Crystal Structure of Poly(lactic acid) Stereocomplex: Random Packing

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Crystal Structure of Poly(lactic acid) Stereocomplex: Random Packing Model of PDLA and PLLA Chains As Studied by X‑ray Diffraction Analysis Kohji Tashiro,*,† Naoto Kouno,† Hai Wang,† and Hideto Tsuji‡ †

Graduate School of Engineering, Toyota Technological Institute, Tempaku, Nagoya 468-8511, Japan Toyohashi University of Technology, Toyohashi 441-8580, Japan

‡

ABSTRACT: The crystal structure model of stereocomplex between poly(L-lactic acid) (PLLA) and poly(D-lactic acid) (PDLA) with the L/D ratio of 50/50 was proposed by several groups [the space group P1 model by Okihara et al. (1991) and R3c or R3̅c model by Cartier et al. (1997)], among which the model of the space group R3c (or R3̅c) had been currently recognized as the most preferable one. However, the thus apparently established model cannot explain such an important experimental fact that the stereocomplex is formed not only for the PLLA/PDLA blend of the L/D ratio 50/50 but also for the blends with the L/D ratio of 70/ 30−30/70. We have proposed here a new model with the space group P3, which can cover the SC structures of the L/D ratio in the range of 70/30−50/50−30/70. This model can show the more quantitative reproducibility of the observed X-ray diffraction data for both the hkl and 000l reflection profiles. In particular the experimental observation of the 0003 reflection is inconsistent with the previous model of the space group R3c, which requests the appearance of only the 000l with l = 6, 12, etc. In the newly proposed P3 model the molecular chains take the regular (3/1) helical conformation; however, the packing mode is not regular. The unit cell consists of the statistically disordered arrangement of the right-handed (R) and left-handed (L) chains of the upward (u) or downward (d) directionality. For example, in the case of the stereocomplex with L/D ratio 70/30, a pair of the left-handed downward (Ld) and right-handed upward (Ru) chains is located at one lattice site at the statistical occupancy of 70/30 ratio and another pair of the left-handed upward (Lu) and right-handed downward (Rd) chains is at the adjacent lattice site at the same 70/30 ratio. The unit cell contains the three sets of these two pairs, which are connected to each other by the symmetric relation of the 3-fold rotation axis. The proposed statistical packing model of the upward and downward chains can explain such various observations as the spherulite formation or the existence of the lamellae with the chain folding structure in the spherulite, the solvent-induced change from the stereocomplex to the α form, and so on.

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INTRODUCTION Poly(lactic acid) (PLA, −[C*H(CH3)−COO]n−), one of the environmentally friendly polymers originated from the natural plants, is known to crystallize into the several different crystal modifications [α, δ (α′), β, and γ forms] depending on the sample preparation conditions.1−43 The crystal structures of these modifications, which are the most important basic knowledge in the study of structure−property relationship of this polymer, were proposed by the several groups including us, though the various problems still remain unsolved up to now about the crystal structures. Before pointing out the structural problem of the stereocomplex, it may be useful to know the structural characteristics of PLLA (or PDLA) itself necessary for the discussion of the stereocomplex. α Form. As for the crystalline α form, after several proposals of the models,44−52 the crystal structure was established on the basis of the quantitative analysis of the 2-dimensional highenergy synchrotron X-ray diffraction data and the 2-dimensional wide-angle neutron diffraction data obtained for the highly oriented and highly crystalline sample.52 As shown in Figure 1a, the (10/3) helical chains are packed in the pseudoorthorhombic (actually triclinic) unit cell, in which the upward © XXXX American Chemical Society

and downward chains of the same handedness are packed at the center and corner of the cell, respectively. Here the (10/3) helical chain indicates that the 10 monomeric units are included and turn 3 times in a repeating period along the chain axis. As known from the presence of no symmetry at each site, these chains do not have the homogeneous regular conformations but are deformed more or less. As a result, the chain packing in the crystal lattice is also distorted to give the energetically stable arrangement of the chains. The regular α form shows a disorder in the domain level. The domains consist of many regularly repeated unit cells, but the domain size is only about several tens of angstroms. These domains of finite size gather together to form a crystallite. The neighboring domains in the crystallite scatter the incident X-ray beam coherently. If the neighboring domains are disordered in their relative height along the c-axis, the intensity of the 00l diffraction peaks is affected sensitively.52,53 Received: July 10, 2017 Revised: September 26, 2017

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DOI: 10.1021/acs.macromol.7b01468 Macromolecules XXXX, XXX, XXX−XXX

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chains are packed in the orthorhombic47,61 or trigonal unit cell.57,58 Quite recently, we have proposed a new model of the space group P1, in which the upward and downward chains of (3/1) helical conformation are packed in a complicated but systematic way (Figure 1c).64 This structure is generated by applying a shear stress to the α crystal lattice along the diagonal direction at a high temperature. In our experiment, the oriented α sample was hung vertically with a small weight and heated up to the high temperature. In the heating process, the sheared α form transforms to the deformed α form at first and then to the δ form. By heating furthermore, the δ form is melted once and recrystallizes into the β form with keeping the chain orientation character almost perfectly.64 γ Form. The γ form was reported to generate by epitaxial crystallization on hexamethylbenzene crystal, the details of which are referred to in the literature.65,66 Stereocomplex. By referring to this basic knowledge about the crystal modifications of PLLA homopolymer, let us see the unsolved problem about the structure of the stereocomplex. PLA has asymmetric carbon atoms in its skeletal chain, and the two types of optically active enantiomers exist: poly(L-lactic acid) [PLLA] and poly(D-lactic acid) [PDLA]. The blend sample of PLLA and PDLA at 1:1 molar ratio was found to create the formation of the so-called stereocomplex (SC).67−74 The SC gives the melting point (ca. 230 °C) higher than that of the α form composed of only PLLA or PDLA homopolymer (ca. 180 °C). The crystallization of the SC from the melt occurs faster than the α form. The mechanical property is also more excellent than the α form. In this way, the SC is attracting many attention from the industrial viewpoint.71,75 The crystal structure of SC may be one of the most important basic knowledge for understanding these characteristic behaviors of SC.50,76−80 But, the details of the crystal structure have not yet been established satisfactorily. Okihara et al. proposed the triclinic unit cell by analyzing the X-ray diffraction data.76 A pair of PLLA and PDLA chains of the (3/1) helical conformation is packed regularly in the cell as illustrated in Figure 2a. Both of

Figure 1. (a) Crystal structure of PLLA α form.52 (b) The structural evolution in the heating process from the mesophase of small crystallite size to the δ form of larger crystallite size with irregular chain packing structure and to the α form of regular chain packing structure of larger size.43 (c) The tension-induced phase transition from the α form to the β form (model 3) via the δ form at a high temperature (the latter process is the melt of the δ form followed by the recrystallization to the β form).64

δ Form and Meso Phase. This type of structural disorder occurs more seriously in the crystal form δ (or α′).1,15,16,26,35,42,53,54 The δ form is prepared by stretching the α form at a low temperature near the glass transition point (∼70 °C). The crystallite size of the δ form is much smaller than that of the α form.53 The (10/3) chain conformation and chain packing mode are appreciably disordered as known from the diffuse X-ray diffraction pattern53 and also from the vibrational spectral data.16,43,54 In such a sense the δ form may be assumed simply as a deformed α form, but it is not correct. The δ form is a crystal form independent of the α form (Figure 1b). The cold drawing of the solution-cast film at room temperature generates the meso phase, in which the more highly disordered (10/3) chains are packed in a crystallite of quite small size, only ca. 30 Å43,53 (Figure 1b). The meso phase transforms to the δ form by heating above the glass transition temperature and then to the α form above 120 °C.16,35,43,53 The biaxial stretching of the meso phase at a high stretching rate was found to give the highly crystalline film with the remarkably tough mechanical property, which was ascribed to the aggregation of a plenty of the highly oriented δ crystallites of small size.56 β Form. As for the β form, which is prepared by stretching the α form at such a high temperature as 160 °C, the crystal structure and the transition behavior were proposed in several papers.38,47,57−64 The upward and downward (3/1) helical

