here we only considered unitary dynamics. Incoherent cavity losses, described by the annihilation operator â, might result in more symmet- ric transitions between subspaces and therefore bigger “no SSA” probabilities. Interestingly, when taking the average of “no SSA” probabil- ity over multiple instances, an optimum value of gN can be ob- served from Figure 4b (∼125meV). Here, the timespan was from 0 to 100 fs in timesteps of 0.1 fs. Figure 4 also demonstrates that, even though electrical excitation may be spatially confined in a thin recombination zone, with strong coupling singlets can be formed outside of it. OLEDs with polariton-improved opera- tional lifetimes were recently reported in ref. [6], to which our analysis ultimately provides an alternative (or complementary) explanation. Adv. Optical Mater. 2025, 2403046 2403046 (6 of 9) © 2025 The Author(s). Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 0, D ow nloaded from https://advanced.onlinelibrary.w iley.com /doi/10.1002/adom .202403046 by D uodecim M edical Publications Ltd, W iley O nline Library on [11/03/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on W iley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.advopticalmat.de Figure 4. Reducing SSA. a) Probability of singlet pairs outside the capture radius (i.e., probability of not getting SSA) as a function of coupling strength and time. b) Arithmetic mean of the “no SSA” probability as a function of gN. The used example parameters are N = 100, Es = 3.5 eV, neff = 2,m = 1, Lc = 100 nm, and k‖ = 0. 2.8. Comparing the Model to Experimental Data We calculated the RISC and TTA rates for six molecules previ- ously studied under strong coupling, using the same parame- ters as in the original works. The chemical structures of these molecules are shown in Figure S5 and the parameters in Table S1 (Supporting Information). To achieve an in-depth understanding of the role of reorganization energies, we scanned the intervals 𝜆s/eV ∈ [0.1, 0.5] and 𝜆±/eV ∈ [0.6, 1.0] (except for 3DPA3CN). Even such rough scans are enough to reveal the polaritonic, large- N effects. Table 1 shows the molecules and their minimum and maximum RISC and TTA rates at these intervals. The bare-film intervals can be notably large, whereas the role of reorganiza- tion energies becomes smaller in the cavity cases. That is, the closer the reorganization energies are to zero (as with the bare- film case), the more their precise values matter. Because we did not consider all the possible OLED processes, some theoretical rates might substantially diverge from the reported experimen- tal values. The first experimental study of the impact of polaritonic states on RISC was realized in ref. [15] with Erythrosine B, a material exhibiting both delayed fluorescence and phospho- rescence. The authors reported a direct transition between molecular-centered and polaritonic states when bringing the LP closer to the first-order triplet. Enhanced RISC was later reported for also 9-([1,1-biphenyl]-3-yl)-N,N,5,11-tetraphenyl-5,9- dihydro-5,9-diaza-13b-boranaphtho[3,2,1-de]anthracen-3-amine (DABNA-2).[18] While our model predicts enhanced RISC for both molecules with very small N, for larger values of N it actually favors TTA. However, if there are enough molecules for TTA to occur, then the harmful, non-emitting SSA may also occur, which we have shown strong coupling to reduce. In other words, enhanced emission can be due to reduced SSA as well. Furthermore, there are other mechanisms behind enhanced emission not included in our model, e.g., Purcell enhancement[40,41] and polariton-induced spectral filtering with refocused emission intensity.