Article pubs.acs.org/Macromolecules
Morphology and Thermal Properties of Precision Polymers: The Crystallization of Butyl Branched Polyethylene and Polyphosphoesters Yi-Ran Zheng,†,‡ Hisachi Tien Tee,† Yujin Wei,§ Xi-Lin Wu,†,∥ Markus Mezger,† Shouke Yan,‡ Katharina Landfester,† Ken Wagener,§ Frederik R. Wurm,† and Ingo Lieberwirth*,† †
Max-Planck Institute for Polymer Research, Mainz, Germany State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Beijing 100029, China § Department of Chemistry, University of Florida, Gainsville, Florida 32611, United States ∥ University of Science and Technology of China, Hefei, China ‡
ABSTRACT: Chemical irregularities such as side chain branches or comonomers in an otherwise regular polymer influence its crystallization. In most polymer systems, these chemical defects are randomly distributed along the chain, and it is difficult to understand in detail their effect on crystallization. We have examined three precision polymers prepared by acyclic diene metathesis (ADMET) polymerization. This synthesis ensures exact placement of the chain defects; here they are all separated by 20 CH2 units. The polymers are two polyphosphoesters with a phosphate or phosphonate group in the main chain and one polyethylene with butyl branches. Although the alkyl part is identical for all three polymers, their thermal and crystal properties differ noticeably. By means of differential scanning calorimetry, X-ray scattering, and transmission electron microscopy, we characterize the lamellar crystals and correlate our findings to the observed difference in thermal behavior.
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branches < butyl2) or excluded from the crystal. In the case of the exclusion type of polymer, this directly influences the maximum achievable lamellar thickness, which is defined by the number of CH2 units between two defects. From a thermodynamic point of view the introduction of defects into the molecular structure will induce a melting point depression, regardless of the inclusion or exclusion model. Either way, the structural defects will cause a melting point depression due to an additional mixing entropy term18 and, in the case of defect inclusion, due to an additional energy term related to the distortion of the crystal lattice.19 Customarily, the melting point Tm of a lamellar crystal is given by the Gibbs−Thomson equation:20
INTRODUCTION The way in which defects in the polymer chain influence the crystallization as well as the mechanical and thermal properties of a polymer has been of ongoing interest in scientific research and industrial application.1−6 Specific examples are the grades of polyethylene with high density (HDPE) and low density polyethylene (LDPE). These achieve their characteristic properties by means of their molecular architecture, especially by adjusting the long- and short-chain branch density in the main chain.7−9 The incorporation of structural defects into the main chain influences the thermal properties of the polymer crystal as well as its crystal structure. Martuscelli and Pracella found that the incorporation of random propylene and butane defects leads to a decrease in the equilibrium melting temperature T0m and to a change in surface free energy σe.6 Furthermore, Balta-Calleja and Martinez-Salazar found by using extensive X-ray measurements that with an increasing number of chain defects the crystals lattice expands.4,5 However, all these studies on the effect of structural chain defects on crystallization were restricted to random copolymers. With the development of the acyclic diene methatesis (ADMET) it became possible to tailor the polymer chain precisely with exactly defined side groups at equidistant chain positions.10 Many examples of precisely tailored polyethylene have been documented in the literature.11−17 Depending on the size of the side chain these are either included (for side chain © XXXX American Chemical Society
⎛ 2σe 1 ⎞ Tm = Tm0⎜1 − ⎟ ΔHm l ⎠ ⎝
(1)
with T0m the equilibrium melting point, σe the surface free energy of the lamellae, l the crystal thickness, and ΔHm the heat of fusion. Hence, the melting point Tm is directly proportional to 1/l. The precision polymers with equidistant structural defects allow us to study the influence of defects on polymer Received: November 28, 2015 Revised: January 30, 2016
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DOI: 10.1021/acs.macromol.5b02581 Macromolecules XXXX, XXX, XXX−XXX
