{ "schemaVersion": 1, "id": "optoelectronics-density-loss", "title": "When triplets accumulate: density-dependent loss and singlet recovery", "question": "Under which assumed rates does faster triplet-to-singlet conversion delay TTA loss, and how does an alternative STA pathway change that conclusion?", "resultKind": "conditional-normalized-steady-state-model", "notAMaterialFit": true, "notDeviceEqe": true, "notLuminanceOrCurrentAxis": true, "defaults": { "ttaLoad": 1e-05, "staLoad": 0.0, "riscRelativeRate": 0.01, "tripletLossRelativeRate": 0.0001, "iscBranch": 0.75, "radiativeBranch": 0.24, "singletGenerationFraction": 0.25, "ttaSingletBranch": 0.25 }, "equations": { "singlet": "0 = fS - s + r*t + f*a*t^2 - b*s*t", "triplet": "0 = (1-fS) + i*s - (r+d)*t - (1+f)*a*t^2", "conservation": "1 = h*s + (1-i-h)*s + d*t + a*t^2 + b*s*t", "monotoneElimination": "lambda*t + B*a*t^2 + i*b*s*t = g; s=(fS+r*t+f*a*t^2)/(1+b*t)", "definitions": { "KS": "kr + knr,S + kISC [s^-1]", "G": "generated excitations per volume per time [cm^-3 s^-1 if density is cm^-3]", "s": "KS*S/G", "t": "KS*T/G", "a": "kTT*G/KS^2", "b": "kST*G/KS^2", "i": "kISC/KS", "h": "kr/KS", "r": "kRISC/KS", "d": "terminal nonradiative triplet decay / KS; excludes RISC", "fS": "singlet fraction of generated excitations", "f": "singlet product fraction of effective annihilating TTA encounters", "lambda": "d+r*(1-i)", "g": "1-fS+i*fS", "B": "1+f*(1-i)" }, "coefficientConvention": "kTT*T^2 is effective annihilating encounters per volume per time. At f=1/4 the singlet source is +(1/4)kTT*T^2 and triplet sink is -(5/4)kTT*T^2. The NET excitation-number loss is kTT*T^2, not 2*kTT*T^2.", "ttaOnlySolution": "t=2*g/[lambda+sqrt(lambda^2+4*B*a*g)]", "ttaOnlyCompetition": "rho=B*a*g/lambda^2; t/t0=2/[1+sqrt(1+4*rho)]", "ttaOnlyHalfTripletLoad": "a_half=2*lambda^2/(B*g), for g>0. This halves T, not photon yield or EQE." }, "assumptions": [ "All defaults are illustrative dimensionless assumptions; no rate is assigned to a selected BNOO, BNSS, BNSSe or BNSeSe emitter.", "Spatially uniform, steady generation in a two-excited-state kinetic system. S1/T1 are coarse-grained states, not a reduction fitted to the separate S1/T1/T2 calculation.", "Fixed first-order coefficients, no state filling, heating, diffusion gradients, charge transport, polaron annihilation, phosphorescence, singlet-singlet annihilation or chemical degradation.", "fS=.25 is an assumed electrical 1:3 singlet:triplet generation fraction. fS=1 describes pure singlet generation, not an entire optical experiment.", "TTA f=.25 is the stated effective branch convention. It is not a measured universal spin yield.", "STA destroys one singlet and leaves one triplet after rapid higher-triplet relaxation.", "Both a and b scale proportionally with G for a fixed material; changing only one load is a channel-isolation counterfactual." ], "interpretationLimits": [ "Photon yield is photons produced per generated excitation, not photons extracted per injected electron (EQE). No outcoupling or charge-balance factor is assumed.", "No conversion to luminance, current, physical concentration, seconds or measured lifetime is available without dimensional coefficients and the recombination profile.", "Gross RISC and TTA singlet formation fluxes may include repeated cycles and must not be plotted as independently assigned emitted photons.", "A yield-versus-density curve does not uniquely identify a microscopic loss mechanism; transient/frequency response, generation calibration and spatial information add constraints.", "TTA can increase light output relative to a weak-RISC baseline by harvesting otherwise nonradiative triplets. Relative photon yield is not universally <=1.", "The quadratic onset scales with lambda^2 only with other parameters held fixed; lambda is a steady-state elimination coefficient, not generally a measured delayed-fluorescence lifetime inverse.", "Lower excitation density or faster RISC in this scenario is not a prediction of operational LT50 or chemical stability." ], "uiGuidance": { "recommendedTtaLoadLog10Range": [ -8, -1 ], "riscRelativeRateChoices": [ 0.001, 0.01, 0.1 ], "staToTtaLoadRatioChoices": [ 0, 1, 100, 1000 ], "ttaSingletBranchFixed": 0.25, "rangeMeaning": "Display ranges chosen to cover linear, crossover and nonlinear limits of the hypothetical scenario, not measured physical bounds." }, "sources": [ { "id": "gruene-2020", "authors": "Jeannine Gr\u00fcne, Nikolai Bunzmann, Moritz Meinecke, Vladimir Dyakonov, Andreas Sperlich", "title": "Kinetic Modeling of Transient Electroluminescence Reveals TTA as an