Influence of molecular designs on polaronic and vibrational transitions in a conjugated push-pull copolymer

Electron-phonon interactions of free charge-carriers in doped pi-conjugated polymers are conceptually described by 1-dimensional (1D) delocalization. Thereby, polaronic transitions fit the 1D-Froehlich model in quasi-confined chains. However, recent developments in conjugated polymers have diversified the backbones to become elaborate heterocylcic macromolecules. Their complexity makes it difficult to investigate the electron-phonon coupling. In this work we resolve the electron-phonon interactions in the ground and doped state in a complex push-pull polymer. We focus on the polaronic transitions using in-situ spectroscopy to work out the differences between single-unit and push-pull systems to obtain the desired structural- electronic correlations in the doped state. We apply the classic 1D-Froehlich model to generate optical model fits. Interestingly, we find the 1D-approach in push-pull polarons in agreement to the model, pointing at the strong 1D-character and plain electronic structure of the push-pull structure. In contrast, polarons in the single-unit polymer emerge to a multi- dimensional problem difficult to resolve due to their anisotropy. Thus, we report an enhancement of the 1D-character by the push-pull concept in the doped state - an important view in light of the main purpose of push-pull polymers for photovoltaic devices.

In-situ (operando) spectroscopy on free carrier induced absorption in π-conjugated polymers displays the pronounced electron-phonon coupling due to π-fluctuations. Similar to Raman modes in the ground state, vibronic terms in doped polymers known as infrared-activated vibrations (IRAVs) display symmetry breaking due to presence of charge carriers [1][2][3][4] . Originally, these modes have been described in doped and photoexcited simple conjugated systems such as polyacetylene and polythiophenes, where all CSC, CCC and CCH vibrations can be assigned to the spectral response. Meanwhile, polymers developed to more complicated macromolecular structures, so that one-to-one vibrational assignments become difficult. However, there exists crucial interest to resolve the doped state electronics as it provides an insight to optoelectronic devices during operation [5][6][7][8][9][10] . In this work we took such an in-situ operando view to these electronic transitions, which emerge only in the doped state. Electronically these are polaron transitions, which qualitatively relate to the coupling of phonons and free charge carriers. Fitting of these transitions allows an estimation of the strength of inter-and intramolecular forces and hence provides substantial information about carrier dynamics, which can be directly proved in device-structures. We elucidate these dynamics for the first time in a sophisticated push-pull polymer such as PBDTTT-c both in the material and in a device-related style. Interestingly we find agreement with earlier results on 1D delocalization, which appears specifically enhanced by push-pull molecular structures.

