Article pubs.acs.org/Macromolecules
Phase Transition Mechanism of Poly(L‑lactic acid) among the α, δ, and β Forms on the Basis of the Reinvestigated Crystal Structure of the β Form Hai Wang, Jianming Zhang, and Kohji Tashiro* Department of Future Industry-Oriented Basic Science and Materials, Toyota Technological Institute, Tempaku, Nagoya 461-8511, Japan S Supporting Information *
ABSTRACT: The crystal structure of poly(L-lactic acid) β form has been reinvestigated on the basis of the 2-dimensional X-ray diffraction diagram measured for the sample obtained by stretching the highly crystalline α form at a high temperature. The six helical chains of (3/1) conformation are packed in a rectangular unit cell of the space group P1 with the complicated but systematic packing mode of the upward and downward chains. This structural model is different from the previously reported trigonal model [Puiggali et al. Polymer 2000, 41, 8921]. The structural phase transition mechanism from the α form to the β form via the δ form has been proposed by assuming the cooperative displacements of the upward and downward helical chains as well as the conformational change. To support this mechanism, the two types of experiments were performed: (i) The highly oriented regular α form was stretched at about 165 °C to the various drawing ratios and cooled to the room temperature with the sample length fixed constantly. The X-ray diffraction data of these samples revealed the transition from the α to the mechanically deformd α (αd), to the δ form, and then to the β form depending on the drawing ratio. (ii) The α sample was suspended vertically with a constant load in the heating process, and the X-ray diffraction pattern was measured as a function of time (temperature). The original α form was found to melt at about 200 °C via the transition to the αd form and then to the δ form, followed by the recrystallization into the highly oriented β form. From these two experiments, the tension-induced structural transition from the α to the β form was found to occur via the disordering of the α form to the αd and to δ form under tension. The structural change process was derived on the basis of all of the knowledge collected from the X-ray structure analysis and the ex-situ and in-situ X-ray diffraction measurements: the molecular chains experience the cooperative translational slippage along the diagonal directions in the ab-plane to give the complicatedly mixed packing of the upward and downward chains to give the characteristic structure of the β form. At the same time, the chain conformational changes from the regular (10/3) to the disordered (10/3) and then to the (3/1) form during the disordering in the chain packing mode.
1. INTRODUCTION Poly(L-lactic acid) (PLLA, −[CH(CH3)−CO−O−]n−) is one of the most popular environmentally friendly polymers, which exhibits the various types of crystal modifications, including the mesophase,1,2 the α form,3−7 the δ (or α′) form,8−10 the β form,4,11−13 the γ form,14 and the stereocomplex between PLLA and PDLA.15 A brief review is made here about the crystal structure analyses of the α, δ, and β forms since these knowledge is needed for the discussion of the phase transition mechanism in a later section, which is a main theme of the present paper. (i) As for the α form, many efforts were made to reveal the chain conformation and chain packing mode in the crystal lattice.3−7,11,16,17 De Santis and Kovacs3 and Kobayashi et al.5 proposed the (10/3) helical conformation, where the 10 monomeric units are included in the three turns around the chain axis in the repeating period. Alemán et al. proposed the © XXXX American Chemical Society
P212121 space group based on the electron diffraction pattern of the α form single crystal.6 Sasaki et al. proposed the crystal structure of the same space group by quantitatively analyzing the X-ray diffraction data measured for a uniaxially oriented sample using a Cu Kα X-ray beam.17 Their structure models were refined furthermore by Wasanasuk et al. using about 700 X-ray diffraction spots picked up from the 2D wide-angle synchrotron X-ray diffraction diagram and also using the 2D wide-angle neutron diffraction diagram.7 The thus-established α crystal structure possesses the orthogonal unit cell of a = 10.683 Å, b = 6.170 Å, and c (fiber axis) = 28.860 Å (fiber axis) at 25 °C. The upward and downward chains of (10/3) helical conformation are packed regularly at the corner and center Received: February 5, 2017 Revised: April 5, 2017
A
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X-ray diffraction data of the β form fibers prepared by solution spinning and proposed the orthorhombic unit cell with a = 10.3 Å, b = 18.2 Å, and c (fiber axis) = 9.0 Å. Sawai et al.13 proposed also the orthorhombic unit cell with a = 10.4 Å, b = 17.7 Å, and c = 9.0 Å for the β form obtained by the melt-extrusion method. By referring to the density 1.27 g/cm3 measured for the bulk β form sample, they suggested that six chains of (3/1) helical conformation are included in a unit cell. However, they did not figure out the chain packing model concretely. Puiggali et al.12 analyzed the electron diffraction data of a thin β form film prepared from a dilute solution, and they proposed a structure model of the trigonal unit cell with a = b = 10.52 Å and c (fiber axis) = 8.8 Å and P32 space group. The three chains of (3/1) helical conformation are included in the unit cell. This simplified model may be useful for the discussion of the frustration of the regularly packed chain structures. However, it must be noticed here that all of these three chains in the unit cell are directed into the same direction along the c-axis (only upward or only downward) from the requirement of the space group. As an experimental fact, it must be realized here that the β form is obtained by stretching the α form, which has the alternately packed structure of the upward and downward chains. Cartier et al.14,24 and Puiggali et al.12 mentioned a possibility of statistical disorder between the upward and downward chains in the β crystal lattice based on the diffraction data as well as the energetic consideration. According to their discussion, the frustration causes such a statistical up−down orientation of helices. However, in order to clarify the transition mechanism from the α form to the β form, we need to establish the details of the crystal structural features of these two crystalline forms as well as that of the δ form. To that end, another such point must be noticed here that the two significant reflections at 2θ = 10.3° and 21.2° at 23 °C (10.6° and 21.3° at −140 °C) cannot be indexed as long as their trigonal unit cell is assumed. Rather, these two reflections can be indexed well using the orthorhombic unit cell proposed by Hoogsteen et al.11 and Sawai et al.13 This point will be reinvestigated later in the present paper. In this way, even at present, we have still several unsolved problems about the crystal structure of the β form: the problem of the upward and downward directionality of the chains and the problem of the crystal system, orthorhombic or trigonal or any others. It is necessary to reanalyze the crystal structure of the β form on the basis of the quantitative analysis of the 2D Xray diffraction data measured for as highly crystalline and highly oriented β sample as possible. The reinvestigation of the crystal structure of the β form is indispensable in the discussion of the phase transition mechanism from the α to β form via the δ form.18,22,23 The present paper reports the results of the crystal structure analysis of the β form and proposes the microscopic mechanism of the stress-induced crystal phase transition between the α and β forms by focusing on the change of the upward and downward chain packing mode.
