Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
Structures of Mixed-Tacticity Polyhydroxybutyrates Maria Haslböck,† Moritz Klotz,† Lisa Steiner,‡ Josef Sperl,‡ Volker Sieber,‡ Cordt Zollfrank,† and Daniel Van Opdenbosch*,† Chair for Biogenic Polymers and ‡Chair of Chemistry of Biogenic Ressources, Technical University of Munich, Campus Straubing for Biotechnology and Sustainability, Schulgasse 16, D-94315 Straubing, Germany
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ABSTRACT: In order to provide parameters that can be used to tailor the crystalline and supramolecular structures of pure polyhydroxybutyrate, we synthesized polymers with fractions of meso groups in the range 0.5−1. We confirmed the random polymerization of R and S enantiomers by the catalyst. From Xray diffractograms, the lattice parameters were determined; they remained constant for the observed range of fractions. We also traced the directional crystallite sizes over tacticity, which change significantly for one unit cell direction. The respective crystalline phase atom fractions were quantified by iteratively fitting amorphous phase diffraction patterns. We found that the crystalline contents of small-crystallite polyhydroxybutyrates have so far been underestimated. X-ray diffraction and transmission electron microscopical observations from polymers with meso group fractions of 0.5 are discussed. To facilitate the quantification of crystalline atom fractions, we refined two accessible infrared absorption spectroscopy-based indices. These indices, and the fundamental correlations between chemical and crystallite structuring reported herein, allow to tune structure-dependent properties, e.g., melting point and toughness, of mixedtacticity polyhydroxybutyrates over wide ranges.
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“rapidly coprecipitate the two components from a nonsolvent”12 in order to avoid phase demixing. One of the aims of this work was to circumvent this issue. Hocking et al. assessed the enzymatic degradability of PHB and found that it is highest for 0.55 < f meso < 0.60.13 They also reported that the heat of fusion of the mixtures is lowest in the same range, which suggests that the crystallinity is lowest as well. Confirming this, Kemnitzer et al. studied the crystallization behavior of partially syndiotactic PHB.14 They deduced a relation between the syndioregularity of polymer chain segments and the thermodynamic behavior of PHB. The latter, in turn, was found to be a factor determining fc. Illustrating the technological relevance, lowered f meso leads to decreased melting temperatures Tm: For f meso = 0.36, Tm = 154 °C14 compared to up to 179 °C reported for isotactic PHB.3 It is an aim of this work to systematically explore the true crystalline atom fractions fc of the prepared materials as well as the resulting crystallite textures for a wide range of f meso. The work presented in the following examines PHB after aging for several days, i.e., its long-term steady state. X-ray diffraction is the method used to assess these properties. However, infrared spectroscopy was found to provide complementary measures thereof: Bloembergen et al. used it to determine a qualitative crystallinity index3 and Iriondo et al. to obtain structural information via changes to the carbonyl absorption bands around k = 1715 cm−1 due to
INTRODUCTION Polyhydroxybutyrates (PHB) are naturally occurring polyesters.1 In several bacteria, submicrometer-sized granules thereof constitute energy storages.2 Because of a number of favorable properties and the possibility to obtain PHB from bioreactors, it is of interest as a renewable replacement for fossil-based polymers, as compiled by Bloembergen and Holden.3 However, the processability of PHB from the melt and its resulting mechanical properties could be improved by tailoring certain characteristics. Among these are the glass transition and melting points, reported as around 0 °C4 and between 160 and 180 °C, respectively.3−6 With regard to the latter, isotactic PHB was reported to degrade significantly in the melt.7,8 It is also brittle, with an accordingly low toughness, which is further reduced with aging, during which the material embrittles through crystallization.6,9,10 Approaches to improve the applicability