Electron microscopic observations of inclusion complexes of α-, β-, and γ-cyclodextrins

Polymer 45 (2004) 6967–6975 www.elsevier.com/locate/polymer

Electron microscopic observations of inclusion complexes of a-, b-, and g-cyclodextrins Machiko Ohmura, Yukiko Kawahara, Keiko Okude, Yasuko Hasegawa, Minoru Hayashida, Ryota Kurimoto, Akiyoshi Kawaguchi* Department of Applied Chemistry, Faculty of Science and Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan Received 19 April 2004; accepted 28 July 2004 Available online 14 August 2004

Abstract Inclusion complexes of a-, b-, and g-cyclodextrins (a-, b-, and g-CyDs) were prepared with poly(ethylene oxide) (PEO), poly(propylene oxide) (PPO), and poly(ethylene adipate) (PEA), respectively. By observing respective inclusion complexes by transmission electron microscopy, it was found that the crystalline complexes grew as follows: (1) a-CyD–PEO complexes formed a hexagonal crystal, (2) b-CyD– PPO complexes crystallized with hexagonal lateral packing of molecular columns with their axes tilted at the basal plane, and (3) g-CyD– PEA crystallized in a tetragonal form with a super lattice with cell dimensions aZbZ13.40 nm, which consisted of sub-cell with cell dimensions a 0 Zb 0 Z1.657 nm. No diffuse scattering was observed in the electron diffraction pattern of complexes of a-CyD–PEO and bCyD–PPO, because disordering of guest molecules within host channels gave no diffuse scattering as long as host molecules were arrayed in an ordered way. g-CyD–PEA complexes gave characteristic streaky diffuse scattering along a* and b*. Stacking faults occurred in g-CyD– PEA complexes. q 2004 Elsevier Ltd. All rights reserved. Keywords: Cyclodextrin; Electron microscopy; Diffuse scattering

1. Introduction A vast number of inclusion complexes of cyclodextrins with simple molecules have been investigated. In such research, Harada and Kamachi first found that a-cyclodextrin (a-CyD) formed an inclusion complex with a polymer: poly(ethylene oxide) (PEO) [1], in which a-CyD was threaded with PEO to form a so-called molecular necklace [2]. Since then, many reports have been published on inclusion complexes of a- [4–12,14,16–18,20], b- [3,5,9,11] and g- [3,5,7,10,11,13–15,19] CyDs in combination with various polymers. In some studies, their structure or conformation of included guest molecules in cyclodextrin hosts was studied, mainly by NMR, IR, X-ray diffraction, and so on. There are a few detailed crystal structure analyses of CyD complexes by X-ray diffraction, involving host * Corresponding author. Tel.: C81-77-566-1111; fax: C81-77-5612659. E-mail address: [email protected] (A. Kawaguchi). 0032-3861/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2004.07.063

cyclodextrins and guest polymers; a-CyD with ethylene oxide oligomer [21], and b-CyD with poly(propylene glycol) [22,23]. It is very difficult to obtain a single crystal of inclusion complex of CyD with polymeric chains, large enough for X-ray structural analyses. In many cases, peculiar techniques were used to form the inclusion complexes with polymers, and hence very small crystallites grew: in some case, inclusion complexes were formed quickly as soon as two solutions of cyclodextrin and polymer were mixed [1], and in another case, the crystallization was carried out under external force, e.g. by ultrasonic agitation [7]. Even though inclusion complex crystals are tiny, transmission electron microscopy (TEM) has the advantage that diffraction technique can be applicable to structural investigation of small single crystals of inclusion complex. The scanning tunneling microscopic (STM) technique, which is very powerful to investigate the nano-scale structure of materials, has been applied to visualize the aggregation behavior of inclusion complexes of a-, b-, and g-CyDs, i.e. the molecular necklace or

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nanotube structure [24]. However, TEM is preferable to STM for studying crystal structure and molecular orientation in crystals. Thus, the results obtained by transmission electron microscopy are described here, focusing on the crystal structure of inclusion complexes of a-, b-, and gCyDs with polymeric chains.