positions of the unit cell.7,10,17,18 However, the observed 00l reflections of odd l values cannot be interpreted with the P212121 space group, as suggested by Sasaki et al.17 Wasanasuk et al. used the space group of the lower symmetry, P1211 or P1.7 The X-ray diffraction pattern shows the diffuse scatterings along the layer lines, which were interpreted as the existence of the disorder in the relative height of the neighboring domains.7 This type of disorder can reproduce the observed profile of the 00l meridional reflections.7 (ii) This type of disorder, in addition to the disorder of chain conformation and chain packing mode, is detected more significantly in the δ form.10 The δ form is generated by annealing the melt-quenched sample at a relatively low temperature below 120 °C. The stretch of the α form or annealing of the oriented mesophase below 120 °C gives the oriented δ form.18 Historically, the existence of the δ form was first suggested in the analysis of the crystallization behavior by Di Lorenzo19 and Cho and Strobl.20 Cocca et al.21 and Zhang et al.8,9 proposed that the δ form should exist as a crystal phase independent of the α form. Zhang et al. showed the discontinuous disorder-to-order phase transition from the δ to α form on the basis of the temperature-dependent measurements of the X-ray diffraction patterns and infrared spectra.8,9,22,23 The detailed analysis of the X-ray diffraction pattern of the δ crystal form was conducted by Wasanasuk and Tashiro.10 The X-ray diffraction pattern contains remarkable diffuse scatterings along the layer lines and some spotlike reflections observed in the X-ray pattern of the α form become quite diffuse and weak. As will be shown in detail in later sections, the positions and relative intensities of the observed Bragg reflections are different from those of the α form, indicating that the δ form is a crystalline phase independent of the α form, not a simple disordered modificaton of the α form (which should be called the deformed α form (αd)). The δ form has the orthogonal unit cell of a = 10.80 Å, b = 6.20 Å, and c = 28.80 Å (fiber axis), which includes the two conformationally disordered (10/3) helical chains. The chain packing mode itself is similar to that of the regular α form in such a point that the upward and downward chains are located at the corner and center positions of the unit cell. Here the upward and downward chains are defined by focusing the direction of the C(O)−O sequence along the chain axis. In addition, the degree of the relative-height disorder between the neighboring domains in the crystallite is higher for the δ form than for the α form. (iii) The disorder-to-order phase transition from the mesophase to the δ form was also studied in details by Tashiro et al. based on the temperature-dependent measurements of the X-ray diffraction and FTIR spectral data.8−10,18 The detailed Xray data analysis revealed that the small crystallites of the mesophase, prepared by stretching the melt-quenched amorphous sample at room temperature, aggregate together to form the larger crystallites of the δ form when heated to around 120 °C. The domains of the δ form are fused into a larger crystal of the α form by heating at a higher temperature as already mentioned above. In this way, the phase transition behaviors of the α, δ, and mesophases were proposed in a concrete way on the basis of the crystal structure information. But, the situation is different for the β form. (iv) As for the PLLA β form, Eling et al. first reported the existence of this crystal modification by stretching the oriented α form at a high temperature.4 Hoogsteen et al.11 analyzed the
2. EXPERIMENTAL SECTION 2.1. Samples. PLLA β form was prepared by the following two kinds of methods.18,25,26 (i) A sheet of PLLA film with ca. 200 μm thickness was prepared by casting from the CHCl3 solution of PLLA (Mw = 700 000 g/mol, Polysciences, Inc.), which was annealed at 150 °C for 2 h to obtain a highly crystalline unoriented α form at first. The β form was obtained by stretching this unoriented α form about 6 times the original length at 170 °C in an oil bath followed by annealing B
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Macromolecules at 150 °C for 2 h under tension. This sample was used for the X-ray structure analysis. (ii) The highly oriented α form was prepared at first by stretching the solution-cast film about 6 times the original length at room temperature and annealing at 165 °C for 2 h under tension.18 This highly oriented α form was tensioned at the various temperatures to get the β form (see Figures 14 and 15). The ultradrawn PLLA β form sample was kindly supplied by Emeritus Professor Tetsuo Kanamoto of Tokyo University of Science, which was prepared by a solid-extrusion method.13,25,26 2.2. X-ray Diffraction Measurement for the Structure Analysis. The 2D-WAXD pattern was measured for the thus-obtained β form at 23 °C using a Rigaku R-axis Rapid II X-ray diffractometer equipped with a cylindrical imaging plate camera. An incident X-ray beam was a graphite-monochromatized Mo Kα line (wavelength 0.71 Å). The sample was also measured at −140 °C using a Rigaku cold nitrogen gas blowing system (GD-1). 2.3. X-ray Data Analysis. The details of the X-ray data analysis were already described in our previous papers.27,28 The brief explanation of the actual process is made here. The positions of the observed X-ray diffraction spots were read manually on the 2D X-ray diffraction pattern. The integrated intensities I of the observed diffraction spots were evaluated by a curve-fitting method using a GRAMS (Thermo, Inc.) software. The structure factor |Fobs| was estimated from the equation I = KALpm|Fobs|2, where K is a scale factor to adjust the total sum of |Fobs| of all the observed diffraction spots to the calculated sum, A is an absorption factor, L is a Lorentz factor, p is a polarization factor, and m is a multiplicity.29 In the estimation of the integrated intensity, the accidentally overlapped reflections were separated using the GRAMS software in advance. The initial crystal structure model of the β form, necessary for the structure refinement, was built up by performing the lattice energy minimization using a commercial software Materials Studio (Accelrys Inc., Version 8.0). The 2D X-ray diffraction pattern and 1D diffraction profiles along the individual layer lines were calculated using a commercial software Cerius2 (version 4.6, Accelrys Inc.) based on the crystal structure model derived from the X-ray structure analysis. The model was refined so that the observed 1D diffraction profiles along the layer lines were totally reproduced as well as possible. The reliability of the thusobtained structure was expressed using a so-called reliability factor (R) defined in the equation
R=
Figure 1. X-ray diffraction patterns of the uniaxially oriented PLLA β form sample measured at 23 and −140 °C using a Mo Kα X-ray line as an incident beam. The cylindrical camera with the 127.4 mm radius was used for the measurement.