of PHB include blending and copolymerization with varieties of polymers and monomers, as comprehensively reviewed by Avella et al.11 Another strategy to tailor the properties of PHB is to copolymerize D- and L-β-hydroxybutyric acid enantiomers. This aims at altering its crystal structure and crystallization behavior via the proportion of meso to racemo diads f meso + f rac = 1. By obtaining smaller fractions of the crystalline phase fc than for purely isotactic PHB (f meso = 1), one can expect to lower the melting temperature and increase toughness. Pearce et al. explored this approach by blending isotactic bacterial PHB with atactic or partially isotactic PHB and indeed found systematically lowered melting points.12 However, they also identified a technological complication, namely the need to © XXXX American Chemical Society
Received: May 17, 2018 Revised: June 15, 2018
A
DOI: 10.1021/acs.macromol.8b01047 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules hydrogen−carbonyl interactions.15,16 It is therefore another aim of this article to provide an accessible infrared spectroscopy-based tool of determining fc. Finally, we assumed that f meso could be readily tuned via the fraction of R-β-butyrolactone monomers f R used as educts for polymer synthesis, and that fc could be tuned by f meso. In this article, we confirm this assumption and provide parameters to correlate fc directly to f R. Since our aim was to investigate PHB that is most readily biodegradable, we studied f meso > 0.5 from predominantly R enantiomers, based on the findings of Kemnitzer et al.17
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the integrals over the absorption intensities I of the meso diads to those of the entire carbonyl peaks (eq 1). fmeso =
meso
∫
∫
tot
ICO(δ) dδ
ICO(δ) dδ
(1)
The signals of the methylene resonance in the range 40.6 ppm < δ < 41.1 ppm presented up to four overlapping peaks from isotactic meso−meso (mm: RRR and SSS), syndiotactic racemo−racemo (rr: SRS and RSR), and two heterotactic triads (mr: SSR and RRS; rm: RSS and SRR).21,22 We deconvolved these peaks with sums of four Lorenztian functions to determine the triad fractions f mm, f rr, f mr, and f rm (eq 2).
EXPERIMENTAL SECTION
triad = (mm, rr, mr, rm)
Polymer Synthesis. Procedure. All syntheses were carried out using standard Schlenk techniques in an argon atmosphere. The racemic and R-β-butyrolactone monomers were purified and dried before polymerization; contaminants were identified by 1H nuclear magnetic resonance spectroscopy (NMR). Butyric, hydroxybutyric, and crotonic acids were removed by treatment with 1.3 mol equiv of barium hydroxide, stirring for 1 day, and subsequent centrifugation. To the collected supernatants, excesses of calcium hydride were added. The mixtures were stirred for 2 days to desiccate. Dried and pure racemic β-butyrolactone was obtained by destillation at 70 °C. For R-β-butyrolactone, only the drying step was necessary. β-Diketiminate (BDI) ligands for the catalyst were prepared according to the literature:18 A solution of 3.0 g of ligands (7.2 mmol, 1.0 equiv) in 5.0 mL of dry toluene was stirred at 0 °C, to which 5.0 mL of a 1.5 mol L−1 solution of diethylzinc in toluene (7.5 mmol, 1.0 equiv) was added gradually. After stirring overnight at 80 °C, the clear solution was cooled to room temperature and dried in vacuo. A light yellow solid was obtained and confirmed as the catalyst ethylzinc (BDI) by 1H and 13C NMR.19 Polymers were prepared with different f R by varying the ratio of R to racemic monomers. 6.0 mL of each monomer mixture was dissolved in 9.0 mL of dry toluene. To each of these solutions, 753.0 μL of a 48.9 mmol L−1 solution of catalyst in toluene (0.04 mmol, 5 × 10−4 equiv; molar ratio of monomer to catalyst: 1999) and 4.6 μL (0.04 mmol, 5 × 10−4 equiv) of the cocatalyst 4-methoxybenzyl alcohol was added. The polymerization solutions were stirred for 24 h at 80 °C. The reactions were quenched with small amounts of methanol, ground with a mortar, and washed with methanol. Bacterial PHB was purchased as the isotactic reference (Biomer, Krailling, Germany). All materials were aged for at least 7 days before usage to decrease the amount of ongoing crystallization processes and provide samples in a steady state. Gas Chromatography. To assess