Supplementary information for the paper

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1 Supplementary information for the paper Structural correlations in the generation of polaron pairs in lowbandgap polymers for photovoltaics Supplementary figures Chemically induced OD 0,1 0,0-0,1 0,1 0,0-0,1 0,05 0,00-0,05 0,05 0,00-0,05 0,05 0,00-0,05 a b c d e 4% doped 3% doped 2% doped 1% doped PCPDT-BDT P 2 P 2 P 2 PCPDT-BT PCPDT-2TTP PC PDT-2TB T P 2 RR P3HT Wavelength (nm Supplementary Figure S1. Hole polaron spectra. Chemically induced differential absorption for the donor-acceptor polymers PCPDT-BDT, PCPDT-BT, PCPDT-2TBT, PCPDT-2TTP and the homopolymer P3HT. A linear increase of the ground state bleach ( at the short wavelength side and of the prominent polaron absorption bands (P1 and P2 in the infrared region can be observed. 1

2 Chemically induced OD PCPDT-BDT, 1800 nm ( PCPDT-DT, 3000 nm (P 2 PCPDT-2TTP, 3000 nm (P 2 PCPDT-2TBT, 1000 nm ( P3HT, 3000 nm (P Dopant concentration (% wt. Supplementary Figure S2. Dopant concentration dependence of polaron absorption. Amplitude of chemically induced differential absorption at the probe wavelength used for pump probe measurements versus doping concentration for all polymers, respectively. The polaron absorption increases linearly up to a doping concentration of 4 % wt. and gets sublinear at higher doping concentrations (not shown here. 2

3 Supplementary Figure S3. Hole and electron polaron spectra from calculations. Computed absorption spectra for the neutral ground state (black, shown on the negative side of the vertical scale and the positive (blue and negative (red polarons (positive sides of the vertical scale. 3

4 Supplementary Figure S4. Energy scheme for polaron absorption. Schematic representation of the typical polaronic transitions for positive (left and negative (right polarons. P+ and P- denote polaronic levels that are spatially confined over the donor (acceptor moeities owing to electronic and geometric relaxation. 4

5 Supplementary tables Polymer Probe wavelength Inclination per % wt. of dopant added Molar absorption coefficient [cm 2 /mol] Polaron cross section [cm 2 ] PCPDT BDT 1800 nm 2.77E E E 16 PCPDT BT 3000 nm 2.00E E E 16 PCPDT 2TBT 900 nm 1.29E E E 17 PCPDT 2TTP 3000 nm 1.78E E E 16 RR P3HT 3000 nm 4.88E E E 17 Supplementary Table S1: Hole polaron cross-sections extracted from Fig.S2 at the specific probe wavelengths. Polymer Polaron band PCPDT BDT PCPDT BT P PCPDT 2TTP P PCPDT 2TBT Supplementary Table S2. Intensities of polaron bands obtained by the combined oscillator strengths for transitions located in a close (~0.2eV vicinity to and P 2 5

6 Supplementary methods Determination of the polaron cross-section and polaron pair yield For the chemical doping measurements the polymers were solved in 1,2-Dichlorobenzene (Sigma-Aldrich with a concentration of 15 μg/ml. Absorption measurements of these solutions filled in fused silica cells (Hellma with a light pass of 10 mm were done with an absorption spectrometer (Cary 5000, Varian covering the spectral range from 175 to 3300 nm. Infrared absorption of the solvent above 3000 nm and of the fused silica cells from 2560 to 2860 nm and below 290 nm limited the measurement to the shown spectral range. After measuring the absorption of the pure solutions, consecutive doping with small amounts of a dilute SbCl 5 solution (90 μg/ml in 1% steps (weight % of dopant relative to weight percent of polymer were added. SbCl 5 is known to be a strong oxidizing agent and to generate a holepolaron in the ground-state of most conjugated polymers 34,35. Measurements in between allowed to observe the changes in absorption due to increasing ionization without inducing further changes to the solution. Subtraction of the ground state absorption measured in undoped solutions lead to the chemically induced absorption spectra of the investigated polymers. Supplementary Figure S1 shows the differential absorption spectra for doping concentrations from 1 to 4 % wt. Up to a doping ratio of four percent a linear increase of the ground state bleaching ( and the polaron absorption bands ( and P 2 intensities can be observed, suggesting that for each SbCl 5 molecule a single hole polaron is generated. For concentrations above 5% the intensities are not linear confirming that less than a polaron is formed for dopant molecule. The optical density of the polaron absorption ( versus the molecular dopant concentration ( allows to calculate their molar absorption coefficient for the desired wavelength used in the pump probe experiments (cell path length x = 10 mm. The measured dopant induced differential optical densities (ΔOD versus the doping concentration together with linear fitting curves are shown in Fig. S2 for all polymers at the relevant wavelengths (photo energies: 0.41 ev (3000 nm; 0.69 ev (1800 nm and 1.24 ev (1000 nm. The resulting positive polaron cross sections have been calculated according to 6