using a rectangular unit cell with the parameters a = 10.41 ± 0.02 Å, b = 18.02 ± 0.04 Å, and c (chain axis) = 9.00 ± 0.01 Å at 23 °C and a = 10.25 ± 0.03 Å, b = 17.80 ± 0.06 Å, and c (f.a.) = 8.92 ± 0.02 Å at −140 °C (47 reflections). These parameters are almost the same as those reported in the literature.11,13 As known from the a and b axial values, this orthogonal unit cell satisfies the relation b/a = √3, suggesting another possibility of utilizing the hexagonal or trigonal unit cell. The spatial relation between the trigonal and orthorhombic unit cells is illustrated in Figure 2. These two cells can be converted geometrically to each other. Then, the indexing using a trigonal unit cell (hexagonal type), as proposed by Puiggali et al.,12 was tried in the present study also. As shown in Figure 3, most of the observed diffraction spots can be indexed successfully using this trigonal cell. But, even after the many trials, the observed hk0 reflection at 2θ = 10.3° and hk4 at 21.2° (at 23 °C) (2θ = 10.6° and 21.3° at −140 °C, respectively) could not be indexed as indicated in Figure 3a,b. These two observed reflections do not come from the other crystal forms (α and δ forms) but intrinsic to the β form. From these analyses, we have concluded that the β form should take the orthogonal unit cell. The lattice spacings (d) of the observed hkl reflections are compared with the calculated values in Table 1. 3.2. Chain Packing Structure. 3.2.1. Building Up the Initial Structure Model. The observed repeating period along the chain axis, c = 9.00 Å, shows that the molecular chain takes a (3/1) helical conformation, as already reported.11,12,16,30 The density measured for the bulk β sample, about 1.27 g/cm3, suggested that the six chains of (3/1) conformation are included in the large rectangular cell.11,13 If we assume this large orthogonal cell belongs to the orthorhombic symmetry system, it becomes immediately quite curious to accept the chain packing structure of these six chains or 18 monomeric units in the unit cell because the orthorhombic space group symmetry supports the existence of 4, 8, 16, or 32 crystallographically asymmetric units in the cell. In other words, we need to apply the crystal system of lower symmetry or the monoclinic or even the triclinic lattice to the β form. (The trigonal unit cell is more preferable and easier to consider since the three chains are contained in the unit cell as indicated in Figure 2. But the indexing problem requested us to abandon this trigonal cell, as already discussed above.) In the construction of the packing structure of the six chains of (3/1) helical conformation, we referred to the following important experimental results reported in the literature: (i) The β form is produced by stretching the α form.25 As will be shown later, the α form crystal structure is created by the alternate packing of the upward and downward chains at
∑ ||Fobs| − |Fcalc||/∑ |Fobs|
where |Fobs| and |Fcalc| are the observed and calculated structure factors, respectively. 2.4. In Situ X-ray Diffraction Measurement under Tension during Heating Process. The purpose was to trace the structural change of the α form in the heating process under the constant load. A long rectangular film of 2 mm × 100 μm cross section was suspended vertically with a constant weight (about 40 g) as shown in Figure S1 of the Supporting Information. A pair of the heater rods were set near the both sides of the sample for heating the sample. The temperature was monitored by setting a thermocouple close to the sample position. The 2-dimensional X-ray diffraction patterns were measured at a constant time interval of 3−5 s during the continuous heating process from the room temperature to about 200 °C. The X-ray diffraction data were collected with a Cu Kα X-ray line (wavelength 1.54 Å) as an incident beam using a 2-dimensional photon-counting detector Pilatus 300k (Dectris Ltd., Switzerland) which was set at about 5 cm distance from the sample holder.
3. RESULTS AND DISCUSSION 3.1. Indexing of Diffraction Spots. Figures 1a and 1b show the 2D-WAXD patterns measured for the uniaxially oriented β form sample at 23 and −140 °C, respectively. (The ultradrawn β form sample supplied by Professor Kanamoto gave essentially the same X-ray diffraction pattern, and so only the data of the above-mentioned sample were used for the analysis.) The 39 observed reflections were successfully indexed C
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Figure 2. Geometrical relation between the orthogonal and trigonal unit cell. (left) real lattice and (right) reciprocal lattice.
gives the packing structure of only the upward (or only downward) helical chains. Figure 4 shows the X-ray diffraction profiles calculated for their model in comparison with the actually observed data. (The unit cell parameters were modified slightly to atrig = btrig = 10.40 Å so that the calculated X-ray diffraction peak positions were fitted to the observed data. The lattice size was 80 × 80 × 80 Å3, the thermal factor 10 Å2, and the lattice strain 0.0% in the calculation.) The agreement between the observed and calculated profiles is good for the hk0, hk1, and hk2 reflection profiles as a whole, but one equatorial diffraction peak (arrow) is totally lack, as already pointed out in the Introduction. Besides, we noticed that the calculated third layer line profile did not give any good agreement with the observed one. (ii) The α form takes the rectangular unit cell of the size a = 10.68 Å, b = 6.17 Å, and c (chain axis) = 28.86 Å. Similarly the δ form takes the unit cell of a = 10.80 Å, b = 6.20 Å, and c (chain axis) = 28.80 Å. The relation between the unit cell parameters among these three crystal modifications is as below (see Figure 16). a(α) ≈ a(δ) ≈ a(β),
b(α) ≈ b(δ) ≈ b/3(β),
c(α) ≈ c(δ) ≈ 3c(β)
Based on the points i and ii, we may imagine the chain packing mode of the β form in the following way. The unit cell of the α form consisting of the upward and downward chains is assumed as a basic unit cell of the β form, the parameters of which are a0 = 10.41 Å, b0 = 6.01 Å, and c0 = 9.00 Å, and the upward and downward (3/1) helices are positioned at the corner and center as shown in Figure 5. The large unit cell of the β form was initially built up by combining these three basic cells along the b-direction, as illustrated in Figure 5. The thusbuilt-up structure was energetically optimized under the assumption of the rigid (3/1) helical chains, where the energy minimization was performed using a Cerius2 software with the COMPASS force field parameters.31 Figure 6 compares the initial model and the thus energetically optimized structure (model 1). The rigid chains rotated around the chain axis to change the orientation from the parallel relation along the aaxis. At the same time they translated along the c-axis to change the relative heights. When compared with the original structure of the initial model 1, the parallel arrays of the upward and
Figure 3. Indexing of (a) hk0 and (b) hk4 reflections observed at 25 and −140 °C on the basis of the trigonal and orthorhombic unit cells. The circles correspond to the ξ values estimated for these observed reflections. At least any one reciprocal lattice point, shown with open spot, must cross these circles to satisfy the so-called Bragg reflection law. The trigonal unit cell cannot satisfy this condition for the black circles.
the corner and center positions of the unit cell, respectively, and so the β form is speculated to have the upward and downward chain in the unit cell. In such a sense, the trigonal structure model with the space group P32 proposed by Puiggali et al.12 is difficult to accept as it is because the space group P32 D
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Table 1. Indices, Lattice Spacing (dobsd and dcald) and Structure Factor (|Fobsd| and |Fcald|) of PLLA β Model 2 and β Model 3 at 23 °C
downward chains along the b-axis were not changed even after the energy minimization. The X-ray diffraction profile calculated for this model 1 is compared with the observed data for the equatorial and several layer lines as shown in Figure 7. This model 1 gives the relatively good reproduction of the observed equatorial and first layer lines. But the agreement is not very high for the other layer line profiles. The structure refinement was tried for the model 1 by manually changing the orientation and relative height of the chains. However, even after the many trials, the model 1 which keeps the linear arrays of the upward (and downward) chains along the b-axis, as observed in the crystal structure of the α form, did not give very good reproduction of the observed Xray diffraction profiles. At this stage, therefore it is difficult to emphasize the preference of the model 1 compared with the trigonal model proposed in the literature.12 There are several possible modes to pack the 3 upward and 3 downward chains in the orthogonal unit cell of the β form. The
above-mentioned model 1, as shown in Figure 5, is one of these possible structures. At first glance, there might be many various candidates of the structure model to pack these six chains in the orthogonal unit cell. But, actually, the independent models are quite limited when the crystallographically equivalent structures are erased. Figure 8 shows the thus-obtained two models (2 and 3), which are different from model 1 in the packing mode of the upward and downward chains. The crystal lattice energies of these two models were minimized by fixing the unit cell size to the experimentally estimated one, where the molecular chains were assumed as the rigid bodies; that is, their conformations were not changed even when the packing mode of these rigid chains was varied. The thus energetically optimized structures were further modified so as to reproduce the observed X-ray diffraction profiles as nicely as possible. Since the observed X-ray diffraction spots are small in number and not enough for the determination of all the structure parameters of the six chains in the unit cell, these chains were E
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Figure 4. Comparison of the observed X-ray diffraction profiles with those calculated for the trigonal structure model.12 The indexing is based on the trigonal cell.