[42,43] With tetracene and DPP(PhCl)2 we have the exact opposite sit- uation; While enhanced TTA was reported,[17,19] our model fa- vors RISC. The discrepancy with tetracene may be explained by the fact that in ref. [17] the physical system was slightly different, utilizing nanoparticle arrays exhibiting surface lattice resonances which have smaller mode volumes compared with planar micro- cavities. In ref. [19], an endothermic TTA process was turned into exothermic by lowering the LP below the S encounter complex. The theoretical model, however, was based on simple Arrhenius Table 1. RISC and TTA rates. The rates are given in units of g2st or g 2 sc. The bare-film intervals were obtained with 𝜆s/eV ∈ [0.1, 0.5] and the polaritonic intervals with 𝜆±/eV ∈ [0.6, 1.0] except for 3DPA3CN, for which we used the reported values of 𝜆s = 0.10 eV and 𝜆± ≈ 0.79 eV. Note also the scaling of the polaritonic rates; The actual rates are obtained by dividing with N, the number of molecules. Molecule Reported enhancement ksRISC∕g 2 st Nk − RISC∕g 2 st k s TTA∕g 2 sc Nk + TTA∕g 2 sc Nk − TTA∕g 2 sc Erythrosine B[15] RISC 109–1011 1010–1011 10−24–1015 1015–1016 1016–1016 DABNA-2[18] RISC 1011–1013 1012–1014 10−164–101 1010–1016 100–1013 Tetracene[17] TTA 10−44–10−6 10−2–10−1 1013–1016 108–1012 1010–1013 DPP(PhCl)2 [19] TTA 10−51–10−7 10−2–10−1 1011–1015 104–107 108–1012 3DPA3CN[16] None 1015 1012 10−79 1016 1014 TDAF[20] None 10−21–101 108–1010 10−22–1015 1014–1016 1013–1016 Adv. Optical Mater. 2025, 2403046 2403046 (7 of 9) © 2025 The Author(s). Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 0, D ow nloaded from https://advanced.onlinelibrary.w iley.com /doi/10.1002/adom .202403046 by D uodecim M edical Publications Ltd, W iley O nline Library on [11/03/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on W iley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.advopticalmat.de rates omitting reorganization energies. While Purcell enhance- ment was ruled out in all the previous demonstrations, it would have been worthwhile to consider experiments that disregard en- hanced emission due to polariton filtering or reduced SSA. We note that a further complication is that all the reported processes correspond to long-lived and mixed-spin encounter complexes, and it may be necessary to incorporate a fuller description of triplet-pair evolution to capture their behavior. In the above four cases, where either RISC or TTA was re- portedly enhanced, the phonon couplings that we assumed weak might have actually played a bigger role. However, even when taking the phonon couplings better into consideration and com- paring the upper bounds of the rates—obtained by omitting the Gaussian damping in Equation (21)—our model alone did not explain the experimental findings. Finally, no enhancement was reported for either 3DPA3CN[16] or 2,7-Bis[9,9-di(4-methylphenyl)-fluoren-2-yl]- 9,9-di(4-methylphenyl)fluorene (TDAF)[20] even though our model predicts major improvement of TTA and, depending on 𝜆s, RISC for TDAF—in fact, TDAF is the only molecule with both RISC and TTA potentially enhanced. However, as already mentioned, the number of molecules did not support TTA with 3DPA3CN. As for TDAF, the number of molecules may very well explain the nonexistent RISC and TTA, yet in ref. [20] both might have been (also) smeared by delayed fluorescence from trapped charge carriers. This highlights the importance of ruling out all sources of delayed fluorescence, whether enhanced or not. To summarize, although we have taken significant steps toward a model connecting all the experimental findings, both more comprehensive theories and experiments are still needed to verify if RISC and TTA can be enhanced in realistic devices. 