Experimental Determination of the Geometrical Relation between

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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Experimental Determination of the Geometrical Relation between Monomer and Polymer Species of 2,5-Distyrylpyrazine Single Crystal in the Topotactic Photoinduced Polymerization Reaction Kohji Tashiro,*,† Hiroko Yamamoto,‡ Kunihisa Sugimoto,§ Tomohiko Takahama,† Masaya Tanaka,† and Masaki Hasegawa∥ †

Graduate School of Engineering, Toyota Technological Institute, Tempaku, Nagoya 468-8511, Japan Aichi Synchrot1ron Radiation Center, Aichi Science and Technology Foundation, 250-3 Minamiyamaguchi, Seto 489-0965, Japan § Japan Synchrotron Radiation Research Institute, SPring-8, Kouto 1-1-1, Sayo 679-5198, Japan ∥ Department of Synthetic Chemistry, Faculty of Engineering, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, Japan

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‡

S Supporting Information *

ABSTRACT: The topotactic polymerization reaction is a special case of more general topochemical reactions, and it is defined as the photoinduced solid-state polymerization reaction, in which the space group symmetry is kept unchanged between the initial monomer and the final polymer crystals and the morphology or crystal shape is also mostly unchanged through this solid-state polymerization reaction. The experimental check of the topotactic reaction is made by analyzing the structure relation between the original monomer single crystal and the resultant polymer single crystal. A half century ago, the 2,5-distyrylpyrazine (DSP) monomer single crystal was discovered as the first example of the [2 + 2]-type cycloaddition topotactic polymerization reaction. However, while the crystal structure of DSP monomer single crystal was analyzed, the crystal structure analysis of the corresponding polymer species had been left pending over these several tens of years, although the unit cell parameters and space group were reported in the literature. Because of such a situation, some argument was given to the proposed reaction system. Using synchrotron X-ray diffraction data, we have succeeded to analyze the crystal structure of the DSP polymer single crystal, by which clear and straightforward evidence of the topotactic polymerization reaction was extracted through the geometrical comparison between the monomer and polymer species.

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INTRODUCTION

show the characteristic physical property. In 1930−1950, diacetylene monomer compounds were found to polymerize by the irradiation of γ-rays.19−22 Through the X-ray structure analysis of the monomer and polymer crystals, Wegner et al. showed this reaction occurs in the topotactic reaction mode as shown in Table 1b: the neighboring diacetylene monomers are linked by the covalent bonds to form the long and welldeveloped polymer chains in the large crystal.23−28 Since then, many types of polydiacetylene derivatives have been synthesized.29 As detected by the Raman and IR spectroscopic measurement,28 the polymer species created in the early stage of the reaction is deformed slightly by the surrounding monomer molecules. The atomic displacements in the polydiacetylene single crystal subjected to an external tensile force were also traced in detail by the vibrational spectral measurement30 and the X-ray structure analysis.31 Another important type of topotactic polymerization reaction is seen for 2,5-distyrylpyrazine (DSP) and its

Topotactic Polymerization Reaction. Various examples are known about the monomer crystals which transform to the polymer crystals under the irradiation of light. The reaction is generally called the photoinduced solid-state polymerization reaction, one of the topochemical reactions.1−14 As shown in Table 1a, the γ-ray-induced solid-state polymerization reaction of trioxane (or tetraoxane) single crystal into polyoxymethylene (POM) is a well-known example of the topochemical polymerization reaction, in which a single crystal of trioxane transforms to the POM crystal, but the resultant polymer product is not a single crystal but it is a multicrystal.15−18 Among many solid-state topochemical polymerization reactions, the topotactic reaction is quite limited, which is a special case of the topochemical reactions, and the space group symmetry is kept unchanged during the reaction. The structural change from a monomer crystal to the corresponding polymer crystal is not very enormous, and the cooperative atomic displacements lead to the reservation of the morphology or crystal shape. As a result, a giant single crystal of polymer is obtained in a size of millimeters to centimeters! Such a polymer single crystal can be assumed as the most ideal state of the partially crystalline polymers and is expected to © XXXX American Chemical Society

Received: January 7, 2019 Revised: February 14, 2019

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DOI: 10.1021/acs.macromol.9b00031 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules Table 1. Solid-State Photoinduced Polymerization Reactions

relatives.32−44 As seen in Table 1c, this reaction was the first example of [2 + 2]-type cycloaddition topotactic polymerization reaction with the formation of cyclobutane rings. The more details will be explained in a later section of the present paper. The third example of the topotactic polymerization reaction system is 1,4-Z,Z-diethyl muconate (EMU) and its relatives, as shown in Table 1d. The irradiation of X-ray beam causes the rapid reaction in a time scale of minute order. The X-ray diffraction data had to be collected in a short time interval to clarify the packing structure of the initial monomer species.45−60 The crystal structure change was also traced as a function of X-ray irradiation time through the time-resolved simultaneous measurement of the wide-angle X-ray diffraction and Raman spectra.49,55,58−60 Topotacticity of DSP. In this way, the topotactic solidstate polymerization reactions were reported for the quite limited monomer species. The concept of the topotacticity must be confirmed on the basis of accurate X-ray crystal structure analysis for both the initial monomer single crystal and the finally obtained polymer single crystal. In the present paper, we will treat the DSP case. The crystal structure analysis was reported for the initial monomer single crystal39−41 and also for the oligomer crystal.61−63 The latter showed the formation of a square cyclobutane ring by the covalent linkage of the ethylene groups between the adjacent two monomers. A similar reaction scheme was speculated for the polymerization reaction of DSP (see Scheme 1).32−44,61 However, it is surprising to notice that the quantitative crystal structure

