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Letter
Deuteration as a Means to Tune Crystallinity of Conducting Polymers Jacek Jakowski, Jingsong Huang, Sophya Garashchuk, Yingdong Luo, Kunlun Hong, Jong Keum, and Bobby G. Sumpter J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b01803 • Publication Date (Web): 25 Aug 2017 Downloaded from http://pubs.acs.org on August 28, 2017
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The Journal of Physical Chemistry Letters
Deuteration as a Means to Tune Crystallinity of Conducting Polymers Jacek Jakowski,∗,†,‡ Jingsong Huang,†,‡ Sophya Garashchuk,¶ Yingdong Luo,† Kunlun Hong,† Jong Keum,†,§ and Bobby G. Sumpter†,‡ Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831 , Computational Sciences and Engineering Division,Oak Ridge National Laboratory, Oak Ridge, TN 37831 , Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC 29208, and Chemical and Engineering Materials Division, Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 37831 E-mail:
[email protected] ∗
To whom correspondence should be addressed Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831 ‡ Computational Sciences and Engineering Division,Oak Ridge National Laboratory, Oak Ridge, TN 37831 ¶ Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC 29208 § Chemical and Engineering Materials Division, Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 37831 †
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The fundamental understanding of the nature of hydrogen vs deuterium (H/D) interactions and associated dynamics is important for a wide range of applications including neutron scattering studies of soft materials (polymers, biological materials, foams, liquid crystals, etc.), 1–3 energy research and optoelectronics, 4,5 biomedical applications and pharmaceuticals (H/D substitution is an efficient labeling technique). 1,6–8 Although recent studies show that the physical properties of polymers can be affected by deuteration, 2,4,5 it is generally regarded that H/D isotope substitution has little effect on crystal morphology and properties of conducting polymers, because different isotopologues exhibit nearly identical electronic structure. An important class of conducting polymer used in organic photovoltaics are poly(3alkylthiophenes). 9,10 These conjugated polymers contain electron rich backbone build of thiophene rings and aliphatic chains. In poly(3-hexylthiophene) (P3HT), which is the best known example, each hexylthiophene unit has 14 hydrogens. One of the hydrogens is directly bound to the thiophene ring on the backbone, while the remaining thirteen hydrogens are part of the side-chain hexyl group. In this work we show that, surprisingly, selective substitution of a single hydrogen atom with deuterium at the thiophene rings significantly reduces the crystallinity of P3HT. In comparison, deuteration of hexyl arms (13 hydrogens in each unit) does not affect the crystallinity of P3HT as much. This finding has very important implications for both fundamental science and electronic and spintronic device engineering: techniques that allow modification of the size of crystal grains and tuning of crystal growth in specific directions provide a powerful order parameter for controlling charge transport properties and mechanisms by which transport occurs (band vs hopping). 11 Here we unravel the mechanism by which selective deuteration of the thiophene rings forming the main chain in P3HT affects its crystallinity. 9,12 We synthesized selectively deuterated and protonated P3HT of different molecular lengths (or hydrodynamic radii) and utilized X-ray diffraction (XRD) measurements to characterize the crystallinity of P3HT. The hydrodynamic radii of the synthesized P3HTs were obtained using gel permetation chro-
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matography (GPC). The experimental measurements are complemented by detailed theoretical studies that involve density functional theory (DFT), quantum molecular dynamics, and discrete variable representation of the H/D nuclear wave function. To analyze the isotope dependence of crystallinity we investigated various factors that contribute to the P3HT crystal binding energy: interchain stacking interaction, changes of the ground state vibrational energy due to H/D substitution, dynamic polarizability of C-H/C-D bonds, concerted motion of H and D in neighboring chains of P3HT that modulate the interactions between chains. Our results suggest that the isotopic purity composition has strong affects on the stability and properties of conducting polymer crystals. We distinguish four different H/D isotopologues of P3HT shown in Figure 1(a) and labeled in Figure 1(b) according to the number of deuterium atoms per hexylthiophene unit: (1) d0 (or P-P3HT) denotes pristine, fully protonated P3HT; (2) d1 (or MD-P3HT) denotes the main-chain deuterated P3HT in which the hydrogen of each thiophene ring on the backbone is substituted with deuterium; (3) d13 (or SD-P3HT) denotes the side-chain deuterated P3HT in which the hexyl arms are deuterated; (4) d14 (or FD-P3HT) denotes fully deuterated P3HT (FD-P3HT), in which both the thiophene ring and the hexyl arms are deuterated. Technical details of the experimental and theoretical methods are available as Supplemental Information. It has been shown that, due to the π-conjugation, the P3HT backbone is relatively rigid and its crystallinity increases with the length of the backbone chain until its molecular weight reaches a critical value (about ∼10kDa which corresponds to about 60 hexylthiophene units). 