Reinvestigation of Crystal Structure and Intermolecular Interactions of

Article pubs.acs.org/Macromolecules

Reinvestigation of Crystal Structure and Intermolecular Interactions of Biodegradable Poly(3-Hydroxybutyrate) α‑Form and the Prediction of Its Mechanical Property Hai Wang and Kohji Tashiro* Department of Future Industry-Oriented Basic Science and Materials, Toyota Technological Institute, Tempaku, Nagoya 461-8511, Japan ABSTRACT: As for the crystal structure of poly(3-hydroxybutyrate) (PHB) α-form, the methyl group was said to locate at an abnormally short distance from the oxygen atom of CO unit, resulting in the formation of CH3···OC hydrogen bond. This idea was proposed on the basis of infrared spectra detecting a band of antisymmetric methyl C−H stretching mode [νas(CH3)] at anomalously high frequency position and the too short CH3···OC interatomic distances calculated from the atomic coordinates derived from the previously reported X-ray structure analysis. However, the crystal structure analyzed by the X-ray method, even the C and O atomic positions, has not yet been established confirmatively because of the appreciably small number of the observed X-ray diffraction spots. We have reinvestigated the crystal structure of PHB α-form by collecting the observed X-ray diffraction spots of about twice larger total number than before, and confirmed the positions of the C, O and H atoms in the unit cell at enough high accuracy. The finally obtained crystal structure gave the reliability factor of 14.5% for the X-ray data at 23 °C (the total number of observed reflections 70) and 16.0% (94 at −140 °C). The thus-established crystal structure was found to exhibit the shortest H···O distance of 2.62 Å, which is shorter than the value expected from the normal van der Waals distance. In order to clarify the relation of this geometry with the observed higher-frequency shift of νas(CH3) band from the viewpoint of space group symmetry, the factor-group analysis and the normal modes calculation were performed for the PHB α-crystal by referring to the presently analyzed crystal structure information. Among the plural possibilities to cause the high-frequency shift of originally doubly degenerated νas(CH3) mode, the normal coordinates calculation has revealed that the vibrational coupling due to the intermolecular interactions between the adjacent molecular chains may be the most significant factor rather than the effect of lowering of C3v symmetry of regular CH3 groups coming from the site group symmetry. Once the crystal structure was established well, then the 3D anisotropic elastic constants matrix was calculated for the first time about the PHB α crystal. The ultimate Young’s modulus along the chain axis was only 5 GPa, which was comparable to the moduli in the direction perpendicular to the chain axis. In other words, the mechanical property of this crystal is mostly isotropic as a whole.

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INTRODUCTION Poly(3-hydroxybutyrate) (PHB, −[−C*H(CH3)CH2COO−]n−) is one of the most typical biodegradable polymers produced naturally by microorganisms.1,2 PHB crystallizes into the two types of crystal modifications, i.e., the α-form of helical chain conformation3−5 and the β-form of the planar-zigzag chain conformation.6 The α-form is normally obtained from the melt, the crystal structure of which was reported by Cornibert and Marchessault4 and Yokouchi et al.5 to take the orthorhombic unit cell with a = 5.76 Å, b = 13.20 Å, and c (fiber axis) = 5.96 Å, in which the two antiparallel chains are packed with a space group symmetry of P212121-D42. However, the accuracy of the X-ray analyzed crystal structure is not necessarily very high judging from the limited number of observed X-ray diffraction spots (24 reflections for Cornibert’s model and 42 reflections for Yokouchi’s model). Sasaki et al. carried out the calculation of electron density distribution of PHB α-form by maximum entropy method on the basis of these previously proposed crystal structures.7 In spite of these ambiguous situations about the © XXXX American Chemical Society