Scheme 1. Predicted Polymerization Reaction of DSP Monomer

analysis of the final polymer product has not yet been completed up to now. The information about the concrete atomic coordinates in the crystal lattice is not given in the literature. On the basis of the X-ray diffraction data, Nakanishi et al. reported the unit cell parameters and the space group symmetry of DSP polymer crystal lattice.41 The space group is just the same as that of the monomer single crystal, Pbca. Their experimental result may support the topotactic reactivity of the B


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Figure 1. 2D X-ray diffraction patterns measured for (a) DSP single crystal and (b) PDSP single crystal. In (a), the X-ray wavelength was 0.711 Å (Mo Kα) and the detector was a 2D imaging plate. In (b), they were 0.355 Å and a 2D CCD camera, respectively.

In the present paper we will report the results of the X-ray crystal structure analysis of both the DSP and polymerized DSP (which is now called PDSP) and will discuss the structural relation of these two species. A comparison of the characteristic features of the solid-state topotactic polymerization reaction is made among the above-mentioned three cases (PDCHD, PEMU, and PDSP). The thus-established topotactic polymerization concept of DSP encourages us also to investigate the [2 × 2]-type cylcoaddition reaction mechanism in the polymerization process, which will be discussed on the basis of the density functional theory (DFT) in a later part of the present report.

DSP single crystal. However, they could not clarify the spatial relation between monomer and polymer molecules in the crystal lattice by determining the atomic coordinates in the crystal lattice. This situation caused the controversy about the solid-state polymerization reaction mechanism of DSP without a final solution. For example, Wegner et al. pointed out that the space group of the DSP polymer is P21ca,61 which is different from the space group Pbca revealed for the monomer species, and that the [2 + 2]-type cycloaddition polymerization reaction occurs heterogeneously or without keeping the single crystal feature.61−63 To discuss the details of the polymerization reaction mechanism including the cyclobutane ring formation process, we need to solve the pending problem about the crystal structure of DSP polymer species above all. The most ideal topotactic reaction should occur by keeping (i) the single crystal morphology and (ii) the space group symmetry before and after the polymerization reaction. Compared with the cases of polydiacetylene (PDCHD) and poly(diethyl muconate) (PEMU), the DSP single crystal is relatively easily strained during the polymerization reaction under the irradiation of light, and the fragmentation of a large single crystal plate occurs. However, this observation does not necessarily mean that the DSP monomer crystal does not follow the topotactic reaction scheme. As will be shown below, the nonhomogeneous irradiation of a light and/or the thick sample causes the heterogeneous reaction in a bulk scale, resulting in such a fragmentation of the crystal. A small and/or thin single crystal gives the homogeneous polymerization reaction, resulting in the successful collection of the clear X-ray diffraction pattern, and the accurate crystal structure of polymer is obtained successfully. The present structure analysis has given the space group Pbca, which is the same as that proposed by Nakanishi et al.,41 leading to such a conclusion that both the monomer and polymer species possess the common space group symmetry. A more important harvest in this study is the clarification of the geometrical relation between these two species in a concrete manner. In this way, the success of the accurate structure analysis of the DSP polymer single crystal has led us to the establishment that the topotactic reaction occurs in the DPS crystal. We have needed a half century to reach the real goal although many textbooks had quoted the DSP solid-state reaction as the first and typical example of the [2 + 2] cycloaddition polymerization reactions without any doubt.