of model 1. The model 2 may be better than the model 3 when judging from the better agreement of the layer line profiles (for example, the third, fourth, and fifth layer lines). The crystal structure of the model 2 viewed from the two different directions is shown in Figure 11, in which the upward and downward chains are indicated by U and D symbols, respectively. The observed (|Fobsd|) and calculated (|Fcald|) Xray structure factors of the models 2 and 3 are compared in Table 1. The C and O atomic coordinates of a helical chain in the models 2 and 3 are listed in Table 2. The R factor estimated for models 2 and 3 is 19.0 and 19.9%, respectively, almost the same as each other within the experimental error. This suggests that both of these two types of structures might be realized in the crystal lattice of the β form as the local domains. The size and distribution of these domains are difficult to estimate concretely. When viewing the crystal structure shown in Figure 11, we notice that one upward chain is surrounded by the 4 downward and 2 upward chains of the similar (3/1) conformation and another upward chain by the 3 downward and 3 upward chains. The similar situation can be seen for the downward chains also. In this way the chains exist in the different circumstances. This type of chain packing mode was discussed in detail by Lotz et al. for the structure of stereocomplex of PLLA and PDLA chains, the structure of isotactic poly(2-vinylpyridine), etc., using a term of the so-called frustrated structure.32 In spite of the complicatedness of chain packing structures, the models 2 and 3 are the cases with the regular packing mode of the upward and downward chain stems in the crystal lattice, although the surrounding circumstance is different depending on the individual chain stem as mentioned above. It is speculated that the packing mode of these upward and downward chains may be disordered more or less with the hybridized structure between the models 2 and 3 because the X-ray diffraction patterns are not very much different between these two structures as mentioned above. The next problem to be solved is how to derive the α-to-β structural transition mechanism. Domain-Disordered Packing Model. Before we discuss the α-to-β transition mechanism in the next section, we need to check a possibility of the aggregation disorder of the domains in
Figure 5. Building up of the initial crystal structure model 1 of the PLLA β form starting from the structure of the α form.
Figure 6. Building up of the energetically stable model 1 starting from the initial model shown in Figure 5.
assumed here also as the rigid bodies. The orientation of the helical chains viewed along the chain axis was changed by rotating about 60° around the c-axis as well as the translation along the c-axis. The relative heights of the methyl groups are indicated in these figures. The comparison between the observed and calculated X-ray diffraction profiles is shown in Figures 9 and 10 for the models 2 and 3, respectively. Here the calculation of the diffraction profiles was performed using a Cerius2 software by assuming the crystalline size of 100 (a) × 100 (b) × 100 (c) Å3, the lattice strain of 0% (a) × 0% (b) × 0% (c), and the isotropic temperature factor 4 Å2. As a whole, these two models give better agreement between the observed and calculated diffraction profiles when compared with the case F
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Figure 7. Comparison of the observed X-ray diffraction profiles with those calculated for the structure model 1.
propiolactone).33 Such an introduction of disorderliness into the inner structure may breaks the relative intensity relation between the calculated reflections on the many layer lines, and so it is inconsistent with the crystal structure model derived from the reflection data analysis. How can we generate the streaks along the layer lines without any significant modification of the Bragg reflections? One way is to introduce the relative height disorder among the domains with the inner structure of the unit cell kept unchanged. This is the case of PLLA α and δ forms.7,10 In fact, the disorderliness of domain heights keeps the inner structure of a domain and modifies only the boundary structure between the neighboring domains, affecting almost negligibly the observed WAXD data, as already discussed in the literature.10 The streak lines detected for the 2D X-ray diffraction pattern of the uniaxially oriented β form can be interpreted also using such a concept. Another checking point of the relative height disorder of domains is to measure the 00l diffraction profile, which was found to be sensitively affected by the degree of the domain height disorderliness.7,10 Then we measured the 00l reflection profile for the uniaxially oriented βform sample as being reproduced in Figure 12. The 003 reflection is the most intense and the other reflections are quite weak. The observation of 001, 002, and so on indicates the symmetrical breakage from the regular 31 helical conformation, consistent with the structure of the P1 space group symmetry as proposed above. We calculated the 00l reflection profile for the crystal structure model 2 (and model 3) without any domain height disorder, which could not reproduce the observed characteristic profile as seen in Figure 12 (the temperature factor along the c-axis = 10 Å2, crystallite size along the c-axis = 100 Å). Rather, it was found that the random shift of the relative height of the neighboring domains (Figure 13) can reproduce the observed profile relatively well as compared in Figure 12. In this way, the PLLA β form may be assumed to take the crystallite structure consisting of many small domains, as illustrated in Figure 13. 3.3. Phase Transition Mechanism. In this section, we are challenged to discuss the transition mechanism from the α form to the β form. For this purpose, however, we need to clarify the various points which are necessary for the derivation of the
Figure 8. Energetically minimized crystal structure models 2 and 3. The U and D denote the upward and downward chains along the caxis, respectively. The figures shown in the pictures indicate the relative heights of the methyl side groups.
the crystal lattice. In the previous reports,7,10 we discussed the disorder of domains in the α and δ forms, in particular the disorder of the relative height of the neighboring domains along the chain axis, on the basis of the observed 00l diffraction profiles as well as the streaks along the layer lines. Here the domain means the X-ray coherent region of regularly packed chain stems with a finite size. The δ form consists of many such small domains with the relative height disorder. By annealing the δ form above 120 °C, these domains coalesce together to form the larger domains of the α form. One method to check the existence of the relative height disorder of domains is to observed the streaks of the layer lines overlapping with the spotlike Bragg reflections (see Figure 1).10 If the inner structure of the unit cell itself is disordered through the sliding of the chains along the chain axis, the streaks are observed significantly and the Bragg reflections become quite diffuse along the layer lines, as seen typically in the case of poly(βG
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Figure 9. Comparison of the observed X-ray diffraction profiles with those calculated for the structure model 2.
Figure 10. Comparison of the observed X-ray diffraction profiles with those calculated for the structure model 3.