9,13 For molecular weights larger than the critical value, the P3HT chains in the crystals appear folded and the crystallinity becomes independent of the chain length. 9,13 Ideally, one wants to compare the crystallinity between different P3HT species with the same chain length and for molecular weight below its critical value. To control P3HT chain length, for each deuterated vs protonated case several batches of P3HT with different molecular weight
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variation error ranges, it appears that the order in the crystallinity of the P3HTs with different deuterium substitution is P3HT-d0 > P3HT-d13 > P3HT-d1 > P3HT-d14. It was also seen that the crystallinity is largely independent of the molecular size in this study (see Supplementary Figure S1 for information on hydrodynamics radius of P3HT samples from GPC). XRD study clearly demonstrates that deuteration of the thiophene ring significantly reduces the crystallinity of P3HT (that is P3HT-d0 > P3HT-d1 and P3HT-d13 > P3HT-d14). This is a remarkable observation since the molecular geometry and electronic structure do not depend on isotopic substitution. It suggests that the difference in crystallinity is related to the dynamics of a single hydrogen (or deuterium) bound to the thiophene ring and, perhaps, to the associated change of the dipole-dipole interactions. Note that the side-chain deuteration also affects the crystallinity of P3HT but to a lesser degree (P3HT-d0 > P3HT-d13 and P3HT-d1 > P3HT-d14) in spite of one order of magnitude larger number of deuterations (a single substition per thiophene unit in the former case and 13 per unit in the latter case). This shows that the reduced crystallinity of MD-P3HT is not caused by a slower kinetics of crystalization due to the increased mass of deuterated P3HT. In fact, the mass of SD-P3HT is larger than that of MD-P3HT but the crystallinity shows the opposite trend (P3HT-d13 > P3HT-d1). In this work we focus on the effect of main-chain deuteration. To understand the effect of main-chain deuteration, we start by examining the interchain interactions. The important interactions influencing self-assembly of nano-structures and defining crystallinity of polymers are, in addition to the dispersion forces, the dipole-dipole interactions. 15 As our electronic structure calculations show, 16 the basic unit of P3HT, i.e., a 3-hexylthiophene, has a dipole moment amounting to ∼ 1.1 Debye. It is located near the thiophene ring and is co-planar with it as shown in Figure 2(a). The alkyl arm practically does not contribute to the dipole moment of 3-hexylthiophene. In crystalline P3HT, 12,17 the relative orientation (packing) of neighboring P3HT chains shows longitudinally displaced stacking of the thiophene rings that leads to an anti-parallel orientation of the dipole moments
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as shown in Figure 2(b). Such anti-parallel, or anti-ferroelectric, arrangement of dipole moments is energetically favorable as it minimizes dipole-dipole interactions. However, such static anti-ferroelectric arrangement alone cannot explain the observed isotopic differences. Another clue comes from the first-principles DFTB 18,19 dynamics results, specifically from the Fourier Transform of the dipole-dipole autocorrelation function (FT-DACF) 20 as shown in Figure 2(c). Only the peaks related to the motion of H/D in a thiophene ring are shown in the figure for clarity. These atoms form a 1-dimensional, column-like chain of H...H...H (or D...D...D) atoms stretching across the entire crystal structure along the stacking direction and coupling neighbouring strands as shown in Figure 3(a). FT-DACF is closely related to the infrared (IR) absorption spectra. The energy of the peaks in FT-DACF corresponds to the IR frequency transitions. For example, C-H and C-D stretch for H/D in the thiophene ring appear as ∼ 3000 cm−1 and ∼ 2200 cm−1 peaks, respectively, thus exhibiting the usual p frequency scaling with the isotope mass as mH /mD . More importantly, the FT-DACF shows differences in the peak intensities as well. The intensities in the FT-DACF and in