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EXPERIMENTAL SECTION

Samples. Pale yellow single crystals of the DSP monomer with flat lozenge shape were prepared from the petroleum ether solution at room temperature. The PDSP crystals were obtained by irradiating ultraviolet light of wavelength 365 nm on the monomer single crystals for 10 h at room temperature. This wavelength was chosen because it caused the most effective polymerization reaction.43,44 The yellow color of the sample disappeared after the polymerization reaction. X-ray Diffraction Measurements. The 2-dimensional X-ray diffraction patterns were measured at room temperature for the DSP monomer single crystal of ca. 0.2 × 0.2 × 0.05 mm3 size using a Rigaku Varimax X-ray diffractometer equipped with the cylindrical imaging plate detector of 127.4 mm radius. The pixel size of the imaging plate was 100 μm × 100 μm. The incident X-ray beam was Mo Kα with the wavelength 0.711 Å. The crystal was set on a goniometer head. The 2-dimensional X-ray diffraction patterns were collected with the oscillation angle Δω 5° in the range of ω = 0− 180°. The X-ray exposure time was 180 s for one diffraction pattern. The X-ray diffraction measurement of PDSP single crystal was performed at the beamline 02B1 of SPring-8, Hyogo, Japan. A tiny PDSP single crystal (ca. 0.03 × 0.03 × 0.01 mm3 size) with no visible trace of crack was chosen for the sample. The wavelength of an incident X-ray beam was 0.355 Å. The detector was a 2D CCD camera (Rigaku, Mercury 2), which was placed at 59.9 mm from the sample center. The detector has a sensitive area of 70 mm × 70 mm. Each pixel has a size of 68 μm × 68 μm. The sample was set on a goniometer head and oscillated with Δω = 5° in the ω range of 0− 180°. The measurement was made at room temperature. The exposure time of X-ray beam was 720 s for one shot. The X-ray diffraction patterns measured for DSP monomer and PDSP crystals are shown in Figures 1a and 1b, respectively. X-ray Structure Analysis. The thus-collected diffraction data were analyzed using a software Auto Run (Rigaku, Japan). At first, the positions of the observed diffraction spots were searched to estimate the unit cell parameters. The integrated intensity I(hkl) of the observed hkl reflections was transformed to the structure factor |F(hkl)| = [I(hkl)/(KALpm)]1/2 by correcting the Lorentz (L) factor, C


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Figure 2. Crystal structure of DSP monomer.

Table 2. Atomic Fractional Coordinates of DSP Crystala

the polarization (p) factor, and the multiplicity (m) and by adjusting the scale factor K. The absorption effect (A) was ignored. The Rmerge (a measure of the accurate collection of the diffraction spots with the equivalent indices) was 6.7% for the DSP monomer and 18.5% for the PDSP. The software Crystal Structure (Rigaku) was used for the structure analysis. The direct method (SIR)64 was applied for the extraction of the initial structure models. The structure refinement was performed with a full-matrix least-squares method. The R factor for the DSP monomer was 5.4% for the 1732 unique reflections (|F|2 > 2σ(|F|2) and 14.2% for PDSP (the 1639 unique reflections, |F|2 > 2σ(|F|2)), where the R factor was defined as R = ∑||Fo|2 − |Fc|2|/ ∑|Fo|2 (|Fo| and |Fc| are the observed and calculated structure factors, respectively). The relatively large R factor for the polymer crystal may come from the strain in the single crystal or from the relatively small X-ray coherent mosaics in the single crystal. Density Functional Theory Calculation. The molecular orbitals and the corresponding energies were calculated for DSP and PSDP crystals with the DFT calculation method. The cyclization reaction of two ethylene molecules was also calculated for the interpretation of the [2 + 2]-type cycloaddition reaction in the DSP monomer crystal lattice. The program used was DMol3 (Materials Studio 2017 version, BIOVIA). The initial structure models of DSP and PDSP crystals were transferred from the X-ray analyzed structures. The functional was the PBE of the GGA (general gradient approximation) category.65 The DFT-dispersion correction was made with the TS method.66 All electrons were included in the calculation. The basis set chosen was DNP (double numerical polarization) functions (version 4.4).

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RESULTS AND DISCUSSION Crystal Structures of DSP and PDSP. DSP Monomer Crystal. The crystal structure of DSP monomer, which was analyzed by following the above-mentioned procedure, is shown in Figure 2. The structure is essentially the same as that reported by Nakanishi et al.39−41 The almost fully extended rodlike molecules are packed in the orthorhombic unit cell with the space group Pbca. The unit cell parameters at room temperature are a = 9.6111 ± 0.0007 Å, b = 7.6534 ± 0.0006 Å, and c = 20.6232 ± 0.0017 Å. The details of the structure analysis information are shown in the Supporting Information. The atomic coordinates are listed in Table 2.

no.

element

x

y

z

1 2 3 4 5 6 7 8 9 10 11 3-H 4-H 5-H 7-H 8-H 9-H 10-H 11-H

N C C C C C C C C C C H H H H H H H H

0.1068 −0.0216 −0.1248 −0.0510 0.0330 0.0077 0.1043 0.0831 −0.0334 −0.1311 −0.1107 −0.2114 −0.1400 0.1170 0.1834 0.1496 −0.0481 −0.2101 −0.1761

0.1233 0.1441 0.0198 0.2964 0.4322 0.5867 0.7225 0.8694 0.8829 0.7503 0.6044 0.0382 0.2910 0.4290 0.7131 0.9577 0.9827 0.7594 0.5148

−0.0110 −0.0365 −0.0249 −0.0768 −0.0850 −0.1253 −0.1262 −0.1639 −0.2012 −0.2019 −0.1635 −0.0437 −0.0980 −0.0621 −0.1004 −0.1646 −0.2269 −0.2277 −0.1634

a The unit cell parameters are a = 9.6111 ± 0.0007 Å, b = 7.6534 ± 0.0006 Å, and c = 20.6232 ± 0.0017 Å. The fractional coordinates of one crystallographically asymmetric unit are given here. The fractional coordinates of the other units in the unit cell are generated using the symmetry operations of the space group Pbca.

