Article pubs.acs.org/JPCC
Molecular Dynamics Simulations of Organic Photovoltaic Materials: Structure and Dynamics of Oligothiophene S. Y. Reddy and Vikram K. Kuppa* School of Energy, Environmental, Biological & Medical Engineering, University of Cincinnati, Cincinnati, Ohio 45221-0012, United States S Supporting Information *
ABSTRACT: Molecular dynamics simulations using atomistically detailed force fields are reported to investigate the behavior of prototypical conjugated polymers in the presence of a fullerene substrate. Four-membered oligothiophene (4TH) molecules are studied adjacent to a C60 phase in an architecture that is typical of the present generation of organic photovoltaic devices. The simulations focus on the structure, orientation, and conformations that develop in the 4TH phase adjacent to the surface and are compared with bulk systems. Effective conjugation lengths in 4TH chains are shifted to significantly lower values as compared with the bulk. Chain backbone torsional transitions between trans and gauche states are counterintuitively accelerated next to fullerene and are found to be strongly correlated with density fluctuations in the polymer phase. The results demonstrate the role of the substrate in controlling nanoscale morphology of the active material in solar cells and reveal qualitative changes in the temperature-dependent behavior of 4TH in the bulk and in the presence of fullerene.
1. INTRODUCTION Alternative sources of energy have rapidly gained importance in the past decade as systems that serve to supplement traditional methods of electricity generation from fossil fuels. Of the numerous such solutions, sunlight is one of the most abundant and is arguably the primary source of all energy and life on Earth. There are many approaches to harnessing solar power, and solar cells made from organic semiconductors are particularly appealing due to their versatility, low cost, ease of production, and mechanical flexibility. The ability of organic photovoltaics (OPVs) to effectively convert incident solar radiation into electricity is controlled not only by inherent material properties such as work functions, absorption coefficients, and bandgaps but is also strongly dependent on the nanoscale morphology of the constituent materials. The discovery of fast (subpicosecond) and efficient electron transfer in a blend of conjugated polymer and C60, from the excited polymer to the fullerene,1 is the basis for most polymeric solar cells today. Such bulk heterojunction devices1−6 are thus called because the region between n-type (fullerene) and p-type (polymer) semiconductors is dispersed throughout the system. A variety of conjugated polymer systems have been used in the construction of photovoltaic devices, including simple polyacetylene,7 functionalized poly(p-phenylenevinylene) (PPV),2 and polythiophenes (PT) [specifically, poly(3-hexylthiophene) (P3HT)].8,9 Thiophene-based polymers have attracted much interest10,11 due to their relatively low band gap (∼2.0 eV), high hole mobility (∼10−3−10−4 cm2 V−1 s−1),12 and optical properties. The present generation of BHJ−OPV devices typically use P3HT as the active material, blended with a fullerene derivative such as (6,6)-phenyl-C61-butyric acid © XXXX American Chemical Society
methyl ester (PCBM). It has been established experimentally that the gross morphology in polymer:C60 solar cells influences charge mobility and the final efficiency13−18 of the device, since the alignment of polymeric entities, the stacking of molecules in crystalline conformations, and the development of interpenetrating contiguous networks of C60 and polymer are crucial to charge transport.19−24 However, the nature of the morphologies at the interface between the fullerene and polymer phases, the role of temperature in influencing these morphologies, and the exact mechanisms by which the structure develops are not completely clear.10,14,17,25−30 Delivering on the promise of organic solar cells demands a comprehensive understanding of the role of the interphase and the interaction between the two phases, specifically of the structural and kinetic processes dictating the yield of OPV devices. In the past few years, simulations have also been used to study the structure and dynamics of conjugated polymers.31,32 Several different force fields for conjugated polymers have been employed,33−35 and all have some trade-off between accuracy and computational expediency. Class-II-consistent (CFF) force fields with bonded and nonbonded interactions and crosscoupling terms for bond−bond, bond−angle, bond−torsion were parametrized for thiophene.36 In general, the weakest aspect of classical potentials was the lack of an accurate interring torsional potential. Marcon and Raos37 addressed this problem with first-principles quantum mechanical calculations Received: December 28, 2011 Revised: June 14, 2012
