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Energetics of Electron-Hole Separation at P3HT/PCBM Heterojunctions Gabriele D'Avino, Sébastien Mothy, Luca Muccioli, Claudio Zannoni, Linjun Wang, Jérôme Cornil, David Beljonne, and Frédéric Castet J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp402957g • Publication Date (Web): 04 Jun 2013 Downloaded from http://pubs.acs.org on June 7, 2013

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The Journal of Physical Chemistry

Energetics of Electron-Hole Separation at P3HT/PCBM Heterojunctions Gabriele D’Avino1, Sébastien Mothy2,3, Luca Muccioli1, Claudio Zannoni1, Linjun Wang3, Jérôme Cornil3, David Beljonne3 and Frédéric Castet2,* 1

Dipartimento di Chimica Industriale “Toso Montanari” and INSTM, Università di Bologna, Viale del

Risorgimento 4, IT-40136 Bologna, Italy; 2Institut des Sciences Moléculaires, UMR CNRS 5255, Université de Bordeaux, Cours de la Libération 351, FR-33405 Talence, France; 3Laboratory for Chemistry of Novel Materials, University of Mons, Place du Parc 20, B-7000 Mons, Belgium.

Corresponding author Dr. Frédéric Castet Institut des Sciences Moléculaires, UMR CNRS 5255, Université de Bordeaux, 351 Cours de la Libération FR-33405 Talence, France Tel. +33 5 4000 3863 [email protected]

Abstract The energetics of electron-hole separation at the prototypical donor-acceptor interface P3HT/PCBM is investigated by means of a combination of molecular dynamics simulations, quantum-chemical methods and classical microelectrostatic calculations. After validation against semi-empirical Valence Bond/Hartree-Fock results, microelectrostatic calculations on a large number of electron-hole (e-h) pairs allowed a statistical study of charge separation energetics in realistic morphologies. Results show that charge separation is an energetically favorable process for about 50% of interfacial e-h pairs, which provides a rationale for the high internal quantum efficiencies reported for P3HT/PCBM heterojunctions. Three effects contribute to overcome the Coulomb attraction between electron and hole: (i) favorable electrostatic landscape across the interface, (ii) electronic polarization and (iii) interfaceinduced torsional disorder in P3HT chains. Moreover, the energetic disorder due to the PCBM polar group is shown to play a key role in increasing the dissociation probability.

Keywords: organic solar cells, bilayer heterojunctions, free charge generation, theoretical calculations

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1. Introduction Although it has fueled a lot of theoretical and experimental studies in the last 1,2,3,4

years

, the mechanism involved in the conversion of bound excitons into free charge

carriers in organic photovoltaic (OPV) cells still remains elusive. The photogeneration of mobile charges in OPV devices proceeds through a succession of events starting with the absorption of a photon to yield a bound electron-hole (e-h) pair. The splitting of the singlet excitons occurs at interfaces with electron-accepting molecules featuring an energy level offset large enough to compensate for the exciton binding energy. Yet, this process produces a charge transfer (CT) state, with a hole and an electron sitting on neighboring donor and acceptor molecules, respectively. The close spatial localization of the opposite charges, along with the low dielectric constant of organic materials, entails very large Coulomb interactions that stabilize the CT state over fully charge separated states, thus favoring charge recombination over dissociation. How a significant amount of these strongly interacting e-h pairs can still escape from their Coulomb well to produce photocurrent – sometimes with an efficiency close to unity5,6 – is currently an open issue. In this respect, the poly(3-hexylthiophene)/1-(3-methoxycarbonyl)-propyl-1-phenyl[6,6]C61 (P3HT/PCBM) heterojunction is one of the archetypal photovoltaic systems7 for which various mechanisms for charge photogeneration have been reported. In particular, although it is established that a typical CT binding energy of at least 0.2 eV needs to be overcome to create separated electrons and holes in polymer-based OPVs8,9,10, the lack of temperature dependence of the internal quantum efficiency of P3HT/PCBM solar cells suggests a barrier-less charge separation11. At least two different mechanisms have been invoked to conciliate these seemingly contradictory results. It was first proposed that the initially ‘hot’ CT states generated just after singlet exciton dissociation use the excess vibrational energy supplied by the light irradiation (∼0.6 eV in P3HT/PCBM blends12,13) to compete against Coulomb attraction 14 , 15 , 16 . This phonon-assisted mechanism requires photogeneration to occur on a timescale shorter than thermal relaxation, which is consistent with a number of experimental results evidencing a sub-picosecond charge separation process in polymer/fullerene solar cells17,18. This mechanism is much faster than internal relaxation processes such as structural relaxations along low-frequency vibrational modes. Recent nonlinear spectroscopy investigations coupled to non-adiabatic dynamics simulations indicate that the hot CT excitons collapse into cold states within one picosecond in a phtalocyanine-


