Quantitative Crystal Structure Analysis of Poly(vinyl Alcohol)–Iodine

Mar 23, 2015 - (32, 33) On the basis of X-ray diffraction and Raman data analysis, Choi et al. proposed the crystal structure of the complex in which ...
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Quantitative Crystal Structure Analysis of Poly(vinyl Alcohol)−Iodine Complexes on the Basis of 2D X‑ray Diffraction, Raman Spectra, and Computer Simulation Techniques Kohji Tashiro,*,† Hideyuki Kitai,‡ Siti Munirah Saharin,† Akira Shimazu,‡ and Takahiko Itou‡ †

Department of Future Industry-Oriented Basic Science and Materials, Toyota Technological Institute, Tempaku, Nagoya 461-8511, Japan Functional Design Technology Center, Nitto Denko Co. Ltd., Shimohozumi, Ibaraki, Osaka 567-8680, Japan

‡

ABSTRACT: The crystal structures of the two types of iodine complexes (complex I and II) of poly(vinyl alcohol) (PVA), which were prepared respectively from the KI/I2 aqueous solution of middle (0.1−0.5 mol/L) and high (1−3 mol/L) concentration of I2, have been analyzed quantitatively on the basis of 2-dimensional X-ray diffraction diagrams and Raman spectral data in addition to the computer simulation method. In the crystal lattice of the original PVA, the PVA chains of zigzag conformation are packed together by intermolecular hydrogen bonds. Once the I3− ions migrate into the crystal lattice of PVA, these hydrogen bonds are deconstructed and the PVA chains are displaced from the original positions so that the I3− ions can be coupled together with the PVA chains through the charge-transfer between the I3− and hydroxyl groups, resulting in the formation of complex I. In this complex, the averaged occupancy of I3− ions is about 0.2, and the PVA−iodine pairs and the original PVA chain pairs coexist to form a kind of super lattice with the disordered packing structure of PVA chains and iodine ion columns. As the iodine concentration is increased furthermore, most of the PVA chains are combined with I3− ions at the occupancy of about 0.7 to create the complex II. The comparison of X-ray end diffraction patterns of the doubly oriented samples clarified the spatial relation of the crystal lattices between PVA, complex I and complex II. In the original PVA sample, the planar−zigzag planes of PVA chains are parallel to the rolled plane of the doubly oriented sample. This geometrical relation is kept in the complex I sample. However, in the complex II, the PVA chains have been found to rotate by 38° around the chain axis in the transition process from complex I to complex II. In this way, the change in the packing mode of PVA chains and iodine ions in the complex formation process has been successfully revealed for the first time from the atomic level.

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Hyde et al.,28 Inagaki et al.29 and Sengupta et al.30,31 analyzed the resonance Raman spectra of PVA−iodine complex to reveal the iodine ion species (I5− and I3−). The I5− ions are existent mainly in the amorphous region of PVA sample soaked in a KI/I2 solution of low iodine concentration of 0.01−0.2 mol/L.3,18 By increasing the iodine concentration furthermore, the crystal lattice absorbs the iodine ions to form the crystalline complex.32,33 On the basis of X-ray diffraction and Raman data analysis, Choi et al. proposed the crystal structure of the complex in which the iodine ions I3− or I5− are surrounded by planarzigzag PVA chains.34−36 However, their X-ray diffraction analysis was not enough quantitative but the qualitative comparison of diffraction intensity between the observed and calculated values was made in terms of “weak” and “strong” expressions only. Shin et al. reported the change in the X-ray diffraction pattern dependent on the iodine concentration but they did not perform any structural analysis.37 A structure model different from that reported by Choi et al. was proposed on the basis of 13C NMR spectra to show the polyiodine ions surrounded by the zigzag PVA chains.38 The various other reports were also published

INTRODUCTION Dipping of an oriented (or even unoriented) film of poly(vinyl alcohol) (PVA, −[CH2CH(OH)]n−) into an aqueous solution of KI and I2 gives the so-called PVA−iodine complex with dark brown-to-blue color.1 This iodine-doped PVA film is useful as an optical polarizer and utilized in such various fields as liquidcrystal display, UV-light-cut sunglass, etc.2 The PVA−iodine complex shows the absorption maximum in the frequency region of visible-ray of 400−600 nm wavelength. The intensity and position of the maximal absorption peak is dependent on many such factors as the stereoregularity of PVA chain, the degree of chain orientation and crystallinity of the PVA film, the content of absorbed iodine ion, temperature, and so on.3−24 The crystal structure information on PVA−iodine complex is indispensable as a basic knowledge in the discussion of these factors from the molecular level. The structural information is important also for the prediction of the electronic and optical properties based on the molecular orbital theory. So far the crystal structure models of PVA−iodine complex were reported in several papers. For example, Zwick25,26 and Teblev et al.27 proposed a helical model of PVA chains with iodine molecules trapped in the center part along the helical axis, which was, however, not derived from the X-ray diffraction data analysis but only by referring to the helical form of starch−iodine complex. © 2015 American Chemical Society