f R in the educts, gas chromatography (GC, GC-2010 Plus, Shimadzu, Kyoto, Japan) was applied. The flow rate and linear velocity of helium in the column (MEGA-DEX DAC-Beta) were 1 mL min−1 and 28 cm s−1, respectively. The column temperature was raised from 80 °C, held for 90 s, to 110 and 170 °C, and held for 2 min each, at a rate of 10 °C min−1. The temperatures of injector and detector were 250 °C each. Nuclear Magnetic Resonance Spectroscopy. The tacticities of the polymers were determined via 13C NMR (ECS 400, JEOL, Freising, Germany) according to Abe et al.20 Spectra were recorded in CDCl3 at 101 MHz and referenced versus the signal of the solvent at a chemical shift δ of 77.0 ppm. All measurements were performed at room temperature, using 13 × 103 accumulations, 5.0 μs pulse width, 45° pulse angle, 5.1 s repetition time, 31 407.0 Hz spectral width, 3.0 s relaxation delay, an acquired size of 65 536 data points, 2.1 s acquisition time, and a resolution of 0.4 Hz. For comparison, all spectra were processed using zero filling (Fourier number 262144). For the determination of the tacticities, the carbonyl signals within 169.1 ppm < δ < 169.5 ppm were chosen. They contained two peaks, from meso (R−R and S−S) and racemic (R−S and S−R) diads.21 The f meso were determined as the ratios of
ftriad =
IL,triad triad
∑
IL
(2)
Here, IL are the scaling factors of the four three-parameter Lorentzians, which determine the areas under the curves. Gel Permeation Chromatography. The number averages of the molecular masses Mn of the polymers and their polydispersity indices IPD were determined by gel permeation chromatography (GPC, SECcurity, PSS, Mainz, Germany, with column arrangement PSS SDV 5 μm precolumn, 103 and 105 Å at 23 °C) using a refractive index detector (1260 Infinity, Agilent, Santa Clara, CA) and polystyrene standards in chloroform with 1 g L −1 tetrabutylammonium tetrafluoroborate as eluent. Powder X-ray Diffractometry. The main method to quantitatively characterize the as-synthesized PHB with varying f meso was powder X-ray diffractometry in Bragg−Brentano geometry (XRD, Miniflex, Rigaku, Tokyo, Japan with silicon strip detector D/teX Ultra). Copper Kα radiation was used, and the samples rotated around thein our setup verticalaxis at half the scattering angle 2θ during measurements. Intensities were recorded in steps of 2θ = 0.02°; Soller slits with angular apertures of 2.5° were used. Samples were prepared as compressed powder beds on aluminum holders. Only scattering into angles 2θ < 35° was considered in order to exclude reflexes from the holders. The obtained diffractograms match those reported for polyesters of D(−)-β-hydroxybutyric acid with Hermann−Mauguin symmetry symbol P212121 and unit cell dimensions of a = 5.7 Å, b = 13.2 Å, and c = 6.0 Å, allowing for a full indexation of the observed reflexes.7,23−26 We use the shorthand isoPHB for this crystal structure. For directional lattice parameter determinations, as well as for crystallite size analyses via Scherrer’s method, a Kα2 correction according to Rachinger was applied. Further, the diffraction reflex broadening stemming from the experimental setup was determined and taken into account. Amorphous phase patterns were obtained by repeatedly casting thin layers of 50 mg of 1 mg g−1 solutions of PHB in chloroform onto monocrystalline silicon substrates in order to suppress crystallization through the quenching effect of rapid solvent evaporation. The substrates showed no Bragg reflexes within the considered scattering angle regime. Their continuous background scattering intensities were recorded separately and subtracted. The obtained exclusively amorphous phase patterns were smoothed over 2θ ranges of 2°, using a first-order Savitzky−Golay algorithm, to reduce their noise below that of the sample diffractograms. Utilizing these smoothed amorphous phase diffraction patterns, fc were determined using an iterative fitting approach applied to the sample diffractograms. We looped through sequences of subtracting increasing multiples of the amorphous phase patterns and Lorentzian fits to the (020) peak at 2θ = 13.5° in the sample diffractograms. The Lorentzians had their respective baselines at the maximum of the multiples of the amorphous background and were calculated for each iteration. Complete fits were achieved when any intensity within 10° < 2θ < 12° was matched by the sum curve (consisting of the scaled amorphous pattern and the last Lorentzian) (Figure 1). B