Figure 2. Crystal structure models proposed in the literature: (a) The triclinic model consisting of a pair of PLLA and PDLA chains.76 In the left-side model, the right-handed (R) and left-handed (L) chains direct upward (or downward), while they are statistically randomly directed in the right-side model. (b) The R3c model composed of the R and L chain stems of only upward (or downward) direction.78 (c) The R3c̅ model composed of the statistically disordered packing of R and L chain stems of upward and downward directions. B


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chains in a crystalline region might exist only at a 30/30 molar ratio and the excess part (or 40 PLLA chains) may exist in the amorphous region. Why do not we have another such possibility that both of PLLA and PDLA chains coexist in a crystalline region at 70/30 molar ratio, or the possibility of cocrystallization of nonequimolar PDLA and PLLA chain components as a whole? If this is true, then the abovementioned crystal structure models (R3c or R3c̅ ) must be reconsidered. The experimental data reported by Cartier et al.78 and Prud’homme et al.87−89 suggest the possibility of the second model, but they did not mention clearly the possibility of this model. We have to check in detail if the formation of the SC phase can be made with the nonequimolar PLLA and PDLA contents. By taking all these situations into account, we have challenged to reinvestigate the crystal structure of the uniaxially oriented SC samples prepared at the various PLLA/PDLA molar ratios by analyzing the 2-dimensional X-ray diffraction data. Our data analysis has concluded the possibility of the random cocrystallization of PLLA and PDLA chains in the common crystallites. The formation mechanism of the SC from the mixture of PLLA and PDLA will be also discussed on the basis of the thus-obtained new model. In the following descriptions, it is assumed that the PDLA chain takes the right-handed helical chain form (R) and the PLLA chain takes the left-handed helical form (L).

these two chains direct upward (or downward) along the chain axis. As another possibility, they proposed also the statistically disordered packing mode of the upward and downward chains of the same handedness, for example, the upward and downward left-handed chains at one lattice site [indicated as L(u/d) and R(u/d) in this figure]. Several years later, their structure model was revised by Cartier et al. on the basis of the analysis of the electron diffraction data collected for a single crystal grown from the solution (followed by the meltrecrystallization).78 Their structure model consists of the trigonal unit cells of a = b = 14.98 Å and c (chain axis) = 8.70 Å (and γ = 120°), where the three pairs of PLLA and PDLA chains are packed at 1:1 molar ratio as illustrated in Figure 2b. However, they proposed the two possible space groups for this unit cell; R3c and R3̅c. In the R3c cell, all the chains are directed commonly to the upward (or downward) direction only. In the R3c̅ cell, the upward and downward chains of the same handedness (right-handed helical chains, for example) are located at a site at the statistical 50% probability, and they are related to the adjacent chains of the opposite sense (upward and downward left-handed helices) by a point of symmetry (Figure 2c). In their reports, they noticed the necessity of the statistical packing of the upward and downward chains in the crystal lattice as discussed by Okihara et al.76 But they kept the above-mentioned R3c (or R3c̅ ) model and introduced the frustrated structural concept to explain the triangular morphology of the grown single crystal. They prepared the single crystal from the nonequimolar mixture of PLLA and PDLA solution. This suggests that the PLLA and PDLA chains can cocrystallize even in an asymmetric L/D ratio. This point was important for them in the discussion of the morphological growth, but they did not make these situations clearer by showing the concrete relation between the frustrated structure and the models of space group symmetry R3c (or R3̅c), the latter requesting the 1:1 ratio of L and D chains. The similar suggestion can be extracted also from the paper by Prud’homme et al.87−89 They measured the DSC data for the various PLLA/PDLA mixtures. The blend sample of PLLA70/PDLA30 content showed almost only the peak of stereocomplex. Similar measurement was made also by Tsuji and Ikada.86 Prud’homme et al. prepared the spherulites from the samples of the asymmetric L/D ratios and observed the twisted shape for the spherulites grown from the sample of unbalanced L/D content, the screw direction of which depends on the excess content of PLLA or PDLA chain component.89 These data suggest the cocrystallization also, but they did not describe this possibility in an explicit manner. By comparing the lattice energies of the SC crystal models on the basis of the Dreiding-type potential functions,81 Brizzolara et al. reported that the parallel packing model of (3/1) helical chains is more stable than the antiparallel model.77 Their discussion was based on the triclinic model proposed by Okihara et al.76 The DSC data collected for a series of the PLLA/PDLA blend samples with the different L/D ratios look quite important for us in the discussion of the SC formation mechanism. The sample with the L/D 70/30 ratio gave the melting peak of the SC phase only, which was supported by the X-ray diffraction data also to indicate the existence of only the SC phase in the sample crystallized from the melt, as will be shown in a later section. As the first plausible interpretation it might be possible to assume the sample consists of the mixture of crystalline SC phase and amorphous phase. For example, in the case of PLLA70/PDLA30 mixture, the PDLA and PLLA

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EXPERIMENTAL SECTION

Samples. PLLA and PDLA samples were synthesized in the present study: the averaged molecular weight was 1.19 × 106 and 1.05 × 106 g/mol, respectively.71 The mixtures of PLLA and PDLA components were prepared at the various weight percentages by casting from the chloroform solutions at room temperature. The cast films were melted above 250 °C (to erase the memory) and quenched into an ice−water bath. The uniaxially oriented samples were prepared by stretching these films about 5 times the original length at about 100 °C. These oriented samples were annealed at the temperature higher than 200 °C under the constant length for 10 h (to erase the α crystal form). The content of the SC phase was checked by measuring the Xray diffraction pattern. Measurements. DSC Thermograms. The as-cast film was put into a DSC (differential scanning calorimeter) aluminum pan, and the thermogram was measured using a TA Instruments DSC Q-1000 in the heating and cooling processes in the temperature range 30−250 °C at the rate of 5 °C/min under the nitrogen gas flow. 1-Dimensional X-ray Diffraction Profiles. The X-ray diffraction profiles were measured using a Rigaku RINT TTR-III X-ray diffractometer for the unoriented samples. The incident X-ray beam was a Cu Kα line (λ = 1.5418 Å) monochromatized using a convergent beam optics (CBO) with a parabollic multilayer mirror.90 The diffraction profile was collected using a high-speed semiconductor detector (Rigaku D/teX Ultra). The simultaneous measurement of Xray diffraction profile and DSC thermogram was also performed using this X-ray diffractometer. A sheet of the film of about 50 μm thickness was put into a DSC pan and set horizontally on the sample stage of the DSC apparatus. 2-Dimensional X-ray Diffraction Patterns. The 2D X-ray diffraction patterns were measured for the uniaxially oriented samples using a Rigaku R-axis Rapid II X-ray diffractometer with a cylindrical imaging plate detector. The incident X-ray beam was the graphitemonochromatized Mo Kα line (λ = 0.7107 Å). The sample was rotated around the stretching axis during the measurement to avoid the anisotropy in the X-ray diffraction intensity coming from the preferential orientation of the crystallites. X-ray Structure Analysis. The process of X-ray structure analysis was essentially the same as that described already in the previous papers.91,92 Briefly speaking, the unit cell parameters were determined C