Results
Typically polarons emerge from electron-phonon interactions. Their binding energy and the intensity of IR absorption due to polaron excitations scales with a dimensionless coupling constant according to Froehlich where m c the effective electron mass and ω Ph is the LO-phonon frequency. In conjugated polymers polaron absorption depends strongly on dielectric function between ε ∞ and ε 0 (high-frequency electronic and static dielectric constant). The term ε ε − ∞ − − ( ) 1 0 1 defines the effective dielectric constant related to the lattice polarisability. For a given electronic polarisability ε ∞ maximizes if the measurable static dielectric constant becomes large. Furthermore it is evident that the electron-phonon coupling and thus the intensity of polaronic absorption increase with electron localization i.e. in case of a high effecitve electron mass m c .
On basis of ground-state and doped-state data we create optical models to visualise polaron differences. Generic oscillators are useful here to assemble these corresponding delta-functions with strong broadening effects (Lorentz-type or Gaussian-type). This allows us to conclude on the molecular interactions dominating the solid-state system 31,32 . Interestingly we find the complex push-pull polymer to suppress intermolecular forces consequently fitting well 1D-delocalization. This is opposite to highly-crystalline rr-P3HT, where the wave functions spread into inter-and intramolecular identities with diverging intensity. Our results show, that the push-pull concept strengthens the 1D-character -it can drive a conjugated polymer with complex molecular structure towards a simple advantageous optoelectronic structural fingerprint.
The experimental optical model for the pristine polymers ( Fig. 1) are shown in the dielectric functions (and the absorption coefficient α) for PBDTTT-c and rr-P3HT, respectively. The latter (Fig. 1a) has maxima at 2.1 and 2.3 eV (imaginary part left scale, ε 2 ). The feature splitting is a signature of intra-and intermolecular alignment and therewith π − π stacking 33 : This is true for the absorption features between 2 and 4 eV. In detail the shoulder at 2.07 eV is attributed to interchain-delocalized exciton, while the following peaks at 2.27 eV and 2.49 eV are phonon replica of the exciton. The broad absorption shoulder at 2.6 eV refers to the screened ππ* transition 34 . The onset of the absorption is found at 1.9 eV 35 . The dispersion -consistent with absorption -is reflected in the plot of the real part ε 1 having two strong variations that are connected with two oscillators with maxima at 1.95 and 2.1 eV. All mentioned assignments fit measurements on films and dilluted rr-P3HT. Thus we derive a consistent value for the average LO-phonon frequency ω Ph at 190 to 200 meV. PBDTTT-c shows different absorption features: Uniting donor (thieno[2,3-b]thiophene) and acceptor (benzodithiophene with alkoxy-side-chains) red-shift the absorption onset to 1.55 eV. The dielectric functions is presented in Fig. 1b with two sharp peaks at 1.75 eV (π-π* transition) and 1.9 eV. Unlike rr-P3HT, this splitting is not originated from π-π -stacking but rather a fingerprint of the push-pull character. In addition to the dielectric function we include the absorption coefficients α for both polymers (Fig. 1c). In rr-P3HT, a different spectral shape of α as compared to ε 2 is apparent -it originates from the important role of the refractive index n i in thin films. The absorption coefficient has a broad peak with maximum at 2.4 eV, which is a result of dispersion from three oscillators describing the optical transitions. Differently, the absorption coefficient for PBDTTT-c correlates better to the ε 1 -function.
For conducting in-situ spectroscopy on the doped-state, we create a long-lived (persistent) species, which allows elucidation by variable angle spectroscopic ellipsometry (VASE) and attenuated total reflection (ATR) FTIR. Persistency is achieved by iodine-doping rr-P3HT and PBDTTT-c while recording spectra. Alternatively, dynamic doping uses the photo-excitation of the polymer in presence of electron acceptor phenyl-C61-butyric acid methyl ester (PCBM). The latter method mimics the charge-separation processes in an organic photovoltaic cell (bulk-heterojunction). We denote that photo-induced in-situ absorption (PIA) measurements are presented for ATR-FTIR in the mid-IR 36,37 . Combined with persistent doping we obtain a complete survey covering the spectral region between 5.5 and 0.075 eV exactly where vibronic transitions (IRAVs), polaron transitions (P 1,2 and ground state transitions occur (Fig. 2).
At first we present datasets in the UV-visible and near-IR (5 to 1.0 eV) of doped-state levels introduced by persistent chemical doping (Fig. 3). We show the real (ε 1 ) and imaginary part (ε 2 ) of the dielectric function of doped polymers rr-P3HT* and PBDTTT-c*, respectively. For P3HT* ε 2 shows a quenched and broad main absorption peak signal with a maximum at 2.3 eV and a transition betweeen localized polaron state at 1.5 eV, denoted as P 1 . Above 3 eV we cannot observe changes as compared to the ground-state, so we conclude that doping affects mainly π-levels (polarons disrupt loosley-bound HOMO and LUMO states). Contributions from iodine are not apparent (rr-P3HT and PBDTTT-c*). The rr-P3HT* real dielectric function ε 1 repeats the ground state oscillator quenching and displays the concomitant formation of an in-gap P 1 transition at 1.5 eV.
For PBDTTT-c*, we see a similar impact: Quenching in the active absorption region and rise of P 1 . The maxima of PBDTTT-c* are red-shifted as compared to rr-P3HT* due to the lower absorption edge in the ground state.
Concretely, P 1 arises at 1.2 eV (ε 2 ) (absorption coefficients in Fig. 3c). Between P3HT and P3HT* the decrease of the original absorption feature is significant, which is not the case between PBDTTT-c and PBDTTT-c* -the quantitative changes due to doping are minor, which correlates to the higher oxidation potential of PBDTTT-c.  To probe the low-energy regime with the continuum polaronic excitations (P 2 ) and the IRAVs, we change to in-situ ATR-FTIR to cover the spectral mid-IR region between 0.6 to 0.075 eV. For P3HT* we see a characteristic broad P 2 feature above 0.18 eV to 0.19 with a maximum at 0.35 eV. Below 0.18 eV IRAVs emerge characterized by multiple, intense absorption peaks. In parallel, PBDTTT-c* exhibits a broad P 2 transition with a maximum at 0.39 eV including IRAVs. The latter are broadened as compared to rr-P3HT.
In ATR-FTIR, photo-inducted absorption is accessible too. We crosschecked, how doped-state levels are affected by the origin of excitation. In both polymers we cannot report on substantial differences in the spectral response (Fig. 4), unless taking into account quantitative evaluations. Persistent doping with iodide yield quantitative changes, while photo-induced changes are relatively small and, though noise-reduced due to lock-in data acquisition, less precise. Qualitatively, we find the maxima for IRAVs and P 2 transitions at the same positions with minor deviations as indicated in Fig. 4, independently, which method for excitation has been applied. For comparison, we sum up all data on in-gap states in Table 1.