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on regioregular (P3HT) in order to study the charge mobility in both packed and disordered regions along intrachain and interchain directions, using the PCFF potentials.52 The phase behavior of sexithiophene was studied by MD simulations,44 and a phase transition from crystal to liquid crystal at 580 K was observed in accordance with experimental results. The influence of chain structure and disorder also holds true for other conjugated polymers and has effectively been demonstrated by the simulations of Kilina et al.,53 in which the role of planar conformations of polyfluorenes on the electronic structure was revealed. Both electron and hole energies and the HOMO−LUMO gap were shown to be strongly dependent on torsional and intermolecular interactions. The electronic and geometric structure of the P3HT/PCBM interface was investigated using a combination of classical and quantum simulation methods.54 In this study, the PCBM phase was disordered, while the initial P3HT structure was crystalline. The simulations showed the change in P3HT electronic states upon contact with the PCBM and traced these changes to the physical behavior of polymer chains in the blend. Specifically, the variation in electronic structure decreased with increasing distance from the P3HT/PCBM interface. Finally, a coarsegrained methodology for studying P3HT and PCBM entities was developed by Huang and co-workers to simulate the structure of typical OPV assemblies over large spatial and temporal scales.55 Despite these efforts, a clear picture of conjugated polymer properties in the presence of the fullerene phase is lacking. Our research attempts to fill in this gap, specifically seeking to elucidate the nanoscale morphology of the polymer chains. In this paper, we use molecular dynamics simulations to investigate the properties of prototypical blends of conjugated polymer (oligothiophene) and fullerene (C60) typically used in organic solar cells. The simulation setup mimics the architecture of a portion of the interpenetrating bulk heterojunction network operative in a real solar cell. We also perform bulk studies for comparison. The use of molecular simulations is particularly apposite, since one can readily probe the structure and dynamics at exactly those lengths at which exciton diffusion and charge transport occur.56 In the next section, we discuss details of the molecular simulations methodology, including the force fields used. After that, we discuss our results in section 3. Finally, we conclude with an overview of our research in section 4.
based on different electron correlation methods. They showed that adjacent rings on the backbone were not planar but were out of phase by about 30°. Their parameters were able to accurately capture the structure of conjugated polymers in the bulk, the crystal lattice of oligothiophene, and alkylthiophenes.38 Thermodynamic information39 as well as the behavior of molecules adsorbed onto flat crystal facets of inorganic salts40 was also successfully investigated using this force field. The stacking of thiophene chains adjacent to graphite planes was probed using a similar potential,41 and it was found that graphite induced liquid-crystal-like ordering of conformationally disordered molecules. MD studies of end-substituted (β-alkylated) thiophenes on graphene surfaces35 demonstrated that the side group influenced the molecular conformation of chains, rotational dynamics of the rings, ring planarity, and adsorption. These simulations were conducted using the OPLS all-atom force field33 with some modifications for ring torsion. Here, too, ordering of the thiophene phase similar to liquid-crystal behavior was observed. Another study used a combined experimental and theoretical perspective (AFM, STM, and molecular modeling) to examine the assembly of α-alkylated thiophenes on substrates of different polarity (mica and graphite).42 It showed that the organization of polymer segments was related to the molecule−molecule and molecule−surface segmental interaction, with various types of supramolecular structures (one-dimensional fibrils, two-dimensional regular layers, and monolayers) being observed, depending on the nature of the end groups of the polymer and the substrate. The amorphous phase of polythiophene was studied using a generalized stochastic computational procedure, followed by a Metropolis Monte Carlo (MC) run.43 The structure of PT was described as a packing of elongated molecular chains aligned in the same general direction, with both parallel or antiparallel displaced π-stacked thiophene rings. Pizzirusso et al. investigated the molecular arrangement of six-membered oligothiophene, using atomistic MD simulations.44 They found smectic and nematic liquid crystalline phases at temperatures corresponding to experimental results. This particular work was performed with AMBER force fields, supplemented with additional terms for partial charges and torsional potentials. Packing of oligothiophenes and its influence on excitation energies were studied45 by using MD simulations in combination with quantum chemical calculations. The effective conjugation lengths of various chains of different lengths were in accordance with experimental data. However, the molecular simulations were performed for extremely short times, about 2 orders of magnitude smaller than those reported in this article. Microstructure and charge transport parameters have been determined for crystalline P3HT by Cheung et al.,46 using a combination of atomistic MD simulations (employing the MM3 potentials for bonded terms,47,48 the OPLS force fields33 for nonbonded atoms, and the Raos potentials mentioned above for torsions37) and quantum chemical calculations. Electronic structure in amorphous PT and P3HT was also studied by a combination of MD and charge-patching (pseudoDFT) methods.49 The simulations clearly demonstrated the influence of structural disorder on the electronic density of states. A class II CFF91 force field36,50 augmented with quantum chemistry-derived torsional potentials for inter-ring rotation was used in this study. Lan et al.51 conducted quantum mechanical (QM) and molecular dynamics (MD) simulations