Received: January 20, 2015 Revised: March 6, 2015 Published: March 23, 2015 2138

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species were dipped into the KI/I2 solutions of 0.5, 1, and 3 mol/L (M) concentrations for 10 h at room temperature. Measurements. Polarized Raman spectra of the iodine-complex films were measured with an excitation laser beam of 532 nm wavelength using a Japan Spectroscopic Company NRS 2100 Raman spectrometer. Since the incident laser beam easily damaged the complex film surface and the spectral pattern (or the relative intensity between the Raman bands) was changed sensitively, the sample position irradiated by the laser beam was moved continuously to avoid such a laser damage during the measurement. The 2-dimensional X-ray diffraction diagrams were measured for the highly uniaxially oriented films using an imaging plate detector of cylinder-type (12 cm radius) which was set on the X-ray generator Rigaku R-Axis Rapid II with a graphite monochromatized Mo Kα line of 0.71 Å wavelength as an incident X-ray beam. It must be pointed out here that the Cu Kα line of 1.54 Å wavelength was not used as an incident X-ray beam since Cu Kα beam was absorbed strongly by iodine atoms and the X-ray diffraction patterns could not be obtained clearly for the thick samples. The end patterns were measured for the doubly oriented samples using a Rigaku X-ray diffractometer R-Axis VII, where the Mo Kα beam was incident along the end direction, i.e., along the chain axis.

about the structure of PVA−iodine complex. Miki et al. analyzed the XANES (X-ray absorption near-edge structure) data of the complex to propose the local coordination structure of PVA and I5− ion.39 Seto et al. investigated the Mössbauer spectra of iodine ion species in the complex.40,41 Miyazaki et al.42 and Yajima et al.43 measured, respectively, the small-angle X-ray and neutron scatterings of PVA−iodine complex to study the higher-order structure consisting of the crystalline and amorphous regions. In this way, the structure of PVA−iodine complex was investigated from the various points of view. But, the crystal structure itself has not yet been established enough satisfactorily because no quantitative X-ray structure analysis had been performed in the long history of PVA−iodine complex since its discovery in 1927 by Herrmann et al.44 and Staudinger et al.45 In the present paper, we have established the two types of PVA−iodine complexes (complex I and II) prepared depending on the iodine concentration, and we analyzed their crystal structures based on the combined experimental data of polarized Raman spectra and 2-dimensional X-ray diffraction patterns measured for a series of uniaxially- and doubly oriented PVA− iodine complex samples of the various iodine contents. We have happened to find the thus-quantitatively analyzed crystal structure of complex II is similar to the structure model proposed by Choi et al.34 although they did not perform the quantitative analysis of the observed X-ray diffraction data as pointed out above. The crystal structure model of complex I has been built up for the first time in the present paper. We have measured also the X-ray diffraction data taken along the end direction of the doubly oriented PVA samples (the end pattern). These data were quite useful to confirm these crystal structure models proposed here for the PVA−iodine complexes. These models have allowed us to derive the geometrical relation between the original PVA crystallites and the resultant iodine complexes from the molecular level. As well-known already, the X-ray diffraction patterns of these complexes show the diffuse streaks along the layer lines, which were interpreted to come from the 1-dimensional disordered array of the iodine species.32,35,46 But, the concrete structure has not yet been clarified enough well. We simulated the diffraction profile successfully by building up an isolated 1-dimensional I3− ion array, showing the existence of appreciably disordered packing structure of iodine ions. As will be mentioned in detail, this paper has succeeded for the first time to describe the concrete structures of PVA−iodine complexes prepared from the iodine solutions of different concentrations as well as the clarification of the geometrical relation between PVA and its complexes. These information will give us a basically important structural knowledge indispensable also for the theoretical prediction of optical properties of these complexes.

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RESULTS AND DISCUSSION (1). Elemental Analysis of Iodine and Potassium Contents. The contents of iodine and potassium elements absorbed in the PVA films may not be necessarily the same as those in the original KI/I2 aqueous solutions. The contents of these elements in the films were analyzed using an X-ray photoelectron spectrometer (XPS) as shown in Figure 1. The contents of iodine and potassium ions increased gradually with an increment of the concentration of KI/I2 solution. The ratio of iodine/potassium elements included in the PVA film was almost constant, about 2.5 for the films of 0.002−0.2 M concentration and about 3 for the films of 0.4−1 M concentration (Figure 1c). These data will be analyzed in a later section by combining with the Raman spectral data. (2). Raman Spectra. Figure 2 shows the Raman spectra measured for (a) a series of KI/I2 aqueous solutions and (b) PVA−iodine complexes dipped in these solutions. The Raman bands detected at 160 and 110 cm−1 are due to the vibrations of I5− and I3− species, respectively.28−31,36 Raman Spectra of the KI/I2 Solutions. The Raman spectra of KI/I2 solutions themselves were not reported so far. Contrary to our expectation, we found that the Raman spectra of the solution of low iodine concentration gave mainly the peak of I3− ion, while the peak intensity of I5− ion increased gradually with an increment of iodine concentration, and I5− and I3− ions coexist together in the solution. The situation was different totally in the PVA solid films. The I5− peak was detected for the film dipped in a low concentration solution, while the film from the high concentration solution showed almost only the I3− peak with a shoulder corresponding to the I5− peak.28−31,36 In this way, the iodine ions were found to exist in a different form depending on the concentration of KI/I2 solution. As will be revealed by the quantitative analysis of X-ray diffraction data in a later section, only the I3− ion can exist in the crystal lattice of the complex and the I5− (and I3−) ions exist in the amorphous region of PVA, as already reported.28−31,36 The comparison of Raman spectra between parts a and b in Figure 2 shows that (i) the I3− ions in the KI/I2 aqueous solution of low iodine concentration change mainly to I5− ions in the amorphous region of PVA film and (ii) when the concentration of aqueous solution is increased, the I5− ions in the solution change to I3− ions in the PVA film, which