When the crystal structure is viewed along the a-axis direction, the rodlike molecules form a layer parallel to the abplane, and these layers are stacked along the c-axis direction in the herringbone-type mode. The C···C distance of the CC units between the adjacent molecules arrayed along the b-axis D


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Figure 3. Crystal structure of PDSP.

Table 3. Atomic Fractional Coordinates of PDSP Crystala

no.

element

x

y

z

1 2 3 4 5 6 7 8 9 10 11 3-H 4-H 5-H 7-H 8-H 9-H 10-H 11-H

N C C C C C C C C C C H H H H H H H H

−0.0974 −0.0196 0.0726 −0.0559 0.0164 −0.0508 −0.0067 −0.0720 −0.1860 −0.2339 −0.1645 0.1201 −0.1444 0.0873 0.0723 −0.0385 −0.2314 −0.3137 −0.1936

0.0639 0.1764 0.1138 0.3764 0.4987 0.5686 0.5489 0.6000 0.6770 0.7001 0.6495 0.1919 0.3875 0.4287 0.5009 0.5833 0.7114 0.7448 0.6760

−0.0402 0.0051 0.0405 0.0063 0.0607 0.1267 0.1963 0.2571 0.2508 0.1813 0.1187 0.0690 0.0162 0.0783 0.1996 0.3037 0.2922 0.1765 0.0717

is 3.93 Å. The CC double bonds and the pyrazine and phenyl rings are as a whole on the common plane of a molecule to give the electronically conjugate system with pale yellow color. The aromatic rings are oriented also in the herringbone mode along the a-axis. PDSP Crystal. Figure 3 shows the crystal structure of DSP polymer (PDSP). The unit cell is of the orthorhombic type with the parameters a = 10.842 ± 0.018 Å, b (chain axis) = 7.411 ± 0.012 Å, and c = 18.12 ± 0.03 Å. The space group is Pbca, the same as that of the DSP monomer crystal. The atomic fractional coordinates are given in Table 3. The details of the structure information are shown in the Supporting Information. The square cyclobutane rings are formed by covalent bonding of the CC units between the neighboring monomers to give the polymer chains along the b-axis. The polymer chains form the layer structure in the ab-plane, and these layers are packed along the c-axis. As seen clearly in Figure 4, the phenyl rings of the monomer species are originally tilted in the bc-plane by about 30° from the b-axis. After the polymerization reaction occurs, these phenyl rings change the orientation and direct almost into the c-axis direction or perpendicularly to the chain axis (the b-axis). Comparison of Geometry between Monomer and Polymer. The local geometries of the DSP monomer and polymer are compared in Figure 5. The cyclobutane ring is not planar but takes a deformed square shape with the C−C bond lengths 1.6 Å. The CCC bond angle of the cyclobutene is almost 90°. It is surprising to note that the formation of such a cyclobutane ring is made by a remarkable contraction of the intermolecular ethylene C···C distance 3.9 Å to the C−C single bonds of 1.6 Å and at the same time by an extension of CC bond length 1.3 Å to C−C bond 1.6 Å. Originally, the ethylene unit, pyrazyl ring, and phenyl ring are electronically conjugated in the DSP monomer molecule. As a result, the ethylene CC bond order decreases to 1.5 from the pure C C bond (bond order 2). After the cyclobutane ring formation, the C−C distances increase due to the disappearance of such

The unit cell parameters are a = 10.842 ± 0.018 Å, b (chain axis) = 7.411 ± 0.012 Å, and c = 18.12 ± 0.03 Å. The fractional coordinates of one crystallographically asymmetric unit are given here. The fractional coordinates of the other units in the unit cell are generated using the symmetry operations of the space group Pbca.

a

E


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Figure 4. Geometrical relation of the crystal structure between DSP (balls and sticks) and PDSP (solid lines).

Figure 5. Structural parameters of DSP and PDSP.

electronic conjugation although the C−C bond length 1.6 Å is longer than the normal value (1.54 Å) because of the strained cyclobutane ring character. The torsional angles are also changed. The torsional angles around the benzene−ethylene and pyrazine−ethylene bonds are 3° and 9°, respectively, in the mostly coplanar DSP molecule, while they change to 80° and 60°, respectively, in the PDSP structure. In this way, the totally electronically conjugated structure of DSP monomer changes to the nonconjugated polymer chain consisting of an alternate array of pyrazine ring and cyclobutane ring with the phenyl rings as the side branches. The conjugation between ethylene unit and phenyl ring disappears. As a result, the pale yellow color of DSP monomer changes to the noncolor of PDSP. The CCC bond angle between benzene ring and

Table 4. Change of the Unit Cell Size in the Topotactic Polymerization Reaction of EMU, DCHD, and DSP Crystals b (chain axis) a c β crosssectional area

EMU

DCHD

DSP

4.931 Å → 4.839 Å (−1.87%) 10.232 Å → 10.403 Å (1.7%) 11.497 Å → 10.992 Å (−4.4%) 107.146° → 107.627° (0.4%) 112.41 Å2 → 108.98 Å2 (−3.1%)