7 on the basis of the reasonable assumption that every inserted SbCl 5 molecule resulting in one positive polaron on the polymer backbone. This assumption is supported by the linear behavior of Supplementary Figure S2 which then saturates for SbCl 5 concentrations above 4%. In this range, which was not used for our estimations of the cross sections, less than one polaron is generated for dopant molecule. SbCl 5 anions are not absorbing in this spectral range. A summary of all obtained values is shown in Table T1. The number of generated excitons was evaluated by with representing the excitation energy density, the pump photon energy and the optical density of the measured sample at the pump wavelength. From the transient absorption signal at the probe wavelength for zero time delay the number of generated positive and negative polarons can be evaluated by where the denominator accounts for the sum of the contributions to the polaron cross-section from positive ( and negative ( polarons. Considering the FWHM of the polaron bands reported in figure 2 (left column, which is typically > 0.3 ev, it is reasonable to consider a contribution of both polarons at the probe wavelengths of the transient absorption experiments. Indeed, while Fig.3(c,d,e,f and Supplementary Figure S3 shows that the calculated polaron bands are not exactly at the same energy for electrons and holes, they still show a substantial overlap, certainly within the inhomogenous broadening of the experimental bands (FWHM >0.3 ev. Without having experimental access to the electron polaron crosssections, we have estimated them from the rescaled by the relative intensity ratio between electron polarons and hole polarons,, for the probed polaron band P x, with x =1 or 2, obtained from the theoretical results of Fig.3(c,d,e,f. The electron polaron cross section reads: 7

8 Table T2 reports the intensities of the positive and negative polaron bands extracted from figure 3 of the main paper. The resulting polaron pair yield is then given by Where is calculated from the sample optical density at the pump photon energy and the pump laser fluence as described above. We have cross-checked the validity of our approach by evaluating the polaron pair yield in blend films of the polymers with the fullerene acceptor PCBM and obtained values above 90% which are consistent with the efficient ultrafast charge separation already reported in the literature for some of these polymers 51. This evaluation was performed considering that in polymer/fullerene blends only holes are left on the polymer and electrons are transferred to the fullerene. Thus considering only the hole polaron cross-section in the formulas above. Quantum-chemical modeling The absorption spectra of the neutral ground state and positive and negative polarons are displayed in Supplementary Figure S3 for all the copolymers. While it is commonly assumed that the two polaronic bands can be assigned to interband transitions ( and intraband transitions (P 2 for homopolymers (see Supplementary Figure S4, the nature of the absorption bands in low bandgap copolymers is somewhat more complex as considerable electronic configuration mixing occurs. For positively charged PCPDT-BT, the P 2 band involves mainly (~80% electronic transitions from doubly occupied levels to the polaronic P+ level and the remaining contributions arise from transitions starting from the polaronic level to unoccupied levels. The band involves two closely lying excited states resulting from a mixing between electronic configurations with comparable intra- and inter-band contributions. The nature of the and P 2 bands calculated for the negatively charged PCPDT-BT is similar to that found for the positive polaron, hence the similar absorption spectra. For very low bandgap copolymers such as PCPDT-BDT, the P 2 band of the positive polaron mainly involves electronic transitions from the polaronic level to the unoccupied levels while transitions from the occupied levels to the polaronic level mostly contribute to. The assignment of the polaronic bands is therefore swapped in comparison to PCPDT-BT, as a result of the strong electron acceptor character of BDT. Indeed, for PCPDT-BDT, the 8

9 HOMO-LUMO bandgap is so small that when an excess positive [negative] charge is added, the resulting polaronic level gets closer in energy to the LUMO [HOMO] level than to the doubly occupied [unoccupied] levels. When using thiophene spacers between the donor and acceptor units, the donor-acceptor character of the copolymer is reduced and the electronic transitions involved in the polaronic bands are similar to PCPDT-BT. Overall, the optical absorption spectra computed for positive and negative polarons in the four copolymers closely resemble each other. There are, however, slight differences that can be traced back to the corresponding charge distributions. As expected, these show that the excess charge is manly confined over the donor [acceptor] moieties for the cations [anions]. For PCPDT-BDT, the positive [negative] charge is almost exclusively (>75% localized on three donor [acceptor] units as a result of the large difference in ionization potential and electron affinity between the two moieties. Thus, in this case, a very similar confinement in the polaronic levels is predicted that in turn leads to very similar optical absorption spectra for excess holes and electrons, see text. Almost complete charge localization over the electrondonating (>80% and, to a lesser extent, electron-withdrawing (>55% units takes place in PCPDT-2TTP and PCPDT-2TBT when merging the charge distributions computed for the PCPDT units and the neighbouring thiophene rings. There, the increased delocalization of the positive charge over the PCPDT-2T segments yields increased absorption cross sections for the positive polaron. In PCPDT-BT, the excess positive [negative] charge is mostly confined (>65% over the PCPDT [BT] units. However, because of the strong electronic coupling compared to the energy mismatch between the frontier energy levels for this donor-acceptor combination, the positive charge partly leaks out over the neighbouring BT units. A similar yet smaller effect is observed for the negative charge. As a result, a slight electron-hole asymmetry is also predicted in this copolymer. Supplementary references 51 Hwang, I.W. et al. Ultrafast electron transfer and decay dynamics in a small band gap bulk heterojunction material. Adv. Mater. 19, (