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fullerene solar cell, opening a short time window for competitive charge separation19. A similar picture emerged from transient absorption measurements on a low bandgap copolymer/PCBM blend20. Finally, infrared pump-push experiments have demonstrated that hot CT states could act as gateways for charge separation at donor/acceptor heterojunctions, yet not because of the resulting excess energy but thanks to the associated larger e-h delocalization21. However, these effects are marginally small in efficient polymer/PCBM heterojunctions such as P3HT/PCBM. A second scenario for charge separation implies a two-step “cold” process where the CT states first fully thermalize before breaking up into free charge carriers, the necessary driving force for charge separation being provided by local electric fields across the interface, and by stabilizing charge polarization effects in the bulk. The interfacial electric fields may originate from a possible ground-state partial charge transfer22 as well as from electrostatic and polarization effects related to the discontinuity in geometric and chemical structure at the heterojunctions 23 . Direct evidence for the existence of significant electrostatic potential variations at the interface between organic materials has been provided by ultraviolet photoelectron spectroscopy measurements22,24,25. Moreover, the possibility for bound e-h pairs to separate through an intermolecular hopping process between relaxed states, rather than through hot CT states, was evidenced in the P3HT/PCBM interface by means of photocurrent spectroscopy measurements, where similar quantum yields of carrier photogeneration were obtained for both exciton dissociation and direct activation of CT states, i.e. by supplying or not excess energy to the system11, 26 . The negligible impact of excess energy on the photocarrier generation was further confirmed by a simultaneous analysis of external quantum efficiency and charge extraction by linear increasing voltage measurements27, as well as by time-resolved microwave conductivity experiments conducted on P3HT/PCBM by Savenije et al.28. The authors attributed the efficient charge generation to the formation of weakly bound (less than a tenth of eV) CT pairs at the interface. Kinetic Monte Carlo simulations of Deibel and colleagues showed that such a small binding energy, together with the resulting efficient e-h pair dissociation at the P3HT/PCBM interface, might originate from the significant hole delocalization along the polymer chains, as well as from the significant energetic disorder at the interfaces29. An alternative, third possible mechanism for charge separation has been proposed by Troisi and coworkers: it has been conjectured that the photogenerated excitons actually split into free e-h pairs via an ultrafast process before reaching the energetically disordered interface. The effective long-distance couplings between


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the donor and acceptor states are then made possible thanks to bridging states provided by spectator polymer chains through a super-exchange tunneling process30,31. In that case, the charge separation rates are expected to decrease exponentially with the donor-acceptor distance. In principle, all charge separation mechanisms listed above can be active in a given solar cell, with one or another prevailing depending primarily on the chemical composition and on the heterojunction geometry; therefore only a specific and detailed modeling can provide a quantitative description of e-h separation. To this end, we report here a theoretical investigation of the e-h separation energetics at the P3HT/PCBM heterojunction using a multiscale modeling approach combining atomistic molecular dynamics, quantum-chemical and classical microelectrostatic calculations. The modeling scheme provides a detailed atomistic description of the local morphology and of the ensuing disordered energetics of the e-h pairs across the interfaces. The model explicitly accounts for the relaxation of electronic clouds, responsible for the stabilization of localized charges in polarizable media, as well as long-range multipolar interactions that have been shown to significantly impact the charge carrier energetic levels at organic/organic interfaces32.