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known from the melting peak at about 180 °C. In the higher temperature region, the SC phase crystallized partially and melted at about 230 °C. Once after being cooled to the room temperature from the melt, the thermal behavior of these samples is classified roughly into two groups, as known from Figure 3b. The samples with the L/D ratio of 100/0−80/20 and 30/70−0/100 showed mainly the melting peak of the α form at around 180 °C with a small peak at about 210 °C due to the melting of the SC phase. These complicated phenomena were not observed for the samples of L/D ratio = 70/30−40/ 60, which showed almost only one melting peak originated from the SC phase. (The slight change of the melting point of the α and SC phases in the second heating process might be due to the lowering of the molecular weight caused by heating above the melting point for a long time.) In this way the samples of the L/D ratio 70/30−40/60 were found to show almost pure SC phase once after the initial solution-cast samples were melted at a high temperature. This observation was consistent with the report by Brochu et al.87 The same results were obtained also from the X-ray diffraction patterns, as will be described in the next section. 1D X-ray Diffraction Profile. The temperature dependence of the 1D X-ray diffraction profile confirms the abovementioned DSC results more clearly. Figure 4 is the case of

by indexing all the observed diffraction spots using the information on their positions on the 2D X-ray diffraction pattern. The 1D diffraction profiles were extracted from the 2D pattern by integrating the diffraction intensity along the individual layer lines over a narrow width. The structural models were constructed using a commercial software Cerius2 (Biovia-Accelrys, version 4.10) and energetically minimized, where the potential energy function parameters of COMPASS force field were used.93 The X-ray diffraction profiles of the various layer lines were calculated for these models, from which the most plausible model giving the best agreement between the observed and calculated diffraction profiles was selected. The degree of the agreement between the observed and calculated profiles was evaluated by calculating the reliable factor (R): R=

∑ |I(hkl)calc − I(hkl)obsd |/∑ I(hkl)obsd hkl

hkl

where I(hkl) is the integrated diffraction intensity.

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RESULTS AND DISCUSSION Thermal Analysis. In the following sections, the term “L/D ratio” will be used for expressing the blend ratio between PLLA and PDLA in a weight percentage. Figure 3a shows the DSC

Figure 4. Temperature dependence of X-ray diffraction profile of solution-cast PLLA sample measured in the heating, cooling, and reheating processes. Only the α form was observed in all the heating and cooling processes.

Figure 3. DSC thermograms measured for (a) the as-cast PLLA/ PDLA blend samples with the various L/D ratios and (b) the crystallized samples obtained by cooling from 240 °C after (a). The endothermic peak at around 180 °C is due to the melting of the α form. The endothermic peak at around 220 °C (in part a) and 210 °C (in part b) corresponds to the melting of the SC phase. The slight fluctuation of the position of the melting peaks may come from the partially occurred thermal decomposition.

pure PLLA sample. At the starting point of heating, the solution-cast film was in the amorphous state and showed no sharp peaks originated from the crystalline phase. The crystalline peaks started to appear at around 90 °C and increased the intensity with an increasing temperature. The diffraction profile is that intrinsic to the pure α phase. These peaks disappeared above 180 °C because of the melting of the α phase. The cooling from the melt induced the crystallization of the α phase which started to occur at about 110 °C. In the second heating process, the diffraction peaks of the pure α phase were detected again up to 180 °C and disappeared finally. In the case of the blend sample with the L/D = 80/20 ratio,

thermograms measured in the first heating process for a series of L/D blend samples cast from the chloroform solutions. All the solution-cast samples were initially almost in the amorphous state with the glass transition point at around 50−60 °C, and the crystallization peak was detected at around 80 °C (for the blends) or 110 °C (for pure PDLA and PLLA samples) in the heating process. As seen in this figure, the samples were found to crystallize at first into the α form as D


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Macromolecules also, the cast film was amorphous at room temperature. The diffraction peaks of the α phase started to appear by heating to 90 °C and disappeared above 180 °C. The cooling from the melt above 230 °C caused the partial crystallization of the SC phase at around 190 °C, and the small peak of the α phase was detected below 130 °C. The second heating gave a clear difference in the melting point between the α and SC phases. The α peak disappeared at around 180 °C and the SC peaks at around 230 °C. In this way, the L/D blend sample of 80/20 ratio consisted of the mixture of the α and SC phases. The samples of L/D 50/50−70/30 ratio are important in the discussion about the formation of SC phase (see Figures 5 and

Figure 6. Temperature dependence of X-ray diffraction profile of solution-cast PLLA/PDLA 70/30 sample measured in the heating, cooling, and reheating processes. The α form was created in the first hearing process from the as-cast sample, which disappeared at about 180 °C. The small amount of SC phase was detected in parallel to this event. In the cooling process from the melt and in the second heating process, only the SC peaks were detected reversibly.

PDLA sample gave only the crystallization of the α phase as likely the case of pure PLLA. Figure 7 summarizes the results of the X-ray diffraction measurements shown in Figures 4−6. The integrated intensity Figure 5. Temperature dependence of X-ray diffraction profile of solution-cast PLLA/PDLA 50/50 sample measured in the heating, cooling, and reheating processes. The α form was created in the first hearing process from the as-cast sample, which disappeared at about 180 °C. The small amount of SC phase was detected in parallel to this event. In the cooling process from the melt and in the second heating process, only the SC peaks were detected reversibly.

6, respectively). In both of the 50/50 and 70/30 blend samples, the first heating of the solution-cast film showed the two-stage increase of the X-ray diffraction peaks due to the appearances of the α and SC phases in the heating process, respectively. These X-ray peaks disappeared at 180 and 230 °C, respectively, corresponding to the melting of these phases. However, the cooling from 230 °C gave the crystallization of the SC phase only. No detection of the α phase signal is not because of the fast cooling of the sample. In fact, pure PLLA sample crystallized into the α phase at the same cooling rate (Figure 4). Even when the cooling rate was reduced, the crystallization of the α form was not detected at all. The second heating showed only the melting of the SC phase at about 230 °C without any detection of the α phase on the way of heating. That is to say, the blend sample of L/D 70/30 ratio gave only the SC phase once after it was melted in the heating process. The similar observation was made for the blend samples of L/D ratio of 70/30−50/50−40/ 60. On the other hand, the blend samples with the L/D ratio 30/70−10/90 and 80/20−90/10 showed the mixture of the α and SC phases. The blend ratio of L/D 30/70 is almost in the boundary between the detection of the pure SC phase and the observation of the appreciable amount of the α phase. The pure

Figure 7. Change of relative content of the α form and SC phase of PLLA/PDLA blend samples with the various L/D contents.

of the (110) diffraction peak of the SC phase, I(SC), and that of the (200/110) diffraction peak of the α form, I(α), were evaluated from the 1D diffraction profiles shown in Figures 4−6, and the intensity ratio I(SC)/[I(SC) + I(α)] or a measure of the SC fraction (XSC) was plotted against the weight percentage of the PLLA component contained in the sample. The fraction of the α form, Xα (= 1 − XSC), is also plotted here with blue solid circles. [It must be noted that the XSC and Xα are not the correct molar fractions of the SC and α phases, respectively, but they are only the measures to show the relative E


