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Elucidation of Chiral-symmetry Breaking in a Racemic Polymer System with Terahertz Vibrational Spectroscopy and Crystal Orbital Density Functional Theory Feng Zhang, Houng-Wei Wang, Keisuke Tominaga, Michitoshi Hayashi, Sunglin Lee, and Takashi Nishino J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b02213 • Publication Date (Web): 01 Nov 2016 Downloaded from http://pubs.acs.org on November 1, 2016

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The Journal of Physical Chemistry Letters

Elucidation of Chiral-symmetry Breaking in a Racemic Polymer System with Terahertz Vibrational Spectroscopy and Crystal Orbital Density Functional Theory Feng Zhang,1 Houng-Wei Wang,2 Keisuke Tominaga,1,* Michitoshi Hayashi,2,* Sunglin Lee,3 and Takashi Nishino3,* 1

Molecular Photoscience Research Center, Kobe University, Kobe 657-8501, Japan

2

Center for Condensed Matter Sciences, National Taiwan University, 1 Roosevelt Rd. Sec. 4,

Taipei 10617, Taiwan 3

Departments of Chemical Science and Engineering, Graduate School of Engineering, Kobe

University, Kobe 657-8501, Japan AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] (M. Hayashi), [email protected] (K. Tominaga), [email protected] (T. Nishino)

ACS Paragon Plus Environment

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ABSTRACT: The conservation of chiral symmetry has been used as a fundamental rule to determine polymer packing-conformations in racemic systems. We have illustrated, through the interplay of polarization THz spectroscopy and solid-state density functional theory, that the chiral symmetry is not conserved in a poly(lactic acid) stereocomplex (scPLA) system. poly(Llactic acid) (PLLA) displays a weaker violation of the 31 screw symmetry than poly(D-lactic acid) (PDLA), and possesses a stronger intramolecular vibrational energy, on average, in the low-frequency gamma-point phonon modes than does PDLA. Polarization THz spectroscopy adds a new dimension to polymer crystallography through which new phenomena are expected to be revealed.

TOC GRAPHICS

KEYWORDS chiral-symmetry breaking • polymer packing conformation • scPLA • THz modes • solid-state DFT


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THz vibrational spectroscopy has attracted increasing attention in crystallography.1-3 One of its promising potential applications is in the determination of the packing conformations of polymers that contain a large fraction of hydrogen atoms. Hydrogen atoms are invisible to X-ray and electron beams; in contrast, THz vibrational spectroscopy probes the collective vibrations of all atoms in a system,4-8 thus implying more complete and delicate structural information. Symmetry conservation has been used as a principle of determining polymer conformations in the crystalline state.9-11 First, the equivalence postulate, formulated by the early pioneers of polymer science, Bunn,12 Huggins13 and Pauling,14 claims the constitutional repeating units— “the smallest constitutional unit, the repetition of which constitutes a regular macromolecule”9— of single polymer chains should be related by symmetry. Second, an enantiomeric polymer chain is assumed to be the exact mirror image of its chiral counterpart when they coexist in a racemic system.9 So far, symmetry breaking of the ideal crystalline chain conformation from the equivalence postulate has been reported in some cases.10, 15 The conservation of chiral symmetry is, however, accepted without question, owing to the electric force, binding atoms and molecules, conserves parity. There is in fact no a priori proof of this reasoning. Quoting Anderson’s wellknown viewpoint of “More is different,” referring to emergence in solid-state physics, “the state of a big system is not implied to have the same symmetry of the laws which govern it”.16-17 The conservation of chiral symmetry, as an underpinning principle of polymer science, should be subjected to rigorous verifications whenever new experimental criteria are available. This letter is devoted to examining the postulate of conservation of chiral symmetry through the interplay of polarization THz vibrational spectroscopy and solid-state density functional theory (DFT).18-20 The poly(lactic acid) stereocomplex (scPLA) provides a prototype system for this embedded purpose. In scPLA, enantiomeric poly(L-lactic acid) (PLLA) and poly(D-lactic acid)


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(PDLA) coexist in equal amounts. The packing conformations of PLLA and PDLA have been resolved from the electron and X-ray diffraction patterns recorded at room temperature of a piece of thin film with the polymer chains uniaxially oriented.21-23 The crystal possesses R3c space group symmetry. In each primitive cell, a left-handed 31 PLLA helix and a right-handed 31 PDLA helix adopt a parallel packing conformation and conserve a perfect chiral relation via glide plane operations (Figure 1).