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synthesis and the chemical characterization of the polymer can be found in the literature.14 Methods. Differential Scanning Calorimetry (DSC). Thermal analysis was carried out using a Mettler-Toledo DSC 822. For nonisothermal crystallization, the samples were heated well above the melting point and kept at this temperature for 10 min. The samples were then cooled at the rate of 5 K/min to −50 °C and heated again at the same rate to 100 °C. For isothermal crystallization, samples were kept at the designated temperature for at least 3 h after eliminating the thermal history by heating the samples 50 °C above their melting point. The samples were then quenched to −50 °C, and DSC thermograms were taken at a heating rate of 5 K/min. Prior to the measurements the instrument was calibrated using an indium, zinc, and n-heptane standard. X-ray Scattering. For wide-angle X-ray scattering (WAXS) and small-angle X-ray scattering (SAXS) experiments samples were prepared by hot pressing an approximately 200−400 μm thick film on a hot stage. A sufficient amount of the sample was placed on a preheated glass slide and allowed to melt. Subsequently, another hot glass slide was pressed on the melt. This sandwich was kept above melting point for another 5 min before cooling it down to room temperature in order to eliminate any shear-induced orientation in the sample. SAXS was recorded using Cu Kα radiation (wavelength 1.54 Å) from a rotating anode source (Rigaku MicroMax 007 X-ray generator) with curved multilayer optics (Osmic Confocal Max-Flux). Polymer foils were measured in transmission geometry. The scattered intensity was recorded on a 2D detector (Mar345 image plate) with a sample− detector distance of 2 m. For WAXS measurements the sample− detector distance was set to 20 cm. For temperature-dependent measurements above the melting point, 1 mm thick polymer samples were contained in a temperaturecontrolled stainless steel cell with 300 μm thick diamond windows. Transmission Electron Microscopy (TEM). A FEI Tecnai F20 transmission electron microscope operated at an acceleration voltage of 200 kV was used to determine the crystal morphology, thickness, and crystal structure. Bright field (BF), parallel beam nano-electron diffraction (NBED), energy-filtered transmission electron microscopy (EFTEM),27 and tomography techniques28 were used for measurements. As solution grown crystals lie flat-on on the supporting carbon film, their thickness was measured by EFTEM. The thickness estimation obtained from EFTEM was determined by27
crystallization and melting. A prerequisite for an accurate evaluation of the thermal data of the precision polymers is a thorough examination of the crystal structure and morphology, which is the main purpose of this article. For our study we selected three polymers with differing defects, but each with an identical defect distance of precisely 20 CH2 units: a polyethylene with a butyl branch at every 21st C atom and two types of polyphosphoesters, each with a phosphate or a phosphonate group in the main chain separated by exactly 20 CH2 units. Because of the steric size of these defects, we assumed that they were excluded from the bulk crystal. In addition to their very special crystallization behavior, polyphosphoesters are increasingly interesting due to their biocompatibility, biodegradability, and their molecular similarity to DNA.21−23 We used two approaches in our experiments: solution-crystallization was applied to check the crystal unit cell parameters by means of single crystal electron diffraction techniques, and melt-crystallization was used to determine the crystal morphology and the thermal data. Interestingly, the results of these two different and controversial crystallization procedures yielded a significantly consistent morphological characterization of our precision polymer lamellar crystals.
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EXPERIMENTAL SECTION
Materials. Polyphosphoesters (PPEs) were synthesized by acyclic diene metathesis (ADMET)10 polymerization with equidistantly placed phosphoester groups. Exactly 20 CH2 units are incorporated between two phosphoester groups (Figure 1). Details on the synthesis
I0 ⎛ t⎞ = exp⎜− ⎟ ⎝ λ⎠ It
(2)