3. Conclusion In this article, we derived polaritonic RISC and TTA rates in the presence of weak phonon coupling. Comparing with the bare- film case, we were able to identify the parameter spaces of en- hanced RISC and TTA, both of which heavily depend on the singlet and triplet free energies, reorganization energies—a fac- tor often omitted from prior works—and number of coupled molecules. Hence, our results help in designing next-generation OLEDs without the need for trial and error. To achieve polaritonic enhancements, the modified energy spacings must counteract both the unfavorable reorganization energies and the effects of large N. Since both can be significant, the change in free energy—and therefore the initial singlet-triplet gap being compared—must also be large. This implies that the original bare-film processes need to be very inefficient to begin with. Processes that are already efficient cannot be further en- hanced by polaritons. Alternatively, one could employ device ar- chitectures that support single- or few-molecule strong coupling. This approach could eliminate the harmful dark states that dilute RISC and TTA. Because the inverse-scaling problem is expected to hinder strong polariton-induced dynamics in the emerging field of po- lariton organic optoelectronics, enhanced RISC and TTA can be somewhat challenging to distinguish from Purcell enhance- ment and polariton filtering. To carefully rule out such alterna- tive sources of enhanced emission in future experiments, both more sophisticated models and experiments are still needed. Such models would, e.g., take into account all the couplings and processes we omitted. Furthermore, one should really consider a continuum of cavity modes as in ref. [44]. Even though it might appear an elusive goal to fully harvest triplets with polaritonic RISC and TTA, strong coupling might influence OLEDs in other, perhapsmore surprising ways. Strong coupling can, in a sense, redistribute excitons. This can benefit fluorescent materials by either enhancing TTA or reducing SSA. While further research is needed to fully understand these fas- cinating new directions, strong coupling clearly holds tremen- dous potential for next-generation OLEDs. In general, our work helps to better understand the rich dynamics occurring in polari- ton OLEDs and paves the way for more advanced hybrid light– matter technologies. Supporting Information Supporting Information is available from the Wiley Online Library or from the author. Acknowledgements This project received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation pro- gramme (grant agreement No. [948260]). The authors would like to thank Ahmed Abdelmagid for useful comments. Conflict of Interest The authors declare no conflict of interest. Data Availability Statement Data sharing is not applicable to this article as no new data were created or analyzed in this study. Keywords organic light-emitting diodes, polaritons, strong coupling Received: November 7, 2024 Revised: December 20, 2024 Published online: [1] S. R. Forrest, Nature 2004, 428, 911. [2] G. F. Trindade, S. Sul, J. Kim, R. Havelund, A. Eyres, S. Park, Y. Shin, H. J. Bae, Y. M. Sung, L. Matjacic, Y. Jung, J. Won, W. S. Jeon, H. Choi, H. S. Lee, J. C. Lee, J. H. Kim, I. S. Gilmore, Nat. Commun. 2023, 14, 1. [3] E. Tankelevicˇiu¯te˙, I. D. Samuel, E. Zysman-Colman, J. Phys. Chem. Lett. 2024, 15, 1034. [4] A. Mischok, S. Hillebrandt, S. Kwon, M. C. Gather, Nat. Photonics 2023, 17, 393. [5] K. Yoshida, J. Gong, A. L. Kanibolotsky, P. J. Skabara, G. A. Turnbull, I. D. W. Samuel, Nature 2023, 621, 746. Adv. Optical Mater. 2025, 2403046 2403046 (8 of 9) © 2025 The Author(s). Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 0, D ow nloaded from https://advanced.onlinelibrary.w iley.com /doi/10.1002/adom .202403046 by D uodecim M edical Publications Ltd, W iley O nline Library on [11/03/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on W iley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.advopticalmat.de [6] H. Zhao, C. E. Arneson, D. Fan, S. R. Forrest, Nature 2024, 626, 300. [7] H. Uoyama, K. Goushi, K. Shizu, H. Nomura, C. Adachi,Nature 2012, 492, 234. [8] S. Diesing, L. Zhang, E. Zysman-Colman, I. D. W. Samuel, Nature 2024, 627, 747. [9] D. Sanvitto, S. Kéna-Cohen, Nat. Mater. 