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A: Spectroscopy, Molecular Structure, and Quantum Chemistry
Elucidating the Effects of Solvating Sidechains on the Rigidity and Aggregation Tendencies of Conjugated Polymers with Molecular Dynamics Simulations Using DFT – Tight Binding Charles J. Zeman, and Kirk S. Schanze J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b12169 • Publication Date (Web): 21 Mar 2019 Downloaded from http://pubs.acs.org on March 26, 2019
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The Journal of Physical Chemistry
Elucidating the Effects of Solvating Sidechains on the Rigidity and Aggregation Tendencies of Conjugated Polymers with Molecular Dynamics Simulations Using DFT – Tight Binding Charles J. Zeman IV† and Kirk S. Schanze*,‡ † Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States ‡ Department of Chemistry, University of Texas at San Antonio, One UTSA Circle, San Antonio, Texas 78249, United States ABSTRACT: Poly(phenylene ethynylene) (PPE) and a series of PPE derivatives were studied using Density Functional Theory– Tight Binding in order to generate molecular dynamics simulations in the gas phase. Dihedral angles between adjacent phenylene units were measured over time to generate a histogram of conjugation lengths where conjugation length was defined by planarity. The average effective conjugation lengths for these polymers were extracted from this data. Notably, it was found that PPE with alkoxy substituents on the phenylene ring of each repeat unit are attributed with causing an increased average conjugation length relative to unsubstituted PPE from 4.7 to 6.4 repeat units. Comparatively, alkyl substituents caused a decrease in conjugation length to 4.5 repeat units. The methods developed here were extended to a wider series of PPE derivatives where a direct link was found between polymer planarity and the electron donating/withdrawing ability of substituents. These results indicate that the solvating sidechains frequently employed in conjugated polymers have an innate effect on the rigidity of the polymer backbone.
INTRODUCTION
underlying reasons why CPEs form aggregates in solution.
Conjugated polymers have been studied extensively since their discovery for their applications in organic electronics and in biology1–4 and remain an area of great interest to this day.5– 15 More recently, conjugated polyelectrolytes (CPEs), characterized by having pendant ionic side groups attached to their conjugated backbone, have garnered much attention due to their solubility in aqueous solution.16,17 One peculiar property of interest for CPEs is that they have been shown to experience fluorescence quenching with Stern-Volmer quenching constants upwards of 109 M-1, an effect that has been referred to as “amplified quenching.”18–20
16,19,25–27
Many different mechanisms have been proposed to explain amplified quenching of CPEs, such as ion pair complex formation between quencher and CPE,19,21,22 long range Forster energy transfer,20 fast exciton migration along the polymer backbone,20,21,23,24 and efficient inter-chain energy transfer.3,4,19 What all of these proposed mechanisms have in common is that they are facilitated by CPE aggregation in solution: In an aggregated state, CPEs experience enhanced conjugation due to increased planarization that is caused by restricted movement of the polymer chains and -stacking interactions.16,19,25,26 This aggregation behavior is typically accompanied by a bathochromic shift in the electronic spectra, and usually accompanied by broadening in band width and reduced fluorescence intensity.10,20 It is this aggregated state that ultimately gives rise to enhanced quenching and much effort has been made to fully characterize and understand the
One of the most obvious explanations for CPE aggregation is intermolecular in nature: Polar solvents that are able to solvate the ionic pendant groups of a CPE are poor solvents for the non-polar backbone; this dichotomy promotes interchain aggregate formation to reduce the unfavorable interaction between solvent and the polymer backbone (the hydrophobic effect).16,26–28 However, recent studies have shown that poly(phenylene ethynylene) (PPE)-based CPEs may be engineered so that they experience minimal aggregation in solution by simply changing the side chain that links the backbone to the ionic pendant from an alkoxy to an alkyl substituent (e.g., -O-CH2- vs. -CH2-).29,30 This effect has not only presented itself for the ionic form of these polymers, but also for charge-neutral PPE-type polymers that are soluble in organic solvents. These effects are more broadly related to recent studies of “side chain engineering” which have shown the dramatic effects of subtle changes in solubilizing groups can have on the packing morphology, secondary structure formation, and photophysical properties of conjugated polymers.14,31–35 Most importantly to this research, experimental probing has revealed that the alkoxy substituted PPE-type polymers have an inherently unique property compared to its alkylsubstituted counterpart,29 to be discussed at length in a forthcoming paper.36 Specifically, this work shows that solutions of PPE-type polymers with -O-CH2-R side groups have a heightened susceptibility to form ordered secondary