2. Experiments According to the procedure in Ref. [1], an inclusion complex of a-CyD with poly(ethylene oxide) (PEO) was prepared by mixing respective solutions of both compounds in water. The molecular weight of PEO was 2000. The precipitated crystals were filtrated, and subsequently the residue was washed out with water to remove the unreacted materials. Inclusion complexes of b-CyD with poly(propylene glycol) (PPO), of molecular weight 1000, were made according to the method in Ref. [5]. Five milliliter of PPO was added to a 0.1 M solution of b-CyD in water, and the mixture was stirred for 12 h at 50 8C. The crystalline precipitates were filtrated, followed by washing with tetrahydrofuran, to remove unreacted PPO. Complexes of g-CyD with poly(ethylene adipate) (PEA) were prepared according to the procedure in Ref. [7]. PEA was dissolved in water at about 50 8C with ultrasonic stirring. An excess of a saturated solution of g-CyD in water was added to the PEA solution. Precipitated crystals were collected by filtration and washed with water, to remove unreacted g-CyD. In all of the above cases, the crystalline inclusion complexes in suspension were filtered onto a poly(tetrafluoroethlene) filter paper and washed with the used solvent at the final step. The remaining paste-like residue was again dispersed in water, to prepare specimens for electron microscopy. The crystalline complexes thus prepared were put on a copper grid covered with a thin carbon film, and they were observed using a JEM 100C transmission electron microscope. For X-ray diffraction work, the residue was dried. a-, b-, and g-CyDs, PEO, and PPO were purchased from Wako Chemicals Co. Ltd and were used as received. PEA was synthesized as described in Ref. [7] and was used as prepared without fractionation. We speculated, from the data in Ref. [7], that the molecular weight ranged from 230 to 2400, although it was not measured.

3. Results 3.1. X-ray diffractions Fig. 1 shows wide-angle X-ray diffraction powder patterns of a-, b-, and g-CyD inclusion complexes prepared as described in Section 2.

Fig. 1. Wide angle X-ray powder patterns of inclusion complexes of (a) aCyD–PEO, (b) b-CyD–PPO, and (c) g-CyD–PEA.

3.2. a-Cyclodextrin complex Fig. 2a and b, respectively, show an electron diffraction (ED) pattern of an a-CyD–PEO complex, and an electron micrograph (EM) corresponding to it. The ED has a definite hexagonal symmetry. The ED pattern is appropriately indexed based on the projected, hexagonal unit cell with cell dimensions aZbZ1.373 nm and gZ1208 [1]. The reflection indicated with an arrow in the X-ray diffraction pattern in Fig. 1a has a lattice spacing of 1.65 nm. It cannot be indexed as an hk0 reflection based on the above unit cell. Here, by indexing it as the 001 reflection, all reflections are appropriately indexed. The hexagonal unit cell parameters are shown in Table 1. The c axis dimension corresponds to

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Fig. 2. (a) Electron diffraction pattern and (b) the corresponding electron micrograph of a-CyD–PEO crystal. By setting the a* and b* axes as in (a), the hexagonal unit cell is constructed.

the height of two a-CyD rings, which are stacked into the channel type by head-to-head or tail-to-tail adjustment. Since the crystalline system is hexagonal, a-CyD–PEO complexes should be expected to crystallize in a hexagonal shape. Usually, a-CyD–PEO complex crystals grew in irregular shapes without facets. In the procedure adopted in the present work, crystals grew so quickly that an energetically stable hexagonal shape was not achieved. Fig. 2b shows an example of a rather well-faceted crystal, exhibiting the hexagonal morphological feature. The diagonal of the ‘hexagon’ corresponds to the h100i direction of the present unit cell. Crystal structure analysis of an a-CyD inclusion complex with oligomeric PEO was carried out [21]. The crystal structure is monoclinic, and a-CyD rings are stacked to form columns in the channel type by head-to-head or tail-to-tail adjustment, including PEO molecules inside their cavity channel. The columnar molecules are slightly oblique at the basal plane. Usually, when such columnar molecules with an oblique crystal structure are aggregated into a crystalline

platelet, the basal surface of the platelet could be the (001) plane if the platelet has a thermodynamically stable form. In normal alkanes with the monoclinic form, platelets are normally formed in such a way, as molecular chains are oblique at the basal plane. In some cases, however, the platelets often grow as if molecular chains are arranged seemingly perpendicular to their platelet surface. This is caused by a roof structure: though the chain axes are oblique to the platelet surface everywhere, some parts of platelets are tilted, forming a roof, thereby retaining a oblique structure, and resultantly, chain axes stand seemingly normal to the platelet surface [25]. If the inclusion complexes could crystallize in the form of a roof shape, a hexagonal ED pattern might be produced, because inclusion complex columns are packed laterally in a hexagonal arrangement [21]. However, judging from the distinguished, highly symmetric ED pattern in Fig. 2a, it is unlikely that the hexagonal symmetry results from such a complicated crystalline morphology. Further, it was found that hexagonal modification is formed in the inclusion

