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An Extension of the Stern-Volmer Equation for Thermally Activated Delayed Fluorescence (TADF) Photocatalysts
扩展热激活延迟荧光 (TADF) 光催化剂的斯特恩-沃尔默方程

Bart Limburg* 巴特-林堡*

Cite This: J. Phys. Chem. Lett. 2024, 15, 10495-10499
引用此文：J. Phys.2024, 15, 10495-10499
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Abstract 摘要

Fluorescence quenching experiments are essential mechanistic tools in photoredox catalysis, allowing one to elucidate the first step in the catalytic cycle that occurs after photon absorption. Thermally activated delayed fluorescence (TADF) photocatalysts, however, yield nonlinear Stern-Volmer plots, thus requiring an adjustment to this widely used method to determine the efficiency of excited state quenching. Here, we derive an extension of the Stern-Volmer equation for TADF fluorophores that considers quenching from both the singlet and triplet excited states and experimentally verify it with fluorescence quenching experiments using the commonly employed TADF-photocatalyst 4CzIPN, and multiple-resonance TADF-photocatalyst QAO with three different quenchers in four solvents. The experimental data are perfectly described by this new equation, which in addition to the Stern-Volmer quenching constants allows for the determination of the product of intersystem and reverse intersystem crossing quantum yields, a quantity that is independent of the quencher.
荧光淬灭实验是光氧化催化过程中必不可少的机理工具，可用于阐明光子吸收后催化循环的第一步。然而，热激活延迟荧光（TADF）光催化剂会产生非线性 Stern-Volmer 图，因此需要调整这种广泛使用的方法，以确定激发态淬灭的效率。在此，我们推导了 TADF 荧光体的 Stern-Volmer 公式的扩展，该公式考虑了单线态和三线态激发态的淬灭，并使用常用的 TADF 光催化剂 4CzIPN 和多重共振 TADF 光催化剂 QAO 与三种不同的淬灭剂在四种溶剂中进行荧光淬灭实验进行了验证。这个新方程完美地描述了实验数据，除了斯特恩-沃尔默淬火常数外，它还能确定系统间和反向系统间交叉量子产率的乘积，这个量子产率与淬火剂无关。