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structures. In summary, experimental results indicate that PPE derivatives that are designed to be soluble in aqueous or organic solvent have a greater tendency aggregate if the solubilizing group is linked to the polyarylene backbone through an alkoxy (-O-CH2-R) rather than an alkyl (-CH2-R) linker. Such a minimal change to the overall polarity and electrostatics of the polymer implies that there is something more fundamental to the explanation of aggregation than solvent effects. Since aggregates of conjugated polymer chains are inherently more planar and linear than their molecularly dissolved counterparts,26 it is not unlikely that the natural planarity and rigidity of the polymer itself aides in the formation of the aggregate. In order to properly study the rigidity of a polymer from a theoretical perspective, molecular
Figure 1. Structures of the conjugated polymers that were studied in this paper: poly(phenylene-1,4-ethynylene), poly(2,5-diethylphenylene-1,4ethynylene), and poly(2,5-dimethoxyphenylene ethynylene), which are named PPE, PPE-C, and PPE-O, respectively, in reference to the atomic composition of their associated side chains (top), along with a series of oligomeric phenylene ethynylene (OPE) derivatives (bottom).
dynamics (MD) must be used. Due to the conformational properties of conjugated polymers being strongly coupled to a delocalized electron system,2–4 the usual molecular mechanics (MM) forcefields do not accurately describe these types of systems.37,38 Alternatively, calculating a dynamics trajectory for a polymer with well over 100 atoms is computationally cost prohibitive for any ab initio method, and therefore some semi-empirical method that accurately describes a system that depends on quantum mechanics is vital. Because density functional theory (DFT) has been shown to predict geometries and electronic structure of conjugated organic compounds, sometimes with greater accuracy than Hartree Fock,39–41 the choice of a semi-empirical method that is derived from DFT is natural.42 By using a tight binding approach to DFT (DFTB) with a properly selected Slater-Koster library, highly accurate MD calculations may be carried out on conjugated polymers containing several hundred atoms in the gas phase with reasonable computational times.43 Here we report the results of an MD study that focuses on the properties of substituted PPE-type polymers in the gas phase. PPE was chosen as the ideal model conjugated polymer because of its naturally linear structure, so that its torsional morphology is largely dictated by its electrons. Additionally, a charge neutral polymer in the gas phase allows for many of the observed properties to be directly attributed to the electronic structure of the polymer backbone. The specific structures chosen for this study are outlined in Figure 1, with the polymers of 25 repeat units comprising the first part of this
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report: using the results of the MD simulations of these polymers to determine a minimal chain length for accurate modeling of polymer properties. The second part of this study then examines the side-chain dependent effective conjugation lengths of a series of oligomeric phenylene ethynylenes (OPE). The overall goal of this research is to uncover trends in the effects of various substituents on the rigidity and planarity of PPE when isolated from solvent, which we hope to correlate with broader polymer properties to be outlined in future work, such as tendency to aggregate in solution. COMPUTATIONAL DETAILS All DFTB calculations were performed using DFTB+ as it is employed in a module in the Materials Studio 17 suite of software from Biovia on a home built, 12-core local machine.44– 46 Polymers of PPE, PPE-C, and PPE-O were constructed to be 25 repeat units long and their geometries were optimized using ultrafine convergence criteria (∆E < 2.0 * 10-5) and selfconsistent charges (SCC) with a SCC tolerance of 1.0 * 10-8 and a Broyden47 charge mixing scheme. The CHNO Slater-Koster library was used in all cases.45 MD trajectories were calculated by using the optimized polymers as starting geometries with randomized initial atom velocities in the gas phase. NVT statistics were used in conjunction with the Nose thermostat and a constant temperature set to 278 K with 1 fs time steps for a total simulation time of 1 ns. The first 10 ps of dynamics were thrown out of data analysis to allow for equilibration of the MD trajectory. Explicit dispersion was not included in these calculations, as the polymers were too rigid and short to ever fully fold back on themselves. These computational methods were repeated for phenylene ethynylene oligomer derivatives with a degree of polymerization of 10. Only 500 ps of dynamics were calculated for these compounds. For oligomers that contained halogens, the HalOrg Slater-Koster library was used.48 All calculations used a k-point separation of 0.04 Å-1. With the results of a 1 ns MD simulation, making a quantitative description about the rigidity of a given polymer becomes trivial. With knowledge of the average end-to-end distance of the polymer with time and the contour length of the polymer, the canonical description of polymer rigidity, the persistence length, may be calculated.49 However, more sophisticated methods must be used in order to attribute effective conjugation lengths to various derivatives of PPE.50,51 By measuring the dihedral angle between adjacent phenylene units of PPE, the distribution of dihedral angles can show a given polymer’s preference towards planarity. To define a break in conjugation, we turn to the Hubbard model to solve this problem. 𝑁 𝐻 = ― 𝑡∑𝑖,𝑗(𝑐𝑖† 𝑐𝑗 + 𝑐𝑗† 𝑐𝑖) + 𝑈∑𝑖 𝑛𝑖↑𝑛𝑖↓
(1)
Here, the subscripts i and j denote a specific atom, 𝑐 is a ladder operator, U is the potential energy from Coulombic repulsion, and 𝑛 is the spin density operator to avoid violation of the Pauli exclusion principle. The operator, t, in the kinetic portion of the
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The Journal of Physical Chemistry Hubbard Hamiltonian is the hopping integral. From the hopping integral alone, the coupling energy between two arylene electron systems may be shown to be proportional to the cosine of the inter-ring dihedral angle.52 A breakage in conjugation is defined as when the coupling energy between two adjacent phenylene units is reduced to 0.5 of its maximum value, which corresponds to a dihedral angle of 60 degrees. This definition is used to generate a histogram of polymer conjugation lengths over which no dihedral angle exceeds 60 degrees and calculate average conjugation lengths from these results. Moreover, it will be shown that the probability distribution of dihedral angles of a smaller oligomer of the corresponding polymer may be used to determine the average conjugation length with minimized computational time.
monitored dihedral angles between adjacent phenylene units serve this purpose by allowing the generation of the probability distributions found in Figure 2. Because the property of interest is planarity and not the topology of the potential energy surface, the data has been fixed to a scale of -90˚ to +90˚ where an angle of 0˚ corresponds to co-planar rings. It is clearly evident from these results that the alkoxy substituents of PPE-O have an effect of increasing the effective planarity of the PPE chain. In order to represent this data in a more easily interpretable fashion, a Monte-Carlo approach was taken. By sampling structures from the MD trajectory every 10 ps, conjugation
RESULTS AND DISCUSSION To determine persistence lengths, the contour lengths of each polymer were taken as the measured end-to-end distance in its geometry optimized conformation. With all three polymers having approximately equal contour lengths, their dynamic end-to-end distance was monitored throughout the MD trajectory to determine persistence lengths. It was found that the polymers PPE, PPE-O, and PPE-C have persistence lengths of 7, 7, and 5 repeat units, respectively. This calculation is described further in the Supporting Information (SI). Because these lengths were calculated for a polymer of 25 repeat units, it would be possible for the true persistence lengths as predicted by scc-DFTB to be longer. However, the important result is the trend, which would remain consistent regardless of the degree of polymerization. These results indicate that the inclusion of certain solubilizing Figure 3. Histograms of conjugation lengths found in snapshots of MD trajectories for PPE, PPE-C, and PPE-O.