Table 1 Lattice parameters of a-, b- and g-cyclodextrin complexes

a-Cyclodextrin

b-Cyclodextrin

g-Cyclodextrin (sub-cell)

c (nm)

a (8)

1.373

1.68

90

1.39 3.6891 1.59a

1.39 2.388 1.59a

1.56 2.3341

90 90

1.9332 1.8726 1.513 1.53 13.40

2.4572 2.4475 1.555 1.53 13.40

1.5961 1.5398 3.034

1.657 1.688

1.657 1.688

a (nm)

b (nm)

1.373

Host: PEO in Refs. [1,10,16]; PPO in Refs. [8,9,12]. a For projected two-dimensional cell.

2.313

b (8)

g (8)

System

90

120

Hexagonal

90 123.084

120 90

Hexagonal Monoclinic

[1] [10]

90 90 90

109.0 110.5 90

90 90 105.94

[8] [9] [12] [12]

90

90

90

Monoclinic Monoclinic Monoclinic Hexagonal Tetragonal

90 90

90 90

90 90

Tetragonal Tetragonal

Ref.

[16]

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Fig. 3. (a) Electron diffraction pattern and (b) electron micrograph of b-CyD–PPO. An encircled crystal in (b) corresponds to the electron diffraction pattern in orientation.

complex of a-CyD with simple molecules [26]. Considering these findings, it is natural to conclude that an a-CyD–PEO complex has a hexagonal form [1]. In the sample used for structural analysis on the crystalline complexes [21], the guest molecules are ‘oligomers’ with three constituent units, while PEO, with a molecular weight of 2000; i.e. the degree of polymerization of w45, was used in the present work. The molecular length of guest molecules might affect the crystalline structure. 3.3. b-Cyclodextrin complex Fig. 3 shows an ED pattern and the corresponding EM of inclusion complexes of b-CyD with PPO. In most EDs, only a pair of spots, with lattice spacing of 0.489–0.498 nm, which are indicated with an arrow in Fig. 3a, were observed. Clearly, such ED patterns were produced by a tilted crystal. The net ED in Fig. 3a happened to be observed. The hexagonal net is set up as seen in Fig. 4. The crystal structure of b-CyD–PPO complex has been analyzed [22,23,27,28]. The crystal structures of these references are quite similar, being monoclinic with a unique angle, bZ109–1108. We shall first examine the ED of Fig. 3a based on these crystal structures, assuming that the platelets were formed with the (001) basal plane; i.e. the columnar axes of complexes are tilted at the basal plane. When such a single crystal is deposited on carbon film for electron microscopy, usually only a few reflections should be observed in ED. When a pair of reflections is observed, it is clear that the columnar axes of inclusion complexes are basically tilted at the basal platelet surface. Here, we shall examine the ED in Fig. 3a as an hk0 net pattern that could be obtained when the incidence of electron beams is nearly parallel to the c axis of the unit cell. Then, the arrowed strong spot is indexed as 050 or 330 diffraction from the lattice spacing, i.e. 0.489–4.98 nm. However, even though the spot of interest could be indexed in such a way, the hk0 net pattern that is produced by the parallel incidence of electron beams to the c axis is never compatible with the actually observed hexagonal net pattern in Fig. 3a.

Alternatively, we also examined another case with the incidence of electron beams not parallel to the c axis; in this case, the strong diffraction spot of interest could be indexed as an hkl reflection with ls0. There are hkl reflections with l of 4–6, with lattice spacing of 0.489–0.498 nm. However, a hexagonal net pattern is never constructed, even if the incidence of electron beams could be coincident to any zone axis. Clearly, the electron diffraction pattern has a hexagonally symmetric feature. As represented schematically in Fig. 4, a hexagonal reciprocal lattice is constructed readily. Thus, we conclude that the columnar inclusion complexes could be packed side-by-side hexagonally, staggered successively in the direction parallel to the columnar axis. Here, the twodimensional unit cell, with projected a 0 and b 0 cell dimensions on the plane perpendicular to the c axis, is obtained as shown in Table 1. Based on the two-dimensional unit cell, the intense spot of interest is indexed as a 210 reflection. It has been reported that two kinds of inclusion complexes are formed out of b-CyD and PPO: complexes A

Fig. 4. Schematic drawing of the electron diffraction pattern, and the orientational relationship between the ED and an inclusion complex crystal in Fig. 3.