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Macromolecules contents of the SC and α phases in the blend sample, since the coefficient k showing the relation between the intensity and the molar fraction [I = k*(molar fraction)] is not known at present.] Figure 7 shows clearly that the sample in the region of L/D 70/30−40/60 gave almost pure SC phase. The blend sample of L/D 30/70 did not give the pure SC phase, but it contained some portion of the α form, opposite to the case of L/D 70/30 blend sample giving the pure SC phase. In this way, strictly speaking, the region of SC formation is not symmetric at the center of L/D 50/50, but it shifts a little from the center line to the higher L component side. The abscissa axis is not a molar ratio but a weight ratio between the L and D components. The slight difference in the averaged molecular weight between these two components might be one possible reason for the asymmetric curve, although the details are not known. In the present paper we say approximately the range of SC formation is from L/D 70/30 to 30/70. The results shown in Figure 7 are consistent with the DSC data analysis shown in Figure 3. These data allow us to speculate the two possibilities as illustrated in Figure 8. In the case of L/D 50/50 blend sample,

common crystal region at the L/D ratio 70/30. In order to check these possibilities, we have performed the X-ray structure analysis using the 2-dimensional X-ray diffraction data. X-ray Structure Analysis. Figure 9 shows the 2D X-ray diffraction patterns measured at room temperature for the

Figure 9. 2-Dimensional X-ray diffraction diagrams of the uniaxially oriented SC phase of the PLLA/PDLA blend samples with the various L/D ratios. The diffraction diagram of the uniaxially oriented PLLA α form is shown here also for comparison.

uniaxially oriented blend samples with the L/D ratios of 50/50, 30/70, and 70/30. The samples were prepared by heating the oriented sample up to 200 °C under tension and cooling to the room temperature. 1. L/D 50/50 Sample. The unit cell parameters were evaluated from the peak positions of all the observed diffraction spots as below: the trigonal (hexagonal-type) cell with a = b = 14.94 Å and c (chain axis) = 8.62 Å. These values are consistent with the trigonal unit cell proposed by Cartier et al.,78 although the c-axial length is a little bit different from theirs (c = 8.70 Å). The repeating period along the chain axis indicates the (3/1) helical conformation as reported already by them. When these (3/1) helical chains are packed in the unit cell, the various possibilities are needed to consider about the space group symmetry. a. R3c and R3̅c Models. Cartier et al. proposed the two possibilities R3c-C3v6 and R3̅c-D3d6.78 Let us investigate at first the reasonableness of these two models in a quantitative manner based on the observed X-ray layer line profiles. As shown in Figure 2, the R3c model consists of the alternate packing of the three right-handed upward chains (Ru) and three left-handed upward chains (Lu). The Ru chains are surrounded by the Lu chains and vice versa, where the upward (u) direction is defined in such a way that the CH3 group directs toward the +c-axis direction (or the direction of the C(O)−O vector). All the chains direct to only the upward (or downward) direction along the c-axis. On the other hand, in the case of the R3̅c model, the upward and downward chains of the same handedness (Ru and Rd, for example) are located at one lattice site at the 50% probability. As a result, the Ru/Rd pairs are connected to the Lu/Ld pairs by a center of symmetry. The comparison of the observed X-ray diffraction profiles was made with the profiles calculated for these structure models, as shown in Figures 10 and 11, where the calculation

Figure 8. Possible modes of PLLA and PDLA chains in the crystalline and amorphous regions of the L/D blend samples. (a) L/D = 50/50. The L and D chains exist at the same ratio in both the amorphous and crystalline regions. (b) L/D = 70/30. The crystalline region consists of the L and D chains at the 50/50 content. The remains are in the amorphous region. (c) L/D = 70/30. The L and D chain components can coexist at the 70/30 ratio in the crystalline and amorphous regions.

the D and L chains may be packed in the crystal lattice at the 50/50 molar ratio, which is consistent with the structure model proposed in the literature.76−78 The case of L/D 70/30 blend sample is different in the situation. Experimentally, this sample gave only the SC peaks in the X-ray diffraction pattern and no α peaks; in other words, the sample consists of the SC and amorphous phases (see Figure 6). If the L/D 50/50 model proposed in the literature78 can be applied as it is, the crystal region must be occupied by the D and L chain stems at the 30/ 30 ratio and the other 40 fractions of the L component must exist in the amorphous region. Another possibility is to assume that the D and L chain components are coexistent in the F


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b. Another Candidate. As mentioned in the previous section, the almost pure SC phase can be formed for the blend samples with the L/D ratio of 70/30−30/70 when the samples are cooled slowly from the melt. However, this experimental fact cannot be explained reasonably as long as the R3c model is assumed as a unique structure model of the SC phase (as deduced from the relatively good agreement of the observed and calculated X-ray diffraction data). A glide plane (simply, a mirror plane) existing between the R and L chain sites causes such a restriction that only the L and R chains exist at the 1:1 ratio in the crystal lattice. As long as the D and L chains are assumed to coexist only at 1:1 ratio in the crystal phase, the surplus PDLA (or PLLA) chains must exist in the amorphous region because the α crystal form is not detected at all for the blend samples of the above-mentioned L/D ratios. Therefore, it is speculated that the degree of crystallinity of the sample should be lower as the D/L ratio deviates from the 50/50 ratio. We have checked the degree of crystallinity of these samples on the basis of both the X-ray diffraction and IR spectral data, but the crystallinity was almost the same within the experimental error, about 45% for all of these samples. From all of these data it may be difficult to accept the R3c model as the common SC structure applicable to all the blend samples of the different L/ D ratios. As another model, we assume that both of PLLA and PDLA chains can coexist at the various ratios in the common crystallite (see Figure 8). For satisfying this requirement, the space group symmetry must be lower than the R3c model; for example, P3 and P3̅.94 In these cases, the glide (or mirror) planes existing in the R3c model (Figure 12a) are removed, and the two neighboring lattice sites (enclosed with a broken ellipse) are symmetrically independent, as known from the symmetry elements shown in Figure 12b. As an example, let us consider the case of the blend sample of L/D 70/30 ratio. One lattice site is occupied by 70% PLLA chain stem and 30% PDLA chain stem. The R and L chains are packed along the upward or downward direction. One possibility is 70% Lu + 30% Ru, 70% Ld + 30% Ru, and so on. As already pointed out before, this type of the statistical packing of R and L chains at one lattice site might be possible also for the model R3c (Figure 13a). In this case, 70% L and 30% R chains can exist at one lattice site, but the presence of a glide plane generates immediately the another pair of 70% R and 30% L chains at the neighboring site. The total amount of chains is 100% L and 100% R, and so the L/D ratio should be necessarily 100/100 (or 50/50), not 70/30. This is a self-contradiction. In this way, the R3c model is limited only to the structure of L/D 50/50 ratio. Similarly, for the model of space group P3̅, also, the site of R70% + L30% pair must be related to another site of L70% + R30% pair by a point of symmetry. Therefore, only a pair of R50% and L50% is possible. In order to interpret the observation of SC samples with the nonequimolar L/D ratios, we need to consider the model without any mirror (glide plane) symmetry or the model of the space group P3. P3 Model for the L/D 50/50 Sample. At first, let us check the validity of the space group P3 for the SC phase of L/D 50/50 ratio (see Figures 12b and 13a). As mentioned above, one lattice site is assumed to be occupied statistically by both of the R and L chain stems at 50% probability. Here we have two possibilities about the directionality of the R and L chains along the c-axis: upward (u) and downward (d). As a result, the neighboring two lattice sites are occupied by a pair of (a) Ru/ Ld and Lu/Rd, (b) Ru/Ld and Ld/Ru, (c) Ru/Lu and Ld/Rd,

Figure 10. (a) Observed X-ray diffraction profiles of PLLA/PDLA 50/ 50 SC sample along the equatorial (hk0) and layer lines (hk1−hk3) in comparison with those calculated for the SC structure model of R3c space group.