Discussion
The interesting part in evaluation of the presented doped-state spectra affects the differences within the polymer systems. Common rr-P3HT has a simple molecular desing but features a complex physical insight: Our approach fitting spectra with a minimum amount of generic oscillators fails, when we stick to a 1D Froehlich-model (details explained in SI). As already discussed in Fig. 1c, rr-P3HT exhibits strong dispersion effects in the ground state likely originating from the strong π-stacking. Therefore the minimum amount of generic oscillators used to reasonably fit the data are 3, which are illustrated in Fig. 4, left. The polaronic absorption lines are then in agreement, if additional intermolecular forces are considered. In the literature, this effect has been also assigned as 2D-polaron 8,38-40 -accordingly we illustrate the in-gap states in a schematic (Fig. 5). In light of its complex electronic insight, PBDTTT-c appears plain and simple, as far as doped-state dynamics are concerned. This is in contrast to its complicated molecular design consisting of two heterocycles and extensive side-chain branches. In PBDTTT-c, we observe classic 1D-delocalization in agreement with the spectral response. The absorption line shape fits a textbook example for 1D Froehlich polaron excitations with relatively high coupling strength and higher effective hole mass. We fit the spectra using two generic oscillators, (Fig. 4, right) and find a proper match with the doped-state spectral features. The latter is not possible in rr-P3HT: P 2 transitions are weaker despite more intense P 1 . We conclude that we have simply more polaronic states, a weaker Froelich coupling constant, thus less 1D-character. These conclusions are furthermore backed by the ground state spectra: In PBDTTT-c dispersion effects are minor as compared to rr-P3HT seen in the qualitative match of ε 2 and the absorption coefficient α. In summary, we show that PBDTTT-c fits the classic description of a 1D Froelich polaron, while rr-P3HT has more complex spectral responses. This structural insight backs the concept of a 1D-polymers hence 1D-delocalization enhanced by push-pull systems. We conclude it is the inferior molecular symmetry of PBDTTT-c, which features suppressed π-stacking and thus translates to a plain doped-state electronic structure. This work aims to visualize the transition from pristine form to a doped-state for PBDTTT-c as part of a prominent family of push-pull type IR-active polymers for high-performance polymer photovoltaic cells. In direct comparison to rr-P3HT having a simpler core unit and stronger tendency to crystallize, PBDTTT-c offers suppressed π-stacking due to its complex structural asymmetry. In first view we find correlative spectral responses -both systems show intense polaron transitions and IRAV bands. The detailed scans, however, reveal the distinct difference, which highlights the simplicity of the electronic structure of PBDTTT-c. The systems resembles a similar response function in the doped state, as found for original conjugated polymers following the concept of 1D-delocalization. This insight points at the impact of molecular design, which can conserve a major polymer fingerprint -a 1D-character packed in an advanced, sophisticated chemical structure. In light of the high performance response from PBDTTT-c family in organic photovoltaics, our study supports the direction to assemble molecular designs, that foster a 1D-character.

Figure 4. Juxtaposition of persistently-and photodoped in-situ spectra by ATR-FTIR exploring P 2 transitions.
In the mid-IR regime rr-P3HT (left) and PBDTTT-c (right) show the broad polaronic transitions (P 2 ) and lower energy IRAV modes. We included generic oscillators (dashed lines) from the underlying model fit -their superposition renders the experimental spectra in precision.

Polymer
absorption edge π-π* π-π-stacking P 1 P 2  Table 1. Summary of all measured optical transitions referring to the peak maxima (all units in eV). We denote the broadened shape of polaronic transitions.

