Ultra-fast triplet-triplet-annihilation-mediated high-lying reverse intersystem crossing triggered by participation of nπ*-featured excited states

The harvesting of ‘hot’ triplet excitons through high-lying reverse intersystem crossing mechanism has emerged as a hot research issue in the field of organic light-emitting diodes. However, if high-lying reverse intersystem crossing materials lack the capability to convert ‘cold’ T1 excitons into singlet ones, the actual maximum exciton utilization efficiency would generally deviate from 100%. Herein, through comparative studies on two naphthalimide-based compounds CzNI and TPANI, we revealed that the ‘cold’ T1 excitons in high-lying reverse intersystem crossing materials can be utilized effectively through the triplet-triplet annihilation-mediated high-lying reverse intersystem crossing process if they possess certain triplet-triplet upconversion capability. Especially, quite effective triplet-triplet annihilation-mediated high-lying reverse intersystem crossing can be triggered by endowing the high-lying reverse intersystem crossing process with a 3ππ*→1nπ* character. By taking advantage of the permanent orthogonal orbital transition effect of 3ππ*→1nπ*, spin–orbit coupling matrix elements of ca. 10 cm−1 can be acquired, and hence ultra-fast mediated high-lying reverse intersystem crossing process with rate constant over 109 s−1 can be realized.

2 of the reaction, the reaction mixture was cooled down, then poured into 60 mL water and extracted with CH2Cl2 (30 mL × 3). The resultant organic phase was washed with brine, and dried over anhydrous Na2SO4. After the solvent was removed, the residue was purified using column chromatography on silica gel employing petroleum ether/CH2Cl2 (1/4). Then recrystallization with n-hexane CH2Cl2/methanol to afford the greenish-yellow solid product. υa-υf is the Stokes shift, f(ε, n) is the orientational polarizability of solvents 3 given by Where ε is the solvent dielectric constant and n is the solvent refractive index. λabs is the absorption peak at the long-wavelength side; b) λem is the emission peak.       After a relatively long delay time of 30 ms, the two emission bands (λem ~590 nm for CzNI, λem ~600 nm for TPANI) are still discernable, which differ from the corresponding steady PL in both shape and position, confirming their phosphorescence character.  A relaxed potential energy surface scan modelling for TPANI conformations in the ground state was conducted by progressively modulating the dihedral angle between the D and A units using toluene as the solvent. As shown in Supplementary Figure 10, for the lowest-energy conformation of TPANI, its dihedral angle is calculated to be ca. 50°, which is quite close to that observed in the single crystal sample (45°). Hence, the D-A dihedral angles for TPANI in toluene may be analogous to that in crystal.  For S2 excited state in TPANI, the "hole" is mainly located at carbonyl six-membered ring, while the "particle" is distributed on the naphthalene skeleton. Therefore, we can conclude that the S0→S2 transition is an nπ*-dominated transition nature. While for T4 excited state in TPANI, both the "hole" and "particle" are mainly located at carbonyl six-membered ring and naphthalene skeleton in TPANI. Therefore, we can conclude that the S0→T4 transition is a ππ* transition nature.
According to El-Sayed rule, the rate of RISC is also determined by the molecular orbital type of singlet and triplet states, for instance, a ππ* triplet state could transition to an nπ* singlet state, but not to a ππ* triplet state, and an nπ* triplet state could transition to a ππ* triplet state, but not to an nπ* triplet state and vice versa 4 . The NTO of T4→S2 in TPANI contains both the ππ* and nπ* transition character, which obeys El-sayed's rule and promotes the m-hRISC process from T4 state to S2 state. Meanwhile, the small ΔEST between T4 and S2 in TPANI also prompts the m-hRISC process. Since the T4→S2 process is calculated to show an ultra-large m-hRISC rate of 2.1 10 9 s -1 , most of the T4 excitons produced by triplet-channel TTA are estimated to be quickly converted to S2 excitons. In view of the different transition characters of the T4 ( 3 LEA-dominated) and T3 ( 3 LED-dominated) states of TPANI (vide Supplementary Table 10), the T4 → T3 internal conversion (IC) process may be not quite fast. Although the T2 state also displays some 3 LEAcharacter, the relatively large ΔE(T2T4) (~0.6 eV) should be adverse to the T4→T2 IC process.
Consequently, both the T4→T3 and the T4→T2 IC processes may be not quite effective.
Nevertheless, considering that the T2→S1 direct hRISC (d-hRISC) process has a moderate rate of 4.9  10 7 s -1 (vide Supplementary Table 11), once T2 excitons are generated through direct electro-injection, the T2→S1 d-hRISC process could occur. The large SOC matrix element (SOCME) value of 9.66 cm -1 between T4 and S2 states of TPANI could be attributed to the quite different transition nature of T4 (ππ*) and S2 (nπ*) states.     process should also contribute to the triplet utilization in this device. In this case, according to the updated formula Idelay/Isteady = ηDF/(ηS + ηDF + ηd-hRISC), the ηDF in Device D could be recalculated to be ca. 13.5% (29% × 46.7%), and thus the corresponding singlet exciton generation proportion from d-hRISC process (ηd-hRISC) was calculated to be 8.2%.

Supplementary equations for the TTA model
When TTA process occurs, after pulse off immediately, the T1 density can be expressed as The intensity of the delayed fluorescence (IDF) induced by the TTA-involved processes can be expressed as Supplementary Equation 6: As shown in Figure 4i and 6f, the EL decay profile of TPANI-based devices in double-log form was well-fitted by the above TTA model, verifying that triplet excitons can be harvested through TTA-involved processes in this device. In the case of CzNI-based Device C, however, only a slope of 1.0 could be observed in the similar time region (vide Supplementary Figure   22d), excluding the significant TTA-involved triplet exciton utilization in this device.

Supplementary equations for triplet dynamics process
The states in Figure 7 can be expressed as follows: The k-1 can be negligible in amorphous film due to the very low diffusion rate of triplet excitons. 8  Considering that the km-hRISC of TPANI is calculated to be as large as 2.1  10 9 s -1 , and meanwhile the relatively large calculated ΔE(T2T4) (~0.6 eV) may lead to a relatively slow T4→T2 IC process, it is assumed that km-hRISC >> k IC Tn , and thus the TTA-m-hRISC/TTA is 3. Consequently, the total ηDF of 13.5% in Device D can be divided into two parts: ηTTA of ca. 3.4% and ηTTA-m-hRISC of ca. 10.1%.
As a reslut, a large km-hRISC of 2.1  10 9 s -1 could be realized.