4.550 Å → 4.887 Å (+7.41%) 13.60 Å → 12.82 Å (−5.7%) 17.60 Å → 17.33 Å (−1.5%) 94.0° → 108.32° (15.2%) 238.78 Å2 → 210.91 Å2 (−11.7%)

7.65 Å → 7.41 Å (−3.14%) 9.61 Å → 10.84 Å (12.8%) 20.62 Å → 18.12 Å (−12.1%) 90° → 90° (0%) 198.18 Å2 → 196.42 Å2 (−0.89%)

F


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Figure 6. Optical microscopic images of DSP single crystals observed under the irradiation of UV light. The relatively large crystals were easily cracked along the b-axis. The fragments jumped outside the microscope image zone. The small (and/or) thin single crystals did not break even after the UV irradiation (red arrow), which were used in the X-ray diffraction measurement.

Figure 7. Structural changes from monomer to polymer species under the irradiation of light: (a) PDSP, (b) PDCHD, and (c) PEMU.

Figure 9. Molecular orbitals and symmetry species of the twoethylene molecular system and cyclobutane molecule. Figure 8. Structural change of the two-ethylene system in the photoinduced cycloaddition reaction. The point groups are shown also.

In the case of EMU crystal, the b-axial length along the chain axis changes from 4.93 to 4.84 Å, which corresponds to the 1.87% contraction.49 For diacetylene with carbazolyl side groups (DCHD), the repeating period changes from 4.55 to 4.88 Å, about 7.4% extension.28 Comparing with these changes, the 3.2% contraction of the b-axis in the polymerization of DSP crystal does not seem curious. The crosssectional area in the ac-plane does not change very much in the former two cases, as seen in Table 4. In the case of DSP, the aaxial length increases and the c-axial length decreases after the

ethylene unit is 123°, which is kept unchanged in the reaction. The remarkable orientation change of the phenyl rings toward the c-axis direction is induced by the change of the hybrid orbitals of C atoms in the ethylene parts from sp2 to sp3. Geometrical Comparison among Three Polymer Species. The repeating period along the b-axis or the chain axis changes from 7.65 Å (DPS) to 7.41 Å (PDSP), about 3.1% contraction. G


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Figure 10. (a) Total energy change of the two-ethylene molecular system in the reaction process, where the inter C···C distance was changed stepwise and the optimization was performed at each fixed distance. (b) The corresponding change of LUMO and HOMO energies.

of large size is easily bent and breaks during an irradiation of light as seen in the optical microscopic image (Figure 6). This phenomenon was observed for the large and/or thick (several tens of micrometers) crystal. The smaller and/or thinner (ca. 10 μm) crystals did not break so easily, which were used in the X-ray diffraction measurements. The UV light irradiated on a thick sample may cause the heterogeneous structural change between the front surface and the inner part of the crystal. Such non-negligible change of the a- and c-axial lengths may come from the orientational change of the phenyl side groups. As illustrated in Figure 7, in the PDCHD case, the linear diacetylene rods rotate and bend under the irradiation of light, and they are linked covalently to the neighboring diacetylene units. The side groups stay at almost the same orientation, attended with a small positional shift. The flexible CH2 units separate the rigid diacetylene rods and the hard carbazole rings. In the case of PEMU, the original CC bonds are combined together to form the C−CC−C skeletal bonds. The ester group positions do not change very much. The flexible ethyl end groups stand up vertically along the chain axis. In these two cases of PDCHD and PEMU, the side groups are comparatively flexible, and the hard skeletal parts are easily rotated and shifted without seriously strong constraint from the side groups. In the case of DSP, the cyclobutane rings are formed between the monomers, and the phenyl rings change their positions with a large shift along the chain axis. This large change of the ring orientation must occur necessarily through the change in the atomic orbitals of the ethylene C atoms from sp2 to sp3, in which the CCC bond angle changes from 120° to 109.5°. Four-Center Cycloaddition Reaction and Polymerization. A key part of the photoinduced [2 + 2]-type cycloaddition reaction observed for PDSP is essentially the same as the well-known photoinduced reaction of the two ethylene molecules into a cyclobutane molecule. However, the situation is different between these two cases: the ethylene groups are free in the latter case, while in the present DSP case, the ethylene units are constrained by the benzene and pyrazine rings and also they are surrounded by the neighboring monomer molecules in the crystal lattice. The adjacent ethylene groups are separated at such a long distance as 3.9

Figure 11. (a) DFT simulation of the polymerization reaction of DSP monomer crystal. The C···C distance was changed stepwise, and the energy optimization was performed. At around the distance 2.7 Å, the molecules start to change their shape to the S-character and form the cyclobutane ring at about 1.6 Å. (b) The zooming up of the local parts.

polymerization reaction. These changes are not very small, but the cross-sectional area a × c does not change very much, or the change of the cross-sectional area is rather smaller than those of PEMU and PDHCD. The relatively large change of the a/c ratio may cause a large anisotropic strain in the unit cell of DSP. In fact, a single crystal H


