Singlet Exciton Fraction in Electroluminescence from Conjugated Polymer

The efficiency of electrofluorescent polymer light-emitting diodes is determined by singlet exciton fraction (χS) formation and its value still remains controversial. In this work, χS in spiropolyfluorene (SPF) is determined by analyzing transient emission of phosphor-dopant probe. The χS is found to range from 50% to 76%, depending on applied voltage. Higher applied voltage gives larger χS. Besides, more rapid increment in χS with applied voltage is observed in the higher-molecular-weight polymer. The voltage or molecular weight dependence of χS suggests the probability of singlet exciton (SE) generation through triplet-triplet annihilation (TTA) is enhanced due to higher triplet exciton (TE) concentration at higher applied voltage or accommodation of more TEs in a polymer chain with high molecular weight, thereby increasing probability of TTA. At lower applied voltage, χS is contributed by charge recombination. Its value (χS ~50%) higher than the statistical limit 25% is in agreement with efficient interconversion between triplet and singlet polaron pairs (PP) and with larger formation rate of SE relative to that of TE.


Supplementary Tables
Supplementary Table 1  Where [T] H is concentration of TE in the host and k ET T is rate constant of triplet-triplet ET from host to guest. k R,G T and k NR,G T are radiative and non-radiative decay rate constants of guest TE, respectively. The second and third terms on the right side of Equation S1 describe TEs in the phosphor are consumed due to radiative and non-radiative decay processes, and those populated through the triplet-triplet ET process is described by the first term. As to be shown later, the contribution of SE transfer from host to phosphor will be included in the initial TE concentration generated in the phosphor because singlet-singlet ET is instantaneous (~several ten ps) relative to the timescale of triplet-triplet ET (~several hundred ns) as mentioned in the main text. Therefore, no additional term related to phosphor TE generated through singlet-singlet ET from host is needed in Equation S1. Similarly, the contribution of charge trapping to phosphor TE can also be included in the initial TE concentration generated in the phosphor due to very fast timescale of electron-hole recombination (~ps) 2

Supplementary Note 3. Correction for efficiency of singlet-singlet ET.
It has been reported that inclusion of phosphorescent heavy-metal complex can enhance ISC rate of host polymer 5 , leading to overestimation of η ET S . Therefore, we have to evaluate this heavy atom effect to obtain η ET,C S in the present system, which can be aided by observing the change in number of TE in the polymer host in a presence and absence of the phosphor guest. In the following, we will show how correction procedures are performed.
The wavelength of probe beam employed to detect TE concentration of SPF is 850 nm, which is near the maximum of TE induced absorption for SPF (812 nm) 5 be observed in (ΔR/R) Y . As can be seen in the Supplementary Fig 2a, a peak and a shoulder around 6-7 kHz and 100-200 kHz appeared in the (ΔR/R) Y (or more clearly from the d(ΔR/R)Y/dω | |versus ω in the inset, in which we can see two local minima in the corresponding positions), indicating existence of two excited state species within SPF LMW /Ir(btp) 2 acac system. We assign them as arising from TE induced absorption of SPF LMW and Ir(btp) 2 acac, respectively. The judgment for shoulder at around 100-200 kHz resulting from induced absorption of Ir(btp) 2 acac TE can be supported by observing dependence of phosphorescence intensity of Ir(btp) 2 acac (615 nm) upon the modulation frequency at the same sample ( Supplementary Fig. 2a). The setup and geometry of this phosphorescence measurement is the same as PIA except no probe beam is involved. The Similar phenomenon was also observed in the Ir(btp) 2 acac doped SPF HMW ( Supplementary   Fig. 2b). Therefore, both TEs of Ir(btp) 2 acac and SPF contribute to the PIA signal at 850 nm.
From the above discussion, we know that the origin of PIA signal at 850 nm in Ir(btp) 2 acac doped SPF is the summation of TE induced absorption from Ir(btp) 2 acac and SPF.
Therefore, it is intuitively required to add an additional term in Equation 4 in the main text to take account of the contribution of induced absorption from phosphor dopant, which is given by: Here, C T Hd and τ T Hd are TE concentration (at steady state) and lifetime of polymer upon phosphor doping in comparison to those without phosphor (C T H0 and τ T H0 ) in Equation 4. I T G and τ T G are steady state TE concentration and TE lifetime of phosphor. The first term and second term on the right side of Equation S8 describe TE induced absorption from Ir(btp) 2 acac and SPF, respectively. Although there are six parameters in the equation above,