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Figure 1. Illustration of the approach to determine fc for samples with (a) f meso = 0.64 and (b) f meso = 1.00 (isotactic reference) via iterative pattern fitting. Thick lines: observed intensities. Thin lines: scaled intensities from amorphous PHB. Dashed lines: sum curves of fitted (020) peaks and scaled amorphous patterns. Dotted line: Chebyshev polynomials, fitted through minima of the observed intensities for comparison. Since our samples were, to our best judgment, homopolymeric, we quantified fc by subtracting the respectively fitted amorphous scattering patterns from the diffractograms to obtain the intensities diffracted from the crystalline fraction Icryst and relating them to the observed intensities Itot within the range 10° < 2θ < 35° via eq 3, adapting Ruland’s approach.27
∫ Icryst(2θ) d2θ fc = ∫ Itot(2θ) d2θ
Table 1. Wavenumbers of the Boundaries of the Enumerated Ranges Used To Calculate the Crystallinity Indices Ic,III, Ic,IV, and Ic and To Trace the Shift of kCO (Vibrational Group Identifications Taken from Wrobel et al.29)
(3)
For comparison (see section Controlling Crystalline Fractions via Tacticities), we calculated “alternative” values of fc by using Chebyshev polynomials, fitted to local minima of the observed intensities, as models for the amorphous backgrounds, based onbut not true toVonk’s approach.28 We term this approach “function fitting”, as opposed to the “pattern fitting” described above. Microscopy. Optical Microscopy. Since we expected the crystallite dimensions and the degrees of crystallinity to be correlated to macroscopical structural features of PHB, we observed sheets thereof with transmission optical microscopy (Dialux 20, Leitz, Wetzlar, Germany with camera α7 RII, Sony, Tokyo, Japan and adapter DSLRCC, Micro Tech Lab, Graz, Austria). The 1 mg g−1 solutions of PHB in chloroform were cast onto microscopy glass slides, dried to yield films of about 5 μm in thickness, and observed under crossed Nicols with an added compensator (Δλ = 530 nm). Transmission Electron Microscopy. Samples that showed no indication of crystalline phases from either XRD or optical microscopy were investigated by low-voltage transmission electron microscopy (LVTEM, LVEM5, Cordouan Technologies, Pessac, France) with an acceleration voltage of 5 kV. 15 mg of 1 mg g−1 solutions of PHB in chloroform were cast as droplets onto copper mesh-supported, 8 nm thick carbon films (S160, Plano, Wetzlar, Germany), dried, and observed in bright-field mode. Infrared Spectroscopy. Since X-ray diffractograms require more expensive machinery, time to record, and attention to detail during evaluation, we recorded infrared absorption spectra (IR, Nicolet 380, Thermo Scientific, Waltham, MA) as a cheap, fast, and robust alternative. They were recorded in attenuated total reflection geometry (Smart Orbit) with a resolution of 2 cm−1. The absorption spectra were transformed to the respective optical depth equivalents for the reflection geometry τref, as calculated from the wavenumber kdependent reflected intensities Iref via eq 4. τref (k) = − ln Iref (k)
kmax (cm−1) kmin (cm−1)
range
vibrational groups
I II III IV
νs(CH2,CH3), ν(CH), νas(CH2,CH3) νas(COO) ν(C−O), δ(OH) nonbonded, τ(CH2) ν(C−C), ω(CH2)
3059 1902 1323 1203
2829 1528 1219 1159
calculated a total of four measures that correlate with PHB’s crystallinities. By integrating the intensities from III and IV, three IR-based indices of crystallinity were derived (eqs 5−7). Of these, Ic is the “main” index resulting from this work, with the other two serving as comparisons. The τref-weighted mean wavenumbers kCO were calculated by eq 8. I
Ic,III =
∫ τref (k) dk III
∫ τref (k) dk
(5)
IV
Ic,IV =
∫ τref (k) dk I
∫ τref (k) dk
(6)
IV
Ic =
∫ τref (k) dk III
∫ τref (k) dk
= Ic,IIIIc,IV (7)
II
k CO =
∫ kτref (k) dk II
∫ τref (k) dk
(8)
Data Fitting. The correlations between all two-dimensional data presented in this work were determined by error-weighted leastsquares fitting, using Python’s Lmfit algorithms (Table 2). A secondorder polynomial served as the basis (eq 9).