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Figure 12. (a) Relative total energy change in the polymerization reaction of DSP monomer crystal and (b) the geometrical change of the ethylene unit part plotted against the C···C distance.

ethylene molecular system and the DSP system, we performed the density functional theory (DFT) calculation for these two systems using the same parameters. The calculation was made in the following way: (i) two ethylene molecules were separated at a far distance, and the energy optimization was made. The result should correspond to the perfectly isolated molecular state. (ii) As illustrated in Figure 8, the C···C distances (d) between these two ethylene molecules were manually shortened, and the energy of the whole system was calculated under the constraining condition of the fixed distances, where the molecular planes were set parallel to each other. The total energy, the energies of HOMO (highestoccupied molecular orbital) and LUMO (lowest-unoccupied molecular orbital) levels, and the related MOs were calculated at each distance. From the viewpoint of group theory, it must be noted that a pair of ethylene molecules arranged face to face possesses the point group symmetry D2h, while the reaction product or cyclobutane molecule is not a planar ring but it is deformed, and so the point group is C2v. Therefore, the discussion is made using the common point group symmetry C2v or a subgroup of D2h. As illustrated in Figure 9, the π-electrons of the initial ethylene pair are stored on the orbitals of the symmetry species a1 and b2. This situation is expressed as a12b22, which is equivalent to the A1 symmetry species. By irradiation of light, one electron of the b2 orbital is excited and transits to the higher energy orbital b1. The electron configuration is expressed as a12b21b11, which corresponds to the A2 symmetry species. As for the cyclobutane, on the other hand, the electron configuration of

Figure 13. Comparison of DSP polymer chain conformation between the X-ray analyzed structure and the DSP prediction.

Å, but they can be covalently linked together under the irradiation of a light. Cyclization Reaction of Two Ethylene Molecules. Before the detailed quantum chemical discussion about the reaction feature of DSP, it may be useful to remind the [2 + 2]-type cycloaddition reaction of the two ethylene molecules concretely. As seen in the literature and the organic chemistry textbooks,67−69 the discussion is made on the basis of the point group theory and the quantum chemical energy calculation. To compare the molecular orbital information between the two I


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Figure 14. MO change in the polymerization reaction of DSP monomer crystal.

Figure 15. (a) UV exposure time dependence of the FTIR spectrum measured for DSP powder sample (365 nm UV). (b) Irradiation time dependence of the molar ratio of DSP monomer species estimated from the IR spectra.

Figure 16. (a) UV exposure time dependence of the X-ray diffraction profile measured for DSP powder sample (365 nm UV). (b) Irradiation time dependence of the molar ratio of DSP monomer species estimated from the X-ray data. It must be noted that the X-ray beam itself did not cause the reaction from DSP to PDSP (refer to the text).

the ground state is a12b22 or the A1 species. The configuration of the one-electron-excited state of cyclobutane is expressed as a12b21b11 or the A2 species. The photoinduced transition route is as follows: A1 (ground state of ethylene pair) → A2 (excited state of ethylene pair) → A2 (excited state of cyclobutane) → A1 (ground state of cyclobutane). Figure 10a shows the total energy change calculated for the ground state and oneelectron-excited state by changing the C···C distance. In these calculations, the total energy of the ground state was evaluated as 2∑Ni=1EMO i , and that of the one-electron-excited state was MO + EHOMO + ELUMO under the approximated as 2∑N−1 i=1 Ei Hückel approximation, where EiMO is the energy of the ith orbital and the total number of electrons is 2N (N = 16 for one ethylene molecule). [Strictly speaking, the energy of the excited state was calculated without any electronic configuration interactions (CI) taken into account. The more

detailed calculation including the CI is beyond the scope of this study.] In the case of thermal excitation, the route is traced from the initial ground state of ethylene pair to the final ground state of cyclobutane (1 → 2′ → 3 → 4 in Figure 10a). The energy increased gradually with a shortening of the C···C distance and crossed the barrier and then steeply decreased to the ground state level of the cyclobutane molecule. The calculated energy barrier was about 60 kcal/mol, which is too high to be excited by the thermal energy at room temperature (kT ∼ 0.6 kcal/mol). On the other hand, in the photoexcited transition, the reaction route is 1 → 2 → 3→ 4, as mentioned above. The energy of the one-electron-excited state (#2) of the ethylene pair decreased gradually and reached the minimal position (#3). Then the route changed to the excited cyclobutane and steeply stabilized to the ground state (#4). The short CC double bond of ethylene changes to the J