X-ray analyzed structure, however, many papers including the vibrational spectral analysis utilized the previously proposed atomic coordinates without any doubt, and they pointed out the existence of the abnormally short C−H···OC distance between the methyl and carbonyl groups in the unit cell. For example, Sato et al. detected the antisymmetric CH3 stretching band [νas(CH3)] at abnormally high frequency of 3008 cm−1 in the observed infrared spectra of PHB α-form compared with the corresponding band of general CH3 group.8−10 The abnormal IR (and Raman) band shifts due to the relatively strong C−H···O interactions were reported in many references for the small organic molecules.11−14 The similar observation of the higher frequency shift of νas(CH3) IR band by Sato et al. might be the first for the polymer substance. In the cases of small organic molecules the wide-angle neutron data confirmed the short Received: October 21, 2015 Revised: December 14, 2015

A

DOI: 10.1021/acs.macromol.5b02310 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules CH···O distances, which were combined with the spectroscopic observations.15 With the similar idea, using the X-ray analyzed structure information reported in the references,4,5 Sato et al. ascribed the abnormally high frequency position of νas(CH3) IR band to the short distance of 2.63 Å between H atom of CH3 group and O atom of the −CO group, which is shorter than the sum of the van der Waals radius of H and O atoms, 2.72 Å.15 However, in general, the positions of H atoms are difficult to determine by the X-ray structure analysis even for single crystals of low-molecular-weight compounds. The usage of only 24−42 X-ray reflections makes it practically impossible to get the accurate positions of even the C and O atoms! The total number of atoms (C, O, and H) included in one crystallographically asymmetric unit is 12 in the present case of PHB α-form. The parameters to be determined are the positions (xi, yi, zi) and temperature parameters (Bjk, j and k = 1−3), or the nine parameters for each atom. Therefore, the detailed analysis requires 109 [=12 atoms × (3 coordinates + 6 anisotropic temperature parameters) + 1 scale factor] parameters in total. If the isotropic thermal parameter is assumed commonly for all the atoms (B), then the total number of parameters is reduced to 38 (=12 atoms × 3 coordinates + 1 isothermal temperature factor + 1 scale factor), where the scale factor is added as one parameter to adjust the total intensity sum [∑jIj(hj, kj, lj), I: diffraction intensity for index (h, k, l)] between the observed and calculated values. For the accurate determination of these many parameters, we need to collect about 2−3 times larger number of the observed reflections, that is, about 80−110! The actually collected reflections were only 24−42 in the references.4,5 In this way, the interpretation of νas(CH3) bands based on the previously reported crystal structure is difficult to accept as long as the intermolecular interatomic distances are used as key factors for the interpretation of vibrational spectral data. In the present case also, it is necessary to establish the positions of the H atoms accurately by performing the refinement of the crystal structure of PHB α-form and reconsider the interpretation of the observed vibrational spectra on the basis of the thus-confirmed structure information. Another point to be noticed in the previous studies of the infrared spectral analyses of PHB α-form is that the quantum chemical calculations were performed to interpret the observed CH3 band positions by using a small PHB chain model of finite length.16 Unfortunately, however, even the factor group analysis of the crystal lattice was not carried out, and no discussion was made about any possibility of the band splitting due to the lowering of the site group symmetry and/or the correlation between the neighboring chains in the unit cell, which should have been performed first of all in the interpretation of the observed spectra. In the present work, we have presented the results on the refinement of the crystal structure of PHB α-form on the basis of the 2D X-ray diffraction data collected with an incident X-ray beam of shorter wavelength and using a highly oriented and highly crystalline sample. Once the structure was established including the H positions, then the infrared spectra were interpreted on the basis of group theory as well as the normal modes calculation by taking into account the symmetries of the site and space groups. In addition, the theoretical calculation of crystallite modulus of PHB α-form was also performed to estimate the ultimate mechanical property as the guiding principle necessary for the industrial improvement of the bulk property of this polymer.

Figure 1. 2D-WAXD pattern of PHB α-form at −140 °C.