the IR spectrum are proportional to the changes in the dipole moment and hence to the nuclear polarizabilities. These observations raise questions about the role of interactions, dynamics and the nuclear quantum effects (NQE) due to the isotopic substitution of protons and deuterons. The isotopic substitution affects primarily vibrational motion of constituting atoms and can appear as a difference in the zero-point vibrational energy (ZPE) of P3HT isotopologus. In principle all atoms in P3HT and its isotopologues contribute to the zero-point vibrational energy (ZPE). The nuclear isotopic effect can be approximated by the difference in dynamics and energy due of the isotope substituted H. To estimate the NQE we analyze the zero-point vibrations of the main-chain hydrogen and deuterium by DFT in the harmonic approximation to the ground electronic state potential energy surface (PES). That is, we assumed that the contribution to ZPE from the same mass atoms in different isotopologues is similar and can be neglected in isotope effect. Our atomistic model is based on the crystallography data. 17 It
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6x10-5
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Figure 2: (a) Schematic orientation of the dipole moment (blue arrow) in a single 3-hexyl thiophene oligomer, obtained from the DFT calculations. 16 The sulfur and hydrogen (or deuterium) atoms on a thiophene ring are shown as yellow and red, respectively. (b) The model of the P3HT crystal consists of four P3HT chains. Each chain consists of four thiophene hexyl units. Relative orientation of the dipole moments leads to the anti-parallel, or anti-ferroelectric, stacking. (c) The simulated IR spectra of pristine P3HT and thiophenedeuterated P3HT from the DFTB-based molecular dynamics 18,19,21,22 of two inner P3HT chains shown in panel (b). The IR spectra are obtained as the Fourier Transform of the dipole-dipole autocorrelation functions. consists of four chains of P3HT (408 atoms). Each chain has four hexylthiophene units (25 atoms) and is terminated with hydrogen atoms – two atoms per chain. The same molecular structure, shown in Figure 3(a), is used for the hydrogen and deuterium version of P3HT, yielding identical electronic structure. Thus, the observed difference in the stability of the crystalline P3HT is related to the difference in dynamics and, particularly, to the difference in the vibrational zero-point energy (ZPE) of H and D. 23 The ZPE is calculated for the main-chain hydrogen and deuterium in crystalline P3HT and compared with that for a a single, i.e., isolated, chain of P3HT employing three different electronic structure methods: LC-ωPBEh, 24 M06L 25 and DFTB 18,19,21,22 including empirical dispersion. 26 Pople’s 6-31G(d) basis set was used for DFT calculations. For all three methods the analysis of the Hessian shows that the crystal field flattens the PES where H/D connects to the thiophene ring, compared to the PES of an isolated P3HT chain. Thus, the force constants and the ZPE are consistently lowered for both H and D. The lowering of the ZPE contributes to the stabilization of the crystalline species, and is larger for the protonated species than for the deuterated one as schematically shown in Figure 4. The corresponding ZPEs are presented 8
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approaches (Figure 3(a)): (1) The outer layer is a Molecular Mechanics (MM) region, where the interatomic interactions are modeled via the point charges; (2) The inner layer is a Quantum Mechanics (QM) region where the electronic structure is described from the first principles via DFT to provide an adequately accurate PES used for the innermost layer; and (3) The innermost layer is the region of the DVR-based quantum dynamics of the proton or the deuteron. Figure 3(b) shows innermost DVR region as a mesh along with the isosurface of the potentials for the H/D motion. The DVR eigestates are shown in Figure S3 (supporting information) and in Table S2 (supporting information) along with dipole and transition moments. 1.5
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Figure 5: ground state wave function for H and D: both functions are shown as functions of displacement from the equilibrium position along the normal mode direction. The nuclear wave functions are calculated within the DVR approach on the ab initio PES computed at the LC-ωPBEh+D3 theory level. (d-e) Contribution to polarizability from motion of main chain H/D. (d) Frequency dependence (in cm−1 ) of the isotropic nuclear polarizability, αiso (ω) = (αxx + αyy + αzz )/3, for H and D in P3HT. Dashed vertical lines correspond to excitation energy poles for bending transitions. (e) Static limit of dynamic polarizability. (f) Dynamic polrizability near the resonance frequencies for the out-of-plane (oop) bend. Center and right panels: The frequency ω denotes the shift from the resonance frequency. The dynamic polarizability changes sign at the resonance frequency; absolute values of polarizability are shown.