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Fig. 5. (a) Electron diffraction pattern and (b) the corresponding electron micrograph of g-CyD–PEA. The electron diffraction pattern was produced from the selected area by a dark disc.

and B [27,28]. Inclusion complexes are not formed of bCyD and guest molecules only; rather, water molecules are incorporated in them. The two crystalline forms are due to the difference in the number of water molecules included in the complexes: six for form A, and two for form B. It was also reported that, when complex A lost water molecules on annealing, the crystal structure was transformed into mesomorphic complex B. Complex B forms a columnar mesophase with hexagonal packing of b-CyD columns. As the present electron microscopic work was carried out in a vacuum, there is a possibility that water molecules could have been lost, and consequently, the mesomorphic phase with a hexagonal molecular arrangement could be formed. The crystalline shape is a lozenge or parallelogram, as seen in Fig. 3b [27]. The ED and a single crystal encircled in Fig. 3 are correctly disposed in orientation. The side planes are the (110) and (010) planes, as sketched in Fig. 4, and the acute angle of the parallelogram is about 678. 3.4. g-Cyclodextrin complex Fig. 5a and b shows the ED pattern of a g-CyD–PEA inclusion complex crystal, and its corresponding morphology, respectively. The ED pattern is a tetragonal net pattern, and correspondingly, the crystal shape is also tetragonally symmetric. From the ED of Fig. 5a, we know that the unit cell is tetragonal with large cell dimensions aZ bZ13.40 nm. In the a* and b* reciprocal axes, every eight h00 and 0k0 reflections are observed with high intensity. Spotty h00 and 0k0 reflections belonging to the super-lattice are also observed weakly (see the arrowed 900 spot in the ED of Fig. 7). This means that the super lattice basically comprises the tetragonal sub-cell, with a 0 Zb 0 Z1.657 nm. It is very interesting that the size of the sub-cell is large enough to involve a g-CyD ring [29,30]. A crystal structure of an inclusion complex with a cell size similar to that of the sub-cell was reported [31], as shown in Table 1. The reflection with a lattice spacing of 0.78 nm, as indicated

with an arrow in Fig. 1c, corresponds to the 003 reflection [31]. No diffraction peaks corresponding to 001 and 002 reflections are observed. Thus, since information on 00l reflections lack and moreover indexing is quite ambiguous because of the super lattice unit cell, it is very difficult to determine the c dimension of a unit cell from the Debye Sherrer X-ray diffraction pattern only, even though the a and b dimensions are known. At the present time, as reflection corresponding to 003 reflection is observed, we speculate that a c axis dimension of 2.34 nm is possible. In the super lattice, eight CyD–PEA molecular complexes that are different in kind and/or orientation can be aligned within the unit length along both a and b axis directions, respectively. Totally, 8!8 molecules are contained in the super lattice cell. The number 8 is very important, because a g-CyD molecule has a quasi 8-fold rotational axis perpendicular to the ring-containing plane [29,30]. How can eight molecules with 8-fold rotational symmetry be disposed in the unit cell length along a and b axes, respectively? One possible answer is as follows: The 8-fold rotational symmetry of g-CyD is destroyed by including poly(ethylene adipate) (PEA) as a guest in its channel. There are 8 equivalent positions in a g-CyD channel where included guest molecule(s) can be disposed. A PEA molecule or a double strand of molecules [7,14,31] could occupy one of the eight positions, and hence eight different configurations of an inclusion complex could be brought about with respect to the orientation of a guest molecule. However, if an included molecule or a double strand of molecules has any kind of symmetry in its projection onto the ring-containing plane of g-CyD, the number of different molecular configurations is reduced. Thus, the following is further needed to understand the present ED: a PEA guest molecule or its double strand should be asymmetric in the projected conformation onto its ring-containing plane of g-CyD. The super-lattice may be set up only when the eight different inclusion complexes, which fulfil the above configurational requirement, are

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arranged in an orderly way. In inclusion complexes of g-CyD with PEO, a unit cell corresponding to the present sub-cell of g-CyD with PEA is reported [31]. Included PEO molecules might have a highly symmetrical conformation in the channel cavity. As mentioned above, however, the present diffraction pattern should be interpreted based on the super lattice.