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EXPERIMENTAL SECTION

Samples. PHB sample of Mw = 500 000 g/mol was purchased from the Polysciences, Inc. The film was cast from the CHCl3 solution at 60 °C and dried up in vacuo. The film was melted at 190 °C and quenched into ice water. The thus-obtained amorphous film was stretched by 10 times the original length at 0 °C in an ice water bath,15 followed by annealing at 155 °C for 2 h. For the infrared spectral measurement, a uniaxially oriented PHB film of ca. 10 μm thickness was prepared by stretching the cast film by 4 times the original length followed by annealing at 140 °C. X-ray Diffraction Measurements. The 2D X-ray diffraction diagrams of the oriented PHB sample were measured at 23 °C and −140 °C using a Rigaku R-axis Rapid-II X-ray diffractometer with a cylindrical camera of 127.4 mm radius equipped with an imaging plate detector.17 The graphite-monochromatized Mo Kα line was used as an incident X-ray beam (λ = 0.7107 Å). The 00l diffraction data were measured with Norman’s method using a Weissenberg camera installed on a Mac Science DIP 1000 X-ray diffractometer (Mo Kα) at 23 °C, where the oriented sample was oscillated by about 180° around the axis perpendicular to the sample draw direction. The X-ray Diffraction Data Analysis. The positions of the observed X-ray diffraction spots were read out manually on the 2D X-ray diffraction pattern. The diffraction profiles of the equatorial and layer lines were obtained by integrating the 2D X-ray diagram over a certain width along each layer line. The integrated intensity I of individual reflection was evaluated by separating the observed diffraction profiles into the components using a GRAMS software (Thermo Fisher Scientific, Inc.). The structure factors |Fobs| were estimated by using the following equation:

I = K ·A ·L ·p ·m |Fobs|2 where K is a scale factor, A is an absorption factor, L is a Lorentz factor, p is a polarization factor, and m is a multiplicity.18,19 The initial models necessary for the structural refinement were built up by referring to the model reported by Yokouchi et al.5 The crystal structure was refined using the constrained least-squares (CLS) program,18 in which the bond lengths and bond angles were fixed to the standard values and only the torsional angles and setting angles of the molecular chains in the crystal lattice were modified. The final structure was obtained so that the structure factors calculated for these initial models showed the best agreement with the observed data as much as possible. The reliability of the thus-obtained structure was expressed using a so-called reliability factor (R) defined in the following equation:

R=

∑ || Fobs| − |Fcalc ||/∑ |Fobs|

where |Fobs| and |Fcalc| are the observed and calculated structure factors, respectively. Infrared Spectral Measurement. The polarized infrared spectra in the frequency region of 400−4000 cm−1 were measured for the oriented PHB films of about 15 μm thickness using a Varian FTS 7000 Fouriertransform infrared spectrophotometer at 23 °C and −190 °C. The far-IR spectra were also measured for the unoriented samples of 120 μm B


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utilizing the Cerius2 software on the basis of the second derivatives method of the potential energy.21 The COMPASS force field was used as the potential function parameters.20

thickness using a JASCO 6100 FV Fourier-transform infrared spectrophotometer. The low-temperature IR measurements were performed using an Oxford Instrument Microscopy cryostat. The Normal Modes Calculation. The normal modes calculation was performed on the basis of the classical mechanics method by Cerius2 software (version 4.6, Accelrys Inc.). The COMPASS force field was used as the potential function parameters.20 Theoretical Prediction of 3D Elastic Constants. The 3D elastic constants were calculated for the X-ray analyzed crystal structure by

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RESULTS AND DISCUSSION Reinvestigation of Crystal Structure. The 2D wide-angle X-ray diffraction of PHB α-form measured at −140 °C is shown in Figure 1. The 2D-WAXD pattern at 23 °C was essentially the

Table 1. Comparison of Structure Factor (|F|) and Lattice Spacing (d) between the Calculated and Observed Values for the PHB α-Form

C


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total number of observed reflections. The fiber period 5.93 Å (at room temperature) suggests a (2/1) helical conformation as already mentioned in the literatures.4,5 The initial torsional angles of the skeletal CC and CO bonds were as below.