2. Theoretical and Computational Approach 2.1 Molecular Dynamics Simulations The interface morphology was obtained by means of atomistic molecular dynamics (MD) simulations, adopting a united-atom force field, which allows a reduction of the computational cost by incorporating hydrogens into the bonded heavier atoms, while preserving to a large extent the quality of an atomistic picture. The force field is based on the AMBER united atom parameterization 33 and was complemented with quantum-chemical calculations for the derivation of united-atom ESP charges34, the adjustment of molecular geometries, and the parameterization of thiophene-thiophene torsional potential. The details of the force field derivation and testing are described in the Supplementary Information (SI). All molecular dynamics simulations were run with the NAMD code35, adopting a cutoff of 15 Å for non-bonded interactions, the Particle Mesh Ewald algorithm36 (mesh size of 1.5 Å) for the evaluation of long-range electrostatic interactions and an integration time step of 2 fs.


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The sample considered, shown in Figure 1, consists in 400 molecules of amorphous PCBM on top of a crystalline slab of regio-regular P3HT, exposing thiophene rings to PCBM. The P3HT phase, composed by 5 lamellae of 16 pi-stacked 20-mers, was obtained from bulk simulations employed for the force field validation (see SI). The dimension of the sample is representative of the typical size of P3HT crystallite and amorphous PCBM clusters, as measured in bulk heterojunctions after thermal annealing37. Interface simulations were performed in the NVT ensemble, using Berendsen thermostat to control temperature and with a simulation box fixed to 78.88 × 84.13 × 350 Å3. The large box length perpendicular to the interface decouples the system from its periodic replica, so that the sample presents a single P3HT-PCBM interface. During simulations, each P3HT 20-mer is bonded to its periodic replica across the simulation box to simulate an infinite polymer chain. The sample was first annealed for 10 ns at 1000 K keeping P3HT fixed, in order to wet the P3HT substrate and randomize positions and orientations of PCBM molecules, and then simulated for 50 ns at 300K (20 ns to reach energy equilibration and 30 ns of production for the calculation of structural observables) leaving the upper 8 layers of P3HT free to move. After the production run, the sample was energy minimized and clusters employed for the electronic structure characterization were extracted from the optimized structure. Minimization was performed to adjust bond lengths to equilibrium values, thus improving the reliability of quantum-mechanical calculations on these structures (classical dynamics may overestimate the amplitude of high-frequency modes), although this procedure is expected to partly reduce structural, and hence energetic disorder, by freezing atomic positions to local minima. 2.2 Energy of Localized Charge Carriers In crystalline or amorphous molecular solids or at interfaces ionization potential (IP) and electron affinity (EA) define the transport levels for charge carriers, i.e. holes and electrons.In the picture of fully localized charge carriers, the energy to create a hole (electron) at molecular site i from a neutral system can be written as: !"! = !"!

!"#

+ !!! !"#

−!"! = −!"!

+ !!!

(1) (2)


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where !"!

!"#

!"#

(!"!

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) is the gas phase IP (EA) of molecule i, and !!! (!!! ) is the so-called

polarization energy for holes (electrons). Equations (1) and (2) introduce two sources of energetic disorder, i.e. intramolecular and intermolecular disorder. The intramolecular contribution arises from the dependence of IPgas and EAgas on the molecular geometry since in MD structures, as in real systems, different molecules present different geometries. Additionally, each molecule experiences a different electrostatic and polarizable environment, leading to different intermolecular interactions between the charge carrier and the surrounding medium, quantified by site-specific polarization energies. The energy to create an e-h pair at sites i-j from the neutral system reads: ∆± !" = !"!