2. SIMULATION DETAILS Molecular dynamics (MD) simulations are employed to examine the behavior of materials relevant to bulk heterojunction OPV devices. The simulation box represents a small fragment of the bulk heterojunction structure seen in modern OPV solar cells and captures the essential feature of a large interface between the polymer and fullerene phases. Oligothiophene molecules are placed adjacent to, and become physisorbed on, the (001) surface plane of the fcc polymorph of fullerene,57 as seen in Figure 1. The interface region is parallel to the XY-plane of the chosen coordinate system, and the oligothiophene phase extends in the positive Z-direction. Note that the interface is shown to be atomistically flat, which is a reasonable assumption at these length scales. Simulations are carried out in the NVT ensemble at six different temperatures, with periodic boundary conditions imposed in all directions. The simulation box contains 100 molecules of oligothiophene (3000 atoms) and 54 molecules of fullerene (3240 B
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each temperature, after which production runs of up to 200 ns (2 × 108 steps) are carried out. Configurations are stored every 10 ps for subsequent analysis. Data collected over 10 ns are used for block averaging. For this first series of simulations reported in this paper, C60 molecules are kept immobile throughout the runs: we expect that in real systems, since the combined mass of the conglomerated C60 in the fullerene phase is much greater than that of the polymers, its inertia is larger and the change in its position, structure, and dynamics on the time scales explored here are insignificant. Thus, although forces derived from the interactions act on the carbon atoms in the C60 as well as all of the atoms belonging to oligothiophene, a counteracting velocity is applied to the C60 carbons, to bring them back to their original positions after each time step. Therefore, the only mobile atoms are those of the polymer. Full interactions between all atoms in the polymer phase are employed, as has previously been used to study oligothiophene systems.37,39,40 Interactions between the polymer and surface are also atomistically detailed 59 and which have been successfully tested with thiophene-based systems.35 All parameters and details of the force- field employed in this research are outlined in the Supporting Information. We mention here that the physical structure of the simulation box does not represent the actual n-type semiconductor used in solar cells. (PCBM is the most commonly used derivative, since processing considerations dictate that the fullerene must be functionalized to make it soluble in organic solvents.) We also note that the oligomers simulated are fairly short and that results could perhaps change as the chain length increases. Nevertheless, the research outlined here is a first step that allows us to establish broad trends governing the physical behavior of typical conjugated polymer/fullerene systems. Each production run is analyzed for the following: density profiles to evaluate segregation and interfacial depth, ring orientation and planarity, chain conformations, extent of π-conjugation, and ring dihedral dynamics.
Figure 1. (a) Snapshot of simulation box used to investigate OPV materials. Fullerene molecules are shown in dark green, on top of which oligothiophene molecules are adsorbed. (b) Snapshot of a single oligothiophene molecule in detail, showing the four rings for each molecule. The sulfur atoms are colored yellow, carbons are green, and hydrogens are gray. The conventions and vectors used in analysis are also shown: chain orientation is investigated via the end-to-end vector, Ve (red arrow), while local ring orientation is studied through the ringnormal vector, VN (black arrow).
3. RESULTS AND DISCUSSION Figure 2 displays the density profiles of all the atoms in the oligothiophene phase as a function of distance from the fullerene surface. Note that the topmost fullerene layer is positioned such that its center-of-mass in the Z-direction is set to 0.0. Results are shown for the total mass density, with a