same as that at low temperature except the relatively diffuse reflections in the wider diffraction angle region. The 94 observed reflections were collected in the quarter zone of the diffraction pattern. The unit cell is of the rectangular shape with a = 5.67 ± 0.01 Å, b = 13.02 ± 0.01 Å and c (fiber axis) = 5.91 ± 0.01 Å at −140 °C. The unit cell parameters at 23 °C were slightly different, a = 5.73 ± 0.01 Å, b = 13.15 ± 0.02 Å and c (fiber axis) = 5.93 ± 0.01 Å, which were determined using the observed 70 reflections. The unit cell parameters at room temperature are essentially the same as those reported by Marchessault et al.4 and Yokouchi et al.5 The systematic absence rules about the hkl reflections were h00 (h = 2n + 1) and 0k0 (k = 2m + 1).22 The indices and |Fobsd| are listed in Table 1. Figure 2 shows the 00l reflections profile measured by a Weissenberg camera. Only the 00l of even l values were detected, confirming the existence of the 21 screw axis along the chain axis. From these extinction rules of the observed reflections, the most plausible space group was determined as P212121-D42 as already reported in the literatures.4,5 As a trial we challenged to extract the initial chain conformation models using the direct method,23,24 but any reasonable structure could not be obtained probably because of the smallness of the

The thus-created initial structure model was refined using the CLS program, where the position and orientation of the rigid (2/1) helical chains were varied in the unit cell so that the reliability factor became the lowest. The structure factor R was reduced to 14.2% for the observed 70 reflection data at 23 °C and 15.8% for 94 reflections at −140 °C. Determination of H Atom Positions. In order to determine the H atomic positions in the PHB α crystal lattice, the F0 − Fc map was calculated using the C and O atomic positions refined by the above-mentioned CLS method, where Fc is the structure factor calculated using only C and O atoms and F0 is the observed structure factor. Figure 3 shows the calculated F0 − Fc

Table 1. continued

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Macromolecules map projected along (a) the c-axis and (b) a-axis, respectively. The C and O atomic positions are overlapped for comparison. Some of the H atomic positions may be detected in this map but not very clearly. Then, as made often in the structure analysis of single-crystal of small organic molecules, the H atoms were added to the C atoms with the standard geometry (C−H = 1.1 Å, ∠H−C−C = 109.5°, and ∠H−C−H = 109.5°). An energy

minimization was carried out for the H atoms using COMPASS force field, where the unit cell parameters and the C and O atomic positions were fixed. The R factor calculated for the energetically minimized crystal structure model was 14.5% and 16.0% at 23 °C and −140 °C, respectively. The comparison of the observed and calculated X-ray layer line profiles is made in Figures 4 and 5 for the data at 23 °C and −140 °C, respectively.

Table 1. continued

E


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Macromolecules Table 1. continued

F


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2.72 Å (van der Waals separation) in general. The 2.62 Å (23 °C) revealed in the present analysis is slightly shorter compared with it. This is consistent with the previously reported neutron diffraction study of the small molecules, in which the H···O distance was checked for many crystals.15 The distance 2.62 Å is almost the same value as that calculated from the Yokouchi et al.’s model. As will be mentioned in a later section, the methyl groups are considered to experience the active thermal motion at room temperature and the non-negligible thermal expansion of the unit cell occurs, different from the structure at −140 °C. The shorter H···O distance at room temperature suggests that the anisotropic thermal expansion and the resultant reorientation of the molecular chain conformation might result in the slightly closer arrangement of CH3 and CO groups between the neighboring chains. These changes might reflect on the temperature factor or the thermal parameters of the H atoms in the X-ray structure analysis. But, the small changes in the X-ray diffraction profiles, as seen in Figures 4 and 5, do not lead to the significant change in the thermal parameters. Vibrational Spectra and Intermolecular Interactions. The polarized FT-IR spectra of the uniaxially oriented PHB film measured at 23 °C are shown in Figure 8. The group theoretical consideration is made here (refer to Figure 9). An isolated single (2/1) helical chain takes the factor group isomorphous to the CS2 symmetry group. The site group or the symmetry of an isolated chain at the crystal lattice position is also isomorphous to the CS2 symmetry group. The crystal lattice symmetry is isomorphous to the group DS2. The factor group analyses were performed as shown below.