EXPERIMENTAL SECTION

Samples. Atactic PVA sample was supplied by Kuraray Co., Ltd., Japan. The degree of polymerization was ca. 1700. The films of ca. 200 μm thickness were prepared by casting from the hot aqueous solution followed by heat treatment at 120 °C for 2 h. Uniaxially oriented sample was prepared as follows: a rectangular piece of film was dipped into a KI/I2 aqueous solution for 4 h, and the thus-swollen film was stretched by 5 times the original length at 50 °C. The KI/I2 aqueous solutions were prepared for the various iodine concentrations (0−5 mol/L), where the molar ratio between KI and I2 species was fixed at the constant ratio of 5:1. In the present paper, the concentration is expressed in terms of I2 concentration. Doubly oriented samples were prepared by rolling the cast films by 5 times the original length at about 120 °C. The rectangularly cut sample 2139

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Figure 3. Schematic illustration of iodine species contained in the amorphous and crystalline regions of PVA sample dipped in the KI/I2 solution of different concentration.

as pointed above. Then, such a speculation can be made reasonably that the PVA sample contains the iodine and potassium ions in the form of I5− and K+ ions at 1:2 ratio in the amorphous region. Since the total system must be electrically neutral, the positive charge of K+ species should be balanced with an anion species of I5−. When the concentration of KI/I2 solution is increased above 0.2 M, the molar ratio between iodine and potassium ions is about 3. As shown in a later section, the X-ray diffraction data indicates that the iodine ions can exit in I3− form in the crystal lattice. The observed molar ratio is reasonable when I3− and K+ coexist at 1:1 molar ratio (3:1 molar ratio for I:K elements) in the crystal lattice. (3). X-ray Diffraction Patterns. (3-1). Uniaxially Oriented Samples. Figure 4 shows a series of 2-dimensional X-ray diffraction diagrams taken at the different dipping times for the uniaxially oriented PVA and its iodine complexes prepared in the KI/I2 solutions of the different concentrations. Pattern a is that of pure PVA sample. Sample b, dipped in 0.5 M solution for relatively short time, shows weak and diffuse streaks along the horizontal line at the position below the first layer line of X-ray pattern of the original PVA. These streak lines increased in intensity as the dipping time was increased as seen in pattern c, suggesting the formation of columnar structure of iodine ions along the fiber direction.32,35 The equatorial line pattern was different between parts c and e measured for the samples dipped in the KI/I2 solutions of different concentration for 48 h. The strong diffractions coming from the pure PVA crystal became weak, although the first layer line peaks corresponding to the fiber period of PVA chain, 2.53 Å, was detected even for the sample dipped in the 3 M solution (e). In the case of PVA sample dipped in a highly concentrated solution for a long time, the Debye−Scherrer rings from the KI crystal powder overlapped with the diffraction pattern of the complex. The KI crystal was deposited on the surface of PVA complex film on drying up the water because of too high concentration of KI in the solution. The deposited KI could be erased by washing lightly by methanol.

Figure 1. Contents of iodine, potassium, and their molar ratios in the PVA samples dipped into the KI/I2 aqueous solutions of the various iodine concentrations. The molar ratio between KI and I2 in the solution was always kept to 5:1.

Figure 2. Iodine concentration dependence of Raman spectra measured for (a) KI/I2 aqueous solutions and (b) the PVA samples dipped in the KI/I2 aqueous solutions of the various iodine concentrations. Notice that the Raman intensity changes depending on the concentration but this tendency is perfectly opposite between a and b cases.

penetrate into the crystalline region. Figure 3 illustrates this situation schematically. As seen from the results of elementary analysis shown in Figure 1, the I/K molar ratio is about 2.5 in the PVA sample dipped into a KI/I2 solution of low concentration (0.001−0.2 M). The Raman spectra showed the existence of I5− ions in the PVA film, 2140

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Figure 4. 2D X-ray diffraction patterns measured for the uniaxially oriented PVA samples dipped in the KI/I2 solutions of the different concentration for the different time. The vertical direction is parallel to the drawn direction.