Figure 1. Crystal structure of scPLA with R3c space group symmetry. The two enantiomeric helices in one primitive cell are projected onto a plane normal to (a) and parallel to (b) the chain axes (z direction). The y-axis lies on a plane determined by the two chain axes of PLLA and PDLA. The red, green and blue lines represent the three primitive cell vectors a, b and c, respectively.

ScPLA samples without preferred orientations were prepared by annealing the casted films of an equimolar mixture of PLLA and PDLA at 200 °C over 3 hours. ScPLA samples with polymer chains uniaxially aligned were prepared for the polarization THz measurements (refer to SI for the experimental details). The sharp X-ray diffraction peaks of the scPLA samples ensure the dominant presence of crystalline regions over


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Figure 2. XRD and THz characterizations of scPLA and the normal mode simulation results. Panel a shows an XRD spectrum of scPLA without preferred orientation. Panel b shows a THz spectrum of scPLA without preferred orientation (top) and THz spectra of scPLA with polymer chains uniaxially parallel (middle) and perpendicular (bottom) to the polarization direction of THz pulses; the frequency region with a reduced signal/noise ratio is shadowed. The XRD and THz spectra were recorded at 293 K and 78 K, respectively. Panels c and d show the normal modes simulated with R3c and P1 space groups, respectively. In each panel, the top, middle, and bottom parts display the simulated normal modes with the corresponding polarization properties with those of Panel b; Lorentzian line shapes with a half-width at half-maximum=2.0 cm-1 are convolved to normal modes for visualization; a frequency distribution pattern of normal modes is shown in the top part (Raman active modes of R3c space group are shown in red).

the amorphous region (Figure 2a), corresponding to very high crystallinity. The peak pattern is completely consistent with that of the resolved crystal structure in the literature, implying the


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existence of a very pure crystalline phase.24 Four bands were resolved (shown in the upper panel of Figure 2b); bands a and d possess polarizations parallel to the chain axes, while bands b and c possess polarizations perpendicular to the chain axes as shown in the middle and bottom panels of Figure 2b, respectively. The polarization dependence of the THz bands indicates these bands originate intrinsically from the crystalline regions because vibrational modes of the amorphous region should not show such strong anisotropy. Concerning the gamma-point phonon modes, which represent the in-phase vibrations of the entire unit cells and have optical activities, the R3c space group has three irreducible representations, A1, A2, and E.25 A1, general to all space groups, represents IR active modes with polarizations parallel to the chain axes. E is given rise to by the 31 screw symmetry, representing double-generate IR active modes with polarizations perpendicular to the chain axes. A2 originates from the glide plane symmetry, representing IR inactive but Raman active modes. In summary, the polarization THz measurements make possible a specific examination of the reproduction of normal modes with A1 and E irreducible representations, respectively. A simulation with using the R3c space group was performed in the CRYSTAL14 software package by complementing the periodic boundary condition.19, 26 The B3LYP-D* functional27-28 augmented by Grimme’s dispersion force correction29-30 and Gaussian’s 6-311G(d,p) basis set31 were employed (refer to SII for the simulation details). The experimental crystal structure resolved at room temperature was used as the starting point for the geometry optimization.21-23 The simulation predicts three bands in the 5-85 cm-1 frequency region with a significant signal/noise ratio (upper panel of Figure 2c). Two modes, #2 and #9 (middle panel of Figure 2c), bearing the A1 irreducible representation, are assigned to THz bands with polarizations parallel to the chain axes; a pair of degenerate modes, #4 and #5 (bottom panel of Figure 2c), bearing the E