Efficiency-Limiting Process in Exciplex-Based TADF OLEDs", "year": 2020, "journal": "Journal of Physical Chemistry C 124, 25667\u201325674", "doi": "10.1021/acs.jpcc.0c06528", "url": "https://doi.org/10.1021/acs.jpcc.0c06528", "accessibleManuscript": "https://arxiv.org/pdf/2007.08862", "locator": "Main text Eqs 1, 3, 5\u20136, manuscript pp. 3\u20135; coefficient-convention derivation in Supporting Information p. 21.", "supports": "Branch-aware TTA produces singlets while consuming triplets; STA removes a singlet but returns a triplet. Main equations use +1/4 kTT T\u00b2 for S and -5/4 kTT T\u00b2 for T.", "system": "m-MTDATA:3TPYMB exciplex OLED; not the BNOO/BNSS/BNSSe/BNSeSe cohort.", "scope": "Adopt the main-text effective rate convention and explicitly define it; do not transfer the fitted coefficients or the mechanism-dominance conclusion.", "sourceAudit": "The arXiv v2 SI p. 21 prints kTT=(9/4)k\u2032TT, but its adjacent equalities require kTT=(4/9)k\u2032TT. We do not use that inconsistent printed conversion. Our effective coefficient is defined directly by the main-text +1/4 and -5/4 terms; it counts annihilating encounters, excluding null quintet returns.", "redistribution": "Article/manuscript not redistributed. Metadata, equations and original paraphrase only." }, { "id": "van-der-zee-2022", "authors": "B. van der Zee et al.", "title": "Numerical Device Model for Organic Light-Emitting Diodes Based on Thermally Activated Delayed Fluorescence", "year": 2022, "journal": "Advanced Electronic Materials", "doi": "10.1002/aelm.202101261", "url": "https://advanced.onlinelibrary.wiley.com/doi/10.1002/aelm.202101261", "locator": "Sections 2.2\u20132.5, Eqs 6\u201311; Figs 2\u20135; Conclusion.", "supports": "Independent +1/4/-5/4 TTA convention, singlet-return STA equation, and the need for a spatial recombination profile and independently constrained ISC/RISC rates when inferring annihilation coefficients.", "system": "Neat CzDBA single-layer OLEDs; multiple active-layer thicknesses and 215\u2013295 K.", "contextualReportedCoefficient": { "quantity": "kTTA", "value": 7e-18, "reportedPlusMinus": 3e-18, "unit": "m^3 s^-1", "equivalentValueCm3S": 7e-12, "equivalentReportedPlusMinusCm3S": 3e-12, "evidenceKind": "coefficient inferred by fitting spatial device simulations to measured roll-off", "spreadMeaning": "As reported; not assigned an unverified SD or confidence level.", "usedInOurCalculation": false }, "scope": "Evidence that TTA can dominate this particular system and that simplifications change inferred constants. Does not justify assigning the same mechanism or coefficient to another host/emitter.", "redistribution": "No full text or figure redistributed; attributed facts only." }, { "id": "king-2026", "authors": "Liam G. King, Kou Yoshida, Arvydas Ruseckas, Ifor D. W. Samuel", "title": "Uncovering the Origin of Efficiency Roll-Off in TADF OLEDs", "year": 2026, "journal": "Advanced Functional Materials", "doi": "10.1002/adfm.202531845", "url": "https://advanced.onlinelibrary.wiley.com/doi/10.1002/adfm.202531845", "locator": "Sections 2.1\u20132.3, Eqs 4\u201310, Table 1; full contextual facts in operando-evidence.json.", "supports": "In-operando frequency-response measurements can distinguish competing annihilation pathways; the studied 4CzIPN device requires STA, singlet-polaron and triplet-polaron terms, whereas TTA is bounded above.", "system": "15 wt.% 4CzIPN:mCBP; separate optical-film and operating-device measurements.", "scope": "A measured counterexample to a universal TTA explanation. Its coefficients, optical-film thickness and estimated device recombination width are not applied to our normalized scenario.", "redistribution": "Source-linked numerical facts and original summaries only." } ], "validation": { "passedAssertions": 496, "stateCases": 120, "independentReference": "70-digit Decimal expanded cubic root", "maxStateBalanceResidual": 5.295032917291241e-16, "maxRelativePopulationDifferenceVsDecimal": 4.570866155483679e-15, "invalidInputsRejected": 8, "scope": "Numerical, algebraic and limiting-case validation only; no experimental validation." }, "landmarks": { "dilute": { "scaledSingletPopulation": 3.855769230769231, "scaledTripletPopulation": 360.5769230769231, "zeroDensityScaledSingletPopulation": 3.855769230769231, "zeroDensityScaledTripletPopulation": 360.5769230769231, "photonYield": 0.9253846153846154, "zeroDensityPhotonYield": 0.9253846153846154, "relativePhotonYield": 1.0, "tripletPopulationRelativeToDilute": 1.0, "fate": { "fluorescence": 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