The family of thermally activated delayed fluorescence (TADF) dyes based on diarylamino-functionalized dicyanobenzenes 1 1 ^(1){ }^{1} has been extensively applied in fields such as organic electronics and photoredox catalysis during the past decade. In the latter field, light excitation of the TADF dye leads to a reactive excited state that can be quenched through electron or energy transfer, leading to reactivity that is otherwise absent in the ground state. 2 2 ^(2){ }^{2} Photocatalysts based on transition-metal complexes of, e.g., Ir or Ru 3 Ru 3 Ru^(3)\mathrm{Ru}^{3} or non-TADF organic dyes 4 4 ^(4){ }^{4} feature emission from a pure excited state. In most cases, the reactive excited state is a triplet that occurs after absorption of light and intersystem crossing (ISC), because triplet states feature longer lifetimes that allow for bimolecular reactivity. TADF dyes, however, are characterized by an excited-state system that, in its simplest form, has two excited states (a singlet and a triplet) that are close enough in energy such that, in addition to ISC, thermal population of the higher-energy singlet excited state from the triplet, known as reverse intersystem crossing (RISC), occurs readily at room temperature. 2 2 ^(2){ }^{2} After excitation, these compounds decay back to the ground state in a biexponential manner according to eq 1 which can be interpreted as a prompt decay of the initially pure singlet excited state (with rate constant k p k p k_(p)k_{\mathrm{p}} ), and a slower delayed decay of an equilibrium state of singlet and triplet excited states (with rate constant k d k d k_(d)k_{\mathrm{d}} ); see Figure 1a.
热激活延迟荧光（TADF）染料系列基于二芳基氨基官能化二氰基苯 1 1 ^(1){ }^{1} ，在过去十年中被广泛应用于有机电子学和光氧化催化等领域。在光氧化催化领域，TADF 染料受光激发后会产生反应激发态，这种激发态可以通过电子或能量转移淬灭，从而产生基态所不具备的反应活性。 2 2 ^(2){ }^{2} 基于过渡金属配合物（如 Ir 或 Ru 3 Ru 3 Ru^(3)\mathrm{Ru}^{3} 或非 TADF 有机染料 4 4 ^(4){ }^{4} 的光催化剂具有纯激发态发射的特点。在大多数情况下，反应激发态是光吸收和系统间交叉（ISC）后出现的三重态，因为三重态的寿命较长，可以产生双分子反应。然而，TADF 染料的激发态系统最简单的形式是有两个激发态（单线态和三线态），这两个激发态的能量足够接近，因此，除了 ISC 外，在室温下，高能量单线态激发态从三线态的热迁移也很容易发生，这就是所谓的反向系统间交叉（RISC）。 2 2 ^(2){ }^{2} 激发后，这些化合物会根据公式 1 以双指数方式衰变回基态，这可以解释为最初纯单线激发态的迅速衰变（速率常数为 k p k p k_(p)k_{\mathrm{p}} ），以及单线和三线激发态平衡态的较慢延迟衰变（速率常数为 k d k d k_(d)k_{\mathrm{d}} ）；见图 1a。
I ( t ) = A e − k p t + B e − k d t I ( t ) = A e − k p t + B e − k d t I(t)=Ae^(-k_(p)t)+Be^(-k_(d)t)I(t)=A \mathrm{e}^{-k_{\mathrm{p}} t}+B \mathrm{e}^{-k_{\mathrm{d}} t}
It is important to note that the experimentally observed rate constants of this biexponential decay ( k p k p k_(p)k_{\mathrm{p}} and k d k d k_(d)k_{\mathrm{d}} ) are not the
需要注意的是，实验观测到的这种双指数衰变的速率常数（ k p k p k_(p)k_{\mathrm{p}} 和 k d k d k_(d)k_{\mathrm{d}} ）并不是
inverse of the lifetime of the pure singlet and triplet states but instead are mathematically defined as follows. 5 5 ^(5){ }^{5}
纯单态和三重态寿命的倒数，而是按以下数学方法定义的。 5 5 ^(5){ }^{5}
k p , d = ( k S tot + k T tot ) ± ( k S tot − k T tot ) 2 + 4 k ISC k RISC 2 k p , d = k S tot + k T tot ± k S tot − k T tot 2 + 4 k ISC k RISC 2 k_(p,d)=((k_(S_(tot))+k_(T_(tot)))+-sqrt((k_(S_(tot))-k_(T_(tot)))^(2)+4k_(ISC)k_(RISC)))/(2)k_{\mathrm{p}, \mathrm{~d}}=\frac{\left(k_{\mathrm{S}_{\mathrm{tot}}}+k_{\mathrm{T}_{\mathrm{tot}}}\right) \pm \sqrt{\left(k_{\mathrm{S}_{\mathrm{tot}}}-k_{\mathrm{T}_{\mathrm{tot}}}\right)^{2}+4 k_{\mathrm{ISC}} k_{\mathrm{RISC}}}}{2}
Here k S tot k S tot k_(S_(tot))k_{\mathrm{S}_{\mathrm{tot}}} and k T tot k T tot k_(T_(tot))k_{\mathrm{T}_{\mathrm{tot}}} are defined as the sum of all rate constants of the unimolecular processes (i.e., not including the bimolecular processes discussed in the following sections) occurring from the singlet and triplet state, respectively. k S tot k S tot k_(S_(tot))k_{\mathrm{S}_{\mathrm{tot}}} and k T tot k T tot k_(T_(tot))k_{\mathrm{T}_{\mathrm{tot}}} as well as the product of the rate constants of ISC and RISC ( k ISC k RISC k ISC k RISC k_(ISC)k_(RISC)k_{\mathrm{ISC}} k_{\mathrm{RISC}} ) can be extracted by considering the ratio of fluorescence intensity between the two individual decays as measured by time-correlated single photon counting, according to eqs 3-5 (see the Supporting Information). 5 5 ^(5){ }^{5} This ratio should be measured with sufficient data points on the prompt decay to ensure the ratio is reliable, and therefore it is best to do one measurement that captures the entire decay and one that mostly captures the prompt decay; see the Supporting Information.
这里的 k S tot k S tot k_(S_(tot))k_{\mathrm{S}_{\mathrm{tot}}} 和 k T tot k T tot k_(T_(tot))k_{\mathrm{T}_{\mathrm{tot}}} 分别定义为从单重态和三重态发生的单分子过程（即不包括下文讨论的双分子过程）的所有速率常数之和。 k S tot k S tot k_(S_(tot))k_{\mathrm{S}_{\mathrm{tot}}} 和 k T tot k T tot k_(T_(tot))k_{\mathrm{T}_{\mathrm{tot}}} 以及 ISC 和 RISC 的速率常数的乘积（ k ISC k RISC k ISC k RISC k_(ISC)k_(RISC)k_{\mathrm{ISC}} k_{\mathrm{RISC}} ）可以通过考虑时间相关单光子计数法测量的两个单独衰变之间的荧光强度之比，根据公式 3-5 提取出来（见《辅助信息》）。 5 5 ^(5){ }^{5} 在测量这一比率时，应充分考虑迅速衰变的数据点，以确保比率的可靠性，因此最好进行一次能捕捉整个衰变的测量，以及一次主要捕捉迅速衰变的测量；请参阅《辅助信息》。
Figure 1. a) TCSPC data (red circles) of 4 CzIPN ( 50 μ M 4 CzIPN 50 μ M 4CzIPN(50 muM:}4 \mathrm{CzIPN}\left(50 \mu \mathrm{M}\right. in THF) at 20 ∘ C , λ ex = 446 nm 20 ∘ C , λ ex = 446 nm 20^(@)C,lambda_(ex)=446nm20^{\circ} \mathrm{C}, \lambda_{\mathrm{ex}}=446 \mathrm{~nm}, showing a biexponential decay, and corresponding fit to eq 1 (black line). b) Simplified Jablonski diagram of TADF fluorophores and possible bimolecular quenching pathways from either the singlet or triplet excited states. c) Molecular structure of TADF-fluorophore 4CzIPN, MR-TADF-fluorophore QAO, and the quenchers employed in this study: triethylamine ( Et 3 N ) Et 3 N (Et_(3)(N))\left(\mathrm{Et}_{3} \mathrm{~N}\right), diisopropylamine (DIPEA), and Hantzsch Ester (HEH).
图 1. a) 20 ∘ C , λ ex = 446 nm 20 ∘ C , λ ex = 446 nm 20^(@)C,lambda_(ex)=446nm20^{\circ} \mathrm{C}, \lambda_{\mathrm{ex}}=446 \mathrm{~nm} 时 4 CzIPN ( 50 μ M 4 CzIPN 50 μ M 4CzIPN(50 muM:}4 \mathrm{CzIPN}\left(50 \mu \mathrm{M}\right. 在 THF 中的 TCSPC 数据（红圈），显示双指数衰减，以及与公式 1 的相应拟合（黑线）。 b) TADF 荧光体的简化 Jablonski 图，以及从单线态或三线态激发的可能双分子淬灭途径。c) TADF-荧光团 4CzIPN、MR-TADF-荧光团 QAO 以及本研究中使用的淬灭剂：三乙胺 ( Et 3 N ) Et 3 N (Et_(3)(N))\left(\mathrm{Et}_{3} \mathrm{~N}\right) 、二异丙基胺 (DIPEA) 和 Hantzsch 酯 (HEH) 的分子结构。
k S tot = k p A A + B + k d B A + B k T tot = k p B A + B + k d A A + B k ISC k RISC = A B ( A + B ) 2 ( k p − k d ) 2 k S tot = k p A A + B + k d B A + B k T tot = k p B A + B + k d A A + B k ISC k RISC = A B ( A + B ) 2 k p − k d 2 {:[k_(S_(tot))=k_(p)(A)/(A+B)+k_(d)(B)/(A+B)],[k_(T_(tot))=k_(p)(B)/(A+B)+k_(d)(A)/(A+B)],[k_(ISC)k_(RISC)=(AB)/((A+B)^(2))(k_(p)-k_(d))^(2)]:}\begin{aligned} & k_{\mathrm{S}_{\mathrm{tot}}}=k_{\mathrm{p}} \frac{A}{A+B}+k_{\mathrm{d}} \frac{B}{A+B} \\ & k_{\mathrm{T}_{\mathrm{tot}}}=k_{\mathrm{p}} \frac{B}{A+B}+k_{\mathrm{d}} \frac{A}{A+B} \\ & k_{\mathrm{ISC}} k_{\mathrm{RISC}}=\frac{A B}{(A+B)^{2}}\left(k_{\mathrm{p}}-k_{\mathrm{d}}\right)^{2} \end{aligned}