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the same as those observed in the [2 + 2] cycloaddition reaction of the two ethylene molecules (Figure 10). The energy gap estimated from Figure 12a is ∼40 kcal/mol (for two sets of two ethylene pairs), which corresponds to the UV wavelength of 358 nm. If this energy gap is assumed to correspond to the photon energy needed for the ethylene cycloaddition reaction, the estimated wavelength is in good agreement with the observed maximal position of the UV spectrum of DSP monomer (∼365 nm).43,44 The comparison of the final PDSP chain conformation is made between the observed and calculated ones, as shown in Figure 13. In the calculation, the benzene rings changed their orientation dramatically, the driving force of which comes from the change of hybridization of the ethylene carbon orbital from sp2 to sp3. The thus-calculated orientation change of benzene ring is a little smaller compared with that detected in the X-rayanalyzed structure. One reason might be a usage of the simplified structure in the DFT calculation. Some of the molecular orbitals (MO) derived at the various reaction stages are extracted in Figure 14. In the ethylene parts of the HOMO state at the initial stage, the lobes of the opposite MO phases were faced to each other between the neighboring units. As the C···C distance became shorter, the contribution of the LUMO became more important, in which the MO lobes of the same phase overlapped together, suggesting the formation of C−C bonding between the neighboring ethylene units. An example of the distance 2.70 Å is clear. At the distance 1.8−1.5 Å, the molecular orbitals characteristic of the cyclobutane ring were created. In this way, according to the DFT calculation, the intermediate state of DSP molecules in the photoinduced reaction is predicted to take the S-shaped conformation (see Figure 11), which could be captured experimentally by the Xray diffraction measurement. Unfortunately, at present, it is actually impossible to do so, since the reaction process might occur in a short time of picoseconds to nanoseconds order. The X-ray diffraction data collected in the long exposure time of seconds to minutes give only a mixture of the original DSP monomer molecules and the produced and stabilized PDSP chain segments. In fact, the IR spectra, which were measured stepwise for the sample exposed to a UV light at a constant time interval, revealed that the IR bands intrinsic to the monomer and polymer species were detected, but their band positions did not change in the reaction process and only the intensity exchange occurred between them (see the Appendix). The IR spectra detected only the molecules relaxed from the excited state to the ground state. The molar fraction of DSP monomer species decreased exponentially with the exposure time, representing the time dependence of the DSP monomer population stabilized to the ground state. The detection of the intermediate state (or the transition state) must be made on a picosecond time scale. The recent development of the synchrotron X-ray diffraction measurement may allow us to trace the transient structural change predicted by the DFT calculation (Figure 11), which should be challenged in future.

longer C−C single bond at the timing of passing through the transient state of the energy maximum (#3). The calculated energy difference between the ground state (#1) and the excited state (#2) of the initial ethylene pair is about 126 kcal/ mol, which corresponds to the wavelength of a light, ca. 230 nm. This is relatively close to the wavelength range of the UV absorption maximum 200−400 nm.67−69 An additional point to be noticed is the similarity between Figure 10a and 10b: the energy change curves calculated for the HOMO and LUMO levels are similar to the changes of the total energy calculated for the ground and excited states. The [2 + 2]-type cyclization reaction is strongly related to the change of π-orbitals of the ethylene units, and so the discussion of the [2 + 2] π-orbital reaction can be made by focusing only on the energy change of the HOMO and LUMO levels. This is the reason why many textbooks describe the transition process using only HOMO and LUMO states.67−69 Cyclization Reaction of Two Ethylene Units in the DSP Crystal. A similar cyclization process might occur also in the DSP system. Because the DSP molecules are packed together closely in the crystal lattice, the reaction may occur cooperatively with the smallest change of the molecular configuration. The DFT calculation was performed for the DSP crystal lattice in the following way under the periodical boundary condition. Because the 4 DSP molecules or 142 atoms are included in the unit cell, the DFT calculation was too heavy using a personal computer. The crystal structure of DSP monomer molecules may be assumed to consist of the repetition of the two layers (bc-plane) along the a-axis. Then, as an approximation, only one bc-plane layer was extracted and packed in the small cell with a half length of the original a-axis (a = a0/2 = 4.8056 Å, b = b0 = 7.6534 Å, c = c0 = 20.6232 Å, and β = 90°). To keep the original symmetry relation between the two molecules at the center and corner positions in the bcplane, the space group symmetry P21/c was employed instead of the original space group P21/b21/c21/a (abbreviated symbol Pbca). The distance between the carbon atoms of the neighboring ethylene units along the b-axis is 3.93 Å. The packing energy optimization was performed by fixing the distance at each step. The thus-minimized structure at a constant C···C distance was used as the initial structure of the next stage, and the C···C distance between the ethylene units was changed by rotating the molecules around the axis perpendicular to the bc-plane at the position of the pyrazine ring center or at a point of symmetry. The total energy of the ground state, the length and order of the ethylene CC bond, and so forth were calculated to monitor the reaction process. Unfortunately, the energy component localized only to the ethylene parts was hard to estimate since the electronic conjugation between the ethylene unit and the phenyl and pyrazine rings made it difficult to extract the local energy value of the ethylene part, though the total energy itself was changed with the reaction. Figures 11−14 show the calculated results. As seen in Figure 11a,b, as the C···C distance between the ethylene units along the b-axis became shorter, the fully extended DSP monomer molecules started to deform into the S-character shape. At around the C···C distance 1.6 Å, the C−C single bonds were created between the neighboring ethylene units to form the cyclobutane ring. Correspondingly, as shown in Figure 12b, the bond order of ethylene unit changed from 1.6 to 1.0. In this reaction process, the total energy became maximal once and decreased steeply (Figure 12a). These behaviors are essentially

