Deuteration as a Means to Tune Crystallinity of Conducting Polymers

Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN ... Oak Ridge, TN 37831 , Department of Chemistry and Biochemist...
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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, Tennessee 37831, United States Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ¶ Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States § Chemical and Engineering Materials Division, Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ‡

S Supporting Information *

ABSTRACT: The effects of deuterium isotope substitution on conjugated polymer chain stacking of poly(3-hexylthiophene) is studied experimentally by X-ray diffraction (XRD) in combination with gel permeation chromatography and theoretically using density functional theory and quantum molecular dynamics. For four P3HT materials with different levels of deuteration (pristine, main-chain deuterated, side-chain deuterated, and fully deuterated), the XRD measurements show that main-chain thiophene deuteration significantly reduces crystallinity, regardless of the side-chain deuteration. The reduction of crystallinity due to the main-chain deuteration is a quantum nuclear effect resulting from a static zero-point vibrational energy combined with a dynamic correlation of the dipole fluctuations. The quantum molecular dynamics simulations confirm the interchain correlation of the proton−proton and deuteron− deuteron motions but not of the proton−deuteron motion. Thus, isotopic purity is an important factor affecting stability and properties of conjugated polymer crystals, which should be considered in the design of electronic and spintronic devices. 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 from gel permetation chromatography (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−

T

he 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 (we refer to most abundant hydrogen isotope 1H as, simply, hydrogen) has little effect on crystal morphology and properties of conducting polymers because different isotopologues exhibit nearly identical electronic structure. An important class of conducting polymers used in organic photovoltaics are poly(3-alkylthiophenes).9,10 These conjugated polymers contain an electron-rich backbone built of thiophene rings and aliphatic chains. In poly(3-hexylthiophene) (P3HT), which is probably 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 13 hydrogens are part of the side-chain hexyl group. In this work, we show that, surprisingly, selective substitution of the 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. © 2017 American Chemical Society

Received: July 12, 2017 Accepted: August 25, 2017 Published: August 25, 2017 4333

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Figure 1. Crystallinity of protonated and deuterated P3HT. (a) Molecular structures of protonated and deuterated P3HT: pristine (P-P3HT), mainchain (thiophene) deuterated (MD-P3HT), side-chain (hexyl) deuterated (SD-P3HT), and fully (hexyl and thiophene) deuterated (FD-P3HT). (b) X-ray (100) diffraction peak intensities of P3HTs as a function of different numbers of deuterium atoms per P3HT monomer. The numbers of deuterium atoms per monomer for P-P3HT, MD-P3HT, SD-P3HT, and FD-P3HT are 0, 1, 13, and 14, respectively. Note that the (100) peak area is proportional to the crystallinity. Detailed information about XRD intensities vs hydrodynamic radii of each P3HT sample are presented in Figure S1.

Next, XRD was used to measure the (100) peak area for (100) crystal reflection for all samples with pristine, main-chain deuterated, side-chain deuterated, and fully deuterated P3HT. Figure 1b shows the (100) diffraction peak intensities of the P3HTs as a function of the number of deuterations where the (100) peak intensities are directly proportional to the crystallinities. Although (100) peak intensities of each P3HT exhibit relatively large 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 > P3HTd14. It was also seen that the crystallinity is largely independent of the molecular size in this study (see Figure S1 for information on hydrodynamic 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 because 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 sidechain deuteration also affects the crystallinity of P3HT but to a lesser degree (P3HT-d0 > P3HT-d13 and P3HT-d1 > P3HTd14), despite a 1 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 slower kinetics of crystallization 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 nanostructures 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, that is, a 3-hexylthiophene, has a dipole moment amounting to ∼1.1 D. It is located near the thiophene ring and is coplanar with it, as shown in Figure 2a. The alkyl arm