Figure 2. Weissenberg diagram and a series of the 00l reflections detected for the uniaxially oriented PHB α-form sample.

The diffraction profile calculation was carried out using a Cerius2 software by assuming the crystalline size of 200 (a) × 200 (b) × 200 (c) Å3, the lattice strain of 0.5% (a) × 0.5% (b) × 0.5% (c) and the isotropic temperature factor 5 Å2. The agreement between the observed and calculated profiles is excellent for all the layer lines. The thus-obtained atomic fractional coordinates are listed in Table 2. The comparison of the observed and calculated lattice spacings (dobsd and dcalcd) and structure factors (|Fobsd| and |Fcalcd|) is shown in Table 1. The torsional angles of the skeletal chain are shown in Table 3 in comparison with the previously reported values. Figure 6 shows the refined crystal structure. As shown in Figure 7, the shortest distances between the carbonyl O atom and methyl H atoms belonging to the neighboring chains are 2.62 Å (23 °C) and 2.71 Å (−140 °C). The standard O···H distance of the corresponding pair is about

Γvib(crystal) = 6A(α′xx , α′ yy , α′zz ) + 4B1(μ′z , α′xy ) + 5B2(μ′ y , α′xz ) + 5B3(μ′x , α′ yz )

where α′ij is the Raman-active polarizability ij component (i, j = x, y, or z) and μ′i is the i component of the IR-active transition dipole moment (i = x, y, or z). Figure 9 predicted the correlation between these factor groups. For example, the A bands of a single chain are predicted to split into two in the crystal lattice: the IR-active B1 band and the Raman-active A band. The B1 band

Figure 3. F0 − Fc Fourier map of the PHB α-form at 23 °C. The red lines denote the skeletal chains, and the red spots denote the positions of the H atoms attached to the skeletal chain using the standard geometry. G


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Figure 4. Comparison of the observed and calculated diffraction profiles along the equatorial and layer lines of the PHB α-form at 23 °C.

Figure 5. Comparison of the observed and calculated diffraction profiles along the equatorial and layer lines of the PHB α-form at −140 °C.

vibrational frequencies and the approximate vibrational modes of the calculated IR bands in comparison with the observed data. The band assignment of CH3 vibrational bands is shown in Figure 10. The methyl group possesses a C3 local symmetry to give the A [νs(CH3)] mode and doubly degenerated E modes [νas(CH3)]. However, such a local symmetry of CH3 group is lost in the crystal lattice. As a result, the originally degenerated νas(CH3) E modes are split into two. Then, the four CH3 units included in the unit cell show the 12 IR bands in principle, which may be classified to the above-mentioned symmetry species. In the actually observed IR spectra, the two parallel-polarized bands at 3009 and 2978 cm−1 and two perpendicularly polarized bands at 2975 and 2968 cm−1 were detected, which may be assigned to

may take the parallel polarization character in the polarized IR spectra. The B bands of an isolated chain should be split into two IR-active bands, B2 and B3, with the perpendicular polarization. Here the parallel and perpendicular polarizations are for the electric vector of an incident IR beam parallel and perpendicular to the chain axis, respectively. By referring to these polarization characters the IR band assignment can be made relatively clearly. For example, the bands at 514, 839, 938, and 1128 cm−1 and so on may belong to the B1 species because of the parallel polarization character. More concrete assignment of the bands may be made by performing the normal modes calculation for the crystal lattice on the basis of classical mechanical method (Cerius2 with the COMPASS force field). Table 4 shows the H


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Macromolecules Table 2. Atomic Fractional Coordinates of PHB α-Form at 23 and −140 °C