In the field of photoredox catalysis, it is important to understand which compound in the complex reaction mixture reacts with the excited state of the photocatalyst, and for this reason so-called luminescence quenching experiments are often an integral part of any mechanistic work. 6 − 14 6 − 14 ^(6-14){ }^{6-14} In such studies, the luminescence intensity of the photocatalyst is probed under varying concentrations of the quencher compound, and the results are plotted using the SternVolmer plot, generally obtaining a linear relationship for wellbehaved dynamically quenched systems when utilizing photocatalysts with a single (emissive) excited state, according to eq 6.
在光氧化催化领域，了解复杂反应混合物中哪种化合物会与光催化剂的激发态发生反应非常重要，因此，所谓的发光淬灭实验通常是任何机理研究工作不可或缺的一部分。 6 − 14 6 − 14 ^(6-14){ }^{6-14} 在此类研究中，光催化剂的发光强度是在不同浓度的淬灭化合物作用下进行探测的，其结果用 SternVolmer 图绘制，根据公式 6，当利用具有单一（发射）激发态的光催化剂时，通常会得到一个线性关系良好的动态淬灭系统。
I 0 I = 1 + K SV [ Q ] I 0 I = 1 + K SV [ Q ] (I_(0))/(I)=1+K_(SV)[Q]\frac{I_{0}}{I}=1+K_{\mathrm{SV}}[\mathrm{Q}]
Many physical and chemical effects, however, can lead to a deviation from linearity such as static quenching, 15 , 16 15 , 16 ^(15,16){ }^{15,16} high viscosity, 17 17 ^(17){ }^{17} and inner-filter effects. 9 , 16 , 18 9 , 16 , 18 ^(9,16,18){ }^{9,16,18} Interestingly, TADF photocatalysts also exhibit nonlinear Stern-Volmer plots portraying a negative curvature. 6 , 19 6 , 19 ^(6,19){ }^{6,19} Within the photoredox catalysis community, however, these fluorophores are typically treated as if they were photocatalysts with a single excited emissive state, which can lead to incorrect interpretations of the luminescence quenching studies. In this work, we derive and experimentally verify an extension of the Stern-Volmer equation that fully takes into account the rapid singlet-triplet interconversions that define the excited state of TADF photocatalysts and considers quenching from both the singlet and triplet excited state (Figure 1b).
然而，许多物理和化学效应会导致偏离线性，例如静态淬火、 15 , 16 15 , 16 ^(15,16){ }^{15,16} 高粘度、 17 17 ^(17){ }^{17} 和内滤器效应。 9 , 16 , 18 9 , 16 , 18 ^(9,16,18){ }^{9,16,18} 有趣的是，TADF 光催化剂也表现出非线性的 Stern-Volmer 图，呈现负曲率。 6 , 19 6 , 19 ^(6,19){ }^{6,19} 然而，在光氧化催化领域，这些荧光团通常被当作具有单一激发发射态的光催化剂来处理，这可能会导致对发光淬灭研究的错误解释。在这项工作中，我们推导并通过实验验证了 Stern-Volmer 方程的扩展，该方程充分考虑了 TADF 光催化剂激发态的单线-三线快速相互转换，并考虑了单线和三线激发态的淬灭（图 1b）。
We first consider the quantum yield of fluorescence since it is proportional to the luminescence intensity I I II. The description of the quantum yield of fluorescence in the absence of bimolecular reactions for TADF fluorophores ( Φ f 0 Φ f 0 Phi_(f)^(0)\Phi_{\mathrm{f}}^{0} ) needs to consider the prompt as well as the delayed components and take into account that the system can go through several cycles of ISC and RISC before ultimately decaying to the ground state. Taking the limit of the resulting geometric series (eq 7) yields the eq 8 . 20 8 . 20 8.^(20)8 .^{20}
我们首先考虑荧光的量子产率，因为它与发光强度 I I II 成正比。描述 TADF 荧光体在无双分子反应情况下的荧光量子产率（ Φ f 0 Φ f 0 Phi_(f)^(0)\Phi_{\mathrm{f}}^{0} ）时，需要同时考虑瞬时成分和延迟成分，并考虑到系统在最终衰减到基态之前可能会经历多个 ISC 和 RISC 循环。对所得到的几何级数（公式 7）进行极限计算，可得到公式 8 . 20 8 . 20 8.^(20)8 .^{20}
Φ f 0 = Φ pf 0 ( 1 + Φ ISC 0 Φ RISC 0 + ( Φ ISC 0 Φ RISC 0 ) 2 + ( Φ ISC 0 Φ RISC 0 ) 3 + ⋯ ) Φ ISC 0 Φ RISC 0 = k ISC k RISC k S tot k T tot , Φ pf 0 = k f k S tot Φ f 0 = Φ pf 0 1 − Φ ISC 0 Φ RISC 0 Φ f 0 = Φ pf 0 1 + Φ ISC 0 Φ RISC 0 + Φ ISC 0 Φ RISC 0 2 + Φ ISC 0 Φ RISC 0 3 + ⋯ Φ ISC 0 Φ RISC 0 = k ISC k RISC k S tot k T tot , Φ pf 0 = k f k S tot Φ f 0 = Φ pf 0 1 − Φ ISC 0 Φ RISC 0 {:[Phi_(f)^(0)=Phi_(pf)^(0)(1+Phi_(ISC)^(0)Phi_(RISC)^(0)+(Phi_(ISC)^(0)Phi_(RISC)^(0))^(2):}],[{:+(Phi_(ISC)^(0)Phi_(RISC)^(0))^(3)+cdots)],[Phi_(ISC)^(0)Phi_(RISC)^(0)=(k_(ISC)k_(RISC))/(k_(S_(tot))k_(T_(tot)))","Phi_(pf)^(0)=(k_(f))/(k_(S_(tot)))],[Phi_(f)^(0)=(Phi_(pf)^(0))/(1-Phi_(ISC)^(0)Phi_(RISC)^(0))]:}\begin{aligned} & \Phi_{\mathrm{f}}^{0}= \Phi_{\mathrm{pf}}^{0}\left(1+\Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0}+\left(\Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0}\right)^{2}\right. \\ &\left.+\left(\Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0}\right)^{3}+\cdots\right) \\ & \Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0}=\frac{k_{\mathrm{ISC}} k_{\mathrm{RISC}}}{k_{S_{\mathrm{tot}}} k_{T_{\mathrm{tot}}}}, \Phi_{\mathrm{pf}}^{0}=\frac{k_{\mathrm{f}}}{k_{S_{\mathrm{tot}}}} \\ & \Phi_{\mathrm{f}}^{0}= \frac{\Phi_{\mathrm{pf}}^{0}}{1-\Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0}} \end{aligned}
Here, Φ pf 0 Φ pf 0 Phi_(pf)^(0)\Phi_{\mathrm{pf}}^{0} is the quantum yield of prompt fluorescence, and Φ ISC 0 Φ ISC 0 Phi_(ISC)^(0)\Phi_{\mathrm{ISC}}^{0} and Φ RISC 0 Φ RISC 0 Phi_(RISC)^(0)\Phi_{\mathrm{RISC}}^{0} are the quantum yields of intersystem crossing and reverse intersystem crossing, respectively. Having defined the quantum yield of fluorescence, we can consider bimolecular reactions occurring from both the singlet and the triplet excited states (Figure 1b). The mathematical description of such reactions is identical for electron transfer and energy transfer reactions. Each possible reaction has its corresponding rate constant and depends on the concentration of the quenching compound, i.e., k q S [ Q ] k q S [ Q ] k_(qS)[Q]k_{\mathrm{q} S}[\mathrm{Q}] or k qT [ Q ] k qT [ Q ] k_(qT)[Q]k_{\mathrm{qT}}[\mathrm{Q}] for reactions of compound Q Q QQ with the singlet or triplet excited state, respectively. The quantum yields defined above are all affected by these reactions, and their definitions in the presence of quencher Q Q QQ are as follows:
这里， Φ pf 0 Φ pf 0 Phi_(pf)^(0)\Phi_{\mathrm{pf}}^{0} 是迅速荧光的量子产率， Φ ISC 0 Φ ISC 0 Phi_(ISC)^(0)\Phi_{\mathrm{ISC}}^{0} 和 Φ RISC 0 Φ RISC 0 Phi_(RISC)^(0)\Phi_{\mathrm{RISC}}^{0} 分别是系统间交叉和反向系统间交叉的量子产率。在定义了荧光量子产率之后，我们可以考虑从单态和三态激发态发生的双分子反应（图 1b）。这种反应的数学描述与电子转移反应和能量转移反应相同。每个可能的反应都有其相应的速率常数，并取决于淬火化合物的浓度，即化合物 Q Q QQ 与单激发态或三重激发态反应的速率常数分别为 k q S [ Q ] k q S [ Q ] k_(qS)[Q]k_{\mathrm{q} S}[\mathrm{Q}] 或 k qT [ Q ] k qT [ Q ] k_(qT)[Q]k_{\mathrm{qT}}[\mathrm{Q}] 。上面定义的量子产率都会受到这些反应的影响，在有淬灭剂 Q Q QQ 的情况下，它们的定义如下：
Φ pf ( Q ) = k f k S tot + k qS [ Q ] , Φ ISC ( Q ) = k ISC k S tot + k q S [ Q ] Φ RISC ( Q ) = k RISC k T tot + k qT [ Q ] Φ pf ( Q ) = k f k S tot + k qS [ Q ] , Φ ISC ( Q ) = k ISC k S tot + k q S [ Q ] Φ RISC ( Q ) = k RISC k T tot + k qT [ Q ] {:[Phi_(pf)(Q)=(k_(f))/(k_(S_(tot))+k_(qS)[Q])","quadPhi_(ISC)(Q)=(k_(ISC))/(k_(S_(tot))+k_(qS)[Q])],[Phi_(RISC)(Q)=(k_(RISC))/(k_(T_(tot))+k_(qT)[Q])]:}\begin{aligned} & \Phi_{\mathrm{pf}}(Q)=\frac{k_{\mathrm{f}}}{k_{\mathrm{S}_{\mathrm{tot}}}+k_{\mathrm{qS}}[\mathrm{Q}]}, \quad \Phi_{\mathrm{ISC}}(Q)=\frac{k_{\mathrm{ISC}}}{k_{\mathrm{S}_{\mathrm{tot}}}+k_{\mathrm{q} S}[\mathrm{Q}]} \\ & \Phi_{\mathrm{RISC}}(Q)=\frac{k_{\mathrm{RISC}}}{k_{\mathrm{T}_{\mathrm{tot}}}+k_{\mathrm{qT}}[\mathrm{Q}]} \end{aligned}