spotlike diffractions are detected in the X-ray diffraction diagram of the initial α form. By stretching the sample up to the drawing ratio (DR) of 3, many layer line diffraction spots become weaker and diffuse except the several strong peaks (for example, the spotlike reflections observed in the higher-order layer lines became quite diffuse although the total pattern was not changed remarkably). This observation does not tell the phase transition of the α form but should be assumed as the mechanical deformation of the crystal structure. So, the crystal form giving this relatively diffuse X-ray diffraction pattern may be called here the structurally deformed α form (αd). Further stretching makes these diffractions broader and more diffuse, and at last the structurally deformed α form transforms to the δ form. (The identification of the δ form can be made by checking the diffuse layer lines. In particular the originally spotlike reflections on the 1st, 4th, 7th, and 10th layer lines
transition mechanism, as will be described in the following several sections. As described below we performed the two different types of the experiments. 3.3.1. High-Temperature Drawing of the Regular α Form. As already published in our preliminary reports,22,23 the original α form sample was stretched at about 165 °C at the various drawing ratios, and it was cooled quickly to the room temperature by keeping the sample length unchanged. In this experiment, the retention of the tensile force along the drawing direction is important. By doing so, the structural state appearing in the high temperature drawing process can be detected even after cooling to the room temperature. If the sample was relaxed in the high temperature region, it changed immediately to the regular α form in addition to the small amount of the β form. The X-ray diffraction data of these variously drawn samples are shown in Figure 14. The sharp and H
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was cooled again on purpose. The highly oriented β form was clearly detected to crystallize in the cooling process. On the way of further cooling, the long arcs appeared, indicating the crystallization of the β form with the lower degree of orientation. By heating up again, these arcs disappeared at first and then only the spots coming from the highly oriented β crystal were observed up to about 230 °C. Figure 15c shows the case of larger weight loading (about 2 MPa). The diffraction pattern of the α phase changed to that of αd at 223 °C and at the next moment (225 °C) the pattern changed to that of the β form. Unfortunately, the data at 224 °C could not be detected, which should be the diffraction pattern of the δ form, as speculated from the above-mentioned two experiments. The β form remained up to 230 °C without breakage. After the end of the experiments, the X-ray diffraction measurement was performed for all of these three samples at room temperature. All samples were observed to be elongated by about 2 times the original length at the heated part, and the β form was detected in the wide area of the elongated zone. In this way, the heating of the oriented α form under the relatively small tensile stress of 1 MPa caused the transition from α to αd and δ at first and then melted. However, this molten sample was not broken, but the highly oriented β form appeared at the higher temperature region. The application of a little larger weight caused the apparently solid-state transition from the α to β form via the αd (and δ) form. But, it might be also the melt-recrystallization phenomenon. From these experimental results we may conclude that the order-to-disorder transition from the regular α form to the β form occur in the two ways depending on the applied tensile force; (i) one is a solid-state transition at a relatively low temperature below the melting point (100−170 °C25), and (ii) another is a melt-recrystallization at a highly superheated state. The former case (i) is the brute stretching of the regular α form up to a high drawing ratio below the melting point. The highly oriented β sample was obtained for the first time by stretching 3−4 times the original length. In this case, the solid-state transformation to the β form occurs via the αd and δ forms. (It must be noted that the sample length was fixed strongly during the cooling to the room temperature. If not, the regular α form would appear.) In the latter case (ii), the applied tension was quite small and the drawing ratio was only 2 times, but the superheating occurred at a high temperature. The strong constraint of the sample generated the oriented molten state, in which the thermal motion of the molecular chains was highly bound and so the entropy change between the crystal and melt became smaller. As a result, the superheating phenomenon occurred to shift the melting point by about +20 °C. This structurally constrained melt seems to play an important role as an intermediate state in the recrystallization phenomenon into the highly oriented β form. (In the former case also, the actual process might be a melt of the α form and a recrystallization to the β form, which may occur through the local heating under the forceful stretching even at such a low temperature as 100 °C.25) 3.3.3. Domain Size Reduction in the α-to-β Transition. As seen in Figures 14 and 15, the diffuse layer lines overlap with the Bragg diffraction spots, indicating the disordering of the relative height of the domains. At the same time we need to notice that the half-width of the equatorial diffraction peaks increases in this process also, indicating the decrease in the Xray coherent domain size. The rough estimation of the halfwidth was made for the innermost spot of 110/200 (α and δ)
Figure 11. X-ray analyzed crystal structure of PLLA β-form (model 2). The U and D denote the upward and downward chains along the caxis, respectively. The O−C(O) direction is used to indicate the chain orientation along the c axis.
become weaker and more diffuse.) At almost the same time, the diffuse scatterings of the β form starts to overlap with those of the δ form, and finally the X-ray diffraction pattern changes to that of the pure β form. In this way, the X-ray diffraction data collected for a series of oriented samples drawn at high temperature at the various drawing ratios indicate that the α-toβ structure change occurs in a manner of order-to-disorder transition via the αd and δ forms. 3.3.2. In Situ X-ray Diffraction Measurement under Tension at High Temperature. More direct observation was tried in the following way. A highly oriented and highly annealed α form sample was suspended vertically with a constant weight and heated up to the melting point continuously, during which the wide-angle X-ray diffraction pattern was measured as a function of temperature. Figure 15 shows the 2D X-ray diffraction patterns measured for the three different weights applied to the samples. Figure 15a is the case of the relatively small weight (about 1 MPa). The X-ray diffraction pattern was that of the α form in the temperature region below 150 °C, around which the reflections changed from the spots to the relatively long arcs, indicating the worse orientation of the crystallites. The further increment of temperature caused the weakening of the diffraction intensity and some reflections became diffuse. By referring to the characteristic X-ray diffraction patterns of these individual crystalline forms, we may assign the observed patterns to the αd and δ forms as indicated in these figures. These diffractions disappeared almost perfectly by heating to about 200 °C, around which the pattern changed to the hallo pattern characteristic of the melt. [The temperature region is too high compared with the melting point of the unoriented α sample (around 175 °C). This may come from the superheating phenomenon of the α form under the constraining condition.] The further heating was found to cause the sudden change of the X-ray diffraction pattern to that of the highly oriented β form with the spotlike diffraction peaks. All the layer lines showed the horizontal streaks, indicating the disorder in the relative height of the chains. Figure 15b shows the similar observations. But, at the moment where the whole crystalline diffraction pattern changed to the amorphous halo, the sample I