atoms) to give a total of 6240 atoms. Initial configurations are generated by placing the polymers randomly in a box at a low density of 0.5 g/cm3 and then slowly decreasing box size over 107 steps until a pressure of ∼0 atm is achieved. The resulting box is then merged with a crystalline slab of C60 in the fcc phase,57 such that the top surface of the C60 crystal is in contact with lowermost atom in the polymer phase. This allows the 4TH molecules to be adsorbed on top of the fullerene. The dimensions of the final box containing both molecule types are 4.266 nm in X- and Y-directions and 7.11 nm along the Z-axes. Note that the large box dimension in Z prevents the oligothiophene phase from interaction with the bottom of the C60 crystal surface. A range of temperatures275, 300, 325, 350, and 375 Kwere investigated for the 4TH/C60 system. To compare and contrast with the effect of the fullerene substrate, simulations of bulk 4TH were also performed in the NVT ensemble at 300 and 375 K. Box dimensions were adjusted such that the total density in the bulk is exactly the same as the density of the 4TH phase in the composite system. A time-step of 1 fs is used to integrate the equations of motion, using a velocity-Verlet algorithm with the LAMMPS simulation engine.58 Long-range corrections for both electrostatic forces (particle−particle and particle−mesh) and dispersive interactions (shift) are employed to account for errors introduced by finite cutoffs (1.2 nm) of the nonbonded potentials. The systems are then equilibrated for 107 steps independently at
Figure 2. Total mass density profile of all molecules belonging to the polymer phase, shown as a function of distance from the fullerene substrate. C
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summation over all species including hydrogen (H), carbon (C), and sulfur (S) atoms. The bin width for this calculation was set to 0.0244 nm, with each bead’s mass (H, C, or S) assigned to the bin in which its center resides. Figure 2 clearly shows that local structure is significantly affected by the fullerene, as is indicated by a strong peak at ∼0.75 nm, followed by a subsequent trough and secondary peaks. This result is similar to those obtained for other simulations of polymers adjacent to surfaces.60−63 The fullerene substrate evidently induces a tendency for the polymer to structure into distinct layers. However, it is also clear that order is quickly dissipated away from the surface, with smooth, liquidlike density profiles being reached within 2 nm of the top C60 layer. All temperatures show evidence of a small first peak at ∼0.6 nm from the surface. This peak corresponds to the momentary residence of the adsorbed thiophene rings at regions corresponding to the octahedral interstitial sites of the (100) FCC fullerene surface. For all temperatures, despite the fairly long simulation times, no evidence of long-range structure was found. The orientation of the oligothiophene molecules was evaluated by considering two different vectors. Local orientation of the thiophene rings was measured through vectors normal to the ring plane. This vector, denoted as VN in the schematic of Figure 1b, is calculated as the average of all normal vectors produced by the dot product of successive vector pairs on the thiophene ring, i.e., VN = (V̂ 1 × V̂ 2 + V̂ 2 × V̂ 3 + V̂ 3 × V̂ 4 + V̂ 4 × V̂ 5 + V̂ 5 × V̂ 1)/5. The end-to-end vectors of chains Ve are calculated from the vector joining the terminal carbon atoms on the molecule, as shown in Figure 1b. Order parameters between any two vectors under consideration are calculated using the relation P2 = 3/2 cos2 θ − 1/2, where θ is the angle between the vectors. Figure 3a shows the order parameter profiles for the orientation of ring normal vectors (VN) with the surface normal (Z-axis) as a function of distance from the fullerene surface for the different temperatures studied. The orientation profile is layered and shows three distinct peaks in which rings are, for the most part, arranged flat along the surface, resulting in strongly positive P2 values. The positions of these peaks correspond to the densification layers in the profiles of Figure 2. The first peak in the ring orientation profile is at exactly the same height (0.59 nm) as the minor first peak in the density and is caused by the small fraction of rings that reside in interstitial cavities on the fullerene surface. However, due to spatial restrictions and due to the curvature of the C60 molecules, the thiophene rings in these pockets cannot lie perfectly flat but are instead canted at a slight angle with respect to the surface normal. Hence, P2 values in this first peak are slightly smaller than those in the second peak at 0.75 nm, which occurs at the same height as the strong densification peak seen in the density profiles of Figure 2. For all temperatures, order parameters follow similar trends as, and are commensurate with, the density profiles. The rings become randomly oriented as their height increases, and isotropic ring orientations are observed at a distance of about 2 nm from the surface, which is also the distance at which density fluctuations smoothen out. Orientation of the 4TH molecules was investigated by calculating order parameters for chain end-to-end vectors. Results for the orientation profiles between Ve and the fullerene surface normal are shown in Figure 3b. Chains were assigned to individual bins (of width 0.0244 nm) based on the vertical distance of their centers-of-mass from the substrate. All chains tend to orient along the XY-plane near the surface, i.e.,
Figure 3. Order parameters profiles, showing the orientation of the oligothiophene chains as a function of distance from the fullerene substrate for all temperatures investigated: (a) Chain planarity order parameters, calculated from angles between thiophene rings and the fullerene surface normal. (b) Order parameter profiles of chain end-toend vectors with respect to Z-axis. (c) Chain planarity order parameters, calculated from angles between successive rings along the chain.
