Importance of Side Chains and Backbone Length in Defect Modeling

Mar 16, 2009 - Handbook of Conjugated Polymers, 3rd ed.; Skotheim , T. A. , Reynolds , J. R. , Eds.; CRC Press: Boca Raton, FL, 2007. ... Sirringhaus ...
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J. Phys. Chem. B 2009, 113, 6215–6218

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Importance of Side Chains and Backbone Length in Defect Modeling of Poly(3-alkylthiophenes) Seth B. Darling* and Michael Sternberg Center for Nanoscale Materials, Argonne National Laboratory, 9700 South Cass AVenue, Argonne, Illinois 60439 ReceiVed: September 10, 2008; ReVised Manuscript ReceiVed: January 6, 2009

Geometric defects in conjugated polymers play a critical role in determining electronic structure and properties such as charge carrier mobility and band gap. Because the relative roles of individual defects are experimentally difficult to discern, computational approaches provide valuable insight if appropriate molecular models are used. Poly(3-alkylthiophenes) are often modeled with very short backbones and without their side chains. We demonstrate the shortcomings of this approach for modeling torsional disorder in poly(3-hexylthiophene) (P3HT). Using a hybrid density functional model, we identify a minimal acceptable model to comprise approximately 10 monomers with explicitly treated alkane side chains. Potential applications of this work extend to polymer electronics and optoelectronics. Polymers containing conjugated backbones have received increasing interest in recent years due largely to their potential application as semiconductors in organic electronics and optoelectronics.1-8 Advantages over traditional inorganic materials include lower cost, lighter weight, mechanical flexibility, and, most important, solution processability. In contrast to inorganic electronic materials, the comparatively large number of electronically significant geometric degrees of freedom extant in organic molecules can have myriad and powerful impacts on the physical properties. Full realization of the potential of conjugated polymers relies, in part, on a complete understanding of how intra- and intermolecular morphology affects relevant parameters such as mobility and band gap.9,10 The challenge lies in the fact that many different types of morphological disorder can occur in polymeric systems, and deconvoluting the relative importance of these different structures is experimentally exigent if not impossible. Computational chemistry methods, however, can be utilized to manipulate individual defects and monitor their influence on the behavior of the molecule without the dilemma of deciphering complementary or competing effects from other defects.11 In order to perform such a calculation, it is critical to select a molecular model and level of theory that balance the needs of accurately capturing the properties while not overly taxing computational resources. In this paper, we examine the prototypical experimentally studied conjugated polymer1,12-14 poly(3-hexylthiophene) (P3HT; Figure 1b). Specifically, we isolate the inter-ring torsion defect and probe various molecular models in order to identify the minimal acceptable structure. Single molecule spectroscopy has shed some light on conformational defects of isolated molecules,15,16 and recent lowtemperature scanning tunneling microscopy (STM) experiments have demonstrated the capacity of directly observing torsion defects in isolated polythiophene analogues on surfaces,17 but computational methods currently remain the only viable approach for elucidating intricate details of the associated structure-property relationships. Previous theoretical investigations of this system have often taken the seemingly simplistic approach of modeling P3HT with * Corresponding author. E-mail: [email protected].

Figure 1. Regioregular (a) PT and (b) P3HT chemical structures.

a thiophene dimer having no side chains.18-24 The reasoning behind this tactic is that the side chains are not involved in the frontier molecular orbitals that dominate optoelectronic behavior and that the inter-ring torsion energy profile can be modeled using just the two rings that directly define the torsion angle. Using this stripped-down model facilitates the application of high-level quantum chemical methods and therefore provides confidence in the accuracy of the results. Here we test both of these assumptions, namely, that additional rings and side chains are deemed not essential to correctly determine torsional energy profiles for P3HT. The first assumption can be interrogated by calculating profiles for polythiophene (PT; Figure 1a) oligomers with varying numbers of rings, while the second assumption can be tested by performing the same calculations with hexyl side chains included. It should be noted that there are other approximations that are made both in previous work and here. One of these is that torsion angles are not correlated with one another, that is, that rotation of one such angle will not affect the geometric arrangement of other rings on the polymer backbone. For solid state systems, this is likely a poor approximation given the substantial intermolecular interactions present.25 For the isolated molecules probed in this study, however, this is a reasonable assumption. A second approximation is that all internal coordinates except the dihedral angle of interest are kept rigid when the latter is rotated away from its planar orientation. Specifically, for each oligomer, the planar structure (usually the ground state, see below) is fully optimized using density functional theory (DFT) with the hybrid B3LYP functional and 3-21G* basis set as implemented in Gaussian 03. Because of the significant