4. Discussion The diffraction patterns of Figs. 2a and 3a are very spotty up to a high order of reflection, and no diffuse and/or streaky scattering is observed. The sharp diffraction feature of Fig. 2a suggests that a-CyD molecules, including a guest molecule, should be arranged in an ordered way. A single guest molecule is incorporated in an a-CyD host channel of a-CyD–PEO complex [1]. Roughly speaking, an a-CyD host molecule has a hexagonal rotational symmetric axis perpendicular to its ring-containing plane. There are six positions to which the guest molecule could be disposed within the channel of an a-CyD host. In reality, the guest molecule can occupy any one of the positions. When a host molecule includes a guest molecule, the hexagonal symmetry may be broken. Further, the orientation of a guest molecule within the host channel changes from host to host molecules over the whole crystal, and diffuse scattering should be expected to be produced due to the incoherent array of included guests. However, no appreciable diffuse scattering is observed in Fig. 2a, or in Fig. 3a as well. Diffuse scattering of the inclusion complex of urea, which incorporated polyethylene and paraffin within its cavity, was discussed in detail by Yokoyama [32]. The diffuse scattering intensity for such a disordered system of an inclusion complex is given by the following equation: I1 ðSÞ Z hjFG ðSÞj2 i K jhFG ðSÞij2

(1)

as detailed in Appendix A. Now, let us consider the diffuse scattering intensity in the case of a-CyD inclusion complex. As one inclusion complex is involved in the unit cell, the above theoretical treatment is readily applied to this system. Three types of orientational disorder can be considered, as shown in Fig. 6. 1. For case I of free rotation of guest molecule within the host channel, HkZJ0(2piRrk) and Hkk 0 ZJ0(2pRrkk 0 ),

Fig. 6. Orientational model of a guest molecule within a host channel of aCyD: (a) free rotation, and discrete disorientations with (b) rZp/6 and (c) rZ0.

where rkk 0 ZjrkKrk 0 j [38]. J0 is the 0th order of Bessel function. In the present inclusion complexes, free rotation of molecules could hardly be considered. 2. For cases II and III, sine terms are diminished in Eqs. (A7) and (A8). When the projection of the guest molecule is symmetric, it is evident. Even though the molecular projection is asymmetric, the sine terms are cancelled out, because the guest molecule can take two conjugated orientations with opposite directions (see Fig. 6). Thus, for discrete orientation of a guest molecule within a host Hk Z

n


p  1X ðm K 1Þ C r cos 2pRrk cos J K n mZ1 n

(2) and Hkk 0 Z

n X n


p   1 X ðm K 1Þ C r cos 2pRrk cos J K 2 n n mZ1 m 0Z1




p  m 0 K 1Þ C r !cos 2pRrk cos J K n (3) In these equations, n denotes the number of orientations in which a guest molecule can occupy within a host, and r is p/6 for case II, and 0 for case III. When the projection of the guest molecule has the point symmetry with respect to the center of the host, the number n is half. nZ3 for a symmetric guest within the hexagonal host, and nZ6 for an asymmetric case, as shown in Fig. 6. For a PEO guest of an a-CyD–PEO inclusion complex, the symmetric case is probable if it could take a nearly planar conformation. In both cases of II and III, Hkk 0 is substantially equal to Hk Hk
; where Hk
is the conjugate complex of Hk. Consequently, the diffuse scattering intensity becomes diminished. For bCDy-PPO and g-CyD–PEA, n is 7 and 8, respectively. The fact that diffuse scattering is weak in these complexes can be understood similarly. Thus, a spotty diffraction pattern without diffuse scattering can be observed as long as host molecules are arrayed regularly, as in Figs. 2a and 3a, even if guest molecules occupy randomly any discrete orientational position within the host channel [32]. The electron diffraction pattern of g-CyD–PEA in Fig. 5a exhibits further interesting features in addition to the superlattice: (1) the h00 or 0k0 reflections are spotty; (2) some off-axial reflections are extended in the direction parallel to the a* or b* axes and fused into a streaky scattering, e.g. 4 24 0 and 5 24 0 reflections; (3) consequently, some diagonal reflections are observed in the shape of an extended diffuse cross, e.g. 880 reflection (see Fig. 7). As discussed above, diffuse scattering is not produced when guests molecules randomly occupy any discrete orientational position within the columnar host channels, as long as hosts are arrayed in an ordered way. The feature (1) mentioned above proves, thus, that columnar g-CyD