perpendicular to the surface normal, as indicated by the value of the order parameter, which is close to −0.5. The flat chain orientation is quickly lost as distance from the surface increases, and the isotropic condition (randomized orientation) is reached after a few nanometers. However, near the free surface of the oligothiophene layer, chains again tend to orient parallel D
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to the XY-plane, along the top surface of the 4TH phase, a result attested to by the values of P2 close to −0.4. This flat arrangement of molecules at the free surface is favored since such configurations maximize contact with the underlying oligothiophene layers, thereby increasing enthalpic interactions and lowering free energy. The electronic structure of conjugated molecules is strongly correlated to chain conformations.11,53,64 We study the physical manifestation of this process by evaluating the planarity of oligothiophene chains. This is done via the calculation of the order parameter for the average angle between the normal vectors of adjacent rings along the molecule. Figure 3c shows the variation of chain planarity with distance from the fullerene surface. The order parameter for each chain is calculated from the average planarity angle, i.e., for a given chain i, Pi2 = 3/2 cos2 θi − 1/2, where θi = (V̂ 0N·V̂ 1N + V̂ 1N·V̂ 2N + V̂ 2N·V̂ 3N)/3, V̂ N is the unit vector normal to the ring plane, and 0, 1, 2, 3 are the identities of rings on the chain. Each such order parameter for every chain is assigned to the bin in which that chain’s center-of-mass resides. Near the surface, 4TH molecules tend to be more planar, as evidenced by the higher values of P2. This is because in the region immediately adjacent to the surface, adsorption forces are able to overcome the inherent dihedral twist in 4TH. This forces a greater degree of planarity in the thiophene rings, as was also observed in studies of oligothiophene adjacent to graphite.35,41 The preference for more planar orientations decreases rapidly with distance from the surface, and values corresponding to unperturbed bulk chains are quickly obtained. Thus, the effect of the surface on chain planarity is only obvious for the first adsorbed layer. A polymer backbone consisting of alternating single and double bonds results in a π-conjugated network which imparts semiconducting electronic properties to that chain. The conjugation permits the electronic wave function to be localized across a larger number of segments along the chain, thereby reducing the energy required for excitation of electrons to the conduction band.46 The extent of π-conjugation of the oligothiophene chains was studied by measuring the conjugation length of chains, which is estimated from the number of adjacent coplanar thiophene rings on a chain. For all saved configurations over all systems and temperatures, the torsional angle formed from the Sa−C−C−Sb dihedral (where Sa and Sb denote S atoms belonging to successive rings on the chain) is calculated. Two adjacent rings are considered to be coplanar if the torsional twist bridging them is less than 40°, since prior research has shown that there exists considerable overlap of the π-electron clouds between the two rings at these dihedral angles.45,51,65 The length of all such coplanar conjugated segments along a chain is recorded, and the largest of such segments on that chain is taken to be the effective conjugation length of the chain, following the protocol established earlier.45 We use the effective conjugation length, rather than the average conjugation length, since it has been shown that the excitation energy of the chain is dependent on the former.45,66,67 Figure 4 shows the effective conjugation length of 4TH chains in both bulk and in the presence of fullerene as a function of temperature. The number of coplanar rings decreases as temperature decreases for both systems, but the bulk system at 300 K has a significantly higher effective conjugation length than all of the 4TH/C60 systems, across all temperatures. Essentially, the existence of higher conjugated lengths is always favored in the bulk. At the highest temperature studied (375 K), the effective conjugation lengths of the two systems are
Figure 4. Effective conjugation lengths of oligothiophene molecules as a function of temperature, in bulk and in the presence of fullerene.
almost identical. The decrease of effective conjugation length with temperature is due to the influence of entropy which favors a decrease in the order of the system, with a concomitant decrease in the planarity of adjacent segments. However, it is interesting to note that the role of temperature is mitigated by the presence of the surface, as demonstrated by the more gradual change in conjugation length temperature, for the system with C60. Our results therefore allude to significant conformational changes in the 4TH structure upon blending with fullerene, thereby substantially affecting the electronic properties. Since the conjugation length has been shown to be directly correlated with the bandgap, our results point to the development of a blue-shift in the excitation wavelength in the presence of fullerene. We were unable to find experimental data for unsubstituted polythiophenes, but our results are corroborated by experimental investigations on thin solid films of P3HT, which reveal a blue-shift of the absorption peak upon blending with both PCBM68−70 and with C60.71,72 The probability distribution of effective conjugation lengths is displayed in Figure 5. Trains of coplanar segments show a prominent trend toward higher lengths for the bulk at 300 K, resulting in the higher effective conjugation length for this state as seen in Figure 4. Longer lengths are penalized at the higher temperatures for both systems, and the population of both single and biconjugated species increases with temperature. In