!"#

!"#

− !"!

+ !!"±

(3)

where, in analogy to the case of single charges (equations 1,2), we introduced the polarization energy for an e-h pair, !!"± , which represents the intermolecular energetic contribution to the creation of an e-h pair, including the Coulomb attraction between the opposite charges in addition to surrounding polarization effects. Polarization energies include both electrostatic interactions between the unperturbed (gas-phase) charge distributions of the molecules within the system, and dynamic polarization effects, originating from the relaxation of electronic polarization in the electric field of charged and neutral molecules38. The polarization energy of hole, electron and e-h pairs can then be decomposed in two terms (molecular indices are dropped): ! ! = ! ! + ! ! , with ! = +, −, ±

(4)

where S is the electrostatic contribution to polarization energy generated by the interaction of gas phase charge distributions (hereafter referred to as static polarization energy), and D is the contribution from dynamic (i.e. reorganization of the electronic clouds) polarization (dynamic polarization energy). Dynamic polarization energies of single charges or e-h pairs in their specific electrostatic environment can be obtained as a difference, i.e. ! = ! − !. In this work, energy levels for single charge carriers and e-h separation energetics at P3HT/PCBM interfaces are assessed with a combination of quantum-mechanical (fragment orbital formalism) and classical (microelectrostatics) methods. 2.3 Fragment Orbital Calculations


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The Valence Bond/Hartree-Fock (VB/HF) scheme 39 adopts a fragment orbital formalism to describe the electronic structure of clusters of non-overlapping molecules, treated at the semi-empirical HF level (here using the AM1 parametrization). With respect to standard quantum-chemical approaches, VB/HF has the advantage of allowing the assignment of a net charge to each individual molecule, and can account for both electrostatic and polarization effects, the latter through a self-consistent relaxation of the orbitals of individual fragments. Thus, it gives direct access to the energy of a supramolecular cluster in a given configuration of charges on molecular fragments. In this work, we have considered three types of clusters: neutral, with a single charge (hole or electron) localized on a given molecule, or with an e-h pair localized on two molecules. !"! (!"! ) is calculated as the energy of the cluster with a hole (electron) at site i minus the energy of the neutral cluster. Hole and electron polarization energies are then calculated through equations (1) and (2), with IPgas and EAgas evaluated at the AM1 level for the same molecular geometry. Similarly, the energy to create an e-h pair, ∆± !" , is the energy of the cluster with a hole at site i and an electron at site j minus the energy of the neutral cluster, and the relevant polarization energy is obtained through equation (3). Total (static) polarization energies are obtained performing VB/HF calculations while relaxing (freezing) the fragment orbitals. 2.4 Microelectrostatics Calculations An original classical microelectrostatic (ME) method, describing molecules in terms of permanent charges and polarizable points (induced dipoles) located at atomic positions, is adopted in this study to evaluate polarization energies. In the ME scheme, the induced dipole at each site k, characterized by its linear polarizability tensor !! , is calculated in the selfconsistent field of permanent charges and dipoles themselves, !! , as !! = !! !! . Selfconsistency is achieved through an iterative scheme, where the electric field and dipole at polarizable points are updated at every step, up to convergence in the system energy: !

!=!

!

!! !!! − !! ∙ !!!

(5)

where !!! (!!! ) is the electrostatic potential (field) at atomic site k due to permanent charges ! , and the sum is extended over atoms bearing charge and/or polarizability. Electric field and potential at a given atomic site are calculated by considering the unscreened contribution form charges and dipoles of all other molecules in the cluster. Convergence of system energy