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(4)
Y = C2(X − X 0)2 + C1(X − X 0) + C0
(9)
RESULTS Polymer Synthesis. From GC and NMR, we found that f R used in the syntheses determined f meso obtained in the final products (Figure 2a). The best polynomial fit to the data (no 1, Table 2) describes a parabola with its vertex close to (f R,
We normalized all resultant spectra of τref(k) to the sum intensities of the C−H-based absorbances, range I in Table 1. We then used difference spectra in relation to those obtained from the isotactic reference to identify wavenumber ranges where τref changed with tacticity and identified the ranges II, III, and IV. From these, we C
DOI: 10.1021/acs.macromol.8b01047 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules Table 2. Summary of Fit Parameters (Eq 2) no.
X/1
Y
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
fR f meso f meso f meso f meso f meso f meso f meso f meso f meso f meso f meso fc fc fc fc
f meso/1 fc/1 a/nm b/nm c/nm La/nm Lb/nm Lc/nm Ic,III/1 Ic,IV/1 Ic/1 kCO/cm−1 Ic,III/1 Ic,IV/1 Ic/1 kCO/cm−1
C2 1.74 −0.38 0.16 0.38 0.05 11 −106 6 −0.06 11.53 2.36 32 0 0 0 0
± ± ± ± ± ± ± ± ± ± ± ±
C1 0.06 0.15 0.06 0.19 0.10 32 53 9 0.11 3.02 0.41 14
0 1.09 −0.25 −0.57 −0.11 −13 206 −6 0.00 −23.51 −4.89 −77 −0.20 −8.48 −2.05 −44
± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
C0 0.23 0.10 0.29 0.16 49 81 14 0.16 4.63 0.63 22 0.04 1.06 0.12 6
0.53 0.09 0.66 1.51 0.66 19 −62 9 0.19 15.01 2.95 1755 0.30 9.76 2.04 1747
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.00 0.09 0.04 0.12 0.06 19 31 6 0.06 1.75 0.24 8 0.03 0.74 0.09 4
X0
R2
0.50 ± 0.01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.999 0.945 0.133 0.064 0.042 0.010 0.557 0.021 0.417 0.806 0.914 0.783 0.283 0.536 0.830 0.509
Figure 2. Plots of the correlations between (a) f meso and (b) f triad and f R in PHB synthesized using ethylzinc (BDI) and 4-methoxybenzyl alcohol. The error bars in direction of f meso and f triad are standard deviations from at least three batches; those in the direction of f R stem from the R/S impurities detected by GC. Line in (a): second-order polynomial fit (no. 1, Table 2). Polynomial fits in (b): f mm (solid line), f rr (dashed line), f mr (dotted line), and f rm (dash-dotted line).