Figure 5. Probability distribution of effective conjugation lengths, for oligothiophene molecules in bulk and in the presence of fullerene, for all temperatures investigated. E
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between flips is significantly smaller for oligothiophenes in the presence of fullerene, across a range of temperatures. Only at the highest temperature studied of 375 K do the bulk and surface-mediated values become similar. Figure 6b reveals the total number of gauche to trans flips per dihedral per nanosecond in the two systems investigated as a function of temperature. Results are shown for ensemble averages over all dihedrals in every chain, over all saved configurations. For all temperatures, the total number of such flips is greater in the case of 4TH molecules adjacent to C60 than for the bulk 4TH. Not only does the substrate reduce the time between flips from gauche to trans states (and vice versa), it also promotes the total number of such flips. Thus, rather than contributing to frozen configurations for the adjacent polymer species, the rigid surface instead induces rich dynamical behavior characterized by rapid local motion. The origins of such behavior are traced back to the role of the surface on adjacent species and have been attributed to long-lived density fluctuations63,75,76 in studies of polymer structure and dynamics in intercalated nanocomposites. With increasing temperature, the total number of flips increases for both systems, albeit at different rates: the transitions for 4TH in the presence of C60 increase more rapidly than in the bulk. The analysis of dihedral flips demonstrates that transitions in the bulk are slower and are less commonplace than for 4TH in the presence of C60. Extrapolating from the physical mechanism to electronic structure, we postulate that transitions from the ground to excited electronic states is much more likely to occur for 4TH molecules adjacent to a substrate. Indeed, we find in experimental systems of P3HT and PCBM that the thermochromatic effects suggested by our data above are corroborated, with a distinct blue-shift77−79 for P3HT/PCBM systems. We note that the structure of the composite 4TH/C60 system as simulated is inhomogeneous in that there are two distinct interfaces for the conjugated polymer phase. One is formed due to the adsorption of the oligothiophene molecules on the fullerene crystal substrate, while the other occurs at the free surface, between the oligothiophene phase and vacuum. Therefore, determining the extent to which the results of the simulations are influenced by the 4TH/vacuum interface region rather than the 4TH/C60 is important. The answer to this issue is in three parts: First, we note that the 4TH/vacuum interface is fairly thin and that the attractive surface clearly has a much greater effect on the structure of the adsorbed face, as revealed by the density profiles of Figure 2. The morphology of the oligothiophene phase shows densification peaks that vanish in the absence of the fullerene. Hence, it is the presence of the fullerene that gives rise to the altered physical state of the oligothiophene and not the free surface. Second, the amount of material in the interfacial region with vacuum is small and is estimated to be about 9% of the total material in the oligothiophene phase, as calculated by integrating over the density profiles. The influence of this diffuse interfacial layer on the entire adsorbed film is negligible, and the behavior of 4TH/ C60 arises from the contact made with the fullerene surface. Third, to further investigate this effect, we plot two major results of this paperthe conformational dynamics and the effective conjugation lengthas a function of the distance from the fullerene surface. Figure 7a shows the transition time from gauche to trans states for the S−C−C−S dihedral as a function of distance from the fullerene surface (black line). The plot is created by calculating the transition times for each such
the case of 4TH/C60 at all temperatures, and for bulk at 375 K, conjugation lengths of just two thiophene rings are the most probable. The transition from π to π* states in organic semiconductors is a process that is influenced by the local physical environment around the segment at which the charge is delocalized. One of the factors that influence the jump to excited states is the motion of the backbone.11,73,74 To probe the physical mechanism responsible for this process, we examined the flipping of the S−C−C−S backbone dihedral, in which the first two and last two atoms belonged to adjacent connected rings along the oligothiophene chain. Each chain has three such dihedrals, corresponding to the three successive ring pairs. Trans and gauche states were defined by considering the angles between the two planes to be between 122° and 162° and 23° and 63°, respectively. The ranges taken for dihedrals to be considered as either trans or gauche are computed from the full width at half-maximum values from the torsional profiles. Each dihedral is then interrogated over all saved configurations as to the state it occupies (trans or gauche). The states in which dihedrals exist, the time taken for transitions between states, and the total number of flips from gauche to trans and trans to gauche for every transitioning dihedral are counted. Figure 6a shows the average time in nanoseconds for a dihedral to flip from trans to gauche state. It is evident that the time taken