Since the ratio of the emission intensities is equal to the ratio of fluorescence quantum yields, we divide Φ f 0 Φ f 0 Phi_(f)^(0)\Phi_{\mathrm{f}}^{0} by Φ f ( Q ) Φ f ( Q ) Phi_(f)(Q)\Phi_{\mathrm{f}}(Q) to derive the extension of the Stern-Volmer equation (see the Supporting Information):
由于发射强度的比值等于荧光量子产率的比值，因此我们用 Φ f 0 Φ f 0 Phi_(f)^(0)\Phi_{\mathrm{f}}^{0} 除以 Φ f ( Q ) Φ f ( Q ) Phi_(f)(Q)\Phi_{\mathrm{f}}(Q) 得出斯特恩-沃尔默方程的扩展（见佐证资料）：
I 0 I = Φ f 0 Φ f ( Q ) = 1 1 − Φ ISC 0 Φ RISC 0 ( 1 + K SV S [ Q ] − Φ ISC 0 Φ RISC 0 1 + K SV T [ Q ] ) I 0 I = Φ f 0 Φ f ( Q ) = 1 1 − Φ ISC 0 Φ RISC 0 1 + K SV S [ Q ] − Φ ISC 0 Φ RISC 0 1 + K SV T [ Q ] {:[(I_(0))/(I)=(Phi_(f)^(0))/(Phi_(f)(Q))],[=(1)/(1-Phi_(ISC)^(0)Phi_(RISC)^(0))(1+K_(SV)^(S)[Q]-(Phi_(ISC)^(0)Phi_(RISC)^(0))/(1+K_(SV)^(T)[Q]))]:}\begin{aligned} \frac{I_{0}}{I} & =\frac{\Phi_{\mathrm{f}}^{0}}{\Phi_{\mathrm{f}}(Q)} \\ & =\frac{1}{1-\Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0}}\left(1+K_{\mathrm{SV}}^{\mathrm{S}}[\mathrm{Q}]-\frac{\Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0}}{1+K_{\mathrm{SV}}^{\mathrm{T}}[\mathrm{Q}]}\right) \end{aligned}
Here, K S V S K S V S K_(SV)^(S)K_{S V}^{S} and K S V T K S V T K_(SV)^(T)K_{S V}^{T} are the Stern-Volmer constants for quenching the singlet and triplet excited states: K SV S = k qS k S tot K SV S = k qS k S tot K_(SV)^(S)=(k_(qS))/(k_(S_(tot)))K_{\mathrm{SV}}^{\mathrm{S}}=\frac{k_{\mathrm{qS}}}{k_{\mathrm{S}_{\mathrm{tot}}}} and K SV T = k q T k T tot K SV T = k q T k T tot K_(SV)^(T)=(k_(qT))/(k_(T_(tot)))K_{\mathrm{SV}}^{\mathrm{T}}=\frac{k_{\mathrm{q} \mathrm{T}}}{k_{\mathrm{T}_{\mathrm{tot}}}}.
这里， K S V S K S V S K_(SV)^(S)K_{S V}^{S} 和 K S V T K S V T K_(SV)^(T)K_{S V}^{T} 是淬灭单重态和三重态激发态的斯特恩-沃尔默常数： K SV S = k qS k S tot K SV S = k qS k S tot K_(SV)^(S)=(k_(qS))/(k_(S_(tot)))K_{\mathrm{SV}}^{\mathrm{S}}=\frac{k_{\mathrm{qS}}}{k_{\mathrm{S}_{\mathrm{tot}}}} 和 K SV T = k q T k T tot K SV T = k q T k T tot K_(SV)^(T)=(k_(qT))/(k_(T_(tot)))K_{\mathrm{SV}}^{\mathrm{T}}=\frac{k_{\mathrm{q} \mathrm{T}}}{k_{\mathrm{T}_{\mathrm{tot}}}} 。
Figure 2. Stern-Volmer plots of TADF-photocatalyst 4CzIPN ( 50 μ M 50 μ M 50 muM50 \mu \mathrm{M} ) in four solvents (toluene, THF, DMF, and MeCN) with three different quenchers ( Et 3 N Et 3 N (Et_(3)(N):}\left(\mathrm{Et}_{3} \mathrm{~N}\right., DIPEA, HEH ) ) )) thermostated at 20 ∘ C , λ ex = 450 nm 20 ∘ C , λ ex = 450 nm 20^(@)C,lambda_(ex)=450nm20^{\circ} \mathrm{C}, \lambda_{\mathrm{ex}}=450 \mathrm{~nm}. Global fits (taken for all three quenchers per solvent) to eq 10 are shown as the black continuous line, and goodness of fit χ 2 χ 2 chi^(2)\chi^{2} and R 2 R 2 R^(2)R^{2} are indicated for each global fit.
图 2.TADF 光催化剂 4CzIPN ( 50 μ M 50 μ M 50 muM50 \mu \mathrm{M} ) 在四种溶剂（甲苯、THF、DMF 和 MeCN）中与三种不同的淬灭剂 ( Et 3 N Et 3 N (Et_(3)(N):}\left(\mathrm{Et}_{3} \mathrm{~N}\right. 、DIPEA、HEH ) ) )) 在 20 ∘ C , λ ex = 450 nm 20 ∘ C , λ ex = 450 nm 20^(@)C,lambda_(ex)=450nm20^{\circ} \mathrm{C}, \lambda_{\mathrm{ex}}=450 \mathrm{~nm} 温度下的 Stern-Volmer 图。式 10 的全局拟合（针对每种溶剂的所有三种淬火剂）显示为黑色连续线段，每个全局拟合的拟合优度 χ 2 χ 2 chi^(2)\chi^{2} 和 R 2 R 2 R^(2)R^{2} 均已标出。
Table 1. Obtained Fitting Constants from Fluorescence Quenching Experiments in Figure 2 and TCSPC (See the Supporting Information) a a ^(a){ }^{a}
表 1.从图 2 和 TCSPC 的荧光淬灭实验中获得的拟合常数（见佐证资料） a a ^(a){ }^{a} .
Solvent 溶剂 Quencher 淬火 K SV S ( M − 1 ) b K SV  S M − 1 b K_("SV ")^(S)(M^(-1))^(b)K_{\text {SV }}^{\mathrm{S}}\left(\mathrm{M}^{-1}\right)^{b} K S V S × 10 3 ( M − 1 ) b K S V S × 10 3 M − 1 b K_(SV)^(S)xx10^(3)(M^(-1))^(b)K_{S V}^{S} \times 10^{3}\left(\mathrm{M}^{-1}\right)^{b} Φ ISC 0 Φ RISC 0 b Φ ISC  0 Φ RISC  0 b Phi_("ISC ")^(0)Phi_("RISC ")^(0)^(b)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0}{ }^{b} k S tot × 10 7 ( s − 1 ) c k S tot  × 10 7 s − 1 c k_(S_("tot "))xx10^(7)(s^(-1))^(c)k_{\mathrm{S}_{\text {tot }}} \times 10^{7}\left(\mathrm{~s}^{-1}\right)^{c} k T tot × 10 5 ( s − 1 ) c k T tot  × 10 5 s − 1 c k_(T_("tot "))xx10^(5)(s^(-1))^(c)k_{\mathrm{T}_{\text {tot }}} \times 10^{5}\left(\mathrm{~s}^{-1}\right)^{c} k q × 10 9 ( M − 1 s − 1 ) k q × 10 9 M − 1 s − 1 k_(q)xx10^(9)(M^(-1)s^(-1))k_{\mathrm{q}} \times 10^{9}\left(\mathrm{M}^{-1} \mathrm{~s}^{-1}\right) k qT × 10 9 ( M − 1 s − 1 ) k qT × 10 9 M − 1 s − 1 k_(qT)xx10^(9)(M^(-1)s^(-1))k_{\mathrm{qT}} \times 10^{9}\left(\mathrm{M}^{-1} \mathrm{~s}^{-1}\right)
Toluene 甲苯 Et 3 N Et 3 N Et_(3)N\mathrm{Et}_{3} \mathrm{~N} 32 ± 1.4 32 ± 1.4 32+-1.432 \pm 1.4 0.855 ± 0.09 0.855 ± 0.09 0.855+-0.090.855 \pm 0.09 0.70 ± 0.006 0.70 ± 0.006 0.70+-0.0060.70 \pm 0.006 6.68 ± 0.97 6.68 ± 0.97 6.68+-0.976.68 \pm 0.97 8.73 ± 0.75 8.73 ± 0.75 8.73+-0.758.73 \pm 0.75 2.2 ± 0.33 2.2 ± 0.33 2.2+-0.332.2 \pm 0.33 0.75 ± 0.10 0.75 ± 0.10 0.75+-0.100.75 \pm 0.10
DIPEA 93 ± 3.3 93 ± 3.3 93+-3.393 \pm 3.3 13.9 ± 0.98 13.9 ± 0.98 13.9+-0.9813.9 \pm 0.98 ( 0.71 ± 0.17 ) c ( 0.71 ± 0.17 ) c (0.71+-0.17)^(c)(0.71 \pm 0.17)^{c} 6.2 ± 0.93 6.2 ± 0.93 6.2+-0.936.2 \pm 0.93 12 ± 0.87 12 ± 0.87 12+-0.8712 \pm 0.87
HEH 125 ± 33 125 ± 33 125+-33125 \pm 33 8.00 ± 0.70 8.00 ± 0.70 8.00+-0.708.00 \pm 0.70 8.4 ± 2.5 8.4 ± 2.5 8.4+-2.58.4 \pm 2.5 7.0 ± 0.86 7.0 ± 0.86 7.0+-0.867.0 \pm 0.86
THF Et 3 N Et 3 N Et_(3)N\mathrm{Et}_{3} \mathrm{~N} 39 ± 0.69 39 ± 0.69 39+-0.6939 \pm 0.69 1.48 ± 0.13 1.48 ± 0.13 1.48+-0.131.48 \pm 0.13 0.54 ± 0.005 0.54 ± 0.005 0.54+-0.0050.54 \pm 0.005 3.65 ± 0.55 3.65 ± 0.55 3.65+-0.553.65 \pm 0.55 6.50 ± 0.58 6.50 ± 0.58 6.50+-0.586.50 \pm 0.58 1.4 ± 0.21 1.4 ± 0.21 1.4+-0.211.4 \pm 0.21 0.96 ± 0.12 0.96 ± 0.12 0.96+-0.120.96 \pm 0.12
DIPEA 100 ± 1.9 100 ± 1.9 100+-1.9100 \pm 1.9 4.70 ± 0.59 4.70 ± 0.59 4.70+-0.594.70 \pm 0.59 ( 0.58 ± 0.15 ) c ( 0.58 ± 0.15 ) c (0.58+-0.15)^(c)(0.58 \pm 0.15)^{c} 3.7 ± 0.55 3.7 ± 0.55 3.7+-0.553.7 \pm 0.55 3.1 ± 0.47 3.1 ± 0.47 3.1+-0.473.1 \pm 0.47
HEH 76 ± 1.5 76 ± 1.5 76+-1.576 \pm 1.5 2.67 ± 0.26 2.67 ± 0.26 2.67+-0.262.67 \pm 0.26 2.8 ± 0.42 2.8 ± 0.42 2.8+-0.422.8 \pm 0.42 1.7 ± 0.23 1.7 ± 0.23 1.7+-0.231.7 \pm 0.23
DMF Et 3 N Et 3 N Et_(3)N\mathrm{Et}_{3} \mathrm{~N} 53 ± 1.2 53 ± 1.2 53+-1.253 \pm 1.2 2.25 ± 0.52 2.25 ± 0.52 2.25+-0.522.25 \pm 0.52 0.33 ± 0.009 0.33 ± 0.009 0.33+-0.0090.33 \pm 0.009 3.96 ± 0.40 3.96 ± 0.40 3.96+-0.403.96 \pm 0.40 8.44 ± 0.58 8.44 ± 0.58 8.44+-0.588.44 \pm 0.58 2.1 ± 0.22 2.1 ± 0.22 2.1+-0.222.1 \pm 0.22 1.9 ± 0.46 1.9 ± 0.46 1.9+-0.461.9 \pm 0.46