M. Ohmura et al. / Polymer 45 (2004) 6967–6975

Fig. 7. Electron diffraction pattern of g-CyD–PEA, patched with the interference function pattern that was computed with D11 and DD12 of 10K3a and 0.01a, respectively, and D21 and D22 of 0.01b and 10K3b, respectively. a and b denote the unit cell length of super lattice in the x and y directions,  reflection of the computed interference function is respectively. The 880 indicated by an arrow. The spot indicated with an arrow in ED corresponds to the 900 reflection of the super lattice. Some part of the interference function is cut out to avoid confusion.

inclusion complexes are regularly arranged in an ordered way, independently of the orientation of guest molecules. A disordered structure, which has an intermediate degree of ordering of guest molecules between the regular array as in the super lattice and the random orientation within the host channels, is speculated. Some reflections due to the super lattice become broad for the disordered structure, depending on the characteristic of the disorder. How can the disorder of guest molecules arise? Streaky extended diffuse scattering was observed, selectively and systematically, on hk0 reflections in syn-polystyrene [33] and syn-polypropylene single crystals [34–36]. This diffraction phenomenon is explained in terms of stacking faults of the extended molecular array [33,35,36]. When stacking disorder takes place frequently, it leads to streaky diffuse scattering. Thus, to explain the streaky scattering in Fig. 5, it is necessary, as a solution, to introduce the idea that host molecules themselves are disordered in stacking. The streaky reflections of syn-polystyrene and syn-polypropylene single crystals are extended in one direction only. In the present electron diffraction pattern of Fig. 5, reflections are extended in both a* and b* directions. It is evident that stacking faults should occur in the x and y directions. It is considered that a kind of net distortion could be formed when such stacking faults occur in the two directions. According to the paracrystalline theory [37,38], we shall consider scattering of a system of molecules with a net distortion. Fig. 7 shows an ED pattern of g-CyD–PAE, patched with the two-dimensional interference function computed by the paracrystalline theory [38]. In Fig. 7, the computed interference function is superposed on an ED that differs from that in Fig. 5a and emphasizes the abovementioned features. The magnitudes of the following lattice

6973

distortion parameters affect the features of the interference function: distant fluctuations D11 and D22 between neighboring molecules, and the angular deviations D12 and D21 of neighboring scattering units in the x and y axes, respectively. The total scattering intensity is expressed by the product of the interference function with the structure factor of molecular complex. Most reflections that should be indexed to the super lattice disappear in the actual electron diffraction pattern, perhaps due to weak structure factors. However, since the diffraction profile is basically formed by the interference function, it is not always required to know them only to survey the diffraction features. The computed interference function reproduces, partly, the characteristic diffuse scattering: the streaky scattering along the a* and b* axes by fusion of extended scatterings in these directions,   e.g. the fused 4240 and 5240 reflections, and the crossed  diffuse off-axial and diagonal scatterings, e.g. the arrowed 880 reflection. However, though the h00 and 0k0 reflections are spotty in a real ED (see Fig. 7), they are extended in the directions parallel to b* and a* axes in the simulated pattern, respectively. This discrepancy implies that the crystalline disorder attributed to streaky scattering should not be explained well based on the paracrystalline net distortion model. To simulate the diffraction features in Figs. 5a and 7, the stacking fault model, as adopted in Refs. [33,35,36], should be applied to the two-dimensional case. But for that, the crystal structure must be known, so it should be analyzed first. The lattice parameters of a-, b-, and g-CyD complexes obtained by the present work are listed in Table 1, together with results by other researchers. There is a possibility that the inclusion complexes could not be composed of CyD hosts and polymer guests only, but water or other solvent molecules could be involved in the crystal formation. As pointed out in Refs. [28,31], the degree of water content affects the crystalline modification and the crystalline disorder. To explain the super lattice of g-CyD–PEA complex, a disorientational model of guest molecules within host channel is put forward here. However, the crystalline structures, modifications, and the disordered structures should be examined considering the contribution of water molecules or other solvent to the crystal formation.