of I3− ion. These ions included in the columns are disordered in relative height. The thus-speculated columnar model of I3− ions are shown in Figures 5c and 6c. As the iodine concentration is increased, the number of iodine ions is increased but they are arrayed in a statistically random way along the columnar axis, as illustrated in Figure 6c. Comparison of the calculated meridional diffraction profile with the observed profile is made in Figure 6b, confirming the reasonableness of the above-mentioned model of iodine column. Now we need to investigate the geometrical relation between PVA chains and iodine columns, as will be analyzed in the next section. (3-2). Equatorial Line Profiles. The equatorial line profile, which was obtained by integrating the 2D diffraction pattern shown in Figure 4, changed remarkably with increasing iodine concentration. As shown in Figure 7, these equatorial line profiles can be classified into 3 types depending on the concentration of the solution: the profile of PVA, the relatively broad profile (I2 concentration of about 0.5 M, complex I) and the relatively sharp profile (I2 concentration 3 M, complex II). (3-3). Crystal Structure of Complex II. Basic Unit Cell Structure. Since the X-ray equatorial line profile of complex II is relatively sharp as a whole (Figure 7), we analyzed at first this diffraction data to get the crystal structure information. In this process we utilized also the X-ray diffraction pattern taken for the doubly oriented PVA−iodine complex sample (3M) in the end direction (the end pattern) or by irradiating the X-ray beam along the chain axis, which is shown in Figure 8c in comparison with that of doubly oriented PVA sample (Figure 8a).49 The unit cell parameters projected to the equatorial plane (a′, b′ and γ′) were estimated from this end pattern as well as the equatorial line profile shown in Figure 7. The reciprocal lattice vectors thus determined are shown in the right side of Figure 8c in comparison with the observed end pattern. The real lattice vectors (a′, b′, and γ′) projected along the chain axis are as below.

The repeating period of iodine ion in the column I may be estimated from the heights of the diffuse scatterings using the following Polany’s equation.47,48 I sin(ϕ) = mλ ,

tan(ϕ) = Δy/R

(1)

where m is the order of layer line, λ is an incident X-ray wavelength, Δy is the height of a diffuse layer line measured from the equatorial line, and R is the camera radius. The ϕ is an elevation angle viewed from the equatorial line to the layer line. In sample a, the repeating period of PVA chain was 2.53 Å, indicating the planar-zigzag chain conformation. The streak lines, intrinsic to the iodine chains oriented along the draw axis, gave the repeating period of about 9.68 Å. This period corresponds well to the effective length of I3− ion (the calculated value of about 9.5 Å with the van der Waals radius of ca. 2 Å taken into account). In fact, the X-ray diffraction profile calculated for a column consisting of iodine ions with 9.68 Å repeating period was found to fit quite well to the observed diffraction profile along the meridional direction, as shown in Figures 5 and 6. In Figure 5, the 2-dimensional X-ray diffraction patterns are compared between the observed and calculated ones, where the calculation was performed for the cell model consisting of isolated I3− ion and also for that containing many but randomly arrayed I3− ion molecules along the c axis. These calculated patterns correspond well to the actually observed pattern shown in Figure 5c. The 1-dimensional diffraction profile calculated for the model in Figure 5b is compared with the observed profile as reproduced in Figure 5c. The I5− ion model with the calculated repeating period of about 15.4 Å could not reproduce the observed diffraction profile at all. Figure 6a shows the diffraction profiles observed for the PVA−iodine complexes prepared from the KI−I2 solutions with the different iodine concentrations. All these samples show essentially the same profile irrespective of the solution concentration, indicating that the iodine species contained in the crystal lattice is commonly existent in the form

a′ = 10.02 Å, 2141

b′ = 7.85 Å,

and γ ′ = 91.0° DOI: 10.1021/acs.macromol.5b00119 Macromolecules 2015, 48, 2138−2148

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Figure 5. Simulation of X-ray diffuse scatterings observed for PVA−iodine complex: (a) isolated I3−, (b) randomly arrayed I3− ions, and (c) actually observed pattern.

Figure 7. X-ray equatorial line profiles measured for the PVA and its iodine complexes prepared at the different concentration of KI/I2 solution.

by 21 screw axis along the chain axis, i.e., the plane group symmetry of complex II is p21, the same as that of the original PVA crystal, the 3D space group symmetry of which is P21/m.50−52 The relative positions of the planar-zigzag PVA chains, I3− columns, and K+ ions were displaced in a trial-anderror way in the a′b′ plane so that the observed X-ray equatorial diffraction profile could be reproduced as well as possible. In the actual calculation, the isotropic temperature factors of these atoms and the occupancies of I3− and K+ were also varied. The calculation of the X-ray diffraction profiles was performed using a commercial software Cerius2 (version 4.6, Accelrys). After many repetitions of trial-and-error calculations of the X-ray diffraction profile, we have reached the most plausible model shown in Figure 9b. The fractional coordinates of the atoms in the unit cell

Figure 6. (a) X-ray diffraction profiles scanned along the meridional line for the uniaxially oriented PVA samples dipped in the KI−I2 solutions of the various concentrations. (b) Comparison of the observed X-ray 00l diffraction profile with that calculated for the randomly packed iodine ions model (see Figure 5b). (c) Columnar model of I3− ions.

Judging from the size of a′b′ plane, a pair of the basic units are included in the cell: one basic unit consists of one PVA chain, I3− and K+ ions, and these basic units are assumed to be connected 2142

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Figure 9. Crystal structures of (a) the original PVA50‑y and (b) the complex II. The large circles (purple color) are iodine atoms. The smaller circles (green color) are potassium atoms.