H/C−D bonds, and 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 effects on the stability and properties of conducting polymer crystals. We distinguish four different H/D isotopologues of P3HT shown in Figure 1a and labeled in Figure 1b 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; and (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 Supporting 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 ∼10 kDa, 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 the P3HT chain length, for each deuterated vs protonated case, several batches of P3HT with different molecular weights (P3HT chain length) have been synthesized.14 GPC with a Malvern viscometer detector was used for each batch sample to establish its hydrodynamic radius based on the molecular weight obtained by a light-scattering detector and the intrinsic viscosity obtained by a viscometer detector. The hydrodynamic radius from GPC is proportional to the P3HT chain length, and hence, comparing X-ray measurments for samples with the same hydrodynamic radius provides a direct way to compare the crystallinity of different P3HTs with approximately the same chain length. Here, the range of variation of the GPC hydrodynamic radius across all samples was between 4.3 and 6.8 nm (see Figure S1 for more information). 4334

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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 hexylthiophene units. Relative orientation of the dipole moments leads to antiparallel, or antiferroelectric, stacking. (c) Simulated IR spectra of pristine P3HT and thiophene-deuterated P3HT from the DFTB-based molecular dynamics18,19,21,22 of two inner P3HT chains shown in panel (b). The IR spectra are obtained as the Fourier transform of the dipole− dipole autocorrelation functions.

Figure 3. Computational model of P3HT: (a) The outer layer (MM region) is represented by point charges from a DFT calculation. The inner layer (DFT region) consists of a single hexylthiophene unit represented via DFT embedded in the external field of point charges (MM region). A selected H/D is treated quantum mechanically via DVR. (b) DVR grid for the quantum H/D. Contours of the actual potential energy for H/D are shown superimposed on the grid. Yellow: sulfur atoms of the thiophene rings. Red: H/D in the main-chain thiophene rings above and below the quantummechanically treated H/D form a column (marked as a vertical dashed line).

in the peak intensities as well. The intensities in the FT-DACF and in the IR spectrum are proportional to 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 (NQEs) due to the isotopic substitution of protons with deuterons. The isotopic substitution affects primarily vibrational motion of constituent atoms and can appear as a difference in the zeropoint vibrational energy (ZPE) of P3HT isotopologus. In principle, all atoms in P3HT and its isotopologues contribute to the ZPE. The nuclear isotopic effect can be approximated by the difference in dynamics and energy due of the isotopesubstituted 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 assume 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 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 3a, is used for the hydrogen and deuterium versions of P3HT, yielding identical electronic structures. Thus, the observed difference in the stability of the crystalline P3HT is related to the difference in dynamics and,

practically does not contribute to the dipole moment of 3hexylthiophene. 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 antiparallel orientation of the dipole moments, as shown in Figure 2b. Such antiparallel, or antiferroelectric, arrangement of dipole moments is energetically favorable as it minimizes dipole−dipole interactions. However, such static antiferroelectric arrangement alone cannot explain the observed isotopic differences. Another clue comes from the first-principles DFTB18,19 dynamics results, specifically from the Fourier transform of the dipole−dipole autocorrelation function (FT-DACF),20 as shown in Figure 2c. 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 one-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 neighboring strands, as shown in Figure 3a. 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 stretches for H/D in the thiophene ring appear as ∼3000 and ∼2200 cm−1 peaks, respectively, thus exhibiting the usual frequency scaling with the isotope mass as mH /mD . More importantly, the FT-DACF shows differences 4335

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The Journal of Physical Chemistry Letters particularly, to the difference in the 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 single, that is, isolated, chain of P3HT employing three different electronic structure methods: LC-ωPBEh,24 M06L,25 and DFTB18,19,21,22 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 that for the deuterated one, as schematically shown in Figure 4. The corresponding ZPEs are presented in Table S1 (Supporing Information).