DIPEA 94 ± 1.8 94 ± 1.8 94+-1.894 \pm 1.8 2.87 ± 0.66 2.87 ± 0.66 2.87+-0.662.87 \pm 0.66 ( 0.35 ± 0.06 ) c ( 0.35 ± 0.06 ) c (0.35+-0.06)^(c)(0.35 \pm 0.06)^{c} 3.7 ± 0.38 3.7 ± 0.38 3.7+-0.383.7 \pm 0.38 2.4 ± 0.58 2.4 ± 0.58 2.4+-0.582.4 \pm 0.58
HEH 57 ± 1.5 57 ± 1.5 57+-1.557 \pm 1.5 2.20 ± 0.37 2.20 ± 0.37 2.20+-0.372.20 \pm 0.37 2.2 ± 0.23 2.2 ± 0.23 2.2+-0.232.2 \pm 0.23 1.9 ± 0.33 1.9 ± 0.33 1.9+-0.331.9 \pm 0.33
MeCN Et 3 N Et 3 N Et_(3)N\mathrm{Et}_{3} \mathrm{~N} 116 ± 1.8 116 ± 1.8 116+-1.8116 \pm 1.8 5.15 ± 1.4 5.15 ± 1.4 5.15+-1.45.15 \pm 1.4 0.29 ± 0.006 0.29 ± 0.006 0.29+-0.0060.29 \pm 0.006 5.13 ± 0.64 5.13 ± 0.64 5.13+-0.645.13 \pm 0.64 8.26 ± 0.74 8.26 ± 0.74 8.26+-0.748.26 \pm 0.74 6.0 ± 0.75 6.0 ± 0.75 6.0+-0.756.0 \pm 0.75 4.3 ± 1.2 4.3 ± 1.2 4.3+-1.24.3 \pm 1.2
DIPEA 218 ± 2.6 218 ± 2.6 218+-2.6218 \pm 2.6 14.9 ± 7.5 14.9 ± 7.5 14.9+-7.514.9 \pm 7.5 ( 0.30 ± 0.06 ) c ( 0.30 ± 0.06 ) c (0.30+-0.06)^(c)(0.30 \pm 0.06)^{c} 11 ± 1.4 11 ± 1.4 11+-1.411 \pm 1.4 12 ± 6.3 12 ± 6.3 12+-6.312 \pm 6.3
HEH 139 ± 5.6 139 ± 5.6 139+-5.6139 \pm 5.6 8.56 ± 1.2 8.56 ± 1.2 8.56+-1.28.56 \pm 1.2 7.1 ± 0.93 7.1 ± 0.93 7.1+-0.937.1 \pm 0.93 7.1 ± 1.2 7.1 ± 1.2 7.1+-1.27.1 \pm 1.2
Solvent Quencher K_("SV ")^(S)(M^(-1))^(b) K_(SV)^(S)xx10^(3)(M^(-1))^(b) Phi_("ISC ")^(0)Phi_("RISC ")^(0)^(b) k_(S_("tot "))xx10^(7)(s^(-1))^(c) k_(T_("tot "))xx10^(5)(s^(-1))^(c) k_(q)xx10^(9)(M^(-1)s^(-1)) k_(qT)xx10^(9)(M^(-1)s^(-1)) Toluene Et_(3)N 32+-1.4 0.855+-0.09 0.70+-0.006 6.68+-0.97 8.73+-0.75 2.2+-0.33 0.75+-0.10 DIPEA 93+-3.3 13.9+-0.98 (0.71+-0.17)^(c) 6.2+-0.93 12+-0.87 HEH 125+-33 8.00+-0.70 8.4+-2.5 7.0+-0.86 THF Et_(3)N 39+-0.69 1.48+-0.13 0.54+-0.005 3.65+-0.55 6.50+-0.58 1.4+-0.21 0.96+-0.12 DIPEA 100+-1.9 4.70+-0.59 (0.58+-0.15)^(c) 3.7+-0.55 3.1+-0.47 HEH 76+-1.5 2.67+-0.26 2.8+-0.42 1.7+-0.23 DMF Et_(3)N 53+-1.2 2.25+-0.52 0.33+-0.009 3.96+-0.40 8.44+-0.58 2.1+-0.22 1.9+-0.46 DIPEA 94+-1.8 2.87+-0.66 (0.35+-0.06)^(c) 3.7+-0.38 2.4+-0.58 HEH 57+-1.5 2.20+-0.37 2.2+-0.23 1.9+-0.33 MeCN Et_(3)N 116+-1.8 5.15+-1.4 0.29+-0.006 5.13+-0.64 8.26+-0.74 6.0+-0.75 4.3+-1.2 DIPEA 218+-2.6 14.9+-7.5 (0.30+-0.06)^(c) 11+-1.4 12+-6.3 HEH 139+-5.6 8.56+-1.2 7.1+-0.93 7.1+-1.2| Solvent | Quencher | $K_{\text {SV }}^{\mathrm{S}}\left(\mathrm{M}^{-1}\right)^{b}$ | $K_{S V}^{S} \times 10^{3}\left(\mathrm{M}^{-1}\right)^{b}$ | $\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0}{ }^{b}$ | $k_{\mathrm{S}_{\text {tot }}} \times 10^{7}\left(\mathrm{~s}^{-1}\right)^{c}$ | $k_{\mathrm{T}_{\text {tot }}} \times 10^{5}\left(\mathrm{~s}^{-1}\right)^{c}$ | $k_{\mathrm{q}} \times 10^{9}\left(\mathrm{M}^{-1} \mathrm{~s}^{-1}\right)$ | $k_{\mathrm{qT}} \times 10^{9}\left(\mathrm{M}^{-1} \mathrm{~s}^{-1}\right)$ | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | Toluene | $\mathrm{Et}_{3} \mathrm{~N}$ | $32 \pm 1.4$ | $0.855 \pm 0.09$ | $0.70 \pm 0.006$ | $6.68 \pm 0.97$ | $8.73 \pm 0.75$ | $2.2 \pm 0.33$ | $0.75 \pm 0.10$ | | | DIPEA | $93 \pm 3.3$ | $13.9 \pm 0.98$ | $(0.71 \pm 0.17)^{c}$ | | | $6.2 \pm 0.93$ | $12 \pm 0.87$ | | | HEH | $125 \pm 33$ | $8.00 \pm 0.70$ | | | | $8.4 \pm 2.5$ | $7.0 \pm 0.86$ | | THF | $\mathrm{Et}_{3} \mathrm{~N}$ | $39 \pm 0.69$ | $1.48 \pm 0.13$ | $0.54 \pm 0.005$ | $3.65 \pm 0.55$ | $6.50 \pm 0.58$ | $1.4 \pm 0.21$ | $0.96 \pm 0.12$ | | | DIPEA | $100 \pm 1.9$ | $4.70 \pm 0.59$ | $(0.58 \pm 0.15)^{c}$ | | | $3.7 \pm 0.55$ | $3.1 \pm 0.47$ | | | HEH | $76 \pm 1.5$ | $2.67 \pm 0.26$ | | | | $2.8 \pm 0.42$ | $1.7 \pm 0.23$ | | DMF | $\mathrm{Et}_{3} \mathrm{~N}$ | $53 \pm 1.2$ | $2.25 \pm 0.52$ | $0.33 \pm 0.009$ | $3.96 \pm 0.40$ | $8.44 \pm 0.58$ | $2.1 \pm 0.22$ | $1.9 \pm 0.46$ | | | DIPEA | $94 \pm 1.8$ | $2.87 \pm 0.66$ | $(0.35 \pm 0.06)^{c}$ | | | $3.7 \pm 0.38$ | $2.4 \pm 0.58$ | | | HEH | $57 \pm 1.5$ | $2.20 \pm 0.37$ | | | | $2.2 \pm 0.23$ | $1.9 \pm 0.33$ | | MeCN | $\mathrm{Et}_{3} \mathrm{~N}$ | $116 \pm 1.8$ | $5.15 \pm 1.4$ | $0.29 \pm 0.006$ | $5.13 \pm 0.64$ | $8.26 \pm 0.74$ | $6.0 \pm 0.75$ | $4.3 \pm 1.2$ | | | DIPEA | $218 \pm 2.6$ | $14.9 \pm 7.5$ | $(0.30 \pm 0.06)^{c}$ | | | $11 \pm 1.4$ | $12 \pm 6.3$ | | | HEH | $139 \pm 5.6$ | $8.56 \pm 1.2$ | | | | $7.1 \pm 0.93$ | $7.1 \pm 1.2$ |
a a ^(a){ }^{a} Uncertainties are the (propagated) standard errors of the fitted constants. b b ^(b){ }^{b} Obtained through fluorescence quenching experiments. c c ^(c){ }^{c} Obtained from fitting the time-correlated single photon counting decays.
a a ^(a){ }^{a} 不确定性是拟合常数的（传播）标准误差。 b b ^(b){ }^{b} 通过荧光淬灭实验获得。 c c ^(c){ }^{c} 通过拟合与时间相关的单光子计数衰减获得。
Equation 10 was experimentally verified by employing the common TADF photocatalyst 4CzIPN, and three different quenchers: triethylamine ( Et 3 N ) Et 3 N (Et_(3)(N))\left(\mathrm{Et}_{3} \mathrm{~N}\right), diisopropylethylamine (DIPEA), and Hantzsch Ester (HEH) in four different solvents (Figure 2; see Figure 1c for chemical structures). The fluorescence quenching was measured in strictly deoxygenated conditions (at least three freeze-pump-thaw cycles) at various concentrations of quencher, and the three-
通过使用常见的 TADF 光催化剂 4CzIPN，以及四种不同溶剂中的三种不同淬灭剂：三乙胺 ( Et 3 N ) Et 3 N (Et_(3)(N))\left(\mathrm{Et}_{3} \mathrm{~N}\right) 、二异丙基乙胺 (DIPEA) 和汉茨酯 (HEH)，对等式 10 进行了实验验证（图 2；化学结构见图 1c）。荧光淬灭是在严格的脱氧条件下（至少三次冷冻-抽气-解冻循环）以不同浓度的淬灭剂测得的，三
parameter eq 10 was used to fit the experimental data as shown in Figure 2. The resulting fitted constants are listed in Table 1. The data in Figure 2 clearly deviate from the typical linear relationship of the Stern-Volmer equation (eq 6), which can be rationalized considering the presence of two excited states where it is easier to quench the triplet state than the singlet state due to the much longer lifetime of the former. As such, efficient triplet-state quenching leads to a considerably larger
如图 2 所示，使用公式 10 中的参数对实验数据进行拟合。得出的拟合常数列于表 1。图 2 中的数据明显偏离了斯特恩-沃尔默方程（公式 6）的典型线性关系，考虑到存在两个激发态，三重态比单重态更容易淬灭，因为前者的寿命要长得多。因此，高效的三重态淬火会导致更大的
Figure 3. Quenching experiment of 4 CzIPN ( 50 μ M ) 4 CzIPN ( 50 μ M ) 4CzIPN(50 muM)4 \mathrm{CzIPN}(50 \mu \mathrm{M}) with Et 3 N Et 3 N Et_(3)N\mathrm{Et}_{3} \mathrm{~N} in THF at 20 ∘ C 20 ∘ C 20^(@)C20^{\circ} \mathrm{C} and various fits. a) Linear fit using only the higher-concentration data points (red), discarding the data at lower concentration (gray). b) Fits using fixed values of Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} demonstrating that it is not possible to fit the data (circles) fixing different values for Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} (cf. χ 2 χ 2 chi^(2)\chi^{2} values), highlighting that the equation is not overparametrized. Only when Φ ISC 0 Φ RISC 0 Φ ISC 0 Φ RISC 0 Phi_(ISC)^(0)Phi_(RISC)^(0)\Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0} is allowed to vary is a good fit obtained (bold black line). c) Simulations using different values for Φ ISC 0 Φ RISC 0 Φ ISC 0 Φ RISC 0 Phi_(ISC)^(0)Phi_(RISC)^(0)\Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0}, using fitted values for K S V S K S V S K_(SV)^(S)K_{S V}^{S} ( 39 M − 1 ) 39 M − 1 (39M^(-1))\left(39 \mathrm{M}^{-1}\right) and K S V T ( 1480 M − 1 ) K S V T 1480 M − 1 K_(SV)^(T)(1480M^(-1))K_{S V}^{\mathrm{T}}\left(1480 \mathrm{M}^{-1}\right) obtained from the bold line fit to the data (circles).