Table 1. Fractional Atomic Coordinates of PVA−Iodine Complex IIa

Figure 8. X-ray end patterns measured for (a) the doubly oriented PVA sample, (b) the complex I, and (c) the complex II. The reciprocal lattices derived from these diffraction data are shown in the right side. In (b), the diffraction spots of PVA and complex II are contained as indicated by white asterisks.

are shown in Table 1. The atactic configuration was assumed for the PVA chain itself. The occupancy is 1.0 for C atom, 0.5 for O atom, and 0.7 for I and K atoms. (The syndiotactic model was used in Table 1 and the occupancy of O atom is 1.0, which is equivalent to the atactic model with 0.5 occupancy of O atom in 2.53 Å.) Figure 10 compares the observed X-ray equatorial reflection profile with that calculated for the model of Figure 9b, where the crystallite size was La = Lb = 100 Å and the lattice strain was 1.0% for both the a′ and b′ axes. The isotropic temperature factor 3 Å2 was assumed for all the atoms. Table 2 compares the lattice spacings and structure factors observed for the equatorial diffraction peaks with those calculated for the model shown in Figure 9b. The reliable factor defined as R = Σ∥Fobs| - |Fcalc∥/Σ| Fobs| is 18.8%, where |Fobs| and |Fcalc| are the absolute values of the observed and calculated structure factors, respectively. After the determination of this crystal structural model, we happened to notice that the similar model was proposed by Choi et al. (substitution model).34 But, as already mentioned in the introduction, they did not choose the best model among the several possible candidates although they compared the X-ray diffraction intensity calculated for the model with the qualitatively estimated intensity data in terms of “strong”, “weak”, and so on.

atomsb

x

y

zc

occupancy

C(H2)1 C(OH)2 O3 C(H2)4 C(OH)5 O6 C(H2)7 C(OH)8 O9 C(H2)10 C(OH)11 O12 I1 I2 I3 K

0.02 0.09 0.08 0.01 0.09 0.22 0.02 0.09 0.08 0.02 0.09 0.22 0.36 0.36 0.36 0.43

0.77 0.72 0.54 0.77 0.70 0.76 0.77 0.71 0.53 0.77 0.70 0.74 0.29 0.29 0.29 0.79

0.00 0.12 0.12 0.25 0.37 0.37 0.50 0.62 0.62 0.75 0.87 0.88 0.94 0.66 0.37 0.64

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.7 0.7 0.7 0.7

a Unit cell parameters a = 10.02 Å, b = 7.85 Å, c (fiber axis) = 9.68 Å, γ = 91.0°. Space group P21 bSyndiotactic configuration was assumed about PVA chains. The atoms of another asymmetric unit in the cell are given by a 21 screw symmetry operation along the c axis at (0.5, 0.5) position. cThe z coordinates of I3− and K+ may be changed depending on the model since the relative heights of these atoms are statistically disordered.

Our model thus determined tells us that the PVA chains are shifted more or less from the original positions to generate the spaces needed for storing the I3− and K+ ions. The occupancy of I3− (and K+) ions is about 0.7. The calculated density of the unit cell is 2.05 g/cm3 by assuming this occupancy of I3− and K+ ions, which is reasonable compared with the observed density of the bulk sample 1.85 g/cm3 when the contribution of the amorphous phase is taken into account. Packing Disorder. In this way, the structure of complex II projected along the chain axis can reproduce the observed 2143

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must be of course maintained in the unit cell model determined above, although the structural model given in Figure 9 shows the regular packing of ions along the c axis for demonstrating a characteristic feature of the packing mode. In fact, a superlattice consisting of 10 × 10 unit cells was built up by starting from the basic structural model shown in Figure 9 and then the relative heights of the iodine ions were shifted randomly. The thuscreated irregular model reproduced the observed 2D X-ray diffraction pattern well as shown in Figure 11a, where the

Figure 10. Comparison of the observed X-ray equatorial line profile with that calculated for complex II model shown in Figure 9.

Table 2. Comparison of Lattice Spacing and Structure Factor of Equatorial Diffraction Peaks between the Observed and Calculated Values for PVA−iodine Complex II index

d(obs)/Å

d(calc)/Å

|F(obsd)|a

|F(calc)|

100 010 110, 11̅0 200 210, 210̅ 020 120 300 310, 220 030 020, 400 02̅0, 13̅0 410, 230 420, 330 500, 51̅0 140, 510

10.21 7.85 6.22 4.99 4.29 3.91 3.66 3.34 3.07 2.60 2.51

9.91 7.85 6.20 5.01 4.25 3.94 3.66 3.37 3.09 2.62 2.54

19.5 55.7 53.6 29.8 107.9 119.0 53.9 52.0 48.6 54.3 54.1

28.0 56.2 51.4 42.4 110.3 97.7 40.3 50.0 48.4 62.5 89.5

2.31 2.07 1.94

2.35 2.09 1.95

42.3 55.7 69.7

50.8 57.2 61.8

Figure 11. (a) Comparison of 2D X-ray diffraction pattern of complex II between the observed and calculated ones, where the model consisted of 10 × 10 × 2 basic unit cells shown in Figure 9 with the translational disorder of iodine columns along the chain axis. The PVA chains are shifted more or less along the chain axis by taking into account the original disorder in PVA crystals. The simulation conditions were as follows: the mean square displacements of atoms 0.2 × 0.2 × 0.1 Å2 along the a, b, and c axes, the crystallite size 100 × 100 × 300 Å, the crystal strains 2 × 2 x 2% and the chain orientation half width 4°. (b) Comparison of 2D X-ray diffraction pattern of PVA crystal between the observed and simulated structures, where the crystal structure reported in the papers50−52 was used for the calculation (the temperature factors 0.2 × 0.2 × 0.1 Å2 along the a, b, and c axes, the crystallite size 100 × 100 × 300 Å, the crystal strains 1 × 1 x 0.5% and the chain orientation half width 2.5°).