was performed using a commercial software Cerius2 (version 4.10, Accelrys-Biovia) with the crystallite sizes 80 Å × 80 Å × 60 Å, the lattice strains 0% × 0% × 4% along the a, b, and c axes, respectively, and the thermal parameters of 0.05 × 0.05 × 1 Å2 for all the atoms. The R3c model gave the good agreement between the calculated and observed profiles for the various layer lines as a whole. Contrarily, as shown in Figure 11, the R3c̅ model could not give very good result when compared with the observed data. Additionally, the diffraction profiles were also calculated for the two types of P1 model shown in Figure 2a.76 As shown in Figure 11, the agreement with the observed data was not good even after many trials were made by modifying the models. The R3c model gave the best agreement among these four structure models (see Figures 10 and 11). In this model the Ru and Lu chains are packed at each lattice site. However, as another candidate of the R3c model, we may build up the structure with the Rd and Lu chains located at one site at 50% probability, where these two chains are used as a pair because they are overlapped together when viewed along the chain axis just likely the regular structure of the R3c model. The existence of glide plane symmetry forces to generate another pair of Ld and Ru chains at the adjacent lattice site. This statistically disordered model can also reproduce the observed diffraction profile along the equatorial line. However, the layer line profiles could not be reproduced satisfactorily well even when the relative heights and orientations of the R and L chains were modified in the various ways. Therefore, judging from the X-ray diffraction data, we may conclude that the regular packing model of Ru and Lu chains in the R3c unit cell may be the best one as long as these five possible models are compared as the candidates of the SC of L/ D 50/50 molar ratio. G


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Figure 11. Comparison of the observed X-ray diffraction profiles along the hk0 and hk2 lines with those calculated for the various structure models shown in Figure 2.

or (d) Ru/Rd and Lu/Ld. Here, Ru/Ld, for example, indicates that the right-handed upward (Ru) helical chain and lefthanded downward (Ld) helical chain are positioned at a lattice site at 50% probability. As illustrated in Figure 13b, we notice the similarity and difference of the chain shape projected along the c-axis: when the projected structures of the statistically positioned two chains are compared, they can be perfectly overlapped or not, depending on the counterparts of the pair.

For example, as shown in case-2 of Figure 13b, the solid and dotted lines in the pairs of (Ru and Lu), (Rd and Ld), (Ru and Rd), and (Lu and Ld) are not overlapped with each other. On the other hand, the pairs of (Ru and Ld) and (Rd and Lu) show the perfectly overlapped structure (case-3). These pairs are located at the two neighboring sites as illustrated in Figure 13a. The projected structure of R3c model (case-1 in Figure 13b) can reproduce the X-ray equatorial line profile quite well, but H


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Figure 12. Crystal structure and symmetry elements of PLLA/PDLA stereocomplex. (a) R3c model. Starting from one monomeric unit, the regular packing structure of Ru and Lu chains is generated. The ratio between the R and L chains is necessarily 1:1 due to the glide symmetry relation. (b) P3 model. Since the glide symmetry is lost from the R3c model, the neighboring lattice site can be occupied by the monomeric unit of R and L components at an arbitrary ratio.

the structure of R3c̅ model (case-2 in Figure 13b) cannot reproduce the data very well (see Figure 11). Therefore, the projected chain structure at one lattice site must be that of R3c type, which should be good candidates of the P3 model (case-3 shown in Figure 13b). In case-3, there are two models (a) and (b). In model (a), we have a pair of (Ru/Ld) and (Lu/Rd) at the neighboring two sites, which are related to each other apparently by a mirror plane symmetry. This packing mode is the copy of that of the space group R3c model, making us expect to get a good agreement between the observed and calculated X-ray data. On the other hand, model (b) shows the same pairs (Ru/Ld) at the two neighboring sites but with the different orientations. We have checked the usefulness of these two models by comparing the observed and calculated X-ray diffraction profiles. Our conclusion is that the P3 model of case (a) can reproduce the observed X-ray diffraction data for all the layer lines. Figure 14 shows the comparison of the observed X-ray diffraction profiles with those calculated for this model. The agreement between the observed and calculated profiles is in almost the same or better level as that of the R3c model. c. Choice of the Best Model. At this stage, we have two plausible candidates for the SC structure with L/D 50/50 ratio: the space groups R3c and P3. In order to choose the better one from them, we checked the 000l diffraction profile. Because of the requirement from the space group symmetry, the observable 000l diffractions are limited to the following conditions.

Figure 13. (a) Various chain packing modes of SC with L/D 50/50 ratio among the different space group symmetries. The R3c model consists of the alternate regular packing of Ru and Lu chains. The R3̅c model gives the statistical packing of Ru and Rd chains (or Lu and Ld) at 50% probability. The statistical packing of Ru and Ld chains at one site is possible for the R3c symmetry, but the ratio of R and L chains is necessarily 1:1. The P3 model can pack the arbitrary ratio of R and L chains at one site, but the X-ray diffraction data can be reproduced well for the pair of Ru and Ld (Rd and Lu). (b) Projected structures of the various symmetric modes of a pair of R and L chain stems located at the adjacent sites. Case-1: Ru and Lu or Rd and Ld stems are located side by side. A pair of Ru and Ld is difficult to use when the R3c mode is referred to. Case-2: statistically disordered packing of Ru and Rd (or Ru and Lu) at one site. The projected structure is not overlapped together between these two pairs. Case-3: the projected structures can be overlapped together. The pairs of the different handedness and directionality (for example, Ru and Ld) are located at one site at the probability determined by the L/D ratio.

R 3c l = 6, 12, ... P3

no condition

Figure 15 shows the observed X-ray meridional diffraction data collected with a Norman’s method (or Weissenberg method), in which the uniaxially oriented sample was oscillated

repeatedly around the oscillation axis perpendicular to the draw direction, and at the same time the cylindrical camera was I


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crystallite size 80 Å × 80 Å × 60 Å, the crystal lattice strain 0% × 0% × 4%, the temperature factors 0.05 Å2 × 0.05 Å2 × 1.0 Å2 along the a, b, and c axes, respectively. The crystal structure is shown in Figure 16. The finally determined atomic coordinates

Figure 16. Crystal structure of PLLA/PDLA stereocomplex. One lattice site is statistically occupied by a pair of Rd and Lu chains and the neighboring site by a pair of Ru and Ld chains: (a) along the c-axis and (b) along the 110 plane.

Figure 14. Comparison of the observed X-ray diffraction profiles along the various layer lines with those calculated for the L/D 50/50 stereocomplex model of the P3 space group symmetry (model (a) in case-3 of Figure 13b). An incident X-ray is the Mo Kα line.

are listed up in Table 1. The R factor is 11% for the hk0 diffraction profile, 15% for hk1, 19% for hk2, 31% for hk3, and 14% for hk4. The comparison in the diffraction intensity is shown in Table 2. (The R factor for the hk3 layer line profile is relatively higher. The slight modification might be needed for the relative height of the neighboring chains, but we did not do it in the present paper.) As reported in our previous papers,52,53 in the case of PLLA α and δ forms, the crystallite was assumed to be an aggregation of the X-ray coherent domains. Each domain consists of the regular packing of the helical chains, but the relative height of the neighboring domains is disordered more or less. This disordered aggregation of domains reproduced the observed 00l diffraction profile well for the α and δ forms. This type of the domain disorder was not suitable for the reproduction of the observed 000l profile in the case of the present SC sample. It must be noted here that the diffuse streak lines overlap with the spotlike X-ray 000l diffractions, as seen in Figure 15. This suggests the existence of the disorder in the relative height of the neighboring chains, as reported by Okihara et al.95 2. X-ray Structure Analysis of L/D 70/30 and 40/60 Blend Samples. The applicability of the above-mentioned P3 model to the SC sample of nonequimolar L/D ratio was checked. As shown in Figure 12b, in the case of L/D 70/30 blend sample, one lattice site consists of the Ru chain at 30% probability and Ld chain at 70% probability, and the neighboring lattice site consists of the Rd chain at 30% probability and Lu chain at 70% probability. The calculated X-ray diffraction profiles were found to satisfy relatively well the observed data for all the layer lines (see Figure 17). The X-ray diffraction data measured for the L40/R60 blend sample was also reproduced relatively well by the structure model of the P3 space group. 3. Effect of L/D Ratio on the Layer Line Diffraction Profiles. When the observed X-ray diffraction profiles are compared among the SC samples with the various L/D ratios, we notice that almost all the layer line profiles are similar to each other