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flexibility associated with these moleculessand the alkyl side chains in particularsfrequency calculations were performed for optimized oligomers containing up to six thiophene rings without and up to four rings with side chains. All eigenvalues were positive at these stationary points, verifying that the geometries do indeed represent minima; the geometric similarity between the shorter and longer chain oligomers suggests that the same holds true for all models in this study. Given the soft nature of the side chains, optimizations using larger basis sets that contained additional diffuse functions were applied to models with ethyl side chains. These shorter chains provide a rough approximation of hexyl side chain behavior without sacrificing computational tractability. Unlike the minima observed using the 3-21G* basis, these models relaxed into more complex nonplanar geometries. Interestingly, in this case, the smaller basis set provides an optimized geometry that more closely matches the known (planar) structure of solid state P3HT.26 Planarity in the physical system is partially the product of intermolecular forces, which are not considered in this modelshence the structural discrepancy with larger bases. Because of their greater physical relevance, the structures resulting from 3-21G* optimizations were utilized throughout this study. Single-point energy calculations were then performed at the B3LYP/6-311G(d,p) level, while the central dihedral angle was stepped in 5° increments from 0° to 180°. The resulting energy profile is shifted to make it relative to the planar (0°) structure for each oligomer. An alternative approach to dihedral rotation in thiophene chains, in which oligomers are twisted end-to-end with nonplanar torsion angles between all constituent rings, was recently reported by Zade and Bendikov.10 These two schemes provide complementary information on related defect structures. Potential energy curves obtained using our method will represent upper limits because the rotated geometries have not been permitted to relax. For models containing only the backbone thiophene rings, this approach can be presumed to provide reasonable profiles; further consideration is required, however, for those models that incorporate the alkyl side chains. As reported previously by others,27,28 we have used 3,4′-dimethyl-2,2′-bithiophene as a computationally tractable model for the effect of the alkyl side chains where the molecule is permitted to fully relax along the torsional potential curve. By comparing this curve with those obtained for our other models using the rigid rotation methodology, we can obtain an estimate regarding the accuracy of the latter as described below. More sophisticated methods such as nudged elastic band models are computationally beyond the present scope. The first consideration at hand is the length of the polymer backbone. Bithiophene, the most basic model option, displays a profile with two minimasat ∼30° and ∼140°sand with a global maximum at 90° that results from breaking the conjugation between the rings (Figure 2a). The 90° geometry is associated with a poor intramolecular charge carrier mobility, as determined by the calculated charge transfer integral,9,18 which is of interest from an applications standpoint. Overall, this profile is in strong qualitative agreement with that obtained using highlevel ab initio quantum chemical calculations,18-23 though the relative energies of the rotated states are slightly higher in the DFT results. Raos et al. have performed detailed comparisons between the B3LYP, MP2, CCSD, and CCSD(T) methods regarding their application to the bithiophene torsion profile.19 Their results also suggest that each of these approaches results in qualitatively similar energy profiles, though the quantitative barrier heights vary. B3LYP has also recently been applied to torsion profiling of polypyrrole, a closely related conjugated

Darling and Sternberg

Figure 2. (a) Calculated inter-ring torsion energy profiles (5° steps) for oligothiophene chains ranging from 2 to 14 monomers. Data are shifted to compare energies to the 0 °C (planar) structure, which represents the global energy minimum for all but the shortest oligomer. (b) Torsion barrier height extracted from (a) as the energy difference between 0° and 90°. Convergence is achieved between 10 and 12 monomers.

polymer.11 If one is interested in highly accurate quantitative data, it would be prudent to select a more sophisticated functional,20-23,29 but the B3LYP hybrid functional appears to provide reliable qualitative results relevant to the present investigation. Increasing the number of thiophene monomers from two to four results in a drastic change in the shape of the potential energy curve, with both minima virtually disappearing and the barrier height increasing substantially. Clearly, bithiophene fails to capture either the qualitative or the quantitative behavior of inter-ring torsion in a polymer like P3HT. Indeed, while the planar state for bithiophene is metastable, its global energy minimum, as found here and in refs 18-23, has a nonplanar geometry. Longer oligomers generally prefer flat backbones, as can be expected. Continuing to lengthen the backbone beyond four units results in a monotonic increase in the torsion barrier height, asymptotically approaching ∼0.16 eV (Figure 2b). Based on these data, one can conclude that models containing fewer than 10 monomers do not accurately identify the potential energy profile for torsion defects. One can rationalize this trend by considering the delocalization of the HOMO and LUMO. From a simple particle-in-a-box perspective, which has some utility for these systems despite questions as to its rigorous applicability,30 longer polymer chains are lower in energy as a result of the broader conjugation system and, therefore, breaking the electron delocalization by torsion defects leads to greater destabilization and

Defect Modeling of Poly(3-alkylthiophenes)

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Figure 3. (a) Calculated inter-ring torsion energy profiles (5° steps) for P3HT chains ranging from 2 to 14 monomers. Data are shifted to compare to the 0° (planar) structure, which represents the global energy minimum for oligomers with less than six substituted thiophene units. Points at 90° have been deleted for the tetramer and decamer due to convergence errors.