图 3. 4 CzIPN ( 50 μ M ) 4 CzIPN ( 50 μ M ) 4CzIPN(50 muM)4 \mathrm{CzIPN}(50 \mu \mathrm{M}) 与 Et 3 N Et 3 N Et_(3)N\mathrm{Et}_{3} \mathrm{~N} 在 THF 中 20 ∘ C 20 ∘ C 20^(@)C20^{\circ} \mathrm{C} 的淬火实验和各种拟合。b) 使用 Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} 的固定值进行拟合，结果表明，固定 Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} 的不同值（参见 χ 2 χ 2 chi^(2)\chi^{2} 值）无法拟合数据（圆圈），这说明方程没有过度参数化。c) 使用不同的 Φ ISC 0 Φ RISC 0 Φ ISC 0 Φ RISC 0 Phi_(ISC)^(0)Phi_(RISC)^(0)\Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0} 值进行模拟，使用从粗线拟合数据（圆圈）中得到的 K S V S K S V S K_(SV)^(S)K_{S V}^{S} ( 39 M − 1 ) 39 M − 1 (39M^(-1))\left(39 \mathrm{M}^{-1}\right) 和 K S V T ( 1480 M − 1 ) K S V T 1480 M − 1 K_(SV)^(T)(1480M^(-1))K_{S V}^{\mathrm{T}}\left(1480 \mathrm{M}^{-1}\right) 的拟合值。
Stern-Volmer constant for the triplet state K SV T K SV T K_(SV)^(T)K_{\mathrm{SV}}^{\mathrm{T}} than for the singlet state K SV S K SV S K_(SV)^(S)K_{\mathrm{SV}}^{\mathrm{S}} (cf. values in Table 1). Upon increasing the concentration of quencher, initially, the quenching is very effective followed by more moderate quenching. After the initial quenching the triplet state is completely deactivated (i.e., RISC is outcompeted by quenching, and the term Φ ISC 0 Φ RISC 0 1 + K SV [ Q ] T Φ ISC 0 Φ RISC 0 1 + K SV [ Q ] T (Phi_(ISC)^(0)Phi_(RISC)^(0))/(1+K_(SV[Q])^(T))\frac{\Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0}}{1+K_{\mathrm{SV}[\mathrm{Q}]}^{\mathrm{T}}} becomes 0 ), after which the TADF photocatalyst behaves as if it were a fluorophore comprising only a singlet excited state, and the plot becomes linear. Literature reports of fluorescence quenching experiments using TADF fluorophores indeed often depict linear Stern-Volmer plots, which can occur when the first data point is taken at a concentration at which full triplet quenching already occurs. However, in such cases, the y y yy intersect (i.e., [ Q ] = 0 [ Q ] = 0 [Q]=0[\mathrm{Q}]=0 ) is at a value greater than 1 (see Figure 3a), which is an easily overlooked indication that eq 6 does not apply. Instead, in the hypothetical limit where Φ ISC 0 Φ RISC 0 1 + K SV T [ C ] Φ ISC  0 Φ RISC 0 1 + K SV T [ C ] (Phi_("ISC ")^(0)Phi_(RISC)^(0))/(1+K_(SV)^(T)[C])\frac{\Phi_{\text {ISC }}^{0} \Phi_{\mathrm{RISC}}^{0}}{1+\mathrm{K}_{\mathrm{SV}}^{\mathrm{T}}[\mathrm{C}]} is 0 , eq 10 predicts that the y y yy-axis intersect of an (inaccurate) linear fit occurs at 1 1 − Φ ISC 0 Φ RISC 0 1 1 − Φ ISC  0 Φ RISC  0 (1)/(1-Phi_("ISC ")^(0)Phi_("RISC ")^(0))\frac{1}{1-\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0}}. In addition, the slope of the linear part of the plot does not have a slope of K SV S K SV S K_(SV)^(S)K_{\mathrm{SV}}^{\mathrm{S}}, but instead K SV S / ( 1 − K SV S / ( 1 − K_(SV)^(S)//(1-K_{\mathrm{SV}}^{\mathrm{S}} /(1- Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} ), therefore overestimating the amount of singletstate quenching if the data was analyzed using eq 6 instead. For the same reason, linear plots might be obtained if dioxygen exclusion is insufficiently performed, which likewise does not yield accurate fitted constants.
三重态 K SV T K SV T K_(SV)^(T)K_{\mathrm{SV}}^{\mathrm{T}} 的斯特恩-伏尔默常数比单重态 K SV S K SV S K_(SV)^(S)K_{\mathrm{SV}}^{\mathrm{S}} 的斯特恩-伏尔默常数高（参见表 1 中的数值）。随着淬灭剂浓度的增加，最初的淬灭效果非常好，随后的淬灭效果较为温和。在最初的淬灭之后，三重态完全失活（即 RISC 被淬灭竞争掉， Φ ISC 0 Φ RISC 0 1 + K SV [ Q ] T Φ ISC 0 Φ RISC 0 1 + K SV [ Q ] T (Phi_(ISC)^(0)Phi_(RISC)^(0))/(1+K_(SV[Q])^(T))\frac{\Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0}}{1+K_{\mathrm{SV}[\mathrm{Q}]}^{\mathrm{T}}} 项变为 0），之后 TADF 光催化剂的表现就像只包含单激发态的荧光团一样，曲线图变为线性。使用 TADF 荧光激发体进行荧光淬灭实验的文献报告确实经常描述线性斯特恩-沃尔默曲线图，当第一个数据点是在三重态完全淬灭的浓度下采集时，就会出现这种情况。然而，在这种情况下， y y yy 交点（即 [ Q ] = 0 [ Q ] = 0 [Q]=0[\mathrm{Q}]=0 ）的值大于 1（见图 3a），这很容易被忽视，表明公式 6 并不适用。相反，在 Φ ISC 0 Φ RISC 0 1 + K SV T [ C ] Φ ISC  0 Φ RISC 0 1 + K SV T [ C ] (Phi_("ISC ")^(0)Phi_(RISC)^(0))/(1+K_(SV)^(T)[C])\frac{\Phi_{\text {ISC }}^{0} \Phi_{\mathrm{RISC}}^{0}}{1+\mathrm{K}_{\mathrm{SV}}^{\mathrm{T}}[\mathrm{C}]} 为 0 的假设极限中，公式 10 预测（不准确的）线性拟合的 y y yy 轴交点位于 1 1 − Φ ISC 0 Φ RISC 0 1 1 − Φ ISC  0 Φ RISC  0 (1)/(1-Phi_("ISC ")^(0)Phi_("RISC ")^(0))\frac{1}{1-\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0}} 。此外，曲线图线性部分的斜率不是 K SV S K SV S K_(SV)^(S)K_{\mathrm{SV}}^{\mathrm{S}} ，而是 K SV S / ( 1 − K SV S / ( 1 − K_(SV)^(S)//(1-K_{\mathrm{SV}}^{\mathrm{S}} /(1- Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} ），因此，如果改用公式 6 分析数据，会高估单态淬火的量。出于同样的原因，如果没有充分进行二氧排除，可能会得到线性图，这同样不会产生准确的拟合常数。
For each solvent, the data obtained for the three different quenchers can be fitted with the same value of Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} (in Figure 2, a global fit was performed with Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} as a shared parameter between the data of the three quenchers in the same solvent; see the Supporting Information for individual fits per quencher). This is expected as this constant is a property of the fluorophore (in a certain solvent) and does not depend on the quencher. In contrast, the fitted value for Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} does differ when changing the solvent due to the dependence of the unimolecular rate constants (e.g., k ISC k ISC k_(ISC)k_{\mathrm{ISC}} and k RISC k RISC k_(RISC)k_{\mathrm{RISC}} ) on the solvent polarity. 21 21 ^(21){ }^{21} The value for Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} obtained through fluorescence quenching experiments closely matches that from fitting the TCSPC data (see Table 1), further confirming that eq 10 describes well the experimental data and that therefore intrinsic properties of the TADF fluorophore can be obtained by simple steady-state fluorescence quenching experiments. Additionally, the precise value of the property Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} can be obtained to greater accuracy using quenching experiments than through TCSPC experiments by