Figure 15. Weissenberg 000l diffraction pattern measured for the L/D 50/50 stereocomplex. The diffraction profile was obtained by scanning the 2D pattern along the line of 000l.

translated along the oscillation axis. As a result, a series of the 000l diffraction were detected on the X-ray film. In particular, the detection of the 0003 peak is quite important, which must not be observed for the R3c model. In other words, the P3 model with the statistically disordered chain packing structure of Ru/Ld and Lu/Rd pairs was found to be the best structure satisfying the observed X-ray diffraction data as a whole. The calculated diffraction profiles for this model are shown in Figure 14, where the structure parameters are as follows: the J


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Macromolecules Table 1. Atomic Fractional Coordinates of the Stereocomplex with L/D 50/50 (P3 Model)a (a) Right-Handed Chains Ru

x

y

1 (C) 2 (CO) 3 (−O−) 4 (O) 5 (M) 6 (C−H) 7 (M−H1) 8 (M−H2) 9 (M−H3) 10 (C) 11 (CO) 12 (−O−) 13 (O) 14 (M) 15 (C−H) 16 (M−H1) 17 (M−H2) 18 (M−H3) 19 (C) 20 (CO) 21 (−O−) 22 (O) 23 (M) 24 (C−H) 25 (M−H1) 26 (M−H2) 27 (M−H3)

0.70 0.67 0.76 0.59 0.68 0.78 0.70 0.60 0.74 0.74 0.69 0.62 0.69 0.85 0.69 0.89 0.84 0.90 0.57 0.65 0.63 0.73 0.48 0.54 0.43 0.51 0.43

0.59 0.65 0.72 0.65 0.49 0.64 0.45 0.44 0.50 0.77 0.69 0.71 0.61 0.86 0.80 0.91 0.90 0.83 0.64 0.66 0.58 0.75 0.66 0.56 0.64 0.74 0.60

Ld 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81

(C) (CO) (−O−) (O) (M) (C−H) (M−H1) (M−H2) (M−H3) (C) (CO) (−O−) (O) (M) (C−H) (M−H1) (M−H2) (M−H3) (C) (CO) (−O−) (O) (M) (C−H) (M−H1) (M−H2) (M−H3)

z 0.08 0.21 0.29 0.23 0.14 0.04 0.04 0.18 0.23 0.42 0.54 0.62 0.57 0.47 0.38 0.37 0.57 0.51 0.75 0.88 0.96 0.90 0.80 0.71 0.71 0.85 0.90 (b) Left-Handed

Rd

x

y

z

28 (C) 29 (CO) 30 (−O−) 31 (O) 32 (M) 33 (C−H) 34 (M−H1) 35 (M−H2) 36 (M−H3) 37 (C) 38 (CO) 39 (−O−) 40 (O) 41 (M) 42 (C−H) 43 (M−H1) 44 (M−H2) 45 (M−H3) 46 (C) 47 (CO) 48 (−O−) 49 (O) 50 (M) 51 (C−H) 52 (M−H1) 53 (M−H2) 54 (M−H3) Chains

0.23 0.31 0.29 0.39 0.14 0.20 0.09 0.09 0.17 0.36 0.34 0.42 0.25 0.35 0.44 0.36 0.40 0.27 0.40 0.35 0.28 0.36 0.51 0.35 0.54 0.56 0.50

0.26 0.32 0.38 0.31 0.16 0.31 0.12 0.17 0.11 0.44 0.35 0.37 0.28 0.53 0.46 0.58 0.57 0.50 0.30 0.33 0.24 0.41 0.32 0.22 0.30 0.40 0.26

0.87 0.74 0.66 0.72 0.81 0.91 0.91 0.72 0.77 0.53 0.41 0.33 0.38 0.48 0.57 0.58 0.39 0.44 0.20 0.07 −0.01 0.05 0.15 0.24 0.25 0.11 0.05

x

y

z

Lu

x

y

z

0.57 0.65 0.62 0.72 0.48 0.53 0.42 0.51 0.43 0.69 0.67 0.76 0.59 0.68 0.77 0.69 0.60 0.73 0.74 0.68 0.62 0.69 0.85 0.69 0.88 0.89 0.84

0.64 0.66 0.57 0.74 0.65 0.56 0.64 0.73 0.60 0.59 0.65 0.71 0.64 0.49 0.64 0.45 0.44 0.49 0.77 0.68 0.71 0.61 0.85 0.80 0.91 0.83 0.89

1.03 0.91 0.83 0.88 0.98 1.07 1.08 0.94 0.89 0.70 0.57 0.49 0.55 0.65 0.74 0.75 0.61 0.55 0.37 0.24 0.16 0.22 0.31 0.41 0.41 0.28 0.23

82 (C) 83 (CO) 84 (−O−) 85 (O) 86 (M) 87 (C−H) 88 (M−H1) 89 (M−H2) 90 (M−H3) 91 (C) 93 (CO) 93 (−O−) 94 (O) 95 (M) 96 (C−H) 97 (M−H1) 98 (M−H2) 99 (M−H3) 100 (C) 101 (CO) 102 (−O−) 103 (O) 104 (M) 105 (C−H) 106 (M−H1) 107 (M−H2) 108 (M−H3)

0.23 0.31 0.29 0.39 0.35 0.20 0.09 0.17 0.10 0.36 0.34 0.43 0.26 0.35 0.44 0.37 0.27 0.41 0.41 0.35 0.29 0.36 0.51 0.36 0.55 0.50 0.56

0.26 0.32 0.39 0.31 0.53 0.32 0.12 0.11 0.17 0.44 0.36 0.38 0.28 0.53 0.47 0.58 0.50 0.57 0.31 0.33 0.25 0.42 0.32 0.23 0.31 0.27 0.40

−0.08 0.04 0.12 0.07 0.30 −0.12 −0.13 0.01 0.07 0.25 0.38 0.46 0.40 0.30 0.21 0.21 0.35 0.40 0.58 0.71 0.79 0.73 0.64 0.54 0.54 0.73 0.68

The central pair of chains shown in Figure 16 is referred to for their positions. The unit cell is a = b = 14.94 Å, c (chain axis) = 8.624 Å, and γ = 120°. M: methyl group.

a

K


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Table 2. Comparison of X-ray Diffraction Intensity of the Stereocomplex with L/D 50/50 between the Observed and Calculated Valuesa,b

a

The calculated intensities were adjusted so that the sum of all the observed intensities along a particular layer line became equal to the sum of the corresponding calculated intensities. The calculation of the reliability factor was made for the individual layer line. bAn observed broad peak contains the several reflections as indicated with parentheses, which could not be separated into the components.