where It is the total intensity of the inelastic spectrum energy, I0 is zero-loss intensity of elastic spectrum energy, λ is the mean free path, and t is the thickness of the specimen. The relative thickness of the specimen t/λ can be directly determined by thickness mapping from EFTEM. The value of the mean free path λ depends on the composition of the specimen and on the convergence and collection semiangles of the TEM. Actually, the mean free path of the carbon support, the PPE-Ph, the PPE-m, and the PE21-butyl were determined to λc = 237 nm, λPPE−PH = 279 nm, λPPE−m = 284 nm, and λPE21−butyl = 294 nm, respectively.29 The information contained in a thickness map image is the relative thickness t/λ and contains the superposition of the crystal lamellae and the supporting carbon film underneath. Accordingly, it is necessary to deconvolve these two in terms of thickness. It is easy to measure the thickness tC of the carbon support alone. From the measured relative thickness t/λ of support and crystal it is then straightforward to calculate the crystal thickness tcrystal. Atomic Force Microscopy (AFM). In order to corroborate the EFTEM thickness measurements, additional AFM measurements were performed. One droplet of the dispersion containing the solutiongrown crystals was dropped onto a freshly cleaved mica substrate, and excess liquid was blotted off with the edge of a filter paper. AFM measurements were performed using a Dimension Icon FS with
Figure 1. Chemical structures of the precision polyphosphoesters (a) PPE-Ph, (b) PPE-m, and the precisely branched polyethylene (c) PE21-butyl. and characterization of the material can be found in the literature.24−26 Here we used two types of PPE differing only in the type of side chain, either a phenoxy group (PPE-Ph) or a methyl group (PPE-m). The respective structures are presented in Figure 1. The weight-averaged molecular weight (Mw) and the molecular weight distribution of the PPE-Ph are Mw = 17.8 × 103 g/mol and Mw/Mn = 2.29. For PPE-m, Mw = 24.0 × 103 g/mol and Mw/Mn = 1.23. After the synthesis, both of these two polyphosphoesters had to be hydrogenated in order to eliminate the unsaturated, central CC bonds. This process was checked by nuclear magnetic resonance spectroscopy (NMR) and yielded a hydrogenation rate larger than 99%. In addition to the PPEs, a precisely branched polyethylene sample containing butyl branches on every 21st CH2 unit (PE21-butyl) was examined. Weight-averaged molecular weight and molecular weight distribution of the PE21-butyl are Mw = 41.5 × 103 g/mol and Mw/Mn = 1.8. Details on the ADMET B
DOI: 10.1021/acs.macromol.5b02581 Macromolecules XXXX, XXX, XXX−XXX
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Figure 2. Nonisothermal crystallization and melting thermograms of (a) PE21-butyl, (b) PPE-m, and (c) PPE-Ph showing the significant difference in the melting temperatures.
Figure 3. Melting thermograms of (a) PPE-m and (b) PPE-Ph after isothermal crystallization at Tc and (c) the corresponding Tm1 versus Tc diagram (Hoffman−Weeks plot). tapping mode. AFM thickness measurements were in good agreement with the EFTEM, yielding a slightly larger thickness (compare Figure 12b and Figure 13). Sample Preparation. Both solution- and melt-crystallization methods were used for sample preparation. To prepare solutiongrown crystals, the polymer was dissolved in hot n-octane at a concentration of 0.02 wt %. The solution was kept in a temperaturecontrolled oil bath, whereby the change of the temperature was controlled by the change of the oil bath. After full dissolution, the solution was slowly cooled down to room temperature for crystallization. Afterward, one droplet of the sample was dropped onto a carbon-coated grid for further TEM measurement. In the case of the PE21-butyl, the sample solution was cooled to 4 °C to induce crystallization, followed by drop-casting onto a carbon-coated TEM grid at the same temperature. The sample grids were then transferred to liquid nitrogen. TEM examination was performed under cryoconditions. Similarly, during X-ray scattering the samples were kept well below the melting temperature throughout the whole experiment. For the melt-grown crystals, the samples were heated above the melting point for 10 min to remove thermal history and slowly cooled down to room temperature. For TEM examination the melt crystallized bulk samples needed to be sectioned by means of microtomy. The bulk samples of PPE were embedded in epoxy, trimmed, and subsequently stained in RuO4 vapor for 24 h, following room temperature sectioning using a Leica ultracut UCT. Interestingly, the PPE samples appeared to be wax-like when clamping them into the ultramicrotome sample holder. As a result, additional epoxy embedding was necessary. To decrease the compression of the sample, a 35° DiATOME ultrasonic oscillating diamond knife was used for sectioning. The thin sections were collected on the copper grids and coated with a thin layer of carbon to stabilize them for further TEM observation.