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within 10-6 eV of tolerance is achieved within 20-50 iterations. To prevent divergent behavior, the update of induced dipoles is damped when oscillations in the system energy are detected40. The ME scheme is formally equivalent to the model introduced by Tsiper and Soos41, but in this case the redistribution of atomic charges is neglected (the atom-atom polarizability matrix is zero), and the whole molecular polarizability is distributed on polarizable points. Our approach improves the ME scheme introduced by Munn38 in two different aspects: (i) the description of molecular permanent charge distribution in terms of point atomic charges goes beyond the multipolar picture, allowing for a careful description of electrostatic potential/field, in particular at close distance. Moreover, the mapping from disordered structures is straightforward and specific chemical features (e.g. polar groups) are naturally accounted for; (ii) the self-consistent solution for induced dipoles is performed in the electrostatic environment provided by permanent charges, while in the approach of Munn ME chargequadrupole and charge-induced dipoles energies are calculated separately, and then summed up assuming an additive scheme. Our ME scheme is also similar to Applequist42 or Thole43 schemes, nowadays implemented in polarizable force fields44,45, the main difference being that our method implements anisotropic polarizabilities calculated for each specific system with quantum-chemical methods. In the ME approach, the polarization energy of a single charge at site i (or of an e-h pair at sites i-j) is obtained as the difference between the energy of the charged and the energy of the neutral system. The difference between ME energies obtained after a self-consistent solution for induced dipoles yields the total polarization energy, P, while unrelaxed energies (interaction between permanent charges), give the static polarization energy, S. ME calculations were performed with an in-house written code, and a thorough description of the method is left to a forthcoming paper. Parameters entering the ME model are the set of atomic charges and polarizabilities of neutral and charged molecular species. In this work, charges and polarizable points were placed at heavy atom positions only. The charge distribution of neutral P3HT was described using B3LYP/cc-pVTZ united-atom ESP charges34 calculated for a 3-propyl-thiophene decamer (from the B3LYP/cc-pVDZ optimized geometry). The charges on the remaining carbon atoms of the alkyl chain were set to zero. As shown in Table S4, the set of atomic charges reproduces rather well the quadrupole moment calculated from electron density obtained at the DFT level. Moreover, charge carrier localization on a polymer chain is


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sensitive to the conjugation length and hence to conformational disorder, mostly due to variations in torsional angles. In order to inject into the ME model the dependence of the hole localization on conformational disorder, the atomic distribution of excess positive charge has been evaluated at the VB/HF-AM1 level for each P3HT geometry, and then summed to the atomic charges of the neutral species. The procedure adopted to derive atomic charges of charged P3HT is reported in detail in the SI, while the localization of the hole on P3HT decamers is shown in Figure 2. ESP-united atom charges of neutral and negatively charged PCBM molecules were calculated at the B3LYP/cc-pVTZ level of theory at their respective B3LYP/cc-pVDZ optimized geometries. In neutral C60 molecules (used here for comparison purposes), all atoms are electrically neutral, while in charged C60 the negative excess charge was uniformly distributed over the atoms. The polarizabilities of the P3HT backbone and of the alkyl chains were evaluated independently. For the conjugated part, we relied on the B3LYP/cc-pVTZ polarizability of sexithiophene (T6), reported in Table S5. One sixth of T6 polarizability tensor was equally distributed over the corresponding atoms of each thiophene unit, fully accounting for its anisotrotropy. As for the alkyl chains, we assigned an isotropic polarizability of 1.66 and 1.81 Å3 to the central (-CH2-) and terminal (-CH3) C atoms, respectively. These values were obtained from B3LYP/cc-pVDZ calculations on linear alkyl chains CH3-(CH2)n-CH3, with n=0,1,2…7, as shown in Figure S9. The B3LYP/cc-pVTZ isotropic polarizabilities of C60 (77 Å3) and PCBM (102 Å3) were distributed uniformly over all non-H atoms. The same polarizability was assumed for neutral and charged species. All DFT calculations were performed with Gaussian0946.