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irreducible representation, are assigned to the THz bands with polarization perpendicular to the chain axes. One may immediately agree that the reproduction of THz bands a and d, with polarizations parallel to the chain axes, is rather satisfactory against both the frequency and intensity criteria, yet the reproduction of THz bands b and c, with polarizations perpendicular to the chain axes, is not satisfactory. Given the reliability of the DFT-D* model applied to normal mode simulations,4-7,

31, 32

this observation indicates that E is not a good irreducible

representation for crystalline scPLA, and the underpinning 31 screw symmetry should not be preserved. If the 31 screw symmetry is removed, the space group would be relegated to the C1 crystallographic point group, which includes the P1 and P-1 two space groups. P-1 corresponds to antiparallel packing of PLLA and PDLA, and the chiral symmetry of the two enantiomers pertains to an inversion center. This possibility, however, has been ruled out via experimentation.21 Consequently, relegating the R3c space group to P1, that is breaking the mirror symmetry between PLLA and PDLA, becomes a unique option to improve the reproduction of THz bands. We thus optimized the R3c-geometry in the P1 space group, i.e., imposing no symmetric restriction on the relaxation of atomic coordinates (refer to SII for simulation details). It is worth noting that the chain axes of PLLA and PDLA, determined by their principal axes with the smallest momenta of 100 translational chain repeating units—“the smallest structural unit of a polymer chain that is repeated by translation in the crystal lattice along the chain axis”9, respectively, persist in a perfect parallel relation in the optimized P1geometry. As shown in the upper panel of Figure 2d, this P1-simulation has qualitatively reproduced all the four of the experimental bands. Compared with the R3c-simulation, the symmetry relegation barely affects the reproduction of normal modes with a polarization parallel


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to the chain axes (middle panel of Figure 2d) but remarkably improves the reproduction of normal modes with a polarization perpendicular to the chain axes (bottom panel of Figure 2d). Having achieved an improvement in the reproduction of THz modes under the P1 space group, we are concerned with a question as to how the R3c geometry changed into the P1 geometry, and especially with that as to what the essential elements are to the improvement. With removing the R3c symmetry, the geometries of PLLA and PDLA would have relaxed in three different ways: external translations along the x-, y- and z-axes, external rotations about the chain axes (i.e., the z direction), and internal displacements. Since the amplitudes are rather small, the internal displacements can be fully characterized by projecting on to a complete set of internal mode coordinates of PLLA and PDLA with the 31 conformations (refer to Appendix in the supporting information). These internal modes are then classified into two groups according to the irreducible representations, E and A. Only by the E-mode displacements can the 31 screw symmetry be broken. Such motions contribute to around 12% of the root-mean-square deviations (RMSDs) for both PLLA and PDLA (Table S5a), and induce a 2.1° average deviation to the PLLA and PDLA backbone conformations in terms of torsion angles (Table S6). Moreover, PLLA and PDLA show nontrivial disparities with respect to some E-mode displacements, especially in the low-frequency end (Table S5b), which causes, in average, a 0.2° disparity in terms of backbone torsion angles (Table S6). Therefore, the E-mode displacement provides the coordinates along which both the 31 screw and mirror symmetry were broken. With respect to the translations, rotations, and internal A-mode displacements, which conserve the 31 screw symmetry, PLLA and PDLA in fact underwent a rather balanced relaxation (Table S5a), implying the conservation of the mirror symmetry; i.e., the three classes of displacements did not contribute to symmetry breaking. These displacements take account of around 84% of the RMSD