23 °Ca C1 C2 C3 C4 O4 O5 H11 H21 H22 H41 H42 H43

−140 °C

x

y

z

0.4446 0.2954 0.1241 0.6094 0.2920 −0.0741 0.5429 0.1988 0.4024 0.7342 0.7099 0.5048

−0.0667 −0.1360 −0.0757 −0.1383 −0.0158 −0.1040 −0.0135 −0.1898 −0.1795 −0.0971 −0.1868 −0.1879

0.2480 0.4008 0.5241 0.1196 0.0896 0.5795 0.3549 0.2945 0.5214 0.0126 0.2355 0.0093

C1 C2 C3 C4 O1 O2 H11 H21 H22 H41 H42 H43

x

y

z

0.4494 0.2928 0.1177 0.5972 0.3000 −0.0803 0.5622 0.1943 0.3943 0.7236 0.6973 0.4788

−0.0722 −0.1402 −0.0780 −0.1465 −0.0114 −0.1077 −0.0229 −0.1937 −0.1847 −0.1060 −0.2003 −0.1912

0.2647 0.4129 0.5312 0.1208 0.1175 0.5780 0.3697 0.3048 0.5378 0.0114 0.2274 0.0109

a The unit cell parameters are a = 5.73 ± 0.01 Å, b = 13.15 ± 0.02 Å and c (f.a.) = 5.93 ± 0.01 Å at 23 °C and a = 5.67 ± 0.01 Å, b = 13.02 ± 0.01 Å and c (f.a.) = 5.91 ± 0.01 Å at −140 °C.

Table 3. Skeletal Torsional Angles of PHB α-Form

present study τ1/deg τ2/deg τ3/deg τ4/deg

Yokouchi et al.5

Marchessault et al.4

23 °C

−140 °C

−52.0 −47.0 −175.0 152.0

−56.7 −31.6 −179.7 141.3

−64.2 −37.4 −168.7 151.3

−53.7 −42.4 −171.5 156.8

Figure 6. Crystal structure of the PHB α-form.

Figure 7. Intermolecular distances of PHB α-form: (a) +23 °C and (b) −140 °C.

the B1(∥), B2(⊥), or B3(⊥) bands modes. IR spectral profiles were predicted theoretically, which are compared with these

observed bands as shown in Figure 10. The positions of the C−H stretching modes calculated by Cerius2 with COMPASS force I


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60−110 cm−1 were observed to split into the complicated band components, which might be assigned to the lattice vibrational modes (see Table 4) such as librational lattice mode (L(Rz)) and so on. The bands observed in the region 160−240 cm−1 are due to the CH3 torsional modes. The half width of the 220 cm−1 band became sharper by decreasing the temperature. As a trial, the half width Δν1/2 was plotted against 1/T by assuming an Arrheniustype equation of the relaxation time τ: τ = τ0eΔE

‡

/ RT

(1)

where τ is the relaxation time (s), ΔE‡ is the energy barrier, R is the gas constant, and T is an absolute temperature. Here we assume that the half-width Δν1/2 is proportional to the inverse of the relaxation time τ. The plot showed the two straight lines with the different slopes, which were crossed at around −100 °C as shown in Figure 13. This spectral change is similar to that observed for isotactic polypropylene, in which the CH3 torsional modes change their motional activity at around −145 °C.27 It must be noted the starting temperature is much higher for PHB α form than isotactic polypropylene. The activation energy barrier ΔE‡ was estimated from Figure 13 to be 0.72 kJ/mol (−100 °C). The thus-evaluated ΔE‡ is in the same range reported for the CH3-compounds in the solid state.28,29 In this way, the methyl groups tend to cease their torsional motion below −100 °C as speculated from the remarkable increase of the energy barrier in this temperature region. The further shift of νas(CH3) band position may be related to this change of thermal activity of the methyl groups: the stronger interaction at a lower temperature. The existence of the secondary force of C−H···OC bond can be supported from such an observation that the starting temperature of activated torsional motion of CH3 group is −100 °C for PHB α-form, which is much higher than −145 °C of isotactic polypropylene case without any strong secondary interactions. Such a change in the H atom motions of the CH3 units may be detected from the electron density map derived from X-ray F0 − Fc calculation, but it was quite difficult at the present stage. The detailed study of the temperature dependence of neutron diffraction may be helpful for this discussion. Theoretical Calculation of 3D Elastic Constants. By referring to the good reproducibility of the observed IR band positions by using the atomic coordinates and COMPASS potential function parameters, the 3D elastic constants tensor and the corresponding compliance tensor were calculated as shown below. Elastic constants matrix