temperatures differ significantly. Especially the polyolefin PE21butyl has a remarkably low melting temperature (Tm = 14 °C) compared to the PPE samples (Tm = 47 and 67 °C for PPE-Ph and PPE-m, respectively). Figure 3 shows the melting thermograms of both PPEs after isothermal crystallization at different crystallization temperatures Tc. With increasing Tc a second melting peak occurs (indicated by Tm2 in Figure 3). This effect is more distinct for the PPE-Ph and might be attributed to a crystal phase transformation similar to that observed in α,ω-alkanediols.30,31 However, when checking the thermograms of the cooling process, an exothermal peak is apparent, caused by incomplete crystallization parallel to the occurrence of Tm2. Consequently, it is reasonable to take the higher melting peak Tm1 as the equilibrium melting point corresponding to the isothermal crystallization at Tc. Figure 3c shows the Hoffman−Weeks plot20 of the isothermal crystallization data. Extrapolation of Tm1 versus the Tm = Tc line yields an intersection at 69.8 and 49.2 °C for PPEm and PPE-Ph, respectively. Noteworthy is the fact that the slope for both PPE data is nearly zero, while bearing in mind that the Hoffman−Weeks extrapolation is a construction which accounts for lamellar thickening processes during the melting process. This does not apply to our samples as the bulky defects in the main chain will definitely hinder any lamellar thickening process. Accordingly, the intersection of the Tm1 line with Tm = Tc does not represent the equilibrium melting temperature of these systems. The significant and unexpected difference in the melting temperature between the PE21-butyl and the PPEs can be attributed to either crystal morphology or structure, which will be examined in detail in the following paragraphs. Morphology and Crystal Structure of PE21-Butyl. Solution-Grown Crystals. The morphology of solution-grown
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RESULTS AND DISCUSSION Thermal Behavior. Figure 2 shows the DSC traces of both PPEs and PE21-butyl as synthesized samples. Although the crystallizing part is the same for all three samples, the melting C
DOI: 10.1021/acs.macromol.5b02581 Macromolecules XXXX, XXX, XXX−XXX
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units for solution crystallized lamellae is in unexpectedly good agreement with the experimental data. Melt-Grown Crystals. SAXS data reveal a single broad peak around q = 1.24 nm−1 (Figure 5). Calculation of the
Figure 4. TEM BF micrograph of solution grown PE21-butyl crystals with the corresponding diffraction pattern (inset). The thickness of the respective crystals (annotations) was measured by EFTEM.
200 nm. Using EFTEM thickness mapping, the mean total lamellar thickness is in the order of tS = 2.9 ± 0.3 nm (Figure 4b). The crystalline lamella is composed of three different parts: the central crystal, the fold surface, and the extruding butyl side chains. All these parts contribute to the measured thickness. Assuming the CH2 groups in the crystal are in all-trans confirmation, as is the case for common polyethylene crystals, we expect a lamellar thickness of (20 − n)/2 × c, where c is the unit cell parameter in the c-direction (c = 2.54 Å) and n is the number of CH2 units needed to form the fold for an adjacent reentry. This is in the order of 4−6 CH2 units.32−34 The tight baxis refold consumes n = 4 CH2 units and contributes to the thickness of the lamellae with approximately 2 × 0.2 nm. The conformation of the extruding butyl side chains is unknown. It might range between totally extended to random conformation, which will contribute to the measured lamellar thickness with 2 × 0.5 nm and approximately 2 × 0.25 nm, respectively. The measured lamellae thickness tS implies a more random conformation of the extruding butyl side chains with tS = 8 × 0.254 nm + 2(0.2 nm + 0.25 nm), which is in good agreement with the measured data. As calculated from the electron diffraction pattern shown in the inset of Figure 4a, PE21-butyl crystallizes in a monoclinic crystal phase with a = 8.0 Å, c = 4.6 Å, and γ = 102.3°. (Please note that in the notation for monoclinic crystal structures the polymer chains are oriented parallel to the crystalline bdirection. Determination of b was not possible because of the flat-on arrangement of the single crystals.) Under normal conditions, polyethylene crystallizes in an orthorhombic phase35 with unit cell parameters a = 7.41 Å, b = 4.94 Å, and c = 2.54 Å. However, under certain conditions PE can crystallize in a monoclinic phase36 with unit cell a = 8.09 Å, b = 2.53 Å, c = 4.79 Å, and γ = 107.9°. Based on the crystal structure data, the crystal lattice of PE21-butyl single crystals appears to be very similar to the monoclinic PE phase with slightly deflated unit cell dimensions. Additionally, n-alkanes can serve as a simple model system in order to allow us to come to conclusions on the fold length. The melting point of PE21-butyl (Figure 2) lies between that of n-pentadecane (10 °C)37 and n-hexadecane (18 °C).38 Accordingly, the above estimation of a fold length of 16 CH2
Figure 5. SAXS data of PE21-butyl acquired at −15 °C and the corresponding correlation function (inset).