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Figure 5(a-c) shows the dependence of the dipole moment for a single P3HT unit on the DVR mesh (Figure 3(b)) along the directions corresponding to various vibrational modes (stretching, in-plane and out-of-plane bending). Clearly, the in-plane with the ring H/D bending leads to the largest changes in the magnitude of the dipole moment. The primary effect for the out-of-plane bending is the change of orientation of the dipole moment, while its magnitude is almost unchanged as shown on panel (a). The anisotropy of the dipole moment combined with anharmonicity of the PES give rise to non-zero transition dipole moments. Table S2 (supporting information) lists the dipole moment integrals, h0| µx |ki obtained from the DVR calculations with both µx and |ki defined on the mesh. Overall, the total dipole moment vector of the P3HT unit consists of a “stationary” dipole moment of a thiophene ring independent of H/D vibrations, and of its instantaneous fluctuations associated with the motion of H/D. To quantify the relative range of fluctuations of the H/D dipole moment we calculated its root mean square (RMS) for the ground vibrational states of H and D. As expected, the range of the dipole moment fluctuations is larger for H (RMSH = [2.9, 11.0, 3.3] mDeb) than for D (RMSD = [1.9, 7.8, 2.2] mDeb). Although the fluctuation appears to be small, they are sufficiently large to dictate the difference. We discussed above the dependence of the local dipoles on the ground state vibrational motion of main chain H/D. Next, we examine contribution to stabilization of crystal structure originating from the interaction between instantaneous dipole change. This contribution is closely related to dispersion energy and is related to polarizability associated with the nuclear motion of quantum H and D. 29,30 As mentioned earlier, the FT-DACF results suggest that the intensity for IR absorption in deuterated P3HT (and hence also polarizability) is reduced compared to that of the protonated case. The polarizability is associated with the induction and dispersion forces between molecules. 31,32 The magnitude of the dispersion interaction is proportional to the electronic polarizability and it arises from the correlated motion between instantaneous dipole moments. Here we analyze the analogous interaction arising from the correlated nuclear motion of H/D. It is expected that the difference in masses of hydrogen
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and deuterium may be manifested in different dynamic responses to the fluctuating local field, since the oscillator mass determines how rapidly it responds to the changing field. To analyze this effect we investigate the nuclear polarizability (dynamic and static) of hydrogen and deuterium in P3HT. The dynamic polarizability is defined from the time-dependent perturbation theory in which the perturbation is an external electromagnetic field, oscillating with the frequency ω. The polarizability tensor component αxy is given by
αxy (ω) = 2
X ωk0 h0| µx |ki hk| µy |ki 2 ωk0 − ω2
k>0
(1)
where ωk0 = Ek − E0 is the resonance frequency of the transition from the ground to the kth nuclear state of hydrogen or deuterium, and h0| µx |ki are the nuclear transition dipole moment integrals. The remaining components (xx, yy, zz, xz, yz) of the polarizability tensor α are given by the expressions analogous to Eq. 1. In the harmonic approximation the transition dipole integrals are obtained from the Taylor expansion of µx up to linear terms with respect to a set of normal mode coordinates ~ Qi at Q=0. For the transition from the ground vibrational state the transition integrals become: h0| µx |ki =
3N −6 X i=1
∂µx ∂Qi
Qi =0
· h0| Qi |ki
(2)
where the summation runs over the normal modes (3N − 3 = 3 in our case); Qi denotes the normal mode coordinate. Then, |ki denotes the kth composite vibrational state represented as a Hartree product of (3N − 6) harmonic modes. In the harmonic approximation only transitions allowed from the ground state are to the first excited state of H/D for each of the 3N − 6 states. Only three such transitions are allowed for a single H or D atom. For a single harmonic oscillator the frequency-dependent polarizability is
α(ω) =
ω0 · | ∂µ h0| Q |1i |2 ∂x m(ω02 − ω 2 ) 12
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where we used Eq. 2 and mass weighting of the normal mode coordinate Q =
√
mx (see