DOI: 10.1021/acs.macromol.7b00272 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules Table 2. Atomic Fractional Coordinates of PLLA β Form Models 2 and 3 Model 2 chain 1 atoms
x
y
C1(1) C1(1) C2(1) O3(1) C4(1) O5(1) C1(2) C2(2) O3(2) C4(2) O5(2) C1(3) C2(3) O3(3) C4(3) O5(3) atoms C1(1) C2(1) O3(1) C4(1) O5(1) C1(2) C2(2) O3(2) C4(2) O5(2) C1(3) C2(3) O3(3) C4(3) O5(3)
0.620 0.620 0.598 0.707 0.675 0.781 0.825 0.954 0.765 0.725 0.666 0.638 0.531 0.590 0.684 0.638
0.493 0.493 0.572 0.495 0.444 0.438 0.448 0.419 0.397 0.448 0.393 0.369 0.319 0.412 0.422 0.484 chain 4 0.839 0.795 0.789 0.731 0.713 0.633 0.721 0.765 0.771 0.775 0.809 0.819 0.7744 0.826 0.157
0.654 0.611 0.705 0.668 0.633 0.620 0.738 0.676 0.789 0.837 0.963 0.793 0.736 0.660 0.765
chain 2 z 0.554 0.554 0.494 0.675 0.431 0.416 −0.098 −0.159 0.022 0.778 0.763 0.227 0.166 0.348 0.104 0.090 0.213 0.092 0.336 0.351 0.865 0.926 0.744 −0.012 0.004 0.540 0.601 0.419 0.662 0.677 0.542
chain 3
x
y
z
x
y
z
0.234 0.234 0.330 0.290 0.200 0.254 0.294 0.332 0.188 0.235 0.122 0.074 −0.061 0.103 0.174 0.232
0.682 0.682 0.740 0.643 0.628 0.575 0.561 0.484 0.558 0.607 0.601 0.600 0.620 0.648 0.610 0.669 chain 5 0.158 0.107 0.099 0.108 0.077 0.059 0.111 0.056 0.034 0.077 0.085 0.148 0.322 0.327 0.275
0.646 0.646 0.586 0.767 0.522 0.508 −0.007 −0.067 0.114 0.870 0.855 0.319 0.258 0.440 0.196 0.182
0.133 0.133 0.115 0.221 0.185 0.290 0.335 0.463 0.273 0.236 0.173 0.144 0.034 0.098 0.193 0.150
0.997 0.997 1.076 0.998 0.947 0.939 0.948 0.917 0.898 0.950 0.896 0.873 0.825 0.916 0.925 0.987 chain 6 0.270 0.281 0.255 0.229 0.280 0.223 0.200 0.147 0.241 0.253 0.314 0.885 0.236 −0.015 0.401
0.566 0.566 0.506 0.687 0.443 0.428 −0.086 −0.147 0.035 0.791 0.775 0.239 0.179 0.360 0.117 0.102
0.677 0.712 0.607 0.562 0.435 0.625 0.662 0.724 0.754 0.800 0.705 0.747 0.269 0.182 0.211
0.421 0.666 0.680 1.195 1.255 1.074 0.318 0.333 0.869 0.748 0.992 1.006 0.490 0.369 0.613
0.105 0.062 −0.069 0.119 0.161 0.218 0.245 0.349 0.295 0.201 0.251 0.541 0.782 0.864 0.295
0.628 1.142 1.202 1.021 0.265 0.281 0.816 0.877 0.695 0.939 0.954 0.273 0.602 0.930 0.550
Model 3 chain 1
chain 2
atoms
x
y
z
x
C1(1) C2(1) O3(1) C4(1) O5(1) C1(2) C2(2) O3(2) C4(2) O5(2) C1(3) C2(3) O3(3) C4(3) O5(3) atoms C1(1) C2(1) O3(1) C4(1) O5(1) C1(2) C2(2)
0.105 0.050 0.189 0.179 0.284 0.323 0.460 0.287 0.226 0.193 0.175 0.093 0.110 0.197 0.126
0.305 0.378 0.320 0.265 0.275 0.290 0.281 0.233 0.277 0.214 0.188 0.124 0.222 0.245 0.298 chain 4 0.772 0.819 0.781 0.834 0.861 0.917 0.808
0.847 0.787 0.968 0.723 0.709 0.194 0.134 0.315 1.071 1.056 0.520 0.459 0.641 0.397 0.383
0.086 −0.042 0.129 0.187 0.252 0.261 0.372 0.303 0.207 0.257 0.275 0.291 0.188 0.224 0.108
0.131 0.011 0.255 0.270 0.784 0.844 0.663
0.705 0.725 0.619 0.577 0.442 0.625 0.676
0.813 0.780 0.713 0.659 0.656 0.558 0.602
y 0.591 0.623 0.635 0.592 0.640 0.667 0.715 0.611 0.619 0.560 0.534 0.454 0.533 0.584 0.595 chain 5 0.172 0.119 0.121 0.135 0.117 0.080 0.127 J
chain 3 z
x
0.835 0.775 0.956 0.712 0.697 0.183 0.123 0.304 1.060 1.044 0.509 0.448 0.630 0.386 0.371
0.603 0.556 0.688 0.672 0.778 0.818 0.955 0.775 0.7202 0.679 0.659 0.569 0.598 0.688 0.623
0.001 0.245 0.260 0.774 0.834 0.653 −0.103
0.150 0.134 0.012 0.106 0.199 0.165 0.153
y 0.494 0.569 0.506 0.452 0.457 0.471 0.456 0.415 0.461 0.400 0.375 0.314 0.411 0.431 0.487 chain 6 0.967 0.992 1.031 0.933 0.949 0.887 0.860
z 1.017 0.957 1.138 0.893 0.879 0.364 0.304 0.485 1.241 1.226 0.690 0.629 0.811 0.567 0.553 0.226 0.740 0.801 0.620 −0.136 −0.121 0.415
DOI: 10.1021/acs.macromol.7b00272 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules Table 2. continued O3(2) C4(2) O5(2) C1(3) C2(3) O3(3) C4(3) O5(3)
0.699 0.636 0.611 0.577 0.698 0.674 0.791 0.791
0.809 0.755 0.730 0.653 0.722 0.776 0.778 0.163
−0.093 −0.078 0.458 0.519 0.337 0.581 0.595 0.121
0.722 0.744 0.802 0.711 0.771 0.326 0.273 0.226
0.067 0.042 0.080 0.098 0.155 0.932 0.972 0.924
−0.088 0.448 0.327 0.571 0.585 0.088 −0.033 0.211
0.157 0.240 0.192 0.303 0.946 0.832 0.838 0.445
0.780 0.866 0.914 0.934 0.794 0.239 −0.016 0.974
0.476 0.294 0.537 0.552 0.191 0.181 0.509 0.148
Figure 14. 2D X-ray diffraction diagrams measured at room temperature for the PLLA α form sample stretched at the different drawing ratio (DR) at 165 °C. The αd indicates the deformed α form. It must be noted that the initial α form is mechanically deformed (αd) and transforms to the δ form, which overlaps with the β form and then changes finally to the β form.
Figure 12. Meridional 00l reflection profile of uniaxially oriented PLLA β form sample in comparison with those calculated for model 2 (Figure 8) with and without domain height disorder (Figure 13).
form into the mosaic-like aggregation consisting of smaller domains in the δ and β crystallites. As discussed above, the inner structure of these small domains are disordered in the relative height along the chain axis. The crystallite size in the lateral direction is almost the same between the δ and β forms, and the δ-to-β transition is considered to occur in such subdivided small domains. In this way, the tensile force causes (i) the cleavage of originally large α crystalline domains into the smaller domains, (ii) the axial slippage of these subdivided domains along the chain axis, and (iii) the inner structural change from the δ to β form. (Unfortunately, we do not know at present whether the inner structural change (iii) occurs af ter the cleavage and slippage of the domains (i) and (ii) or at the same timing.) 3.3.4. Chain Conformational Change. In Figure 14, the layer lines of the β form locate at the lower positions than those of the δ form, which corresponds to the longer helical pitch of the β form chain compared with that of the δ (and α) form. According to the above-mentioned X-ray analyzed results, the molecular chains change the conformation from (10/3) to (3/ 1) type in the process of α(δ)-to-β transition, which occurs through the small changes of the torsional angles of the skeletal chain. As shown in Figure 16, the local conformation of one monomeric unit may be roughly expressed as TT′G, where T (and T′) and G are the trans and gauche angles, respectively.10 But, the averaged values of T and G angles change from 150− 170° to 155−180° and 70° to 76°, respectively, in the transition process. As a result, the helical pitch increases from 2.89 to 3.00 Å/monomeric unit. 3.3.5. Change in the Chain Packing Mode. Now let us discuss the change of chain packing mode in the unit cell. As seen in Figure 11, PLLA β form takes a complicated and low
Figure 13. A domain aggregation model with the relative height disordering along the chain axis (derived from model 2).
