An insight into non-emissive excited states in conjugated polymers

Conjugated polymers in the solid state usually exhibit low fluorescence quantum yields, which limit their applications in many areas such as light-emitting diodes. Despite considerable research efforts, the underlying mechanism still remains controversial and elusive. Here, the nature and properties of excited states in the archetypal polythiophene are investigated via aggregates suspended in solvents with different dielectric constants (ɛ). In relatively polar solvents (ɛ>∼ 3), the aggregates exhibit a low fluorescence quantum yield (QY) of 2–5%, similar to bulk films, however, in relatively nonpolar solvents (ɛ<∼ 3) they demonstrate much higher fluorescence QY up to 20–30%. A series of mixed quantum-classical atomistic simulations illustrate that dielectric induced stabilization of nonradiative charge-transfer (CT) type states can lead to similar drastic reduction in fluorescence QY as seen experimentally. Fluorescence lifetime measurement reveals that the CT-type states exist as a competitive channel of the formation of emissive exciton-type states.

. The Huang-Rhys factor S and the main intramolecular vibrational energy 0 were calculated to be 1 and 0.18 eV, respectively, from a Franck-Condon analysis for the fluorescence spectra of triblock in toluene. Therefore, the expression for extracting excitonic coupling energy J 0 becomes the following: 1 The average oscillator strength, ̅ 0→ , relative to that of the average optically bright state, ̅ 0→ 1 . The arrow indicates the position of the distance cutoff, = 3.5 Å, used to distinguish the more strongly light-emitting exciton from weakly light-emitting polaron states. Figure 7  (a) A plot of the average energy of the lowest CT-type and exciton-type states. The plot contains two sets of exciton-type data. The data labeled 'raw' (solid red) is that which was generated explicitly with simulations (see Fig. 8a).

Supplementary
The data labeled 'corrected' (dashed red) represents the raw data plus a linear shift. (b) A plot of the average oscillator strength, relative to that of the average optically bright state, for the 'raw' and 'corrected' data described in Panel (a).

Supplementary Tables
Supplementary Table 1  Force field parameters. Units of energy, length, and angle are given in kcal/mol, angstrom, and radians respectively.

Supplementary Note 1 FCS curve fitting and correlation amplitude correction
The FCS curves were fitted with the following equation 8 : where, ( ) is the correlation function of fluorescence fluctuations, (0) is autocorrelation amplitude at correlation time = 0, D is the diffusion time, and and is the radius and half-length of the observed volume, respectively.
The fitted correlation amplitude is 0.52 and 0.58 for the exemplary toluene and toluene/methanol samples shown in Supplementary Fig. 2, respectively. It should be noted that the measured amplitude should be corrected by a factor of <F (t) > 2 /[<F (t) ><F BG >] 2 , where <F (t) > and <F BG > are the time-averaged total fluorescence signal and background signal, respectively. 9 With the same excitation powder density ( 6 W), the <F (t) > for triblock in toluene and toluene/methanol is  17.0 kHZ and 2.1 kHZ, respectively. And the background <F BG > is ~ 1.3 kHZ for both toluene and toluene/methanol. Therefore, for the toluene sample, the background

Supplementary Note 2 Distinguish different characters of the excited states
Individual excited states were characterized as being exciton-type, polaron-type, or CT-type based on the following criteria. First, for each excited state the excess charge on molecule 1 due to the excitation, denoted as (1) , was computed. Supplementary   Fig. 6a illustrates that this gives rise to two distinct populations of states: polaron-like and, as illustrated in Supplementary Fig. 6c, are poorly light-emitting. Using the information plotted in Supplementary Fig. 6c we identified that there is a steep drop-off in oscillator strength for states with > 3.5 Å. Since these states are not likely to contribute very much to the fluorescence quantum yield we use this observation as the basis to exclude such states from being characterized as 'excitons'.

Supplementary Note 3 Sensitivity of fluorescence QY to simulation details
The quantitative behavior of the fluorescence quantum yield as a function of solvent dielectric is sensitive to simulation details. Supplementary Fig. 7 illustrates this sensitivity. Specifically we examine how the predicted fluorescence quantum yield responds to a small linear shift on the exciton energy levels. Such a shift is artificial but allows a systematic exploration of the consequences of slightly widening the energy gap between CT-like and exciton-like states. For the raw data the predicted fluorescence QY plotted in Supplementary Fig. 7b (compare to Fig. 5b in the main text) saturates to a value of approximately 20%. However, if the excited state energy levels include a subtle linear shift such as that shown in Supplementary Fig. 7a the fluorescence quantum yield is very similar to that seen experimentally. While we are not advocating that such a shift be applied to the data without justification, but make this comparison in order to highlight the sensitively. This suggests that in this regime even small computational inaccuracies can have large influence on details such as the particular value at which quenching is predicted to occur.

Theoretical simulation method
The potential energy function governing the configuration of the nuclei is given by, where the subscript conj refers to the collection of atoms contributing to the conjugated pi-electronic system and the subscript sat-conj refers to the interactions between saturated and conjugated atoms. Following the notation of Ref. 10 , the first term in the above equation is given by, Values of the force field parameters used in this study are included in Supplementary  Table 1.