3. Results 3.1 Morphology and Dynamics of P3HT/PCBM Interfaces The structural characterization of MD trajectories at 300 K shows that the initial structure, consisting in a sharp interface between crystalline P3HT and amorphous PCBM, remains stable during the spanned timescale (50 ns). No mixing between the two materials occurs, with the exception of a few PCBM molecules that partially penetrate within the alkyl chains of P3HT lamellae. The crystalline/amorphous nature of P3HT/PCBM is confirmed by


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!

molecular orientations, as quantified by the orientational order parameter !! = ! cos ! ! ∙ !

! − ! , where u is the molecular (monomer for P3HT) axis and z the direction perpendicular to the interface47: P2=0.98 for P3HT, P2~0 for PCBM. Nevertheless, the interface with PCBM locally affects the conformational order of P3HT chains. Figure 3a shows the distribution of thiophene-thiophene dihedral angles for the polymer chains at the interface with PCBM and in the bulk (NpT simulation at 300 K and 1 atm, see SI). The most probable conformation is always the planar one, but the P3HT layer in contact with PCBM presents higher torsional disorder than inner layers, whose distributions resemble that of the bulk. The higher degree of torsional disorder at the interface is retained also in minimized structures (see Figure 2). The density profile in a direction perpendicular to the interface, shown in Figure 3b, confirms the higher disorder in interfacial P3HT. While the smoothed density profile (red line) increases from 1.1 in bulk P3HT to 1.5 g cm-3 in bulk PCBM, the density peaks corresponding to P3HT layers (green line) broaden upon approaching the interface and the peak to peak distance increases. Higher torsional disorder and lower positional order at the P3HT/PCBM interface have been also reported by McMahon et al.30. The existence of short range order in the amorphous PCBM is revealed by three broad peaks in the radial distribution function (Figure S4) at about 10, 18 and 28 Å, while no significant spatial correlation has been found between molecular dipoles. Interestingly, PCBM molecules, similarly to C60 fullerenes, rotate at room temperature, with characteristic rotation time of 300 ns, as extrapolated from the fit of the time correlation function of molecular axes (Figure S5). Due to the presence of the bulky substituent, the rotation time of PCBM is at least one order of magnitude longer than in C60 (15 ns at 300 K)48. Additional probability distributions and time correlation functions of P3HT and PCBM torsions are reported in the SI. 3.2 Electrostatic landscape in model 2D clusters: VB/HF vs ME results Semi-empirical VB/HF and classical ME energy landscapes are first compared in order to cross check results obtained with the two different approaches. The comparison is performed on model 2D clusters consisting in stacks of 10 P3HT decamers with 24-26 PCBM molecules above, extracted from the minimized sample in Figure 1 (five 2D clusters, one for each P3HT stack, have been considered). Hydrogen atoms have been added to united atom structures by means of geometrical criteria. A snapshot of a P3HT/PCBM 2D cluster considered is shown in Figure 4a.