对于每种溶剂，三种不同淬火剂获得的数据可以用相同的 Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} 值进行拟合（图 2 中，用 Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} 作为同一溶剂中三种淬火剂数据的共享参数进行了全局拟合；关于每种淬火剂的单独拟合，请参阅《辅助信息》）。这是意料之中的，因为该常数是荧光团（在特定溶剂中）的属性，并不取决于淬灭剂。相反，由于单分子速率常数（如 k ISC k ISC k_(ISC)k_{\mathrm{ISC}} 和 k RISC k RISC k_(RISC)k_{\mathrm{RISC}} ）取决于溶剂的极性，当改变溶剂时， Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} 的拟合值确实不同。 21 21 ^(21){ }^{21} 通过荧光淬灭实验得到的 Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} 值与 TCSPC 数据拟合得到的值非常吻合（见表 1），这进一步证实了公式 10 很好地描述了实验数据，因此 TADF 荧光团的固有特性可以通过简单的稳态荧光淬灭实验得到。此外，与 TCSPC 实验相比，利用淬灭实验可以更精确地获得属性 Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} 的精确值，具体方法是
performing global fitting on data sets with more than one quencher. Using a combination of steady-state fluorescence quenching and a single TCSPC experiment in the absence of quencher, the quenching rate constants k q S k q S k_(qS)k_{\mathrm{q} S} and k qT k qT k_(qT)k_{\mathrm{qT}} can be determined, since k S tot k S tot  k_(S_("tot "))k_{\mathrm{S}_{\text {tot }}} and k T tot k T tot k_(T_(tot))k_{\mathrm{T}_{\mathrm{tot}}} can be obtained from the biexponential fit of the TCSPC decay (vide supra). Table 1 lists the quenching rate constants, showing that quenching of both the S 1 S 1 S_(1)S_{1} and T 1 T 1 T_(1)T_{1} state of 4CzIPN is very efficient and close to the diffusion limit, with only small variation between the two, even though the Stern-Volmer constants K S V S K S V S K_(SV)^(S)K_{S V}^{S} and K S V T K S V T K_(SV)^(T)K_{S V}^{\mathrm{T}} are 2 orders of magnitude different.
对含有一种以上淬灭剂的数据集进行全局拟合。结合使用稳态荧光淬灭和无淬灭剂时的单次 TCSPC 实验，可以确定淬灭速率常数 k q S k q S k_(qS)k_{\mathrm{q} S} 和 k qT k qT k_(qT)k_{\mathrm{qT}} ，因为 k S tot k S tot  k_(S_("tot "))k_{\mathrm{S}_{\text {tot }}} 和 k T tot k T tot k_(T_(tot))k_{\mathrm{T}_{\mathrm{tot}}} 可以从 TCSPC 衰减的双指数拟合中获得（见上文）。表 1 列出了淬灭速率常数，表明 4CzIPN 的 S 1 S 1 S_(1)S_{1} 和 T 1 T 1 T_(1)T_{1} 状态的淬灭非常有效，接近扩散极限，两者之间的差异很小，即使斯特恩-沃尔默常数 K S V S K S V S K_(SV)^(S)K_{S V}^{S} 和 K S V T K S V T K_(SV)^(T)K_{S V}^{\mathrm{T}} 相差两个数量级。
The data of a fluorescent quenching experiment cannot be fitted correctly by any other combination of constants using different values for Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0}, therefore excluding overparameterization of the three-parameter equation; see Figure 3b. The higher the Φ ISC 0 Φ RISC 0 Φ ISC 0 Φ RISC 0 Phi_(ISC)^(0)Phi_(RISC)^(0)\Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0}, the more TADF character the fluorophore possesses. In contrast, if this parameter is equal to 0 , we obtain the normal Stern-Volmer equation (6), and the fluorophore only emits from the initial singlet state (i.e., it does not demonstrate TADF). Closer to a value of 1 , the fluorophore has a rapidly established equilibrium of S 1 S 1 S_(1)S_{1} and T 1 T 1 T_(1)\mathrm{T}_{1} excited states, and the data show a very clear curvature in the Stern-Volmer plot. Indeed, when we compare the curves in Figure 2, the data obtained in toluene have a more pronounced curvature compared to the data in acetonitrile ( Φ ISC 0 Φ RISC 0 = 0.70 Φ ISC  0 Φ RISC  0 = 0.70 (Phi_("ISC ")^(0)Phi_("RISC ")^(0)=0.70:}\left(\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0}=0.70\right. vs 0.29 , respectively). Figure 3c further demonstrates the effect of simulating a change in Φ ISC 0 Φ ISC  0 Phi_("ISC ")^(0)\Phi_{\text {ISC }}^{0} and Φ RISC 0 Φ RISC  0 Phi_("RISC ")^(0)\Phi_{\text {RISC }}^{0} while keeping K SV S K SV S K_(SV)^(S)K_{\mathrm{SV}}^{\mathrm{S}} and K SV T K SV T K_(SV)^(T)K_{\mathrm{SV}}^{\mathrm{T}} constant, showing more pronounced curvature at higher values. The limits of eq 10 were further scrutinized by employing the MR-TADF (multiple resonance) fluorophore QAO (also called DiKTa; see Figure 1c), 22 , 23 22 , 23 ^(22,23){ }^{22,23} which has a much smaller value for Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC 0 Phi_("ISC ")^(0)Phi_(RISC)^(0)\Phi_{\text {ISC }}^{0} \Phi_{\mathrm{RISC}}^{0}, limited by the low efficiency of intersystem crossing, Φ ISC 0 = 0.03 Φ ISC  0 = 0.03 Phi_("ISC ")^(0)=0.03\Phi_{\text {ISC }}^{0}=0.03 (see the Supporting Information). 23 23 ^(23){ }^{23} Even at such low efficiency of TADF, a small amount of curvature was still observed in the Stern-Volmer plots (see the Supporting Information), highlighting the importance of considering both excited states in fluorescence quenching for any photocatalyst displaying TADF.
使用不同的 Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC  0 Phi_("ISC ")^(0)Phi_("RISC ")^(0)\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0} 值，任何其他常数组合都无法正确拟合荧光淬灭实验的数据，因此排除了三参数方程的过参数化；见图 3b。 Φ ISC 0 Φ RISC 0 Φ ISC 0 Φ RISC 0 Phi_(ISC)^(0)Phi_(RISC)^(0)\Phi_{\mathrm{ISC}}^{0} \Phi_{\mathrm{RISC}}^{0} 越高，荧光团的 TADF 特性就越强。相反，如果该参数等于 0，则得到正常的斯特恩-沃尔默方程 (6)，荧光团仅从初始单色态发射（即不显示 TADF）。当数值接近 1 时，荧光团迅速建立起 S 1 S 1 S_(1)S_{1} 和 T 1 T 1 T_(1)\mathrm{T}_{1} 激发态的平衡，数据在斯特恩-沃尔默曲线图中显示出非常明显的曲率。事实上，当我们比较图 2 中的曲线时，在甲苯中得到的数据比在乙腈中得到的数据具有更明显的曲率（ ( Φ ISC 0 Φ RISC 0 = 0.70 Φ ISC  0 Φ RISC  0 = 0.70 (Phi_("ISC ")^(0)Phi_("RISC ")^(0)=0.70:}\left(\Phi_{\text {ISC }}^{0} \Phi_{\text {RISC }}^{0}=0.70\right. vs 0.29 ，分别为 0.29 和 0.29）。图 3c 进一步展示了在保持 K SV S K SV S K_(SV)^(S)K_{\mathrm{SV}}^{\mathrm{S}} 和 K SV T K SV T K_(SV)^(T)K_{\mathrm{SV}}^{\mathrm{T}} 不变的情况下模拟 Φ ISC 0 Φ ISC  0 Phi_("ISC ")^(0)\Phi_{\text {ISC }}^{0} 和 Φ RISC 0 Φ RISC  0 Phi_("RISC ")^(0)\Phi_{\text {RISC }}^{0} 变化的效果，在数值较高时显示出更明显的曲率。通过使用 MR-TADF（多重共振）荧光团 QAO（也称为 DiKTa；见图 1c），进一步仔细研究了式 10 的限制， 22 , 23 22 , 23 ^(22,23){ }^{22,23} 的 Φ ISC 0 Φ RISC 0 Φ ISC  0 Φ RISC 0 Phi_("ISC ")^(0)Phi_(RISC)^(0)\Phi_{\text {ISC }}^{0} \Phi_{\mathrm{RISC}}^{0} 值要小得多，这是受低系统间交叉效率 Φ ISC 0 = 0.03 Φ ISC  0 = 0.03 Phi_("ISC ")^(0)=0.03\Phi_{\text {ISC }}^{0}=0.03 的限制（见辅助信息）。 23 23 ^(23){ }^{23} 即使 TADF 的效率如此之低，在 Stern-Volmer 图中仍然可以观察到少量的曲率（见佐证资料），这凸显了对于任何显示 TADF 的光催化剂而言，在荧光淬灭过程中考虑两种激发态的重要性。
In conclusion, an extension of the Stern-Volmer equation was derived to describe the nonlinear behavior introduced by the complex excited-state system of TADF photocatalysts that are currently experiencing a rapid growth in their application in photoredox catalysis. This new model comprises three constants: the Stern-Volmer constants for quenching of the
总之，我们对斯特恩-沃尔默方程进行了扩展，以描述 TADF 光催化剂复杂激发态系统带来的非线性行为。这个新模型由三个常数组成：用于淬火的 Stern-Volmer 常数、用于淬火的 Stern-Volmer 常数、用于淬火的 Stern-Volmer 常数。
singlet and triplet excited states and the quantum yield of successive ISC and RISC. The model was experimentally verified by using three quenchers in four different solvents, showing congruent behavior with rate constants matching those that were independently obtained from time-correlated single photon counting experiments.
单态和三重激发态以及连续 ISC 和 RISC 的量子产率。通过在四种不同溶剂中使用三种淬灭剂对该模型进行了实验验证，结果表明该模型的行为与时间相关单光子计数实验独立获得的速率常数一致。