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CONCLUSIONS In the present paper the details of the crystal structure of PDSP have been revealed experimentally on the basis of the X-ray diffraction data analysis. The long-year ambiguity about the topotacticity of the photoinduced polymerization reaction of DSP crystal was erased at last, allowing us to discuss the reaction process from the quantum chemical point of view K


Article

Macromolecules

1, we have the relation of Im = −(εm/εp)Ip + εm. The plot of Im versus Ip should form a linear straight line. The coefficient ratio (εm/εp) was estimated from the slope of the plot, and then the content ci was evaluated. The result is shown in Figures 15b and 16b, respectively. The logarithm of the monomer content cm decreases almost linearly with the irradiation time for both the IR and X-ray diffraction data: log(cm) = −kt, which apparently corresponds to the behavior characteristic of the first-order chemical reaction: −dcm/dt = kcm. The reaction rate is higher for the irradiation of 365 nm UV light than 254 nm light. The observation of the maximal reaction rate at around the 365 nm wavelength is consistent with the UV spectral data showing the absorption maximum at this wavelength.43,44 An apparently first-order chemical reaction was observed also for DCHD and EMU cases.48 However, the reaction mechanism viewed from the molecular level cannot be deduced from such a macroscopic and stationary state observation. The experimental trace of the transient state is needed.

using the DFT calculation. The structural change in the photoinduced reaction was compared between PDSP, PDCHD, and PEMU, from which the role of the side branches in the structural change from monomer to polymer was estimated. The flexible side groups do not affect the drastic structural change in the skeletal chain segments as seen for PDCHD and PEMU. In the case of PDSP, the orientation of the phenyl rings changes toward the horizontal direction through the change of the hybrid orbitals of the C atoms from sp2 to sp3. At the same time, the ethylene units change the bond order from 1.6 to 1.0 in the structural change to the cyclobutane ring. According to the DFT calculations performed for the two ethylene molecules and the DSP crystal system, the transition of the ethylene unit from the ground state to the one-electron-excited state is one of the important stages to cause the photoinduced cyclization reaction. The energy gap of this excitation is found to correspond to the UV light region. The hard and straight DSP molecules composed of the totally conjugated elements of pyrazine, benzene, and ethylene units change their shape drastically but in the organized manner under the irradiation of light. It is surprising to realize that the C atoms separated about 3.9 Å distance approach together under the irradiation of light and induce the chemical reaction attended by a large structural change. Such a remarkable change is induced neither by an addition of thermal energy nor by the irradiation of X-ray beam of a higher energy. According to the quantum mechanical theory, the transition condition is hν = ΔE, where ΔE is an energy gap between the ground state and the excited state. The too small thermal energy cannot give enough large energy for this transition. The high-energy X-ray beam also cannot satisfy this condition because the X-ray photon energy hν is too large compared with the energy gap ΔE. The application of an external perturbation with a proper energy (UV light) is needed for this reaction. In fact, the transition scheme derived by the DFT calculation indicates that the energy gap between the ground state and the one-electron excited state corresponds well to the UV abruption maximum.

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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.macromol.9b00031. Crystal structure of 2,5-distyrylpyrazine (PDF) Crystal Structure of poly(2,5-distyrylpyrazine) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (K.T.). ORCID

Kohji Tashiro: 0000-0002-7543-2778 Kunihisa Sugimoto: 0000-0002-0103-8153 Present Address

M.H.: Department of Materials Science and Technology, Faculty of Engineering, Toin University of Yokohama, Aoba,Yokohama 225-8503, Japan. Notes

APPENDIX

The authors declare no competing financial interest.

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IR and X-ray Diffraction Measurements of the Stepwise UV-Irradiated DSP Monomer Crystal

ACKNOWLEDGMENTS This study was supported financially by MEXT “Strategic Project to Support the Formation of Research Bases at Private Universities (2010−2014 and 2015−2019)”. The synchrotron X-ray experiment was performed at SPring-8 beamline 02B1 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal Nos. 2017B1215 and 2018A1410).

The IR spectra and X-ray diffraction profiles were measured stepwise for the DSP powder sample subjected to a UV light irradiation (254 and 365 nm wavelengths) at a constant irradiation time interval. Figure 15 shows the irradiation time dependence of the IR spectra in the frequency region of 780− 710 cm−1. The monomer bands decreased the intensity, and the polymer bands increased instead. Figure 16 is the change of X-ray diffraction profile measured for the UV-irradiated sample. The diffraction peaks characteristic of the monomer and polymer crystal lattices were detected clearly. They changed the relative peak height with an increase of UV irradiation time. The relative molar contents of the monomer and polymer species were evaluated quantitatively by analyzing these data. The integrated intensity of the i component was assumed to be linearly proportional to the molar content ci [Ii = εici, i = m (monomer) or p (polymer species)]. The crystalline regions of the DSP and PDSP species are assumed to coexist in the reaction system. Because Im = εmcm and Ip = εpcp and cp + cm =

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REFERENCES

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Experimental Determination of the Geometrical Relation between

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