Figure 8. Polarized FT-IR spectra of the uniaxially oriented PHB film at 23 °C.

Figure 9. Correlation of the factor groups predicted for the PHB α-form.

field are found to correspond relatively well to the observed data. Among these bands, the 3009 cm−1 band was found to shift remarkably by cooling to −190 °C (Figure 11), indicating this band is affected sensitively by the intermolecular interactions.8−10 The normal modes calculation supported this point. The bands predicted for the isolated chain (Figure 10b) were found to shift to the higher frequency side by 26 cm−1 in the calculation made the intermolecular interactions taken into account (Figure 10c). In this way, the normal modes calculation using the atomic coordinates revealed by the X-ray structure analysis reproduced the anomalously high frequency positioning of νas(CH3) band, which was interpreted on the basis of the factor group analysis well. The X-ray structure analysis revealed the CO bond distance, 1.24 Å, which was not very much different than the standard value (about 1.23 Å). This is reasonable because the CH···O interactions are secondary interactions compared with the stronger hydrogen bond affecting the CO bond distance remarkably. The position of CO stretching band was also checked, but it was almost in the same frequency range as the standard case (1730−1750 cm−1).25 The calculated frequency of ν(CO) was a little higher because of the overestimation of the corresponding potential function. The far-IR spectral region gives us the information on the correlation splitting of the vibrational bands more clearly. Figure 12 shows the temperature dependence of far-IR spectra of PHB α form. As already reported,26 some bands in the region

⎡ 4.35 ⎢ ⎢1.68 ⎢ 3.43 c (GPa) = ⎢ ⎢ 0.0 ⎢ 0.0 ⎢ ⎣ 0.0

1.68 7.40 2.97 0.0 0.0

3.43 2.97 8.11 0.0 0.0

0.0 0.0 0.0 2.18 0.0

0.0

0.0

0.0

0.0 ⎤ ⎥ 0.0 ⎥ 0.0 ⎥ ⎥ 0.0 ⎥ 0.0 ⎥ ⎥ 0.0 2.46 ⎦

0.0 0.0 0.0 0.0 9.32

Compliance tensors matrix ⎡ 0.35 −0.02 −0.14 0.0 0.0 0.0 ⎤ ⎢ ⎥ ⎢−0.02 0.16 −0.05 0.0 0.0 0.0 ⎥ ⎢−0.14 −0.05 0.20 0.0 0.0 0.0 ⎥ s (GPa−1) = ⎢ ⎥ 0.0 0.0 0.46 0.0 0.0 ⎥ ⎢ 0.0 ⎢ 0.0 0.0 0.0 0.0 0.11 0.0 ⎥ ⎢ ⎥ ⎣ 0.0 0.0 0.0 0.0 0.0 0.41⎦ J


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Macromolecules Here the first axis ∥ a-axis, the second axis ∥ b-axis and the third axis ∥ c-axis. The calculated Young’s modulus along the chain axis, Ec, is quite low, 5.0 GPa, which is close to the crystallite modulus reported for poly(ethylene oxybenzoate) α-form and poly(trimethylene terephthalate) (2−3 GPa).30,31 In the latter 2 cases, the deformation energy distributes mainly to the torsional angle change of the skeletal chains.32,33 This type of torsional angle deformation may occur also in the PHB α-form chain, resulting in the very low Young’s modulus. The anisotropic curves were calculated for Young’s modulus and linear compressibility in the plane perpendicular to the chain axis using eqs 2 and 3.32