Acknowledgements This work was partly supported by a Grant-in-Aid for Scientific Research on Priority Areas: ‘Mechanism of Polymer Crystallization’ (No. 12127207), and partly by the High Technology Research Project 2001, from the Ministry of Education, Culture, Sports, Science, and Engineering.

Appendix A. Diffuse scattering The general formula for scattering from an assembly of

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molecules is XX IðSÞ Z Fj ðSÞFk ðSÞexpð2piðSrjk ÞÞ j

(A1)

k

jth atom in the host and a kth atom of guest molecules. The structure factor for a guest molecule of present interest is X fG;k expð2piðS$rk ÞÞ (A5) FG ðSÞ Z k

where F(S) is the structure factor of a molecule, S is a scattering vector, and rjk is the intermolecular vector between jth and kth molecules. When molecules are displaced and/or disoriented from their regular lattice points, the observed scattering intensity is expressed by the averaged intensity over the whole system of molecules, as follows [37,38]: 2

2

IðSÞ Z NðhjFðSÞj i K jhFðSÞij Þ C LðSÞjhFðSÞij

Now, let us introduce the cylindrical coordinate systems; that is, r, j, and z for the real space, and R, J, and Z for the reciprocal space. Eq. (A5) is rewritten in the cylindrical coordinate system in the following way: X FG ðSÞ Z fG;k expð2piðZzk C Rrk cosðJ K ðjk C rÞÞÞ k

(A6)

2

Z I1 ðSÞ C I0 ðSÞ

(A2)

where L(S) is the Laue function, and N is the number of molecules. I0(S) and I1(S) denote the Bragg diffraction and the diffuse scattering, respectively. The structure factor of an inclusion complex is described by the sum of those of host and guest molecules: F(S)Z FH(S)CFG(S), where FH(S) and FG(S) stand for the structure factors of host and guest molecules, respectively, and suffices H and G denote the host and guest molecules, respectively. Here, we assume that host molecules are disposed regularly at the lattice points while guest molecules are disordered, taking the irregular orientation inside the host channel. The following equations hold for averaged scattering for the disordered system of molecular complexes: hjFðSÞj2 i Z jFH ðSÞj2 C hjFG ðSÞj2 i C hFG ðSÞiFH
ðSÞ C hFG
ðSÞiFH ðSÞ

By averaging with respect to j, X hFG ðSÞij Z fG;k expð2piZzk ÞHk

(A7)

k

where Hk Z hexpð2piRrk cosðJK ðjk C rÞÞÞij : The mean square of structural factor with respect to j is given as follows: XX hjFG ðSÞj2 ij Z fG;k fG;k 0 expð2piRzkk 0 ÞHkk 0 (A8) k

k0

where Hkk 0 Z hexpð2piRrk cosðJ K ðjk C rÞÞÞ !expðK2piRrk 0 cosðJ K ðjk 0 C rÞÞÞij In the two-dimensional a*–b* reciprocal space, which corresponding to the present ED pattern, Eqs. (A7) and (A8) are reduced into (A9) and (A10), respectively, by setting ZZ0. X fG;k Hk (A9) hFG ðSÞij Z k

and

hjFG ðSÞj2 ij Z

jhFðSÞij2 Z jFH ðSÞj2 C jhFG ðSÞij2 C hFG ðSÞiFH
ðSÞ

XX k

fG;k fG;k 0 Hkk 0

(A10)

k0

C hFG
ðSÞiFH ðSÞ; where the symbol hi means an average. From these relations, we get the following diffuse scattering expression: I1 ðSÞ Z NðhjFðSÞj2 i K hFðSÞij2 Þ Z NðhjFG ðSÞj2 i K jhFG ðSÞij2 Þ:

References (A3)

From this relation, we see that diffuse scattering should originate only from disordering of guest molecules. The structure factor of an inclusion complex is expressed by the equation: X FðSÞ Z fH;j expð2piðS$rj ÞÞ

[1] [2] [3] [4] [5] [6] [7]

j

X C

fG;k expð2piðS$rk ÞÞ

(A4)

k

where fH,j and fG,k denote the atomic scattering factors of a

[8] [9] [10] [11]