For a more accurate description of the NQE associated with the isotope substitutions in P3HT, the protonic and deuteronic energy eigenstates were obtained using the Discrete Variable Representation (DVR)27 and ARPACK diagonalization routines.28 In this approach, the wave function of the quantum nucleus is represented on a three-dimensional Cartesian mesh. The advantage of the current DVR treatment is that it includes (i) the effects of anharmonicity of the PES and (ii) the variance of the dipole moment from the DFT calculations. The computational model is composed of three layers treated with different theoretical approaches (Figure 3a): (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 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 DVRbased quantum dynamics of the proton or the deuteron. Figure 3b shows the 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 and Table S2 (Supporting Information) along with dipole and transition moments. Figure 5a−c shows the dependence of the dipole moment for a single P3HT unit on the DVR mesh (Figure 3b) along the directions corresponding to various vibrational modes (stretching, in-plane, and out-of-plane bending). Clearly, the in-plane with 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 gives rise to nonzero transition

Figure 4. Effect of crystallization on the ZPEs: In a crystalline environment, the force constants are decreased compared to isolated P3HT; hence, the ZPEs are lowered for both hydrogen and deuterium species. The net effect is the increase in stability of the crystalline P3HT (black) compared to a single P3HT chain (blue).

Figure 5. (a−c) Ground-state wave functions and dipole moments 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−f) 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 polarizability near the resonance frequencies for the outof-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. 4336

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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

dipole moments. Table S2 (Supporting Information) lists the dipole moment integrals, ⟨0|μx|k⟩ obtained from the DVR calculations with both μx and |k⟩ 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 rootmean-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 that for D (RMSD = [1.9, 7.8, 2.2] mDeb). Although the fluctuations appear 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 the contribution to stabilization of the crystal structure originating from the interaction between instantaneous dipole changes. This contribution is closely related to the 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 the 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 and deuterium may be manifested in different dynamic responses to the fluctuating local field because 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 timedependent 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 ∑ k>0

α(ω) =

(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 ⟨0|μx|k⟩ 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 Q⃗ = 0. For the transition from the ground vibrational state, the transition integrals become 3N − 6

⟨0|μx |k⟩ =

∑ i=1

⎛ ∂μ ⎞ ⎜⎜ x ⎟⎟ ⎝ ∂Q i ⎠

·⟨0|Q i|k⟩ Q i=0

2

(3)

where we used eq 2 and mass weighting of the normal-mode coordinate Q = m x (see Atkins33). In contrast to the dynamic polarizability, the frequency-dependent polarizability of the 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 because 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 Figure 5d−f. Panel (d) shows the isotropic dynamic polarizability. The resonance frequencies corresponding to excitation of out-of-plane and in-plane bending for hydrogen appear as poles (shown as vertical dashed lines) at, respectively, 752 and 1190 cm−1 (533 and 844 cm−1 for deuterium). The static polarizability limit of the isotropic dynamic polarizability is shown in panel (e). Contrary to the harmonic approximation, the DVR approach reveals about 1% difference in the static polarizability of H and D (αH = 2.82 au, αD = 2.79 au), which is (i) due to the anisotropy/nonlinear dependence of the dipole moment on the displacement of H/D from the equilibrium position and (ii) due to the difference in delocalization and the 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. Panel (f) 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 Figure 2c). Because the dynamic polarizability exhibits poles at the resonant frequencies that are different for H and D, we compare the polarizabilities of the same vibrational modes near their respective frequencies. Out of the three vibrational modes, the out-of-plane bending shows the largest dynamic polarizability and is shown in Figure 5f. It is about 30% higher for H than that 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 the harmonic approximation, eq 3, near the transition frequency. 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, and (ii) it is easier to excite the

ωk 0⟨0|μx |k⟩⟨k|μy |k⟩ ωk 0 2 − ω 2

∂μ ⟨0|Q |1⟩ ∂x m(ω0 2 − ω 2)

ω0 ·

(2)

where the summation runs over the normal modes (3N − 3 = 3 in our case); Qi denotes the normal-mode coordinate. Then, |k⟩ denotes the kth composite vibrational state represented as a Hartree product of (3N − 6) harmonic modes. In the harmonic 4337

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Figure 6. Interchain 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.