β(θ ) = (s11 + s12 + s13) cos2 ϕ + (s21 + s22 + s23) sin 2 ϕ (3)

where sij is the compliance tensor component and ϕ is the angle measured from the a-axis. The results are shown in Figure 14, where the case of the poly(L-lactic acid) α crystal is also shown for comparison.33 In the case of the PHB α lattice, Young’s modulus along the b-axis is rather higher. It is difficult to ascribe this anisotropy to the short H···OC bonds revealed in the present study since the corresponding force constant is not very extremely large to give an one-order large force constant than the H···H bonds between the neighboring chains.32 The modulus perpendicular to the chain axis is in the same order as that parallel to the chain axis, indicating that the PHB α-form is mechanically almost isotropic. The Young modulus of the PLLA

1/E(θ ) = s11 cos 4 ϕ + 2s12 sin 2 ϕ cos 2 ϕ + s22 sin 4 ϕ + 2s66 cos2 ϕ sin 2 ϕ

(2)

Table 4. IR Band Assignment of PHB α-form at 23 °Ca

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α crystal is as a whole higher than that of the PHB α form. The Ec of the PLLA α form is about 14.7 GPa, 3 times higher than the latter.32

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CONCLUSION In the present paper, the refinement of the crystal structure of PHB α-form was performed successfully to establish the atomic

Table 4. continued

a Key: (a) The vibrational mode frequencies calculated by COMPASS force field. (b) Normal modes; Tx, Ty, Tz: translations; L(Tx), L(Ty), L(Tz): translational lattice modes; L(Rx), L(Ry), L(Rz): librational lattice modes; τ: torsional mode; δ: bending mode; γ: rocking mode; ν: stretching mode; ω: wagging mode; t: twisting mode; νas: antisymmetric stretching mode; νs: symmetric stretching mode.

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Figure 13. Logarithmic plot of relaxation time against 1/T to estimate the activation energy (ΔE‡) of methyl group torsional motion of the PHB α-form.

Figure 10. Comparison of the observed FT-IR spectra at 23 °C with the calculated spectra of the PHB α-form.

Figure 14. Anisotropic curves of Young’s modulus and linear compressibility in the plane perpendicular to the chain axis calculated for the PHB α-form and the PLLA α-form.33 Figure 11. FT-IR spectra of the PHB α-form at different temperatures in the frequency region of 2900−3050 cm−1.

X-ray structure analysis supported the interpretation about the higher frequency shift of the originally doubly degenerated νas(CH3) IR bands, as reported by Sato et al.8−10 Another effect of this secondary interaction was detected in such an experiment that the starting temperature of CH3 torsional motion is much higher than the case of isotactic polypropylene as clarified from the temperature dependence of the far-IR spectral data. In the present paper, furthermore, the polarized IR and far-IR spectra were analyzed quantitatively by performing the factor group analysis and normal modes calculation for the 3-dimensional crystal structure as well as the isolated chain, which revealed the sitesymmetry splitting of the doubly degenerated bands and their shift by the strong intermolecular interactions. As a result of these discussion, the 3-dimensional elastic constants matrix of PHB α-form was calculated for the first time using the thus-established crystal structure. Young’s modulus along the chain axis is only 5 GPa, and so the almost isotropic modulus was expected for this polymer as the ultimate mechanical property.

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Figure 12. Temperature dependence of far-IR spectra of the PHB α-form.

AUTHOR INFORMATION

Corresponding Author

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

coordinates in the lattice. In particular, the C−H···OC distance between the neighboring chains was confirmed to be appreciably short compared with the normal case. This conclusion by the

Notes

The authors declare no competing financial interest. M


Article

Macromolecules

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ACKNOWLEDGMENTS This study was supported financially by MEXT “Strategic Project to Support the Formation of Research Bases at Private Universities (2010-2014)”.

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