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amplitudes for both PLLA and PDLA. Refer to SIII and SIV for details about the above discussion. In order to clarify whether the relatively weak symmetry-breaking element is essential to the improvement in the reproduction of THz modes, we removed its contribution from the P1-geometry, and performed a frequency calculation. Consequently, a negative frequency appears, indicating that the structure has become unstable (Figure S2). Therefore, we conclude that the symmetry breaking plays a crucial role in the determination of the packing conformation for scPLA. We next quantify the symmetry-breaking element without referring to the R3c frame. We first examine how far the 31 screw symmetry is broken. In terms of the torsion angles of the back bone, In the example of PLLA, we fixed the atomic positions of the constitutional repeating unit #4, and evaluated the RMSD of the other two repeating units, #5 and #6, from the artificially created ones with perfect 31 screw symmetry with respect to #4 (Figure 3a, refer to SV for details). PDLA was analyzed in the same way (Figure 3b). We then quantified the structural disparity between PLLA and PDLA at the configurational and conformational levels, respectively. Concerning the configurational disparity, we examined the RMSD of a mirror image of a single constitutional repeating unit, e.g., unit #5, of PLLA from the corresponding unit #1 of PDLA by overlapping them as much as possible (Figure 3c, refer to SVI for details). Similar analyses were performed for the translational chain repeating units (containing three constitutional repeating units) to examine the conformational disparity (Figure 3d). The RMSD evaluations of the 31 screw and mirror symmetry breaking were taken with respect to all of the chemically irreducible atoms comprising the constitutional repeating units.


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Figure 3. Examination of the symmetry breaking extents for PLLA and PDLA simulated with P1 space group. Panels a and b show the RMSDs from the 31 screw symmetry for PLLA and PDLA, respectively. Panels c and d show the RMSDs from the mirror reflection symmetry for one constitutional repeating unit and one translational chain repeating unit, respectively. RMSDs in each panel are examined with respect to all the chemically irreducible atoms.

In inspecting the four panels in Figure 3, one may agree that the hydrogen atoms of the CH3 groups and the oxygen atoms of the C=O groups undergo the strongest deviations in the symmetry breaking process. This result is consistent with the IR experimental results that the interactions between the CH3 and the C=O groups play an important role in the formation of scPLA.24 The relaxation of these functional groups from their symmetric sites restricted by the R3C space group may result in a stronger interaction between PLLA and PDLA and lower the electronic energy by 0.098 kJ/mol. Note that this work adopts Grimme’s empirical approach to take into account the dispersion forces, whose accuracy in terms of a lattice-energy prediction is


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several kJ/mol.33-34 The energy calculation result is therefore sound at a qualitative level. One may also notice that the structural disparity is rather weak if evaluated with respect to single constitutional repeating units and is generally less than 0.003 Å (Figure 3c). However, the structural disparity is almost doubled if evaluated with respect to the translational chain repeating units (Figure 3d), implying that the mirror-symmetry breaking takes place primarily at the conformational level. This is caused by the much stronger, but imbalanced, violations of the 31 screw symmetry in PLLA and PDLA, as shown in Figures 3a and 3b, respectively. If we eliminate the conformational structural disparity by replacing PDLA with a mirror image of PLLA, a negative frequency appears in the normal mode simulation, implying that the system has been moved to a transition state (Figure S7). We therefore conclude that the conformational mirror-symmetry breaking would be an indispensable element of the scPLA samples. We present a discussion of the symmetry breaking from the perspective of the vibrational energies of PLLA and PDLA. If the chiral symmetry is conserved, the potential energy,

Vi = 12 ωi2Qi2 , of a certain normal mode

Qi

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reflection operation; hence PLLA and PDLA should make equivalent contributions to the potential energy (refer to SVII for details). Upon the symmetry breaking, such a balance is certainly not guaranteed. Figure 4a shows the percentage contributions of the five fundamental vibrational components of PLLA, namely three intermolecular translational vibrations along the x-, y- and z-axes, an intermolecular principal libration about the chain axis (i.e., the z direction), and an intramolecular vibration, to the potential energy of every P1-mode. Figure 4b shows the differences of PDLA from PLLA in the above five aspects. PLLA and PDLA have pretty balanced energy contribution in terms of intermolecular translations and libration. By contrast, the symmetry breaking leads to significantly imbalanced distributions of the intramolecular


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vibrational energy in PLLA and PDLA, especially in the high-frequency normal modes where intramolecular vibrations show dominance. 25

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The imbalanced energy contributions of the intramolecular vibrations in PLLA and PDLA represent imbalanced energy distributions of certain internal modes of the two vibrational bodies. Since PLLA and PDLA possess a virtually identical set of internal modes, the imbalance shown in the bottom panel of Figure 4b would be averaged out over all of the optical normal modes in the entire frequency region. However, concerning the vibrational dynamics of matter at ambient