among the samples. Of course, the equatorial line profile is common to the various SC samples. It is reasonable since the structure projected along the c-axis is the same for all the SC samples. Even for the layer line profiles, also, the diffraction profiles are similar among the various SC samples. In fact, the computer simulation confirms it: the main strong peaks along the hkl, hk2, and hk3 layer lines are almost common to the SC samples with the various L/D ratios. The reason for the similarity of the whole X-ray diffraction pattern among the various SC samples is speculated to come from the similarity of the relative height of the Ru, Rd, Ld, and Lu chains as seen from the side view shown in Figure 16b. Even when the ratio of L and D chains is changed, the atomic positions are almost the same. Strictly speaking, when the simulated diffraction profiles are investigated more carefully along the hk1 layer line, some weak peaks (101, 501, 511, and so on) are predicted to appear when

the L/D ratio is deviated from the symmetric L/D 50/50 ratio. In particular, the SC structure of L70/D30 (and L30/D70) was predicted to show the 101 diffraction peak detectable intensity at around 5.7°. Unfortunately, however, in the actually observed diffraction pattern, the thus-predicted 101 peak might be overlapped with the arc originated from the quite strong 110 equatorial peak and also with the horizontally developed streak line connecting the right and left 211 strong peaks on the diffraction pattern. These situations make it impossible to check this prediction about the 101 reflection. Besides, the slight change in the relative height between the neighboring chains may modify the relative intensity of the 101 peak sensitively and the 101 peak intensity might become much weaker. Another possible modification of the 101 reflection intensity may be made by changing the chain conformation. The P3 model presented here assumes the rigid conformation of the (3/1) helical chain. This is because the total number of the L


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into the α (δ) form by heating above the glass transition point (cold crystallization). As already analyzed, the helical chains of the same handedness are packed in the crystal lattice of the α form (see Figure 1). Therefore, it is reasonable to speculate that the PDLA and PLLA chains in the blend sample create their own domains separately in the cold-crystallization process of the cast-film. The SC crystals start to appear for the first time when the film containing these α phase crystal domains is melted and cooled down to a certain temperature. Once the SC crystals are formed in this way, they do not transform to the original α form even after many repetitions of melting and cooling. This observation was made for all the blend samples in the range of L/D ratio of 70/30− 30/70. The initial formation of the α-phase crystal domains and the SC phase formation after the melting of the α-phase domains can be interpreted by assuming the heterogeneous distribution of PDLA and PLLA chain stems in the crystals. If the alternately arranged regular model of the PLLA and PDLA chain stems is assumed, the PDLA and PLLA chain stems trapped in the individual α crystalline regions must migrate and rearrange their spatial positions appreciably largely. It may take a long time for these chains to escape from the α phase regions and form the SC crystal region again. It is rather easier for the chains to be trapped into the SC region through the small change of the spatial distribution. The structure model with the P3 space group symmetry or the structure of the randomly packed L and D chain stems is consistent with this type of formation mechanism. (b) We have performed a new experiment. The uniaxially oriented or unoriented samples containing only the SC phase were exposed for the several hours in the atmosphere of acetone or chloroform vapor at room temperature. These samples were found to transform to the mixture of the SC and α form (Figure 18). An important point is that the relative content of the SC phase decreased in parallel with the increment of the α form. If only the amorphous region is crystallized into the α form by the solvent effect, the whole amount of the original SC phase may not be changed. The decrement of the SC phase content by supplying the solvent indicates the transition from the SC phase to the α phase. In the case of uniaxially oriented SC sample, the orientation of the thus-recovered α form was not very high when compared with the original SC phase, but it was not perfectly randomized. From these experimental observations it may be reasonable to speculate that the outer edge of the SC crystallites is dissolved partially by the penetration of the organic solvent molecules and recrystallizes as the α crystal on the crystal surface part. It is important to notice that the partial dissolution of the SC phase and the recrystallization into the α form occurred at the same time. This observation supports also the heterogeneous distribution of the D and L chains in the SC phase. One important point to be noticed is that the crystallization of the molten SC phase at a high temperature gives only the SC phase in the cooling process, while the partial dissolution of the SC phase at room temperature gives the crystallization of the α form. The crystallization of the L/D blends at high and low

Figure 17. Comparison of the observed X-ray diffraction profiles along the various layer lines with those calculated for the L/D 70/30 stereocomplex model of the P3 space group symmetry. An incident Xray is the Mo Kα line.

observed reflections is too small to refine all the possible structure parameters enough well. In this way, the appearance of the 101 peak (and the other much weaker peaks) predicted for the SC structure with the nonequimolar L/D ratio is difficult to check at present. The experimentally observed similarity of the X-ray diffraction pattern among the SC samples with the various L/ D ratios might recall such a story that the SC sample is created at the L/D ratio of 50/50 only with the R3c symmetry. But, as already discussed above, the 000l diffraction profile is not consistent with it (Figure 15). We cannot help abandoning the R3c and R3̅c models with the L/D 50/50 ratio. Besides, as will be reported in a separate paper, other experimental data collected from the perfectly different point of view, that is, the vibrational circular dichroism measurement, confirm the reasonableness of the random packing structure model of the P3 space group symmetry. 4. Formation Mechanism of SC Phase and Heterogeneous Distribution of L/D Chains. In the previous sections we have proposed a new model of SC crystal. In the limited range of L/ D ratio, 70/30−30/70, the PDLA and PLLA chains are statistically randomly packed in the common crystal lattice, that is, the so-called random cocrystallization of these two enantiometric species. This indicates the heterogeneous distribution of the PDLA and PLLA chain stems in the crystal lattice. The heterogeneous distribution concept is supported by the various experimental facts as summarized below. (a) As seen in Figures 4−6, the solution-cast film is almost amorphous at room temperature, and it is crystallized M


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from the PLLA and PDLA blend, the L and D chain components are distributed statistically randomly; the domains of only L chain component, the domains of only D chain components, and the domains of randomly mixed L and D chain components are existent together, all of which are almost in the amorphous state. These domains crystallize partially into the δ form when the film is heated above the glass transition temperature. At a higher temperature, the δ form transforms to the α form, and finally these α crystallites are melted totally. In the molten state, the molecular chains may migrate to some extent to mix more homogeneously, but it is hard to imagine that they change their spatial distribution drastically to realize the regularly alternate packing of the PDLA and PLLA chain components in the crystallization process. It is more natural to speculate that the heterogeneously distributed PDLA and PLLA chains cocrystallize together as the SC phase without remarkably large change of their spatial positions. Figure 19 illustrates this situation schematically. The above-mentioned points (b) and (d) can be interpreted reasonably by applying this idea. Figure 18. X-ray diffraction patterns measured for (a) the stereocomplex of L/D 50/50 ratio, (b) the same sample but after being exposed in the acetone or chloroform vapor for 3 h, and (c) the diffraction pattern of highly oriented PLLA α form as a reference. The X-ray exposure time was same between (a) and (b). It must be noted that the SC peak intensity was weakened, and the α peaks were detected to appear with the low degree of orientation.

temperatures results in the formation of the different crystalline phase, which may be related to the difference in the thermodynamic stability of the α and SC phases as well as the kinetic factor or the energetic barrier. A detailed discussion is a future work. (c) As already mentioned, the SC phase prepared from the L/D 70/30−30/70 mixtures was kept in the repeated processes of melt and crystallization (see Figure 6). On the other hand, the PDLA/PLLA blend with the L/D ratio higher or lower than the above-mentioned range gave the mixture of the SC and α crystals (Figure 7). This means that a critical L/D ratio may exist, beyond which the α phase becomes more stable and coexists with the SC phase. The SC crystal is made of the random distribution of the PLLA and PDLA chain stems. The small α-phase-like domains, composed of only the L or D chain stems, may exist locally in the SC phase (for example, in the boundary between the SC crystal regions). Once the size of these domains exceeds a critical point, then they are stabilized as the α phase and separated from the SC crystal region to give the mixture of the SC and α phases. (d) Another experiment was performed additionally. A sheet of pure PLLA film was contacted directly with an SC film of L/D 50/50 ratio and melted together for a while above the melting point of the SC phase. The relative content of the SC phase was found to increase after being cooled to the room temperature as known from the Xray diffraction data. This indicates the increment of the SC phase of the unbalanced L/D ratio by taking PLLA chains of the original α form into the SC film. These four important points allow us to conclude about the SC phase in the following way. In the as-cast film prepared

Figure 19. A model of stereocomplex formation from the solution cast L/D blend sample. The locally heterogeneous D (or L) chain stems in the as-cast film can crystallize into the α crystallites by heat treatment. Once after the α crystallites are melted at a higher temperature, only the stereocomplex crystallites are obtained by cooling. It should be noted that the chain stems of the asymmetric L/D ratio can be included in the SC crystallites. If many L (or D) chain stems are aggregated together in a local region, they form the α crystal domain.