Atkins 33 ). In contrast to the dynamic polarizability, the frequency-dependent polarizability of harmonic oscillator (Eq. 1) in the ω = 0 limit (the static polarizability) depends on the force constant and on ω0 but not on the mass. That is, the static polarizabilities of H and D in the harmonic approximation are equal. Within our DVR/DFT approach for eigenvalues the transition moment integrals and nuclear polarizabilites can be evaluated directly from the perturbation-theory based Eq. (1) since both the nuclear wave function and the electronic dipole moments (beyond linear terms used in Eq. 2) are available on the mesh. The nuclear polarizabilities computed from the DVR eigenvectors as a function of frequency are shown in Fig. 5(d-f). Panel (d) shows isotropic dynamic polarizability. The resonance frequency corresponding to excitation of out-of-plane and in-plane bending for hydrogen appear as poles (shown as vertical dashed lines) at, respectively, 752 cm−1 and 1190 cm−1 (533 cm−1 and 844 cm−1 for deuterium). The static polarizability limit of the isotropic dynamic polarizability is shown on the (e) panel. Contrary to harmonic approximation, the DVR approach reveal about 1% difference in the static polarizability of H and D (αH =2.82 a.u, αD =2.79 a.u.), which is (i) due to the anisotropy/non-linear dependence of the dipole moment on the displacement of H/D from the equilibrium position and (ii) due to the difference in delocalization and spatial span of the protonic/deuteronic wave functions. This suggests that the difference in the static polarizability of deuterated and protonated species can be used to probe the anharmonicity/anisotropy of the potential and of the dipole moment. The (f) panel in Figure 5 shows the absolute value of dynamic polarizabilities for H and D near the resonance frequency defined by the vibrational excitation energies. As expected from Eq. (1), the polarizabilities are singular at the resonance frequency. These singularities directly correspond to the peaks in the IR spectra (see Fig. 2(c)). Since the dynamic polarizability exhibits poles at the resonant frequencies which are different for H and D, we compare the polarizabilities of the same vibrational modes near their respective frequencies.
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Out of the three vibrational modes, the out-of-plane bending shows the largest dynamic polarizability and is shown in Figure 5(f). It is about 30% higher for H than for D and also has the lowest resonance frequency. The magnitude of dynamic polarizability for H is consistently larger than that for D for all three vibrational modes. This trend agrees with the mass dependence of the dynamic polarizability within harmonic approximation, Eq. (3), near the transition frequency. The analysis of the dynamic polarizabilities indicates that: (i) the out-of-plane bending is the easiest and the stretching mode is the hardest to excite/polarize, as their polarizabilities are the largest and lowest respectively; (ii) it is easier to excite the vibrations of H than those of D, since near the resonant frequencies the polarizability of H is significantly larger than that of D. In the crystalline P3HT there is an internal source of the resonant field due to the C-H and C-D vibration from the neighboring P3HT chains. For verification we performed quantum molecular dynamics of H and D in the electrostatic field due to vibrations of the neighboring C-H and C-D bonds at the resonant frequencies as described below. We have above discussed the dynamic polarizability for the nuclear motion of main chain H/D. Now we analyze the inter-chain correlation effect between two H/D atoms placed on different (neighboring) P3HT chains. As shown on the panel (d) in Figure 5, the large magnitude of polarizability of H and D occurs at different resonance frequencies. This suggests that the motion of mixed species H and D is largely independent of each other while some correlation might be expected in the dynamics of the same species. To verify that, a set of four first-principles dynamics simulations was performed using our 408-atom model of P3HT with different combinations of H or D being the emitter and the receiver of the oscillating field. All atoms were frozen except for the two selected H/D atoms: a single oscillating H/D atom (the emitter of the field) and a single H/D (the receiver responding to the field). The emitter and the receiver H/D atoms were the closest H/D atoms belonging to the neighboring poly-thiophene chains (see H/D column (red) on panel of Figure 3). The initial velocity of the receiver H/D was set to zero, while that of the emitter H/D was
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Figure 6: The inter-chain response of H/D to the local oscillating field caused by oscillating H/D of the neighboring P3HT chain. The displacement of H/D out of the thiophene plane is a function of the number of MD steps (the time-step is 0.5 fs). The displacement of the receiver atom is scaled by 2 for clarity. The out-of-plane displacement corresponds to the out-of-plane bending vibrational mode. set randomly with its kinetic energy matching the ZPE (0.22eV for D and 0.30 eV for H). Freezing the rest of the atoms allowed us to eliminate other possible sources of the oscillating field, such as coupling to the intra-chain vibrational modes, which could mask the effect of inter-chain H/D coupling. Figure 6 shows the response of the receiver H/D to the oscillating field originating from the zero-point vibration of the nearest inter-chain neighbor H/D. The displacement of H and D shown in the panels is in the direction normal to the thiophene ring corresponds to the out-of-plane bending. According to the simulations, there is a resonance between the same species (two hydrogen or two deuterium atoms). This is remarkable since both H (or D) atoms, i.e., the emitter and receiver, do not belong to the same P3HT chains and, therefore, are not coupled through the bonding network. The oscillating electrostatic field from H/D is sufficiently strong to affect the dynamics of H/D belonging to a different P3HT chain and can result in inter-chain resonance effect. The motion of two protons or deuterons coupled 15