and 130/200 (β) reflection: 0.12°, 0.26°, and 0.27° for the α, δ, and β forms, respectively, which may correspond respectively to the crystallite size of about 305 Å (α) and 140 Å (δ and β) in the lateral direction perpendicular to the chain axis, where we used the Scherrer’s equation with the formula ⟨crystallite size⟩ = 0.9λ/(Δ(2θ) cos(θ)) for the wavelength λ, the half-width Δ(2θ), and the Bragg angle 2θ.29,34 As reported in the previous paper,18 the crystallite size along the chain axis is also reduced in the transition from the α to δ form (150 and 100 Å, respectively). In this way, the tensile force applied along the draw direction causes the cleavage of the large domain in the α K
DOI: 10.1021/acs.macromol.7b00272 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules Figure 15. continued
long arcs disappeared at first, and only the spotlike diffraction peaks of the highly oriented β form were detected with the streaks along the horizontal direction. (c) Temperature dependence of 2D X-ray diffraction pattern of highly oriented α form under a constant tensile force (about 2 MPa). The diffraction pattern changed to that of αd at 223 °C, and then that of the oriented β form was detected at 225 °C. (Unfortunately, the data at 224 °C could not be detected, which should be of the δ form as speculated from the data (a) and (b).) The β form was detected up to 227 °C and then melted. For comparison, the diffraction pattern of the β form measured at room temperature is shown also (right downward).
Figure 16. Comparison of molecular chain conformation between the α and β forms. The skeletal torsional angles and helical pitch are also shown for comparison. The torsional angles are the roughly averaged values among the widely distributed values coming from the low symmetry of the helices in the crystal lattice.7,10
symmetric packing structure (P1) consisting of the six chains in the orthogonal unit cell. However, the chain packing mode is not very random, but the upward and downward chain stems are located in a systematic way. The geometrical relation of the crystal structure between the α (and δ) and β forms is shown in Figure 17. The unit cell size and the chain positions in the abplane are almost the same among these three crystalline forms. The main difference in the chain packing mode is seen for the arrangement of the upward (U) and downward (D) chain stems in the crystal lattice. In the cases of the α and δ forms, the U and D chain stems are arrayed respectively at the corner and center positions of the unit cell, and these arrays form the alternate alignments along the a-axis. In the crystal lattice of the β form, the U and D chain stems are arranged in a complicated way as already explained in Figures 8 and 11. Therefore, we need to introduce the translational displacement of the U and D chains in the crystallites. There might be many possible modes to displace the U and D positions in the crystal lattice, among which we need to estimate the several simplest ways as the elementary processes. Figure 18 shows an illustration of one possible way to cause the transition of the packing mode from α to β form. We pick up the arrays of U and D chain stems along the diagonal direction in the crystal lattice of the α form. By applying the tensile force along the chain direction, the shear stress component might cause the displacement of the chain arrays. In Figure 18, the diagonal slippage is assumed to
Figure 15. (a) Temperature dependence of 2D X-ray diffraction pattern of highly oriented α form under a constant tensile force (about 1 MPa). The pattern change reveals the transition from the α to the mechanically deformed αd, the δ form, and to the oriented melt, which recrystallizes into the highly oriented β form. (b) Temperature dependence of 2D X-ray diffraction pattern of highly oriented α form under a constant tensile force (about 1 MPa). In the cooling process after the disappearance of all the crystalline diffractions at about 202 °C, the pattern of the highly oriented β form (spotlike reflections) started to appear at around 168 °C, and then the long arcs of the lessoriented β form overlapped at 165 °C. In the reheating process the L
DOI: 10.1021/acs.macromol.7b00272 Macromolecules XXXX, XXX, XXX−XXX
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shape ([process (b)]). The thus-obtained structure corresponds well to the chain arrangement detected in the model 2. Since the slippage can occur in the diagonal directions of the opposite tilting angles along the 110 and 11̅0 planes, there may exist a pair of the twinned structures as a result (Figure 18). The model 3 can be obtained by shifting the UUD arrays (for example) along the b-direction furthermore. It might be a little unnatural to accept the diagonal slippage of one U D array with fixing the neighboring two UD arrays. Actually, it may occur in the mutual slippage mode of the neighboring arrays. Figure 19 illustrates this situation concretely. We can focus on the three arrays of U and D chain stems, which cause the mutual slippages into the opposite directions. This more rational mutual movement of U and D chain stems is equivalent to that shown in Figure 18. Unfortunately, at present, we cannot tell a reason why the pairs of three diagonal arrays consisting of the alternately arranged U and D chain stems must show such a mutual slippage by the application of the tensile force along the chain axis. The present discussion is to show one possibility of the transition mechanism to induce the structural change from the α form to the β form by focusing on the displacement of the U and D chain stems. The energetic calculation based on the molecular dynamics is now being carried out. 3.3.6. Total Image of Structural Change in the α−δ−β Phase Transition. So far we have discussed the structural changes to occur in the α−δ−β phase transition from the different points of view on the basis of the X-ray analyzed crystal structures of the α, δ, and β forms. For this purpose, the crystal structure of the β form was reinvestigated to show the complicated packing mode of the U and D chains in the large rectangular unit cell. These information can be combined together to build up the whole image of the structural change in this transition. The information obtained is listed as below.
Figure 17. Comparison of the unit cell ab-plane structure between the α (δ) and β forms, where the model 2 is employed for the β form. The U and D indicate the upward and downward helical chains along the caxis, respectively. In the crystal of α (δ) form, the array composed of only the U (D) chain stems is formed along the b-axis. These U and D arrays are alternately arranged along the a-axis. In the β form crystal, these U and D chain stems are arranged in a complicated manner (refer to Figures 8 and 11).
occur for the every third array, resulting in the mutual exchange of positions between the U and D chain stems [process (a)]. As a result, the change of the regular alignments from UUU to UUD and from DDD to DDU occurs along the b-axis. These UUD and DDU pairs are packed alternately along the a-axial direction. During this process, the tensile force induces the conformational change from (10/3) to (3/1) form as explained above (Figure 16). This structure will change furthermore to the more energetically stable packing structure of rectangular
Figure 18. An illustration of one possible process of structural change from the α form to the β form. (a) The tensile force causes the slippage of U/ D chain stem arrays along the 110 planes and (b) the thus-created structure of the deformed unit cell shape transforms furthermore to more energetically stable structure of the β form (model 2). The slippage into another diagonal direction (along the 1−10 planes) causes the twin structure. M
DOI: 10.1021/acs.macromol.7b00272 Macromolecules XXXX, XXX, XXX−XXX
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(ii) The crystallite size is large for the α form, about 150 Å in the c-axial direction and about 300 Å in the ab-plane.18 The crystallite becomes smaller in the δ and β forms because of the effect of externally applied tensile stress: about 100 Å along the c-axis18 and 140 Å in the lateral direction. The size is almost the same between the δ and β forms. (iii) The crystallite consists of the X-ray-coherent domains. The relative height of the neighboring domains is random as estimated from the X-ray 00l diffraction profile. (iv) The helical chain conformation changes from (10/3) (or (3.33/1)) in the α and δ forms to (3/1) of the β form. The repeating period increases in this process through the slight but significant torsional angle changes of the skeletal CC and CO bonds (Figure 16). (v) The spatial positions of some U and D chain stems in the crystallite are exchanged systematically in the transition from the α, δ, and β forms. The regular packing of the D and U chains in the α and δ forms changes to the more complicatedly arranged packing in the β form. The environment of the U (D) chains is not necessarily the same at the various lattice points, giving a frustrated structure. But this complicated packing mode is not necessarily totally disordered. If the perfectly disordered chain packing structure is realized, one lattice site is occupied statistically by the U and D chain stems at 50% probability, and so all the lattice sites become equivalent to each other. If so, the unit cell of the β form should be assumed to be much smaller than that proposed in the present paper. The complicated but systematic packing of the U and D chain stems in the β crystalline domain is induced by the cooperative slippage of the UD arrays in the unit cell. From these items (i) to (v), we can build up the whole structure of a crystallite as shown in Figure 20. The crystallite of the α form is a kind of single domain with regular chain packing mode of the U and D chains. The application of a tensile force deforms the crystallite of the α form and induces the disorderliness of the chain conformation and chain packing mode (structurally deformed α form). The further increment of the tensile force breaks the originally large domain into the aggregation of small domains with the relative height disorder
Figure 19. Equivalence of (a) the slippage mode of one array in the every 3 arrays to (b) the mutual slippage mode of the neighboring arrays included in the set of the three arrays enclosed with the blue broken lines.