Harada A, Kamachi M. Macromolecules 1990;23:2823–4. Harada A, Kamachi M. Nature 1992;356:325–7. Harada A, Li J, Kamachi M. Macromolecules 1993;26:5267–8. Harada A, Li J, Kamachi M. Macromolecules 1994;27:4538–43. Harada A, Okada M, Li J, Kamachi M. Macromolecules 1995;28: 8406–11. Harada A, Kawaguchi Y, Nishiyama T, Kamachi M. Macromol Rapid Commun 1997;18:535–9. Harada A, Nishiyama T, Kawaguchi Y, Okada M, Kamachi M. Macromolecules 1997;30:7115–8. Huang L, Allen E, Tonelli AE. Macromolecules 1998;20:4857–65. Huang L, Allen E, Tonelli AE. Polymer 1999;40:3211–21. Lu J, Shin ID, Nojima S, Tonelli AE. Polymer 2000;41:5871–83. Okumura H, Okada M, Kawaguchi Y, Harada A. Macromolecules 2000;33:4292–8.

M. Ohmura et al. / Polymer 45 (2004) 6967–6975 [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]

Huh KM, Ooya T, Sasaki S, Yui N. Macromolecules 2001;34:2402–4. Wei M, Tonelli AE. Macromolecules 2001;34:4061–5. Lu J, Mirau PA, Tonelli AE. Macromolecules 2001;34:3276–84. Porbeni FE, Edeki EF, Shin ID, Tonelli AE. Polymer 2001;42: 6906–12. Rusa CC, Luca C, Tonelli AE. Macromolecules 2001;34:1318–22. Pozuelo J, Mendicuti F, Saiz E. Polymer 2002;43:523–31. Rusa CC, Bullions TA, Fox J, Porbeni FE, Wang X, Tonelli AE. Langumuir 2002;18:10016–23. Li J, Yan D, Jiang X, Chen Q. Polymer 2002;43:2625–9. Huh KM, Tomita H, Ooyama T, Lee WK, Sasaki S, Yui N. Macromolecules 2002;35:3775–7. Harada A, Li J, Kanachi M, Kitagawa Y, Katsube Y. Carbohydr Res 1998;305:127–9. Kamitori S, Matsuzaka O, Kondo S, Muraoka S, Okuyama K, Noguchi K, Okada M, Harada A. Macromolecules 2000;33:1500–2. Udachin KA, Wilson UD, Ripmeester JA. J Am Chem Soc 2000;122: 12375–6. Ohira A, Sakata M, Taniguchi I, Hirayama C, Kunitake M. J Am Chem Soc 2003;125:5057–65. Keller A. Phil Mag 1960;6:329–43. Noltemeyer M, Saenger W. J Am Chem Soc 1980;102(8):2710–22.

6975

[27] Panova IG, Matukhina EV, Popova EI, Gerasimov VI, Topchieva IN. Polym Sci Ser A 2001;43:771–7. [28] Popova EI, Topchieva IN, Zhavoronkova EV, Panova IG, Matukhina EV, Garasimov VI. Polym Sci Ser A 2002;44:72–6. [29] Ding J, Steiner T, Saenger W. Acta Cryst 1991;B47:731–8. [30] Steinger T, Saenger W. Acta Cryst 1998;B54:450–5. [31] Panovia IG, Gerasimov VI, Kalashnikov FA, Topchieva IN. Polym Sci Ser B 1998;40:415–9. [32] (a) Yokoyama F, Monobe K. Polymer 1983;24:149–54. (b) Yokoyama F. Dissertation. Kyoto University; 1986 [33] Tsuji M, Okihara T, Tosaka M, Kawaguchi A, Katayama K. MSA Bull 1993;23(1):57–65. [34] Lovinger AJ, Davis DD, Lotz B. Macromolecules 1991;24:552–60. [35] Lovinger AJ, Lotz B, Davis DD, Padden Jr FJ. Macromolecules 1993; 26:3494–503. [36] Hamada N, Tosaka M, Tsuji M, Kohjiya S, Katayama K. Macromolecules 1997;30(22):6888–92. [37] Hosemann R, Bagchi SW. Direct Analysis of Diffraction by Matter. Amsterdam: North-Holland; 1962. [38] Vainshtein BK. Diffraction of X-rays by chain molecules. Amsterdam: Elsevier; 1966.