Figure 2. Distribution of dihedral angles between adjacent phenylene units in PPE, PPE-C, and PPE-O, with each dihedral measured every 100 fs over the course of 1 ns of MD.
substituents may decrease the inherent rigidity of PPE. Moreover, this implies that some substituents have a more dramatic impact on the rigidity of the polymer than others. While the apparent decrease in rigidity by adding alkyl substituents could be explained as a manifestation of increased degrees of freedom, the lack of discrepancy between PPE and PPE-O indicates that there is a more complicated interplay between various mechanisms that might govern the mechanical properties of PPE, which are discussed at length here. For a more rigorous consideration of the rigidity of PPE and its derivatives, something must be said about its planarity. The
lengths could be measured by counting the number of repeat units for which no dihedral angle exceeds 60˚ for a total of 100 different snapshots. Example snapshots of each polymer are shown in the SI. The conjugation lengths found from these results were used to produce the histograms shown in Figure 3. Using this data, the average conjugation lengths for PPE, PPE-O, and PPE-C were 4.3, 6.3, and 4.1 repeat units, respectively. Here, conjugation length is effectively synonymous with increased planarity, and the results reinforce the notion that the alkoxy substituents increase the effective planarity of the PPE backbone. An interesting reflection on these numbers is that, although alkyl substituents decrease the persistence length of PPE, alkoxy substituents greatly increase the conjugation length. The implication is that PPE-O does not exhibit a decreased persistence length like PPE-C because the alkoxy substituents give rise to an increased coupling energy between the systems of adjacent phenylene units in a way that the alkyl substituents of PPE-C do not. In fact, PPE-C appears to experience the opposite effect: a slight decrease in planarity in comparison to unsubstituted PPE. In order to elucidate the underlying basis for the effect of different substituents on the rigidity and planarity of PPE, we determined the effective planarity of a much wider range of substituted PPE chains. By reducing the polymer to 10 repeat units, an MD trajectory can be computed in a computationally
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accessible time period, to produce dihedral angle distributions that are in good agreement with the results previously discussed for polymers of 25 repeat units. Additionally, chains lengths of 10 repeat units were deemed to be sufficient for modeling planarity while simultaneously taking into account the innate flexibility of the polymer backbone by virtue of being several units longer than their respective polymer persistence lengths. Shorter chain lengths were found to produce inconsistent data and the results of a chain length dependency study on the dihedral angle between adjacent phenylene units may be found in the SI. An unfortunate consequence of decreasing the degree of polymerization is that the persistence length may no longer be measured for these oligomers. Another difficulty that reducing the degree of polymerization presents is that it would also reduce the measured conjugation length in turn. To counteract this problem, the produced Table 1. Average conjugation lengths53 found from MD trajectories of deca(2,5-diX-phenylene-1,4-ethynylene) (OPE-X) extrapolated to polymers of 100 repeat units. Substituent (-X) -H -CH3 -CH2CH3 -CH2CH2CH3 -NH2 -NHCH3 -NHCH2CH3 -OH -OCH3 -OCH2CH3
Conj. Length (Repeat Units) 4.67 4.55 4.49 4.49 5.43 5.40 5.02 7.31 6.43 6.05
Substituent (-X) -F -Cl -Br -I -CHO -CH2CHO -N(CH3)2 -CN -NO2 -CF3
Conj. Length (Repeat Units) 5.94 5.84 4.79 3.88 4.37 4.39 5.46 5.52 4.53 6.35
dihedral angle distributions were integrated outside of ±60˚ to obtain the probability of a conjugation breakage at any given torsion along the chain. This probability was then used to generate an artificially produced histogram of conjugation lengths by considering all possible combinations of angles >60˚ and