same species (two hydrogen or two deuterium atoms). This is remarkable because both H (or D) atoms, that is, 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 an interchain resonance effect. The motion of two protons or deuterons coupled through the field is clearly correlated: both atoms move with similar phases. The interchain 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 interchain binding. Compared to D, the rate of the initial response of H to the oscillating field is stronger (top left and bottom right panels 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 5f). 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 synthesized and characterized pristine, main-chain deuterated, side-chain deuterated, and fully deuterated P3HT. Gel permeation chromatography equipped with triple-detector has been used to characterize the relative length of P3HT chains of different samples. XRD has been used to compare the 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 amount of deuterium substitution but rather related to the dynamics of a single hydrogen (or deuterium) bound to the

vibrations of H than those of D because 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 vibrations 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 interchain correlation effect between two H/D atoms placed on different (neighboring) P3HT chains. As shown in panel (d) in Figure 5, the large magnitude of polarizability of H and D occurs at different resonance frequencies. This suggests that the motions of mixed species H and D are 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 firstprinciples 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 polythiophene chains (see the H/ D column (red) in Figure 3). The initial velocity of the receiver H/D was set to zero, while that of the emitter H/D was set randomly with its kinetic energy matching the ZPE (0.22 eV 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 intrachain vibrational modes, which could mask the effect of interchain 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 interchain neighbor H/D. The displacement of H and D shown in the panels is in the direction normal to the thiophene ring and corresponds to the out-of-plane bending. According to the simulations, there is a resonance between the 4338

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thiophene ring and to the associated change of the dipole− dipole interactions. The experimental measurements are complemented by detailed theoretical studies involving DFT, quantum molecular dynamics, and analysis of nonstatic quantum correlation contributions to the molecular properties. The dynamic polarizabilities associated with the protonic/deuteronic motion were computed using DVR for the nuclear wave functions and the PES from LC-ωPBEh+D3 calculations. Finally, the firstprinciples dynamics based on the DFTB level of electronic structure has been used to study interchain H/D coupling. 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 antiparallel, or antiferroelectric, interchain 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 interchain interaction and π−π stacking cause 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 that for deuterium, as illustrated in Figure 4. (iii) Isotopic substitution leads to a 30% increase of dynamic polarizability for H compared to that for 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 the 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 that for H and a 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 interchain 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 does not cocrystallize in the same domain but forms independent crystal domains.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jacek Jakowski: 0000-0003-4906-3574 Jingsong Huang: 0000-0001-8993-2506 Kunlun Hong: 0000-0002-2852-5111 Bobby G. Sumpter: 0000-0001-6341-0355 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS 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, which are U.S. Department of Energy Office of Science User Facilities. S.G. 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.

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REFERENCES

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b01803. Description of synthesis and experimental measurements (gel permeation chromatography and X-ray diffraction intensities) and details of computational modeling (description of the molecular structure, DFT, and DFTB calculations), ZPE from the harmonic approximation, nuclear eigenstates for H/D from DVR, and corresponding transition dipoles (PDF) 4339

DOI: 10.1021/acs.jpclett.7b01803 J. Phys. Chem. Lett. 2017, 8, 4333−4340

Letter

The Journal of Physical Chemistry Letters (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.; et al. 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 QChem 4 Program Package. Mol. Phys. 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 DensityFunctional Tight-Binding Method for Simulations of Complex Materials Properties. Phys. Rev. B: Condens. Matter Mater. Phys. 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.; Schmitt, 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. (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-RangeCorrected Density Functional That Performs Well for Both GroundState 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 Thermo- chemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent In- teractions. J. Chem. Phys. 2006, 125, 194101. (26) Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787−1799. (27) Colbert, D. T.; Miller, W. H. A Novel Discrete Variable Representaiton for Quantum Mechanical Reactive Scattering via the SMatrix Kohn Method. J. Chem. Phys. 1992, 96, 1982−1991. (28) Lehoucq, R. B.; Sorensen, D. C.; Yang, C. ARPACK Users Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods; SIAM: Philadelphia, PA, 1994. (29) Bishop, D. M. Molecular Vibrational and Rotational Motion in Static and Dynamic Electric Field. Rev. Mod. Phys. 1990, 62, 343−374. (30) Van Hook, W. A.; 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., A: Phys. Sci. 1994, 49, 563−577. (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, 4th ed.; Oxford University Press: New York, 2005; p 425. 4340

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