a The observed structure factor |Fobs| was evaluated from the integrated intensity Iobs of a diffraction spot using the equation Iobs = kALp|Fobs|2, where L, p, A, and k are the Lorentz factor, polarization factor, absorption coefficient, and scale factor, respectively. The intensity integration of an individual peak was made after the curve separation of the observed X-ray diffraction profile shown in Figure 10.

equatorial line profile well. Now we need to consider the 3D structure by taking into consideration the relative height of PVA and iodine ions. The repeating period of PVA chain along the c axis is 2.53 Å. The repeating period of I3− ions in the column is about 9.68 Å (see Figures 5 and 6). These two repeating periods cannot be adjusted to one another by a simple integer relation, but they should be in a so-called incommensurate relation. The approximately estimated least common multiple of them is 65.8 Å (=2.53 Å × 26 − 9.68 Å × 7). Since this common repeating period is too long for the structural analysis, the simpler unit cell model containing a pair of four VOH monomeric units + I3− ion + K+ ion is considered here as the first approximation. The observed repeating period along the chain axis 9.68 Å was used for the c axis, which is a little shorter for the ideally extended zigzag form of PVA chain. As already discussed in Figures 5 and 6, the diffuse meridional scatterings can be reproduced well using a columnar structure model consisting of randomly arrayed I3− ions. This situation

comparison was made also for the original PVA crystal (Figure 11b) to show the clear difference of the iodine complex effect on the X-ray diffraction pattern (refer to the crystal structures shown in Figure 9). Spatial Relation between PVA and Complex II. Figure 8 compares the X-ray diffraction end patterns between the original PVA and complex II. The planar-zigzag chains are packed in the unit cell of PVA crystal so that the intermolecular hydrogen bonds are formed between the chains positioned face-to-face within the unit cell along the 110 plane and also between the chains arranged along the b axis.49−52 As known from the observed end pattern, the original PVA takes a twin structure, in which the a (and b) axis orients in the 4 directions with the 2144

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Figure 13. Comparison of the observed X-ray equatorial line profile with that calculated for complex I model shown in Figure 14

Figure 12. Spatial relation of the crystal orientation between PVA and complex II derived from the X-ray end pattern shown here (refer to Figure 8).

hydrogen bond direction parallel to the rolled plane in all the crystallites (Figure 12a). On the other hand, the unit cell of complex II is found to orient so that the a axis is parallel to the rolled plane as known from the analysis of the end pattern. In this case also the twin structure is possible. Since the rolled plane is common to both of the original PVA and the complex II, we can conclude that the PVA zigzag chains rotate by about 38° around the chain axis in the formation process of complex II, as illustrated in Figure 12b. In this figure, the comparison of the observed X-ray end pattern is made again for understanding the structural relation between PVA and complex II more clearly. (3-4). Crystal Structure of Complex I. Basic Crystal Structure. In this section, we analyze the X-ray diffraction data of the complex I, which was prepared from the KI/I2 solution of relatively low-concentration of ca. 0.5 M. The equatorial line profile of complex I given in Figure 7 was analyzed starting from the structural model determined for the complex II, because these two diffraction profiles are similar to each other in the high 2θ region. The calculated X-ray diffraction profile was fitted to the observed profile by changing the unit cell size, the positions of planar-zigzag chains, the positions and occupancy of I3− and K+ ions as well as the crystallite size and crystalline strain. The results are as below: asub′ = 10.1 Å,

Figure 14. Crystal structure model of complex I derived from the X-ray data analysis in the higher angle region (refer to Figure 13). The relation of the unit cells between the smaller cell (a′sub and b′sub) and the super lattice (a′super and b′super) is also shown here.

equatorial profile between the observed and calculated ones for the complex I. The crystal structure model is shown in Figure 14, where K+ ions are neglected to avoid the complicatedness in the further discussion. Superlattice Structure Model of Complex I. The X-ray end pattern is useful for the consideration of the cell geometry. As seen in Figure 8 (b) we have to notice the existence of some reflection spots with lattice spacing of about 13 Å near the beam stopper. The observation of this diffraction peak was reported already by Choi et al. for the complex prepared from the relatively low concentration solution.34 However, a careful observation tells us one important point that the 13 Å reflection is not single but they can be detected in the two different directions (100 and 010 of the superlattice shown in the right-side picture of Figure 8 (b)) with slightly different 2θ values. Then the following unit cell parameters which satisfied all the observed diffraction spots including these low-angle spots:

bsub′ = 8.60 Å,

c(chain axis) = 9.68 Å,

asuper = 13.50 Å,

and γsub′ = 91.0°

bsuper = 13.90 Å,

and γsuper = 106.0°

As shown in Figure 14 these larger unit cell vectors asuper and bsuper can be correlated roughly to the above-mentioned smaller unit cell vectors (a′sub and b′sub), derived from the higher diffraction angle data, in the following approximate equations.