corresponding correlation function, assuming a two-phase lamellar system, yields thicknesses for the two different phases at 1.7 and 2.8 nm (Figure 5). Depending on the crystallinity χ of the sample, the thickness d from the correlation function represents either the crystalline (χ < 0.5) or the amorphous (χ > 0.5) layer.39 Unfortunately, we have not yet been able to assess the exact value of χ, and accordingly the interpretation of the correlation function data remains ambiguous. TEM examination of bulk samples failed because of issues with the staining at temperatures below the melting of PE21-butyl. However, when we look at the lamellar thickness of the solution-grown crystals, we might assign d to the amorphous layer thickness. In this case, the crystallinity of the PE21-butyl bulk sample would amount to χ = (L − d)/L = 0.6. Furthermore, the transition zone dtr can be extracted from the correlation function, which is found to be in the order of 0.4−0.5 nm. As reported previously, we can identify two peaks in the WAXS diffractogram corresponding to lattice distances of 4.5 and 3.9 Å.14 These peaks can be indexed as (001) and (200), which is in good agreement with the WAXS data found in the literature40 and with the electron diffraction (Figure 4). Morphology and Crystal Structure of PPE-m. SolutionGrown Crystals. Figure 6 shows a TEM micrograph of solution-grown crystals. From observation of TEM and AFM measurements the crystal lamellae always formed some kind of clustered objects rather than displaying nicely separated individual crystals. Possibly this agglomeration of crystals happens during the drying process. Using the EFTEM thickness mapping, we observed lamellar thicknesses ranging from 6.2 nm up to several tens of nanometers. AFM examinations yield a similar result (Figure 7). The crystals are found to be agglomerated, and the heights of the individual crystal terraces range from 35 down to 9.5 nm, which was the thinnest lamella found in the AFM measurements. In neither of the TEM and AFM thickness measurements were we able to identify a crystal featuring a thickness corresponding to a single D
DOI: 10.1021/acs.macromol.5b02581 Macromolecules XXXX, XXX, XXX−XXX
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reported in the literature,16,43 the pseudohexagonal form of polyethylene shows one single diffraction peak in WAXS at q = 14.52 nm−1, whereas the orthorhombic form shows two diffraction peaks at q = 16.09 nm−1 (110) and 16.83 nm−1 (200). Hence, from WAXS data we can see that PPE-m crystallizes in the pseudohexagonal form with slightly closer molecular packing and accordingly with smaller unit cell dimensions in crystalline a and b directions, similar to the crystal structures of the atactic poly(octadecyl acrylate) (PODA) and the ethyl branched PE (PE1E) shown by Qui et al.16 Furthermore, the crystal structures obtained from TEM and X-ray scattering are in good agreement and indicate that the PPE-m crystallizes in a pseudohexagonal crystal structure, whether formed from solution or from melt. In addition to the strong peak at q = 15.32 nm−1, WAXS reveals another very distinct peak around q = 2.51 nm−1. This peak indicates an interplanar spacing of 2.5 nm which is exactly the length of 20 CH2 groups in all-trans conformation. In the SAXS diffractogram the low angle peak from the WAXS appears again, indicating a long period of 2.6 nm (Figure 8). This long period is most likely the same as found in the WAXS measurement at q = 2.51 nm−1. The SAXS measurement shows a prominent peak at a scattering vector q of 2.39 nm−1 and a weaker peak around q = 0.75 nm−1 corresponding to a long period of 2.6 and 8.6 nm, respectively (Figure 8a). Analysis of the correlation function is the usual method to characterize the lamellar and amorphous thickness of a lamellar, bimodal system. However, the presence of the two characteristic peaks in the SAXS scattering, which are nonharmonic, should be viewed with caution. Here (Figure 8a), the correlation function analysis yields a long period of 2.5 nm, with an average lamellar thickness of 1.0 nm. Accordingly, the average amorphous layer thickness is 1.4 nm. These small dimensions are an indication that the correlation function analysis should be interpreted carefully. Possibly, the PPE-m system cannot be explained by a two-phase lamellar system, making the above correlation function analysis an inappropriate tool in this case. Combination of SAXS and TEM Data. In order to determine the lamellar structure of the melt-crystallized PPEm sample in detail, only the combination of SAXS and TEM is able to produce a thorough characterization. TEM directly images the lamellar structure. Figure 10a shows a TEM BF micrograph of a stained thin section of the same sample examined by SAXS. The lamellar morphology showing the crystalline lamellae (bright) and the amorphous regions (dark) can be easily identified. In order to compare the SAXS
Figure 6. TEM BF micrograph and the ED pattern (inset) of PPE-m solution grown crystals. The thickness of the lamellae (annotations in the image) was measured by EFTEM.