Figure 6. (a) Average time for dihedral flips from trans to gauche states, in the bulk and in the presence of C60, as a function of temperature. (b) Average number of dihedral transitions from trans to gauche states, in the bulk and in the presence of C60, as a function of temperature. F
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length of each chain in the system is calculated and then added to the bin in which the Z-coordinate of its center-of-mass resides at that configuration. As with the previous figure, exactly the same bin width as the density profile was chosen, so as to facilitate comparison. Results are shown for one representative temperature, 375 K: results for other temperatures were similar. The 4TH/vacuum interface exhibits very little anomalous behavior when compared with the rest of the adsorbed layer. The effective conjugation length in the boxed region corresponding to the free surface interface does not show a pronounced deviation from the interior of the film, except for some minor peaks which arise due to poor statistics. The ensemble averaged effective conjugation length, shown by the green circle, is representative of the interior of the film and the density fluctuations caused by the 4TH/C60 interface and not by the free surface of the 4TH phase. Our analysis on both dihedral transition dynamics as well as the effective conjugation length of chains clearly reveals that the interface of the adsorbed 4TH phase with the C60 crystal surface is responsible for the behavior of the entire film. The effect on chain conformations and dynamics engendered by this particular interface gives rise to the substantially different behavior that is observed in the composite system, as compared with the pure− bulk−4TH system. In contrast, the free surface of the 4TH phase shows very little influence on the properties of the film. Not only is the fraction of the material in this region quite small, but the properties also do not deviate substantially from the rest of the adsorbed phase. To further investigate the density-dependent behavior of the composite systems, correlations between dihedral transitions as a function of distance from the surface and the polymer density profiles were computed. Profiles of transition times in the Zdirection as well as profiles of the number of gauche−trans transitions were measured for all runs in the 4TH/C60 system. Using the statistical analysis program R, correlations between the density profiles and the dihedral dynamics profiles were estimated and are shown in Figure 8a as a function of temperature: the correlations for both gauche−trans flip times as well as the number of such flips were calculated. The high positive value of the correlations demonstrate that there is a significant covariance between the density in the Z-direction (mass distribution perpendicular to the surface) and 4TH backbone dynamics in the composite system. Both the total number of transitioning dihedrals between gauche and trans states as well as the times taken to make such transitions are higher in regions of higher density. The former effect is due to the fact that there are many more dihedrals that flip between states in regions of higher density, while the latter occurs because these higher density domains restrict motion, thereby increasing the time for such transitions to occur in the vicinity. In contrast, the correlations as computed in the bulk were time much lower (ϕnumber density = 0.05, ϕdensity = 0.01 at 300 K) and show almost no correspondence of dihedral libration with density. The correlations in 4TH/C60 also display interesting temperature dependencies that accentuate the extent to which the adjacent fullerene substrate has a bearing on the behavior of the polymer phase. Simulation analysis indicates that, as expected, an increase in temperature is accompanied by an increase in the total number of backbone transitions between gauche and trans states (Figure 6b). This is because the density inhomogeneities that exist in the polymeric phase permit these new flips to occur only at those places where there is a greater amount of the polymer. Hence, the correlation between the number of
Figure 7. (a) Comparison of mass density profile (red line, right vertical axis) and time for gauche−trans S−C−C−S dihedral transition as a function of distance from fullerene surface (black line, left vertical axis) at 275 K. The region enclosed by the dashed line corresponds to the 4TH−vacuum interface. The ensemble averaged gauche−trans flip time at 275 K is also shown (green circle). (b) Comparison of mass density profile (red line, right vertical axis) and effective conjugation length of 4TH chains as a function of distance from fullerene surface (black line, left vertical axis) at 375 K. The region enclosed by the dashed line corresponds to the 4TH−vacuum interface. The ensemble averaged effective conjugation length at 375 K is also shown (green circle).