Methods
PBDTTT-c was purchased from Solarmer Inc., and used as received. P3HT bought from Rieke Metals (98%) and has been purified prior to use by re-crystallization in n-hexane. As electron acceptor the soluble fullerene derivative, (6,6)-phenyl-C61-butyric acid methyl ester (PCBM) was used. PCBM was purchased from Solenne Inc.
(Groningen, The Netherlands). PBDTTT-c or P3HT and PBDTTT-c:PCBM or P3HT:PCBM (1:1 weight ratio) were dissolved in chlorobenzene with concentration of 10 g L −1 and 20 g L −1 , respectively. To measure the optical properties of the pristine and doped materials, NIR-Vis-UV variable angle spectroscopic ellipsometry (VASE) is used. The characterization is performed using a Woollam M-2000 (rotating compensator) ellipsometer (spectral range 0.73 to 6.5 eV). VASE results are analysed using WVASE software on basis of three phase layer model. The polymer film dielectric function is fitted using a parametric dispersion model based on generic oscillators. The layer thickness is measure beforehand by DekTak (Bruker). The as-derived preliminary optical model is consequently refined by point-to-point fits and the resulting ε 1 -and ε 2 -functions. The results are crosschecked in terms of the Kramers-Kronig consistency 41,42 . All VASE measurements are performed on polymer layers deposited by spin coating of the polymer solution on a glass substrate. Doped-state in-situ spectra are generated by exposing the sample to iodine vapor -after a saturation time (10 min) numerous VASE-spectra are recorded subsequently 31 .
The mid-IR spectra are recorded using a FTIR spectrometer (Bruker IFS66S) in attenuated total reflection (ATR) mode. A ZnSe crystal is used as the reflection element. The setup used for in-situ probing is presented in the supplementary part. Doped-state spectra are recorded in presence of an iodine crystal, which is placed in a closed volume box on top of the polymer-film and ATR-FTIR spectra are recorded in-situ. The plots relate the ground state signal (T ref , T is transmission) and subsequent doped-state spectra Ts to a differential spectra (− Δ T/T). We denote that (− Δ T/T) is absorbance A, in first approximation. For quantitative evaluations, we consider the intensity of transmission T as product of all 6 reflections (T equals R 6 ). We can calculate intensities including Fresnel reflection coefficients assuming an isotropic material and the single attenuated total reflection from ZnSe-parallelepiped at 45° total reflection. In ATR-mode also photo-induced absorption is measured. We apply a lock-in mode, amplified by the FTIR spectrometer and a mechanical shutter. The polymer-fullerene blend is deposited on a ZnSe crystal and photo-excited at 532 nm (P3HT) and 664 nm (PBDTTT-c) diode-lasers thought the shutter. A differential spectra (−Δ T/T, T dark and T light ) are calculated from sequences of 1000 repetitions of recording 10 single beam spectra in the dark and light, respectively, to reduce the noise level. We denote that photo-induced VASE is not accessible with our equipment to date.
To evaluate the ATR-FTIR spectra for a quantitative analysis we relate the intensities of polarons and IRAVs to the electron-phonon coupling. The Froehlich interaction turns out to be suitable for polymers: The basis of the model is given by following Hamiltonian 41 : where the prefactor C F is given by In those equations q is a phonon wave vector, + c q and c.c. are creation and annihilation operators, ω Ph is a phonon frequency, N is the number of charges and V is a volume. The values of ε ∞ and ε 0 are high-and low-frequency dielectric constants. In this picture, electron phonon coupling is either enhanced, if the phonon frequency ω Ph increases, or when the ''static'' dielectric constant ε 0 (below the energy of a selected vibronic transition) is strongly different from the dielectric constant ε ∞ (above the energy of a selected vibronic transition), or equivalently, 1 0 1 0 0 decreases. Our assumption is now based on the substitution of the phonon frequency by vibrational frequenciesin particular the IRAVs, which appear due to symmetry breaking (polymer deformation). Each one contributes to the difference (ε 0 − ε ∞ ), as well as in the strength of the polaron transition. For the case of chemical doping of rr-P3HT it is clear that the static dipole moment ε 0 increases, which means that ε − 0 1 vanishes and the coupling coefficient increases in the Fröhlich model -thus allowing a quantitative interpretation.