Figure 7. AFM micrograph (z-contrast) of PPE-m solution-grown crystals (right). Height profile along the indicated bar in the micrograph reveals that the lamellae have no uniform thickness (left).
folded lamella, which is expected to be around 2.6 nm assuming that the phosphonate groups are excluded from the crystal.41 The crystal lattice parameters were determined from the flaton oriented crystals by electron diffraction to a = 8.3 Å and b = 4.8 Å, forming an orthorhombic unit cell (inset of Figure 6). (From ED data the c parameter could not be determined.) These values are rather close to those of pseudohexagonal polyethylene, which has unit cell parameters of a = 8.46 Å, b = 4.88 Å, and c = 2.45 Å.42 As a result, we consider that the PPEm crystallizes in the pseudohexagonal phase. Usually, the hexagonal PE phase forms during crystallization at high pressure yielding extended chain crystals.42 Melt-Grown Crystals. WAXS of melt-grown films of PPE-m reveals only one single peak at q = 15.32 nm−1, which corresponds to a lattice spacing of 4.10 Å (Figure 8b). As
Figure 8. (a) SAXS diffractogram with the corresponding correlation function inserted and (b) WAXS diffractogram of PPE-m. E
DOI: 10.1021/acs.macromol.5b02581 Macromolecules XXXX, XXX, XXX−XXX
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Nonetheless, in the TEM micrographs we can identify lamellae with a typical thickness of approximately 2.6 nm (indicated in Figure 10). In summary, the combination of SAXS and TEM yields a lamellar structure with a typical thickness between 8 and 10 nm. The prominent SAXS peak at 2.6 nm corresponds well to the all-trans length of 20 CH2 units (20/2 × 0.254 nm) in a polyethylene crystal. The TEM measurements are relatively blind this structural feature but are very sensitive to showing the larger structures. However, in the given case that the lamellae are perfectly oriented edge-on with regard to the incident electron beam, TEM micrographs reveal a substructure within the observed lamellae. Figure 11 shows a digital
and TEM data, we analyzed the TEM data as proposed by Haubruge et al.44,45 From each TEM micrograph a onedimensional power spectral density (PSD) was calculated, and a correction was applied in order to account for the lamellar structure of the sample. In contrast to the SAXS results, the corrected PSD of the TEM micrographs features a clear peak in the low-frequency region around q = 0.75 nm−1, corresponding to a long period of 8.3 nm (Figure 9). In the higher frequency
Figure 9. Comparison of SAXS and TEM data.
region, the corrected PSD shows a very broad distribution slowly dropping off around 2.51 nm−1. We should point out here that the TEM micrographs used for the computation of the corrected PSD are projections from an approximately 60 nm thick section through the lamellar morphology. This is the reason why the calculated PSD needs correcting.44,45 However, optical sections from a reconstructed tomogram are relatively thin and will avoid the problem of projecting a finitely thick structure (Figure 10b). Accordingly, this data needs no Figure 11. Zoom into a TEM BF micrograph revealing the stacking of individual sublamellae (top). The intensity profile was taken from the area marked in the micrograph and clearly reveals the substructure of the thick lamellae (bottom). However, this is only visible in TEM when the lamellar structure lies in perfect edge-on orientation with the incident electron beam.
magnification of a TEM bright field micrograph and the corresponding intensity profile of the marked area. From the intensity profile we see that a thick lamella is in fact a stack of approximately 2.6 nm thick lamellae. This might explain why the correlation function analysis failed in this case. Morphology and Crystal Structure of PPE-Ph. Solution-Grown Crystals. For the PPE-Ph solution-grown crystals, TEM BF and EFTEM micrographs are shown in Figure 12 revealing a very distinct polymorphism. The single crystals have an irregular shape, and two different populations can be observed: one small-sized population with a lateral size