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through the field is clearly correlated: both atoms move with similar phases. The inter-chain in-phase correlated displacement of H/D suggests that the fluctuations of the instantaneous dipole moments are also in-phase, which can contribute to the stability of the inter-chain binding. Compared to D, the rate of the initial response of H to the oscillating field is stronger (panels a and d in Figure 6). This observation is consistent with the larger dynamic polarizability of H near the resonance frequencies for the out-of-plane bending (see Figure 5(f)). For the mixed H/D combination of the emitter/receiver the response to oscillations is practically negligible. This is consistent with the fact that the dynamic polarizability of D near the resonance frequency of H is very small (and vice versa). All-in-all the dynamics simulations confirm that the oscillating field from H/D of a selected P3HT chain is sufficiently strong to influence the dynamics of H/D in neighboring chains, which may lead to the interchain resonance effect. In summary, we have synthesised and characterized pristine, main-chain deuterated, sidechain deuterated and fully deuterated P3HT. Gel permeation chromatography has been used to characterize relative length of P3HT chains of different samples. The XRD has been used to compare crystallinity of different P3HT samples. XRD studies demonstrate that deuteration of the thiophene ring reduces the crystallinity of P3HT. It suggests that the difference in crystallinity is not merely a kinetics problem depending on the number of deuterium substitution but rather related to the dynamics of a single hydrogen (or deuterium) bound to the thiophene ring and to the associated change of the dipole-dipole interactions. The experimental measurements are complemented by detailed theoretical studies involving density functional theory, quantum molecular dynamics and analysis of non-static quantum correlation contributions to the molecular properties. The dynamic polarizabilities associated with the protonic/deuteronic motion were computed using the DVR for the nuclear wave functions and potential energy surface from LC-ωPBEh+D3 calculations. Finally, the first-principles dynamics based on the DFTB level of electronic structure has been used to study inter-chain H/D coupling.
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The results obtained indicate the following: (i) Although crystalline P3HT is bound by the dispersion forces, the specific parallel shift in stacking minimizes the dipole-dipole interactions. The resulting equilibrium structure exhibits the anti-parallel, or anti-ferroelectric, inter-chain stacking which is attractive (interaction between parallel dipoles is repulsive). (ii) The reduced crystallinity due to the main-chain deuteration in P3HT is caused by the difference in the ZPE of protonated and deuterated species in the crystal vs isolated P3HT chain. The inter-chain interaction and π −π stacking causes lowering of the force constants and decreases the ZPE of hydrogen and deuterium, adding to the stability of crystalline P3HT. The ZPE stabilization is more pronounced for hydrogen than for deuterium as illustrated in Figure 4. (iii) Isotopic substitution leads to a 30% increase of dynamic polarizability for H compared to D near the frequencies corresponding to the underlying vibrational modes. This result is consistent with the increase of the IR intensities in the IR spectra obtained from the Fourier Transform of dipole-dipole autocorrelation function (panel c in Figure 2). Overall, the higher stability of protonated vs deuterated P3HT results from a combination of lower ZPE for D than for H and larger dipole-dipole interaction for H. (iv) The oscillating field from the zero-point vibrational motion of H/D is sufficiently strong to affect dynamics of H/D in different chains and can lead to correlated inter-chain H/D motion. (v) Isotopic purity or its lack is an important factor that affects the stability and properties of conducting polymer crystals. Our work suggests that a mixed blend of pristine P3HT and main chain deuterated P3HT do not co-crystalize in the same domain but form independent crystal domains.
