The Excited-State Lifetime of Poly(NDI2OD-T2) Is Intrinsically Short

Conjugated polymers composed of alternating electron donor and acceptor segments have come to dominate the materials being considered for organic photoelectrodes and solar cells, in large part because of their favorable near-infrared absorption. The prototypical electron-transporting push–pull polymer poly(NDI2OD-T2) (N2200) is one such material. While reasonably efficient organic solar cells can be fabricated with N2200 as the acceptor, it generally fails to contribute as much photocurrent from its absorption bands as the donor with which it is paired. Moreover, transient absorption studies have shown N2200 to have a consistently short excited-state lifetime (∼100 ps) that is dominated by a ground-state recovery. In this paper, we investigate whether these characteristics are intrinsic to the backbone structure of this polymer or if these are extrinsic effects from ubiquitous solution-phase and thin-film aggregates. We compare the solution-phase photophysics of N2200 with those of a pair of model compounds composed of alternating bithiophene (T2) donor and naphthalene diimide (NDI) acceptor units, NDI-T2-NDI and T2-NDI-T2, in a dilute solution. We find that the model compounds have even faster ground-state recovery dynamics (τ = 45, 27 ps) than the polymer (τ = 133 ps), despite remaining molecularly isolated in solution. In these molecules, as in the case of the N2200 polymer, the lowest excited state has a T2 to NDI charge-transfer (CT) character. Electronic-structure calculations indicate that the short lifetime of this state is due to fast nonradiative decay to the ground state (GS) promoted by strong CT–GS electronic coupling and strong electron-vibrational coupling with high-frequency (quantum) normal modes.

T2-NDI-T2 and NDI-T2-NDI were synthesized following a previous report of analogous compounds with different N,N'-substituents; 1 the precursors NDI-Br 2 and NDI-Br were synthesized as previously reported [1][2][3] and the synthetic scheme is shown below.

UV-Vis Spectroscopy Details:
The samples for UV-vis spectra were prepared in dry ortho-dichlorobenzene (oDCB) in ambient conditions.The spectra were recorded in transmission mode using a Cary 5000 UV-vis-NIR spectrophotometer in a quartz cuvette with path length of 1 cm.For the molar extinction coefficient experiment, the stock solution of NDI-2T-NDI and 2T-NDI-2T was prepared at 0.1 mM concentration in oDCB and different aliquots of stock were added into oDCB to vary the concentration as follows: Photoluminescence spectra were collected using a custom-built Princeton Instruments spectrometer.A liquid nitrogen-cooled, front-illuminated Si CCD (PyLoN) was used for collecting visible-NIR spectra (425-900 nm) and a 1D liquid-nitrogen cooled InGaAs array (PyLoN-IR) was used for SWIR measurements (850-1550 nm).Vis-NIR spectra were intensity calibrated using an IntelliCal USB-LSVN (9000-410) calibration lamp.SWIR spectra were calibrated using a SWIR quartz tungsten halogen lamp from Princeton Instruments.Dual monochromators (HRS 500) were used to achieve pseudo-monochromatic excitation from an Energetiq EQ99x laser driven light source, with typical FWHM bandwidths ca.16 nm using a 1200 g mm −1 , 750 nm blaze grating.A single monochromator was used for detection (Princeton HRS-300) with 1200 g mm −1 (500 nm blaze) and 150 g mm −1 (800 nm blaze) gratings used for measuring vis-NIR and SWIR spectra, respectively.Typical exposures were 0.5-1 s with 0.25-1 mm detection slit widths.PL spectra for the model compounds and N2200 were collected using 550 nm and 700 nm excitation light respectively.

Strickler-Berg Analysis:
Further details of the Strickler-Berg analysis can be found in the literature. 4Briefly, the reduced extinction coefficient spectrum was produced by dividing the extinction coefficient at each energy value by the energy in cm −1 .The photoluminescence spectrum was bandwidth-corrected by multiplying the intensity at each wavelength by the square of the wavelength and plotting vs. energy.The photoluminescence vs. energy plot was reduced by dividing by the cube of the energy in cm −1 .The intrinsic radiative rate constant k r was then calculated from the reduced extinction coefficient and reduced PL plots as follows: where n f is the refractive index of the medium in which the PL spectrum was taken, n a that of the medium in which the absorption spectrum was taken, ϵ(ν) ν d(ν) was taken over the CT band only, and the integrals over the PL spectrum ( F (ν)dν and F (ν) ν 3 dν) were taken over the entire range.5 Cyclic Voltammetry:      7 Supplemental Calculations:

Figure S3. 1 :
Figure S3.1:Steady-state photoluminescence spectra of model compounds and N2200 in various solvent environments and across both visible-NIR and SWIR detectors, in order to capture entire emission tail out to ca. 1200 nm.Spectra are normalized to 1 at the cross-over from the visible-NIR detector to the SWIR detector.

Figure S6. 1 :
Figure S6.1:Transient absorption spectra of N2200 in oDCB photoexcited at 700 nm.The spectra are normalized to the ground-state bleach at 715 nm to show the pronounced growth of the 760 nm feature assigned to the N2200 polaron.

Figure S6. 3 :
Figure S6.3:Linear-scaled transient absorption spectra of all samples dissolved in oDCB showing short (a) and long (b) timescales

Figure S7. 2 :
Figure S7.2:Experimental and simulated line-shapes of the reduced emission of NDI-T2-NDI.The experimental band was measured in toluene.The theoretical curve was obtained by fitting the experimental line-shape in the framework of the Marcus-Levich-Jortner model.The following best fitting microscopic parameters were obtained (see methodology section): λ c =0.20 eV, Sqm=1.027,ω qm =1600 cm −1 , E CT = 1.98 eV, and T=300 K.

Table S6 . 1 :
Kinetic fit parameters for the data in Figure 4(b)

Table S6 . 2 :
Kinetic fit parameters for the data in Figure4(a)

Table S7 . 1 :
Excitation energies and oscillator strengths of the lowest excited states in NDI-T2, as calculated at the LC-ωhPBE/6-31G(d,p) level of theory with the consideration of o-dichlorobenzene as an implicit solvent.TableS7.2:Excitationenergiesandoscillatorstrengths of the lowest excited states in T2-NDI-T2, as calculated at the LC-ωhPBE/6-31G(d,p) level of theory with the consideration of o-dichlorobenzene as an implicit solvent.TableS7.5:Atomiccartesiancoordinates of the NDI-T2 molecule at the optimized S 1state geometry and the nonadiabatic coupling (NAC) constants between the S 1 and S 0 states, as obtained at the LC-ωHPBE/6-31G** level of theory with the consideration of o-dichlorobenzene as an implicit solvent.TableS7.6:Frequencies(ω),relaxationenergies (L) and Huang-Rhys (S) factors related to the S 1 → T 1 and S 1 → T 1 transitions in T2-NDI.The calculations are performed at the LC-ωhPBE/6-31G(d,p) level of theory with the consideration of o-dichlorobenzene as an implicit solvent.TableS7.7:Spin-orbit coupling constants (in cm-1) between the lowest singlet and triplet states in T2-NDI computed at the LC-ωhPBE/6-31G(d,p) level of theory with the consideration of o-dichlorobenzene as an implicit solvent.The calculations were performed at the ground-state geometry.
TableS7.3: Excitation energies and oscillator strengths of the lowest excited states in NDI-T2-NDI, as calculated at the LC-ωhPBE/6-31G(d,p) level of theory with the consideration of o-dichlorobenzene as an implicit solvent.