The subscript “sub” means a sublattice as will be explained later. The occupancy of C and O atom is 1.0 and 0.5, respectively. The I3− occupancy is 0.3. The temperature factor is 5 Å2. The crystallite size and lattice strain are 40 Å and 1.0%, respectively, in both of the a and b directions. Figure 13 shows the comparison of

a super = a′sub + b′sub , 2145

b super = a′sub − b′sub

(1a)

DOI: 10.1021/acs.macromol.5b00119 Macromolecules 2015, 48, 2138−2148

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Macromolecules The actually calculated values are asuper = 13.2 Å, bsuper = 13.4 Å, and γsuper = 85.4°, which are roughly closer to the abovementioned parameters obtained experimentally for the larger cell. The initial model of the super lattice was built up starting from the basic structure model shown in Figure 14. In this model the occupancy of iodine atoms 0.2 is quite low, suggesting that PVA chains might exist at the positions of iodine atoms instead. That is to say, we may build up a hybrid structure model between PVA and PVA−iodine complex. Some positions are occupied by the hydrogen-bonded PVA chain pairs and some other positions by PVA−iodine complex pairs. By changing the locations and orientations of these pairs as well as occupancy of K+ and I3− ions, the good structure model was searched. The finally obtained model is shown in Figure 15a. The fractional coordinates of the

Table 3. Fractional Atomic Coordinates of PVA−iodine Complex Ia atomsb

x

y

zc

occupancy

C1 O2 O3 C4 O5 O6 I3/K7 I3/K8 C9 O10 O11 C12 C13 O14 O15 C16

0.14 0.06 0.23 0.14 0.05 0.22 0.14 0.16 0.51 0.41 0.59 0.50 0.50 0.41 0.58 0.50

0.21 0.13 0.17 0.27 0.30 0.34 0.56 0.83 0.14 0.06 0.10 0.20 0.36 0.40 0.44 0.30

0.67 0.67 0.54 0.40 0.40 0.27 (0.88, 0.73, 0.59) /0.98 (0.89, 0.75, 0.61) /0.99 0.52 0.52 0.40 0.46 0.53 0.53 0.41 0.47

0.5 0.25 0.25 0.5 0.25 0.25 0.22 0.22 0.5 0.25 0.25 0.5 0.5 0.25 0.25 0.5

a

Unit cell parameters asuper = 13.5 Å, bsuper = 13.9 Å, csuper (fiber axis) = 19.36 Å, γsuper = 106.0°. Space group P21 bThe atoms of another asymmetric unit in the cell are given by a 21 screw symmetry operation along the c axis at (0.5, 0.5) position. cThe z coordinates of I3− and K+ may be changed depending on the model since the relative heights of these atoms are statistically disordered.

Figure 16. Comparison of the observed X-ray equatorial line profile with that calculated for complex I superlattice model shown in Figure 15.

assumed. The occupancy is 0.5 for C atoms, 0.25 for O atoms (atactic) and 0.22 for I and K atoms. Table 4 shows the comparison of lattice spacings and structure factors between the observed and calculated values. The R factor is 13.5%. The PVA chains form the columns along the bsuper axis and the PVA−iodine complexes also form the columns in parallel. As shown in Figure 8b, the reciprocal lattice vector asuper* is perpendicular to the rolled plane of the complex I sample, and so the real lattice vector bsuper axis is parallel to the rolled plane. This means that the PVA columns and the PVA−iodine columns are arrayed in parallel to the rolled plane. The pairs of PVA chains are considered to form the intermolecular hydrogen bonds along the bsuper axis judging from the O···O distance of about 3.2 Å, a little longer than 2.9 Å in the PVA crystal lattice itself. The oxygen atoms of PVA chains

Figure 15. (a) Crystal structure model of PVA−iodine complex I superlattice. The hydrogen-bonded PVA chains form the arrays along the b′super axis. The PVA−iodine complex forms also the arrays. The potassium ions are erased for simplicity. (b) One possibility of the local structure of the statistic structure of part a.

atoms are listed in Table 3. The comparison of X-ray diffraction profiles is made in Figure 16 between the observed and calculated ones, where the lattice size is 40 × 40 Å2 and 1% × 1% for the asuper and bsuper axes. The isothermal temperature factor 5 Å2 was 2146