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Acknowledgement This research was sponsored by the Laboratory Directed Research and Development (LDRD) Program of Oak Ridge National Laboratory. The work was conducted at the Center for Nanophase Materials Sciences and the Spallation Neutron Source, U.S. Department of Energy Office of Science User Facilities. SG acknowledges support by the National Science Foundation under Grant No. CHE-1565985. The XSEDE allocation TG-DMR110037 and use of the USC HPC cluster funded by the National Science Foundation under Grant No. CHE-1048629 are also acknowledged.
Supporting Information Available Description of synthesis and experimental measurements (gel permeation chromatography and X-ray diffraction intensities) and details of computational modeling (description molecular structure, DFT and DFTB calculations, zero-point vibrational energy from harmonic approximation, nuclear eigenstates for H/D from DVR and corresponding transition dipole.
References (1) Meilleur, F.; Weiss, K. L.; Myles, D. A. In Micro and Nano Technologies in Bioanalysis Methods and Protocols; Lee, J. W., Foote, R. S., Eds.; Springer: New York, 2009; pp 281–292. (2) White, R. P.; Lipson, J. E. G.; Higgins, J. S. Effect of Deuterium Substitution on the Physical Properties of Polymer Melts and Blends. Macromolecules 2010, 43, 4287–4293. (3) Higgins, J. S.; Benoit, H. C. Polymers and Neutron Scattering; Oxford Series on Neutron Scattering in Condensed Matter; Clarendon Press: Oxford, UK, 1997; Vol. 8. (4) Shao, M.; Keum, J.; Chen, J.; He, Y.; Chen, W.; Browning, J. F.; Jakowski, J.;
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Sumpter, B. G.; Ivanov, I. N.; Ma, Y.-Z. et al. The Isotopic Effects of Deuteration on Optoelectronic Properties of Conducting Polymers. Nature Commun. 2014, 5, 3180. (5) Wang, L.; Jakowski, J.; Garashchuk, S.; Sumpter, B. G. Understanding How Isotopes Affect Charge Transfer in P3HT/PCBM: A Quantum Trajectory-Electronic Structure Study with Nonlinear Quantum Corrections. J. Chem. Theory Comput. 2016, 12, 4487– 4500. (6) Tung, R. The Development of Deuterium-Containing Drugs. Innovations in Pharmaceutical Technology 2010, 32, 24–28. (7) Harbeson, S. L.; Tung, R. D. Deuterium Medicinal Chemistry: A New Approach to Drug Descovery and Development. Med. Chem. News 2014, 8–22. (8) Halford, B. Deuterium Switcheroo Breathes Life into Old Drugs. Chem and Eng News 2016, 94, 32–36. (9) Lim, J. A.; Liu, F.; Ferdous, S.; Muthukumar, M.; Briseno, A. L. Polymer Semiconductor Crystals. Materials Today 2010, 13, 14–24. (10) Ludwigs, S., Ed. P3HT Revisited – from Molecular Scale to Solar Cell Devices; Advances in Polymer Science; Springer-Verlag: Berlin Heidelberg, 2014; Vol. 265. (11) Poelking, C.; Daoulas, K.; Troisi, A.; Andrienko, D. Morphology and Charge Transport in P3HT: A Theorist’s Perspective. Adv. Polym. Sci. 2014, 265, 139–180. (12) Pascui, O. F.; Lohwasser, R.; Sommer, M.; Thelakkat, M.; Thurn-Albrecht, T.; Saalwachter, K. High Crystallinity and Nature of Crystal-Crystal Phase Transformations in Regioregular Poly(3-Hexylthiophene). Macromolecules 2010, 43, 9401–9410. (13) Liu, J.; Arif, M.; Zou, J.; Khondaker, S. I.; Zhai, L. Controlling Poly(3-Hexylthiophene) Crystal Dimension: Nanowhiskers and Nanoribbons. Macromolecules 2009, 42, 9390– 9393. 19