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We start discussing gas-phase IP and EA, evaluated at the AM1 level for molecular geometries in 2D clusters. The knowledge of !" !"# and !" !"# , representing the intramolecular contribution to single charge and e-h energies (c.f. Equations 1-3), is required to extract VB/HF polarization energies and hence perform the comparison with ME, the latter being limited to intermolecular interactions only. !" !"# of the individual P3HT chains (Figure 5a, black circles, left scale) decreases upon moving away from the interface, with an average difference between interfacial and bulk chains of 0.12 eV, which agrees well with the 0.15 eV decrease in the P3HT valence band edge calculated by Troisi and coworkers for the same system30. !" !"# of the individual PCBM molecules (Figure 5a, green dots, right scale) instead do not show a net trend, but are rather spread over a ~0.1 eV span. VB/HF and ME single charge polarization energies in P3HT/PCBM 2D clusters are shown in Figure 5b. The comparison is limited to static polarization energies, excluding all effects arising from mutual polarization of the molecular electronic clouds. Polarization effects cannot be quantitatively assessed in clusters of reduced dimensionality like these; on the other hand, the full relaxation of fragment orbitals with VB/HF is not computationally affordable. Both VB/HF and ME predict a stabilization of ~0.5 eV for holes in P3HT bulk with respect to the interface, resulting from the discontinuity in the quadrupolar field, similarly to what is found in other donor/acceptor organic interfaces49,50. On the PCBM side, ! ! values present a ~0.5 eV scattering, without showing a net trend. The large electrostatic disorder is caused by the random orientation of the PCBM polar group, associated to the buckyball rotations (see section 3.1). Electrostatic disorder has therefore a dynamic nature in time, although the characteristic rotation time of PCBM molecules is much slower than charge transfer dynamics. In order to disentangle the effect of PCBM polar groups from the intrinsic discontinuity of the electrostatic potential at the interface, P3HT/C60 2D clusters have been created artificially, by replacing PCBM molecules with C60 fullerenes (see Figure 4b). C60 molecules have the same molecular geometry (from crystal bulk structure) and are placed with random orientation at PCBM position (by imposing the coincidence of the C60-cage centroid). C60-based structures should not be considered as realistic interfaces, but just as a mean to “switch off” the electrostatic disorder of PCBM substituents. Static polarization energies for holes and electrons in P3HT/C60 2D clusters are shown in Figure 5c: as expected, by eliminating PCBM polar groups, the trend in polarization energies becomes smoother, both for P3HT, where the picture of holes being more stable in the bulk is confirmed, and on


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the C60 side. More interestingly, upon removal of electrostatic disorder, a neat trend in ! ! emerges, with values ~0.2 eV higher at the interface. The destabilization of the electron at the interface results from the electrostatic repulsion between between the π-electronic clouds of the polymer and the electron on C60, as already observed for several organic-organic interfaces49,50,51. However, the few C60 molecules within a few Å from the interface (see inset in Figure 5c), which are partially immersed into P3HT alkyl regions, do not experience this electrostatic effect, and present lower ! ! values. These low-energy molecular sites are likely to behave as traps for electrons created at the interface upon exciton dissociation. Figure 5d shows static polarization energies for e-h pairs in P3HT/PCBM, calculated at the VB/HF and ME levels for selected couples of electron and hole positions. A more detailed analysis of e-h polarization energies is presented in the next section; here we simply point out that we also observe a good agreement between VB/HF and ME results for e-h pairs. ! ± decreases in magnitude with the e-h distance as expected. Compared to P3HT/PCBM, an even better agreement is obtained in the P3HT/C60 interface (Figure S14). Overall, the agreement with static VB/HF results validates the ME approach, giving us confidence in its application to quantitatively evaluate polarization energies in larger 3D structures, this time fully accounting for molecular polarizability effects. 3.3. Energy landscape for single charge carriers A quantitative evaluation of the effect of the polarizable medium on localized charge carriers requires ME calculations to be performed on 3D structures. Five 3D clusters have been extracted from the sample shown in Figure 1, consisting in 3 P3HT stacks and (209-219) PCBM molecules above (see Figures 4c-d). In ME calculations, excess charges are placed only at molecular sites in the inner region of the cluster (red molecules in Figures 4c-d), in order to ensure a polarizable environment of similar size around each charge carrier position. ME calculations on 3D clusters of larger size (see Figures S12 and S13) demonstrate that the size of the system in Figure 4c-d is appropriate for our purposes. Besides P3HT-PCBM clusters, we again considered artificial fullerene-based interfaces, obtained by replacing PCBM molecules with C60. ME energies for single charge carriers are shown in Figure 6, which separately shows static (upper panels), dynamic (middle panels) and total polarization energies (lower panels) for P3HT/C60 (left panels) and P3HT/PCBM (right panels). Static polarization energies in the C60-based system (Figure 6a) confirm the picture that emerged from 2D clusters (Figure 5b),


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with both holes on P3HT and electrons on PCBM repelled by the interface. We also notice the presence of low-! ! trapping sites for electrons at the interface (z

PCBM

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