2016, 15, 1061. [10] J. Feist, J. Galego, F. J. Garcia-Vidal, ACS Photonics 2018, 5, 205. [11] M. Hertzog, M. Wang, J. Mony, K. Börjesson, Chem. Soc. Rev. 2019, 48, 937. [12] L. A. Martínez-Martínez, E. Eizner, S. Kéna-Cohen, J. Yuen-Zhou, J. Chem. Phys. 2019, 151, 054106. [13] R. Bhuyan, J. Mony, O. Kotov, G. W. Castellanos, J. Gómez Rivas, T. O. Shegai, K. Börjesson, Chem. Rev. 2023, 123, 10877. [14] A. Mukherjee, J. Feist, K. Börjesson, J. Am. Chem. Soc. 2023, 145, 5155. [15] K. Stranius, M. Hertzog, K. Börjesson, Nat. Commun. 2018, 9, 2273. [16] E. Eizner, L. A. Martínez-Martínez, J. Yuen-Zhou, S. Kéna-Cohen, Sci. Adv. 2019, 5, eaax4482. [17] A. M. Berghuis, A. Halpin, Q. Le-Van, M. Ramezani, S. Wang, S. Murai, J. Gómez Rivas, Adv. Funct. Mater. 2019, 29, 1901317. [18] Y. Yu, S. Mallick, M. Wang, K. Börjesson, Nat. Commun. 2021, 12, 1. [19] C. Ye, S. Mallick, M. Hertzog, M. Kowalewski, K. Börjesson, J. Am. Chem. Soc. 2021, 143, 7501. [20] A. G. Abdelmagid, H. A. Qureshi, M. A. Papachatzakis, O. Siltanen, M. Kumar, A. Ashokan, S. Salman, K. Luoma, K. S. Daskalakis, Nanophotonics 2024, 13, 2565. [21] S. R. Forrest, Organic Electronics: Foundations to Applications, Oxford University Press, Oxford 2020. [22] F. Herrera, F. C. Spano, Phys. Rev. A 2017, 95, 053867. [23] J. J. Hopfield, Phys. Rev. 1958, 112, 1555. [24] J. A. Campos-Gonzalez-Angulo, J. Yuen-Zhou, J. Chem. Phys. 2022, 156, 194308. [25] J. Jortner, J. Chem. Phys. 1976, 64, 4860. [26] C. Lin, P. Han, S. Xiao, F. Qu, J. Yao, X. Qiao, D. Yang, Y. Dai, Q. Sun, D. Hu, A. Qin, Y. Ma, B. Z. Tang, D. Ma, Adv. Funct. Mater. 2021, 31, 1. [27] T. W. Schmidt, F. N. Castellano, J. Phys. Chem. Lett. 2014, 5, 4062. [28] D. Y. Kondakov, T. D. Pawlik, T. K. Hatwar, J. P. Spindler, J. Appl. Phys. 2009, 106, 124510. [29] P. Bharmoria, H. Bildirir, K. Moth-Poulsen, Chem. Soc. Rev. 2020, 49, 6529. [30] D. G. Bossanyi, M. Matthiesen, S. Wang, J. A. Smith, R. C. Kilbride, J. D. Shipp, D. Chekulaev, E. Holland, J. E. Anthony, J. Zaumseil, A. J. Musser, J. Clark, Nat. Chem. 2021, 13, 163. [31] J. Kim, D. C. Bain, V. Ding, K. Majumder, D. Windemuller, J. Feng, J. Wu, S. Patil, J. Anthony, W. Kim, A. J. Musser, Nat. Chem. 2024. [32] A. J. Musser, J. Clark, Annu. Rev. Phys. Chem. 2019, 70, 323. [33] D. Polak, R. Jayaprakash, T. P. Lyons, L. A. Martínez-Martínez, A. Leventis, K. J. Fallon, H. Coulthard, D. G. Bossanyi, K. Georgiou, A. J. Petty, II, J. Anthony, H. Bronstein, J. Yuen-Zhou, A. I. Tartakovskii, J. Clark, A. J. Musser, Chem. Sci. 2020, 11, 343. [34] K. E. Smyser, J. D. Eaves, Sci. Rep. 2020, 10, 18480. [35] M. Nakano, S. Ito, T. Nagami, Y. Kitagawa, T. Kubo, J. Phys. Chem. C 2016, 120, 22803. [36] C. K. Yong, A. J. Musser, S. L. Bayliss, S. Lukman, H. Tamura, O. Bubnova, R. K. Hallani, A. Meneau, R. Resel, M. Maruyama, S. Hotta, L. M. Herz, D. Beljonne, J. E. Anthony, J. Clark, H. Sirringhaus, Nat. Commun. 2017, 8, 15953. [37] T. Suzuki, Y. Nonaka, T. Watabe, H. Nakashima, S. Seo, S. Shitagaki, S. Yamazaki, Jpn. J. Appl. Phys. 2014, 53, 052102. [38] S. M. King, D. Dai, C. Rothe, A. P. Monkman, Phys. Rev. B 2007, 76, 085204. [39] M. C. Gather, A. Köhnen, K. Meerholz, Adv. Mater. 2011, 23, 233. [40] K. Vahala, Nature 2003, 424, 839. [41] C. Y. Peng, M. J. Wei, R. J. Huang, K. P. Guo, Y. L. Jing, T. Xu, B. Wei, Key Engineering Materials 2015, 645, 1087. [42] K. S. Daskalakis, F. Freire-Fernández, A. J. Moilanen, S. van Dijken, P. Törmä, ACS Photonics 2019, 6, 2655. [43] T. Khazanov, S. Gunasekaran, A. George, R. Lomlu, S. Mukherjee, A. J. Musser, Chem. Phys. Rev. 2023, 4, 041305. [44] N. Lydick, J. Hu, H. Deng, J. Opt. Soc. Am. B 2024, 41, C247. Adv. Optical Mater. 2025, 2403046 2403046 (9 of 9) © 2025 The Author(s). Advanced Optical Materials published by Wiley-VCH GmbH 21951071, 0, D ow nloaded from https://advanced.onlinelibrary.w iley.com /doi/10.1002/adom .202403046 by D uodecim M edical Publications Ltd, W iley O nline Library on [11/03/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on W iley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License