As a final discussion in this section, we need to add some comments about the chemical structural change between PLLA and PDLA chains or the possibility of the so-called ester exchange as another explanation way of the formation of SC crystal in the blend samples with the nonequimolar L/D ratio. By heating PLLA (or PDLA) at a high temperature near the melting point for a long time (in a span of days), some parts of PLLA chain change their configuration to the PDLA form. If N


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chain stem. We can speculate the various possibilities of the local packing mode of PDLA and PLLA chains in the crystal lattice. At first, let us consider the case of the SC phase of L/D 50/ 50 ratio. One possible model is the perfectly random packing of the PDLA and PLLA chain stems at each lattice site (Figure 20a). Another possible packing model is the random

this type of ester exchange occurs during keeping the sample in the melting state, the ratio between D and L components might be changed to increase the formation probability of the SC with 50/50 ratio. However, it is difficult to imagine the chemical reaction occurring for a short time in an order of several minutes at 230 °C. The ester exchange reaction was reported to occur for such a long time as 25−30 weeks.96 Besides the effective D (and L) chain sequential length necessary for the SC formation is about 16 monomeric units.71 The probability to get such a long sequential array of D (and L) units by the ester exchange reaction is almost zero. Besides, the shorter sequences generated in the original chains might make it more difficult to cause the SC formation. In addition, one point to note is that if the ester exchange occurs actually in PLLA chains, it should occur also in PDLA chains at the same probability, causing no change of the D and L contents. 5. Possibility of Chain Folding. The SC sample forms a large spherulite in the isothermal crystallization process from the melt, which shows the lamellar structure as known from the small-angle X-ray scattering data. These lamellae are formed with the chain folding on the surfaces. A similar situation can be seen also for the single crystals of the SC phase. For introduction of such a chain folding structure, we have to have necessarily the chain packing mode with the upward and downward directions along the chain axis. As long as the structure model of R3c space group is adopted, all the chains direct upward (or downward), and so it is difficult to imagine the occurrence of the chain folding on the lamellar surface. The statistical packing of the upward and downward chains in the SC crystallites is consistent with the observations of spherulites and single crystals. Since the D and L helical chains are mixed together, the chain folding or chain reentry should occur randomly on the surface. The structure models of R3̅c, P1, P3̅ , and P3 space groups may be possible for the explanation of chain folding. However, as already checked, the first three models cannot be adopted here since they cannot reproduce the observed X-ray diffraction data satisfactorily. The P3 model is reasonable in the interpretation of the chain folding. Brizzolara et al.77 and Cartier et al.78 presented the growing mechanism of lamellar structure, where they discussed it including the chain folding possibility. For example, in the latter case, they show beautiful thin single crystals of the SC phase with only the equatorial diffraction spots. This should indicate the high possibility of the chain folding on the crystal surfaces of the SC crystals! Unfortunately, however, they did not mention the chain folding phenomenon of the SC phase with clear words. Besides, they did not discuss which space group (R3c and R3̅c) may give the possibility of the chain folding in a definite manner. As mentioned above, we know already how it is curious to apply the R3c and R3̅c models in the discussion of chain folding phenomenon. Chen et al.97 analyzed the solidstate NMR spectral data collected for the SC samples and estimated the various types of chain folding modes. Although they did not mention clearly in their paper, they suggested the preference of the R3c̅ model with the upward and downward chain directionality from the viewpoint of the chain folding analysis. But this structural model cannot be accepted anymore from the X-ray data analysis. 6. Structure of the Domain Boundaries. In the SC structure of P3 space group symmetry, the PLLA and PDLA chain stems are statistically randomly positioned at each lattice site depending on the L/D ratio. However, in the actual crystal lattice, one site must be occupied by either PDLA or PLLA

Figure 20. Local packing modes of L and R chain stems. The case of the blend sample with the L/D 50/50 ratio is illustrated as an example. (a) Random packing of R and L chain stems. (b) Regular packing of R an L chain stems in a domain. In the domain boundaries, the chain stems of the same handedness are adjacent to each other.

aggregation of the domains composed of the regular packing of PDLA and PLLA chain stems as illustrated in Figure 20b. One domain consists of the regular alternation of PDLA and PLLA chain stems. The neighboring domains are also composed of the regular packing of these two types of chain stems. The chain stems of the same handedness may encounter side by side at the boundary between these two domains. These aggregated domains are called the antiphase domains. The array of PLLA and PDLA chain stems is expressed as ...(RLRL...RL)(LRLR...LR)(RLRL...RL)... along a line, as illustrated in Figure 20b. By referring to the above-mentioned many experimental facts the random packing model (a) should be employed as the suitable structure of the stereocomplex. A similar discussion can be made for the SC crystal of the asymmetric L/D ratio. The chance of the local aggregation of the helical chains with the same handedness becomes higher as the asymmetry of the L/D ratio is increased. As the L/D asymmetry is increased up to some critical value, they will finally form the α form domains, which coexist with the domains of the stereocomplex.

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CONCLUSIONS The present study has proposed a new model for the crystal structure of the stereocomplex between the PDLA and PLLA chains on the basis of the X-ray diffraction data analysis. The O


Article

Macromolecules

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PDLA and PLLA chains coexist in the SC crystal lattice at the various ratios in the range of L/D = 70/30−50/50−30/70. Beyond these ratios, the α and SC phases coexist. The space group symmetry is not very high as the previously proposed R3c model, but it is simply P3, resulting in the statistically disordered packing structure of the D and L chains. One lattice site is occupied by the Ru or Ld chain stems at the probability given by the L/D ratio and another lattice site by the Rd or Lu chain stems. Beyond the L/D ratio 70/30, the D and L chain stems cannot coexist stably in the SC crystal lattice, but they show the phase separation of the α crystal phase from the SC phase. This newly proposed concept of the unbalanced packing of the PDLA and PLLA chain components in the common SC crystallites explains the various kinds of experimental facts described in the present paper. We need to confirm this concept from a different point of view. One idea is to check the systematic change in the optical activity of the crystal lattice, not the bulk sample. The optical activity should change from the right-handed value to the left-handed value as the L/D ratio in the crystal lattice changes from 0 to 100%. The measurement of the circular dichroism is one of the best methods for this purpose. But, this experiment must be performed by focusing on the crystal lattice, not the amorphous region. This requirement can be realized by applying the vibrational circular dichroic IR spectral measurement. The result was quite nice since the circular dichroic ratio of the crystalline IR bands was found to change systematically corresponding to the change of the L/D ratio. This experimental result supports confirmatively the above-mentioned new SC structure model proposed by the X-ray data analysis. The details will be reported in a separate paper.98

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected], Tel +81-52-1792, Fax +81-521793 (K.T.). ORCID

Kohji Tashiro: 0000-0002-7543-2778 Hideto Tsuji: 0000-0001-9986-5933 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported financially by the MEXT, Japan “Strategic Project to Support the Formation of Research Bases at Private Universities (2010−2014) and also (2015−2019)”.

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REFERENCES

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