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temperature, only a portion of the low-frequency vibrations are thermally active. The thermal energy at 293 K amounts to 200 cm-1; we thereby have a special interest in examining such an average effect within the optical normal modes below 200 cm-1. By averaging the difference between PDLA and PLLA in terms of the energy contributions of intramolecular vibrations over 23 optical normal modes in the 0-200 cm-1 frequency region (refer to SVIII for complete information), we find PLLA has an advantage of 0.039% over PDLA. In contrast, this average effect is 0.000% and 0.001% for energy contributions of the intermolecular translations and libration, respectively, which should be attributed to the numerical inaccuracy of the simulation and used as the margin of error. In summary, PLLA and PDLA show an energetic disparity with respect to intramolecular vibrations in the low-frequency region. Note that this conclusion is warranted for only the gamma-point phonon modes and is open to verification for other branches of phonon modes. Because the electric force conserves parity, two molecular systems with opposite chirality should have the same energy. We have examined a mirror image structure of the symmetrybroken (PLLA, PDLA) system, thus designated as (PDLA, PLLA)*, where an asterisk indicates a mirror-reflection operation (Figure S10). The difference of electronic energy between the two systems (PLLA, PDLA) and (PDLA, PLLA)* is as marginally small as 1.03×10-4 kJ/mol. Thus the mirror-symmetry breaking structure of scPLA does not violate the basic physical law. Within the theoretical accuracy in this report, the crystal structure with the R3c space group deduced by the electron and X-ray diffraction spectroscopy at room temperature may not be the global minimum of the potential energy surface of scPLA. To be more precise, the experimental R3c-geometry refers to only the backbone conformations of PLLA and PDLA, due to a lack of


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information regarding the hydrogen atoms. Moreover, the accuracy of the backbone atoms was greatly affected by the thermal motions. Refer to SX for a further discussion. The lowtemperature polarization THz spectroscopy indicates a strong possibility that the P1-geometry is a more accurate description of the crystal structure of scPLA. The disparity between PLLA and PDLA thus revealed would have some far-reaching significance. The crystalline polymers in this study undergo spontaneous symmetry breaking toward the (PLLA, PDLA) direction but not the (PDLA, PLLA)* direction. The application of the principle of conservation of chiral symmetry, generally assumed in polymer science, requires extra caution, especially when a large fraction of hydrogen atoms are involved. Future insights into this problem are expected to be obtained through a careful examination of other well-known racemic polymer systems with high crystallinity such as α-isotactic polypropylene and form I of isotactic polybutene.10 ASSOCIATED CONTENT Supporting information Materials and experiments, ab initio solid-state calculations, characterization of the structural change induced by the symmetry relegation from the R3c to P1 space group in terms of external and internal displacements, evaluation of the changes in torsion angles for the P1-geometry with reference to the R3c-geometry, evaluation of the violations of the ideal 31 helical symmetry for PLLA and PDLA, evaluation of the violation of the mirror-reflection symmetry between PLLA and PDLA, characteristics of optical normal modes simulated with using the R3c and P1 space groups in the frequency region below 200 cm-1 are included in this section, a schematic demonstration of the counterpart system (PDLA, PLLA)* of (PLLA, PDLA) with respect to


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mirror-reflection symmetry, and comparison between the experimental XRD pattern and the simulated ones with using the R3c- and P1-geometries. AUTHOR INFORMATION Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work was partially supported by an Industry-Academia Collaborative R&D Program from Japan Science and Technology Agency and Special Coordination Funds for Promoting Science and Technology, Creation of Innovative Centers for Advanced Interdisciplinary Research Areas (Innovative Bioproduction Kobe), MEXT, Japan. MH would like to thank the Ministry of Science and Technology of Taiwan (MOST) (105-2113-M-002-002) for financial support. The theoretical computations were performed using the Research Center for Computational Science, Okazaki, Japan.


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