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Macromolecules

(C) Structural Transition Model from PVA to Complex I and to Complex II. On the basis of the X-ray diffraction patterns measured for the uniaxially oriented and doubly oriented PVA, complex I, and complex II samples, we have clarified the spatial relation between these crystal structures. Figure 17 summarizes the illustrative explanation of the structural changes between these three phases. The molecular chains in the complex I orient almost in parallel to the rolled plane as similarly to that of PVA. Once when the iodine ions (and K+) penetrate into the PVA crystallite the PVA chains are shifted to make empty parts, into which the I3− ions (and K+) are trapped to form the complex. The PVA columns are still remained in the complex I. Some parts are not yet filled by the I3− ions. The total amount of trapped iodine ions is about 20%. The I3− ions are statistically randomly positions along the chain axis to give the horizontal streak lines. During these changes, the intermolecular hydrogen bonds between the neighboring PVA chains must be broken so that the PVA chains form the charge transfer complex with iodine (and K+) ions. (The preliminary investigation of infrared spectra revealed the shift of O−H stretching band toward the higher frequency side, suggesting the weakening of hydrogen bonds between PVA chains. Similar observation was made also in the complex formation process of aliphatic nylons with iodine ions.53−56 It may be necessary to study the change in intermolecular interactions in detail during the complex formation process.) By dipping the sample into a solution of higher concentration, about 70% of PVA chains form the complex II with I3− ions. Many positions in the complex I are occupied by many I3− ions to form the well-developed complex structure as a whole. At the same time, we notice that the zigzag chains in the complex II rotate ±38° around the chain axis. Such a reorientation of planarzigzag chains is considered to occur cooperatively over a wide range so that the degree of packing becomes higher and the total energy of the system is much lowered. In order to confirm the structural evolution in the complex formation process, we need to perform the energy calculation to clarify the transition route from PVA unit cell to the complex II via the complex I.

Table 4. Comparison of Lattice Spacing and Structure Factor of Equatorial Diffraction Peaks between the Observed and Calculated Values for PVA−iodine Complex I index

d(obs)

d(calc)

|F(obsd)|a

|F(calc) |

100 020 300 14̅0, 230, 040 330, 440, 240 540, 45̅0, 600

13.67 6.71 4.30 3.29 2.70 2.35

13.05 6.68 4.46 3.30 2.71 2.42

52.4 81.8 264.1 88.5 78.1 89.1

49.8 89.9 273.2 65.6 64.4 57.1

The observed structure factor |Fobs| was evaluated from the integrated intensity Iobs of a diffraction spot using the equation Iobs = kALp|Fobs|2, where L, p, A, and k are the Lorentz factor, polarization factor, absorption coefficient, and scale factor, respectively. The intensity integration of an individual peak was made after the curve separation of the observed X-ray diffraction profile shown in Figure 16. a

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CONCLUSIONS In the present paper, the crystal structures of PVA−iodine complexes have been analyzed quantitatively on the basis of X-ray diffraction patterns taken for uniaxially and doubly oriented samples dipped into the KI/I2 aqueous solutions of the various concentrations. The complexes were found to exist as two types, complex I (0.5−1M) and complex II (1−3M). In the complex II, iodine and potassium ions are sandwiched by PVA chains through the charge transfer mechanism. Complex I shows a superlattice consisting of statistically random distribution of domains with and without the occupation by I3− (and K+) species. The X-ray end pattern taken for the doubly oriented sample revealed the geometrical relation of the basic unit cells between PVA and these complexes. The complex I contains both of PVA columns and PVA−iodine complex columns alternatively and so it is assumed as an intermediate phase in the transition process from PVA to complex II. Once the complex II is formed, the zigzag PVA chains are rotated by 38° around the chain axis cooperatively. The transition from PVA to complex I and complex II occurs gradually as known from the length of dipping time of the sample into KI/I2 aqueous solution, but these phases are coexistent during this process, indicating that these transitions occur in a discontinuous way, in other words, they are of the thermodynamically

Figure 17. Spatial relation between PVA, complex I and complex II. The twin structures are shown here. (a) PVA: the planar-zigzag planes are parallel to the rolled plane. The intermolecular hydrogen bonds are formed between these chains. (b) Complex I: the PVA chains and PVA− I3 complex form the arrays arranged in a statistically disordered manner. The PVA chains are shifted in the lateral directions from the original positions to create the voids or complex with iodine species. (c) Complex II: the molecular chains rotate about 38° from the original direction when the complex formation is almost completed.

are linked with iodine atoms at about 4.7 Å distance, which is almost the same as that of complex II (4.9 Å). (Of course these distances might change more or less depending on the relative height of PVA and iodine chains.) In other words, the complex I may be assumed as a superlattice between PVA arrays and PVA− iodine arrays with statistically disordered arrangement. The concrete image of a local structure with the statistical disorder taken into account is illustrated in Figure 15b. Such a statistical disorder can be said also about the relative height of neighboring chains to give the streak lines in the 2D X-ray diffraction image. 2147

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Macromolecules first-order type. The time-dependent measurement of the X-ray diffraction or the kinetic data collected during the transition at the various temperatures may reveal the motivating force of the transition clearly. In such a discussion, it must be noticed that the formation of these complexes is affected sensitively by the various factors.3−24 For example, in the present paper the contribution of K+ ion is not discussed in detail, although this ion must be coexistent with iodine ions necessarily to neutralize the total system as shown in Figure 9. In another experiment, we have found that the structure of the PVA−iodine complex is affected by changing the counterion. The study about these various factors governing the complex formation process will be reported in a separate paper.

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AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was financially supported by a MEXT “the International Project on the Basic Research Promotion for the Development of Highly-Controlled Multi-Purpose Polymer Materials” in “the Strategic Project to Support the Formation of Research Bases at Private Universities” (2010−2014).

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DOI: 10.1021/acs.macromol.5b00119 Macromolecules 2015, 48, 2138−2148