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(14) Tamba, S.; Shono, K.; Sugie, A.; Mori, A. C–H Functionalization Polycondensation of Chlorothiophenes in the Presence of Nickel Catalyst with Stoichiometric or Catalytically Generated Magnesium Amide. J. Am. Chem. Soc. 2011, 133, 9700–9703. (15) Talapin, D. V.; Shevchenko, E. V. Dipole-Dipole Interactions in Nanoparticle Superlattices. Nano Lett. 2007, 7, 1213–1219. (16) Shao, Y.; Gan, Z.; Epifanovsky, E.; Gilbert, A. T. B.; Wormit, M.; Kussmann, J.; Lange, A. W.; Behn, A.; Deng, J.; Feng, X. et al. Advances in Molecular Quantum Chemistry Contained in the Q-Chem 4 Program Package. Molecular Physics 2015, 113, 184–215. (17) Dudenko, D.; Kiersnowski, A.; Shu, J.; Pisula, W.; Sebastiani, D.; Spiess, H. W.; Hansen, M. R. a Strategy for Revealing the Packing in Semicrystalline P-Conjugated Polymers: Crystal Structure of Bulk Poly-3-Hexyl-Thiophene (P3HT). Angew. Chem. Int. Ed. 2012, 51, 11068–11072. (18) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai, S.; Seifert, G. Self-Consistent-Charge Density-Functional Tight-Binding Method for Simulations of Complex Materials Properties. Phys. Rev. B 1998, 58, 7260–7268. (19) Zheng, G.; Lundberg, M.; Jakowski, J.; Vreven, T.; Frisch, M. J.; Morokuma, K. Implementation and Benchmark Tests of the DFTB Method and Its Application in the ONIOM Method. Int. J. Quantum Chem. 2009, 109, 1841–1854. (20) Kim, J.; Schmitti, U. W.; Gruetzmacher, J. A.; Voth, G. A.; Scherer, N. E. The Vibrational Spectrum of the Hydrated Proton: Comparison of Experiment, Simulation, and Normal Mode Analysis. J. Chem. Phys. 2002, 116, 737–746. (21) Witek, H.; Morokuma, K. Systematic Study of Vibrational Frequencies Calculated with the Self-Consistent Charge Density Functional Tight-Binding Method. J. Comput. Chem. 2004, 25, 1858–1864. 20
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(22) Parameter Set “mio-1-1”. http://www.dftb.org/parameters/download/mio/mio-1-1-cc/ (accessed May 30, 2017). (23) Scheiner, S.; Cuma, M. Relative Stability of Hydrogen and Deuterium Bonds. J. Am. Chem. Soc. 1996, 118, 1511–1521. (24) Rohrdanz, M. A.; Martins, K. M.; Herbert, J. M. A Long-Range-Corrected Density Functional That Performs Well for Both Ground-State Properties and Time-Dependent Density Functional Theory Excitation Energies, Including Charge-Transfer Excited States. J. Chem. Phys. 2009, 130, 054112. (25) Zhao, Y.; Truhlar, D. G. A New Local Density Functional for Main-Group Thermochemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions. J. Chem. Phys. 2006, 125, 194101. (26) Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a LongRange Dispersion Correction. J. Comput. Chem. 2006, 27, 1787–1799. (27) Cokbert, D. T.; Miller, W. H. A Novel Discrete Variable Representaiton for Quantum Mechanical Reactive Scattering Via the S-Matrix Kohn Method. J. Chem. Phys. 1992, 96, 1982–1991. (28) Lehoucq, R. B.; Sorensen, D. C.; Yang, C. ARPACK Users Guide: Solution of LargeScale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods; SIAM: Philadelphia, 1994. (29) Bishop, D. M. Molecular Vibrational and Rotational Motion in Static and Dynamic Electric Field. Rev. Mod. Phys. 1990, 62, 343–374. (30) Hook, W. A. V.; Wolfsberg, M. Comments on H/D Isotope Effects on Polarizabilities of Small Molecules. Correlation with Virial Coefficient, Molar Volume and Electronic Second Moment Isotope Effects. Z. Naturforsch. 1994, 94a, 563–577. 21
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(31) Jeziorski, B.; Moszynski, R.; Szalewicz, K. Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of Van Der Waals Complexes. Chem. Rev. 1994, 94, 1887–1930. (32) Chalasinski, G.; Szczesniak, M. M. State of the Art and Challenges of the Ab Initio Theory of Intermolecular Interactions. Chem. Rev. 2000, 100, 4227–4252. (33) Atkins, P.; Friedman, R. Molecular Quantum Mechanics; Oxford University Press: New York, 2005; p 425, 4th Ed.
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MM region (charges)
DFT region
Quantum H/D (DVR)
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