Figure 4. Close-up view of the environment in the vicinity of the rotating torsional motion, for the case of the hexamer, with an inter-ring angle of (a) 15° and (b) 150°sthe two angles that represent local maxima in the P3HT torsion potential energy profiles that were not present in analogous data for polythiophene.

a greater barrier height. All of these data are qualitatively similar to those obtained for the fully relaxed 3,4′-dimethyl-2,2′bithiophene model (data not shown), suggesting that the angular position of the minima and maxima acquired with the rigid rotor method are reasonably accurate. The second major consideration when selecting a model is inclusion of alkyl side chains. Calculations for oligomers of P3HT with all atoms explicitly included were carried out as with the PT backbone described previously; results are presented in Figure 3. Incorporating side chains significantly increases the demands on computational resources because the number of so-called heavy atoms more than doubles. The question is whether this additional investment is worthwhile. It is important to note that shorter chains will be insufficient in terms of capturing essential behaviorseven more so than without the side chains because the chains bound to the rotating thiophene rings need to “see” side chains on neighboring rings, though it is not immediately obvious whether only simple nearestneighbor, next-nearest-neighbor, or even further interactions are important. One difference between the data in Figures 2a and 3 is that the principal torsion barrier height is decreased for all chain lengths studied. This effect is the result of destabilization of

the planar structure arising largely from new interactions between backbone atoms and side chain atoms rather than a stabilization of the rotated geometry. As this effect has essentially no dependence on the number of monomers involved, its interpretation is relatively straightforward. Another, more complex change that occurs upon introduction of side chains is the appearance of new local maxima at ∼15° and ∼150°. These features only become apparent as peaks as the backbone length reaches 10 rings; that is, there is a noticeable chain length dependence. While not definitive, Figure 4 depicts aspects of the geometry at these torsion angles that are likely the source of the destabilization. In each case, hydrogen atoms on the first carbon of the side chain attached to one of the rotating rings play an important rolesonce each via steric interactions with the sulfur atom (at 15°) and a hydrogen atom (at 150°) of the neighboring rotating thiophene ring. At the angles associated with these peaks, the steric hindrance is maximal and, since the other internal coordinates are not permitted to relax, atoms cannot adjust to accommodate for this unfavorable interaction. Accepting the local maxima as a potential artifact, and ascribing their origin to a single localized structural effect, still calls for an explanation of the remarkable chain length

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dependence of their height. One possible source for this dependence is that there could be differential geometric reorganizations of the environment around the central (rotating) thiophene rings in the fully optimized (planar) structures of different backbone spans. This possibility was investigated, and it was determined that the geometry displays no significant change as the number of monomers increases. Since the atomic geometry is not the basis of the observed effect, it must be a result of an electronic interaction. Mulliken charge analyses do indeed indicate that the electronic structure reorganizes to place lower density on the sterically interacting atoms as the dihedral angle nears the peak locations. This result lends credence to the ascribed source of the observed peaks. Yet, these atomic charges do not exhibit a clear trend with chain length that would rationalize the variance in potential energy barriers. However, there is a molecular property that does depend on the backbone length, namely, the dipole moment. The moment vector, which reorients substantially during torsional rotation, interacts with the atomic charges of the hydrogen and sulfur atoms. At a given angle, the dipole moment varies by roughly an order of magnitude over the range of chain lengths examined in this study (from nearly zero for the dimer and tetramer increasing to ∼4.5 D for the 14-mer for the untwisted species). While the full interactions are certainly more complex than simple atomic charge-dipole communication, the latter is likely a major contributor to the chain length dependence of the auxiliary maxima in the potential energy profile. Taken together, these results suggest that simple models such as bithiophene fail to capture many of the important physical characteristics of the technologically significant polymer P3HT. Rather, computational models ought to incorporate at least 10 monomers with the side chains treated explicitly. Calculations using these more robust models have provided insight into the influence of inter-ring torsion defects on molecular properties such as electronic structure and potential energy profiles. It is likely that similar requirements apply to other important conjugated polymer systems, with ramifications extending to organic electronics and optoelectronics. Specifically, dihedral twists such as that modeled here can significantly impact the molecular band gap, ionization potential, and mobility.9,10 Taking the case of band gap, for example, dihedral disorder reduces the conjugation length of the polymer backbone, which in turn will raise the HOMO-LUMO energy gap. This is especially important for technological applications considering the rather low energetic cost of rotating the inter-ring torsion angles. Beyond understanding the structure-property relationships in these materials, one can also utilize this connection to develop polythiophene sensors, artificial enzymes, and other devices.31-33 Acknowledgment. Use of the Center for Nanoscale Materials was supported by the U.S. Department of Energy, Office of

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