- ASSOCIATED CONTENT - 相关内容

(5) Supporting Information
(5) 辅助资料

The Supporting Information is available free of charge at https:// pubs.acs.org/doi/10.1021/acs.jpclett.4c02609.
辅助信息可从 https:// pubs.acs.org/doi/10.1021/acs.jpclett.4c02609 免费获取。
Mathematical derivation of the equations used, general methods, TCSPC data and fits, and additional SternVolmer plots and fits (PDF)
所用方程的数学推导、一般方法、TCSPC 数据和拟合以及其他 SternVolmer 图和拟合 (PDF)
Transparent Peer Review report available (PDF)
提供透明同行评审报告 (PDF)

◻ ◻ ◻\square AUTHOR INFORMATION
◻ ◻ ◻\square 作者信息

Corresponding Author 通讯作者

Bart Limburg - Secció de Química Orgànica, Facultat de Quimica, Universitat de Barcelona, 08028 Barcelona, Spain; Institut de Química Teòrica i Computacional (IQTC, 08028 Barcelona, Spain; ©orcid.org/0000-0002-7996-2485; Email: blimburg@ub.edu
Bart Limburg - Secció de Química Orgànica, Facultat de Quimica, Universitat de Barcelona, 08028 Barcelona, Spain; Institut de Química Teòrica i Computacional (IQTC, 08028 Barcelona, Spain; ©orcid.org/0000-0002-7996-2485; Email：blimburg@ub.edu
Complete contact information is available at:
完整联系信息请访问
https://pubs.acs.org/10.1021/acs.jpclett.4c02609

Notes 说明

The author declares no competing financial interest.
作者声明不存在任何经济利益冲突。

ACKNOWLEDGMENTS 致谢

The Spanish Ministry of Science, Innovation and Universities, is acknowledged for a Researcher Consolidation grant CNS2023-144535, financed by MICIU/AEI/10.13039/ 501100011033 and by the European Union NextGenerationEU/PRTR and a Maria de Maetzu grant CEX2021-001202M financed by MICIU/AEI/10.13039/501100011033. Xavier Companyó is acknowledged for fruitful scientific discussion.
感谢西班牙科学、创新和大学部（MICIU/AEI/10.13039/ 501100011033）和欧盟 NextGenerationEU/PRTR 资助的研究人员巩固基金 CNS2023-144535，以及 MICIU/AEI/10.13039/501100011033 资助的 Maria de Maetzu 基金 CEX2021-001202M。感谢 Xavier Companyó 进行的富有成效的科学讨论。

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  1. Received: September 6, 2024
    收到：2024 年 9 月 6 日
    Revised: October 7, 2024 修订：2024 年 10 月 7 日
    Accepted: October 9, 2024
    接受：接受： 2024 年 10 月 9 日