(i) The transition occurs from the α form to the β form via the αd and δ forms, meaning that the phase transition is that of the order-to-disorder transition type. The transition may occur apparently in two ways; one is a solid-state transition at a relatively low temperature below the melting point (100−170 °C, Figure 14 and ref 25), and another is a melt-recrystallization at a highly superheated state (Figure 15). The present discussion is made mainly for the former case. In the latter case also, the process itself might be similar to the former one but the oriented amorphous (or oriented liquid crystalline) phase may play a role as an intermediate state.
Figure 20. A schematic illustration of the tension-induced phase transition from the α form with a large single domain to the β form with the aggregated domains of smaller size via the δ form of the structurally disordered structure and smaller domains (refer to the structural change shown in Figures 18 and 19). Depending on the different external conditions, there might be two routes from the δ form to the β form: one is a direct transformation from the δ to the β form, and another is via the intermediate state between the two solid states. N
DOI: 10.1021/acs.macromol.7b00272 Macromolecules XXXX, XXX, XXX−XXX
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constrained entropy change shifts the melting point of the α form and induces the formation of liquid crystalline phase as an intermediate state) may allow us to interpret these experimentally observed transition behaviors more systematically than that shown in Figure 20. The α crystal is deformed easily to the δ form by the application of tensile force at a relatively low temperature near the glass transition point (70 °C). The δ form consists of the disordered structure with the smaller crystallite size. Jarivasakoolroj et al. produced the biaxially oriented PLLA film at the high drawing rate (75 mm/s) at 90 °C, which was found to exhibit the remarkably high mechanical property compared with that produced at a normal drawing rate (5−10 mm/s).35 The film is highly crystalline but consists of many highly oriented δ form domains of small size. In this way the δ form is important in the production of the practically tough PLLA film. Compared with the case of the δ form, the β crystal is difficult to prepare because the tensile deformation must be performed at a high temperature, near the melting point of PLLA α form. But the ultimate mechanical property is higher than those of the α and δ forms.26 In such a sense, it might be challengeable to produce the biaxially oriented PLLA β form film at a high tensile stress and at a high temperature, which can be induced by the mechanical slippage of the molecular chains as described in the present paper. The ultradrawn β sample is another candidate of the mechanically tough PLLA product.25,26 As reported in the present study, the highly oriented pure β form can be prepared by heating the oriented α form in the melting region under a relatively small tensile load (Figure 15), which is another useful method to prepare the ultradrawn β sample with the higher Young’s modulus in addition to the method reported in refs 25 and 26.
and causes also the disorder in the conformation and packing of the helical chains. As a result, the α form transforms to the δ form. The further application of tensile force at a higher temperature allows the easy slippage of the chain arrays along the diagonal direction and then the systematic mixing of the U and D chain stems occurs in the small domains. At the same time, the contracted helical chains of (10/3) form is stretched and changes to the (3/1) form through the change of torsional angles. In this way, the mechanical deformation finally creates the β form, the crystallite of which consists of the small domains with the disorder in the relative height. It must be noted here again that Figure 20 contains the two routes for the description of the phase transition from the α to β form. The large deformation was made for the original α form at such a low temperature as 100−160 °C to induce the solidstate transition (Figure 14 and ref 25). On the other hand, as reproduced in Figure 15, the α-to-β transition occurs also through the melt-recrystallization process under the superheated condition. The (10/3) helices subjected to a tensile force can keep the chain orientation even in the molten state, and so the highly oriented liquid crystalline state is created. The structural change itself may be quite similar to that given in Figures 18 and 19, and the thermally activated chain stems can move more easily to the lattice positions of the β form. In this case, anyway, one picture must be inserted additionally between the δ form and β form in Figure 20, which illustrates the parallel packing of the conformationally disordered and thermally activated chain stems.
4. CONCLUSION With the purpose to clarify the α-to-β phase transition mechanism of PLLA crystal, the crystal structure of PLLA β form has been reinvestigated by the quantitative analysis of the 2-dimensional X-ray diffraction data. The unit cell is of the rectangular shape, not the trigonal type. We have proposed here the two models (2 and 3) which can reproduce the observed layer line profiles as a whole. In the structure model 2, which can reproduce the observed X-ray data better than the model 3, one linear array consists of the repetition of UUD set along the b-axis. Another consists of DDU repetition. These UUD and DDU arrays are packed alternately along the a-axis. We have proposed one transition mechanism: the regular arrangements of UUU and DDD lines in the α form crystal change to those of the β form crystal through the mutual slippages along the diagonal directions between the neighboring lines, which may be caused by the shearing motions of the chain stems under the application of a tensile force along the chain direction. At low temperature the tensile force causes the disordering of the regular α form into the δ form. But, the mechanical tension at such a higher temperature as 160−170 °C (Figure 14) allows the easier and more drastic structural deformation in both the chain conformation [from (10/3) to (3/1)] and the chain packing mode to cause the formation of the β crystal form as a result (Figures 18 and 19). In the present study, we found out another transition behavior (Figure 15): the high-temperature superheating of the α form under a relatively low tensile stress caused the meltrecrystallization into the highly oriented β crystal. As illustrated in Figure 20, we may have two different routes to the creation of the β form. However, the balanced consideration of both of the kinetic factor (for example, an energy barrier between the α and β forms, which is controlled by a tensile force) and the thermodynamic factor (for example, a superheating caused by a
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b00272. Figure S1: illustration of a homemade sample cell for the X-ray diffraction measurement under a constant tensile force at the various temperatures (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (K.T.). ORCID
Jianming Zhang: 0000-0002-0252-4516 Kohji Tashiro: 0000-0002-7543-2778 Present Address
J.Z.: Key Laboratory of Rubber-Plastics, Ministry of Education, Qingdao University of Science and Technology, Qingdao 266042, China. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by “the Strategic Project to Support the Formation of Research Base at Private University (2010− 2014) and also (2015−2019)” of MEXT, Japan. The authors thank Dr. Tetsuo Kanamoto, Emeritus Professor of Tokyo O
DOI: 10.1021/acs.macromol.7b00272 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules University of Science, for his kind supply of an ultradrawn β sample.
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