dihedral in the system and then adding that transition time for each of the bins perpendicular to the substrate, in which the Zcoordinate of the chain’s center-of-mass resides. This procedure is carried out over all saved configurations followed by normalizing to give the height-dependent dihedral relaxation times. The bin width chosen was the same as that for the mass density profile, which is also shown (red line). Results are demonstrated for a representative temperature of 275 K, and similar curves are obtained at other temperatures as well. It is evident from the figure that the 4TH/vacuum interfacial region (enclosed by the box bounded by dashed lines) accounts for very marginal deviations from the rest of the film. Only at the end of the density tail do the dihedral flip times show an anomalous increase. Because of the extremely low densities, there is insufficient interaction between chains to promote dihedral transitions here. Overall, the transition times of the oligothiophene phase is not affected by chains existing at the vacuum interface: the ensemble-averaged value over the entire film is shown by the green circle and is in concert with the behavior of much of the adsorbed oligothiophene phase. Figure 7b reveals the effective conjugation length of chains with respect to height from the fullerene surface. The conjugation G
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closely at higher densities. With increasing temperature, although the effect of entropy on the conjugation length is increased, chain conformation is even more prominently controlled by the density in the surrounding regions. Hence, chains can adopt more extended and planar conformations (leading to higher effective conjugation lengths) only when the surrounding phase permits permits such structural changes, and so the correlations between the density profiles and the effective conjugation lengths are slightly higher. Our analysis of the dynamics and the effective conjugation lengths reveals that the interaction between the C60 surface and the oligothiophene phase is critical in dictating the behavior of the composite system. The root cause of the polymer motion, dihedral relaxations, chain conformations, and the temperature dependence of these effects is the proximity of the surface, which induces substantial density fluctuations in the structuring of the 4TH phase. These inhomogeneities are long-lived and contribute to the dramatically different behavior of individual chains in the 4TH/C60 composite system, when compared with the unperturbed bulk case. The density fluctuations and the surface effects alter molecular conformations in the oligothiophene phase and suppress the development of ordered structures. Significant changes in the nanoscale morphology of the 4TH molecules are induced, as indicated by the density and order parameter orientation profiles. Despite the presence of alternating regions of high and low local density, rather than exhibiting a moderating influence on chain dynamics, the opposite effect is observed. The disorder in the 4TH phase leads to accelerated conformational dynamics and enhanced dihedral transitions. Such behavior has also been observed in studies of intercalated polymer films and points to the role of the surface in causing heterogeneous densification and modifying adsorbed film behavior.63,75,80 To ensure that our results are not unduly influenced by the ordered, atomistically smooth facet of the fullerene crystal phase, we have also performed simulations with different surface roughnesses. Even with a nonuniform adsorbing substrate, dihedral librations and chain conformations are still very different than the bulk case. A comparison of the different substrates and their influence on oligothiophene behavior as well as results across different chain lengths will be addressed in a future publication.
Figure 8. (a) Correlations between density profiles (mass distribution perpendicular to the surface) and dihedral dynamics as a function of distance from the fullerene surface, for all temperatures investigated. Correlations for number of gauche−trans flips (black circles) and time between flips (red squares) with density are shown. (b) Correlations between density profiles and effective conjugation length as a function of distance from the fullerene surface, for all temperatures investigated (black circles).
gauche−trans backbone flips and the density profiles of the 4TH increases with temperature. On the other hand, correlations between dihedral flip times and the density decreases with increasing temperature. Figure 6a demonstrates that the rate of dihedral flips is heightened with temperature due to the increasing entropy. This reduction in the dihedral libration time occurs across the system over all regions of the polymer, irrespective of the density. Therefore, the lower influence of density on flip times is observed, since the rate of increase is relatively unaffected by the surrounding region’s density. The effect of the adsorbed layer structure on the effective conjugation length of chains is studied by considering correlations between the density profiles and the effective conjugation length as a function of distance from the fullerene crystal surface. Results of this correlation are shown in Figure 8b for the different temperatures studied. Correlations calculated in the bulk were significantly smaller (ϕρ(z) Ecl = 0.1) than in the composite system. A high positive correlation is revealed between the effective conjugation length and the density profile, indicating that higher local densities lead to enhanced chain conjugation in 4TH/C60. This is because an increase in density leads to more ordered chain conformations, with a corresponding influence on the effective conjugation length: planarity of successive rings and the sharing of the πelectron are further facilitated when chains are packed more
4. CONCLUSIONS Using molecular dynamics simulations with atomistically detailed force fields, we have studied the behavior of fourmembered oligothiophene (4TH) molecules in the presence of a fullerene substrate at a range of temperatures. To highlight the influence of the rigid C60 phase, we have also performed simulations of the bulk−neat−4TH system. Our results elucidate molecular details of the structure of oligothiophene chains in a simulation that mimics the nanoscale structure of a plastic solar cell upon the segregation of its material constituents into an interpenetrating, bulk heterojunction network. The simulations reveal that the interface has a substantial effect on the structure of the adjacent 4TH phase, with density profiles displaying the classic behavior of polymer−surface systems. Order parameters of ring and chain orientation demonstrate that the substrate drives the orientation and stacking of the 4TH, but unlike studies of polymers on graphene sheets, we find no evidence of liquidcrystal-like behavior. Dihedral transitions between trans and gauche states are shown to be substantially accelerated in the presence of C60, and the effective conjugation lengths of the H
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chains in the composite systems are significantly lower than those in the bulk phase. Our results are in concert with experimental studies which show a blue-shift for thiophene systems upon blending with functionalized fullerene.
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ASSOCIATED CONTENT
S Supporting Information *
Details of the force-field parameters employed in this research. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by startup funds from the University of Cincinnati and by computing time and resources from the Ohio Supercomputer Center.
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