approach the values ( f c , f meso ) = (0, 0). However, predominantly syndiotactic PHB crystallizes in a different structure than isotactic PHB.14,30 The absolute values of crystallinity for any f meso differ by factors of at least 2, depending on whether the pattern or function fitting approach was used. From the latter, a maximum fc = 0.45 was determined for f meso = 1, whereas fc → 0 for f meso → 0.5. The determined lattice parameters (Figure 4) match those reported from the literature.23−25 They do not change significantly with f meso, as expressed by the polynomial fit parameters 0 < C2 < 0.25C0 and −0.38C0 < C1 < 0, and their uncertainties, which are of the same order as the uncertainty of C0, as well as the values of R2 < 0.15 (nos. 3−5, Table 2). The determination of crystallite sizes via the Scherrer method incurs large errors, especially when diffraction peaks from small crystallites overlap. Although the reflexes used for the determination of the directional sizes La,b,c were carefully chosen, the obtained values scatter by factors up to 0.4 around the fitted polynomial functions (Figure 5). Nevertheless, it is
f meso) values of (0.5, 0.5) and running through (0, 1) and (1, 1), considering the margin of error. Similarly, f R determined f mm, f rr, f mr, and f rm (Figure 2b). Their polynomial fits are parabolic and converge on values of (f triad, f R) of (0.25, 0.5). Save for f mm, which approaches 1, all f triad → 0 for f R → 1. Since f meso and all f triad show the same absolute qualitative progression, we chose the former as the unifying parameter. GPC analysis showed that the polymers from all batches had Mn = 93 ± 13 kg mol−1 and IPD = 1.12 ± 0.05. No conclusive correlation between Mn and f R was detected. Using the unit cell dimensions of iso-PHB, this means that single molecule chains were 650 ± 91 nm long. Powder X-ray Diffractometry. A clear correlation between f meso and fc was determined (Figure 3). Both the pattern fitting and the “pseudo-Vonk” function fitting approaches show the same qualitative progression of the degrees of crystallinity: With decreasing f meso, they decrease almost linearly. The fitting value C0 = 0.09 ± 0.09 (no. 2, Table 2) suggests that rather conveniently the crystallinity would D
DOI: 10.1021/acs.macromol.8b01047 Macromolecules XXXX, XXX, XXX−XXX
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Figure 3. Development of fc in PHB, 2 weeks after synthesis, with changing f meso. Triangles and line: fc and second-order polynomial fit (no. 2, Table 2), obtained by the pattern fitting approach. Circles: fc, obtained when considering only the areas within the crystalline peaks by the function fitting approach (compare with Figure 1).
Figure 5. Crystallite dimensions along the lattice directions a, b, and c of PHB in steady state, with changing f meso. Lines: second-order polynomial fits (nos. 6−8, Table 2).
Figure 6. Diffractogram obtained from f meso = 0.54, overlaid with the amorphous phase pattern (thin line).
intuitively run counter to the crystallite sizes calculated from diffractograms: The sample with f meso = 0.54 presented elongated objects with uniform optical axes up to 20 μm in length, whereas f meso = 0.75 and f meso = 1.00 showed circular crystalline assemblies with decreasing diameters (Figure 7). Birefringent objects showed blue or red coloration, depending on whether their optical fast axes were parallel or perpendicular to that of the compensator. Transmission Electron Microscopy. The carbon film holders prepared with f meso = 0.54 were covered by dispersed objects of similar appearance, as in Figure 8a. In light of the average molecule lengths of 650 ± 91 nm, we interpret these objects as folded and partially overlapping single molecular chains. We calculated this length from the c dimensions of the iso-PHB unit cell. Therefore, the 21 helix is included in this lengtha direct path going along atomic bonds of the molecule from end to end would be longer. Occasionally, linearly extended objects were observed (Figure 8b). At regular intervals of 39 nm along their lengths, they showed dark spots, marked by arrows. We assume that these are due to diffraction contrast arising from a repeated folding pattern of the chains. Since, on closer inspection, the shapes of the linear objects undulate with regular intervals
Figure 4. Lattice parameters a, b, and c for PHB of orthorhombic space group P212121 with changing f meso. Lines: second-order polynomial fits (nos. 3−5, Table 2).
observed that La and Lc remain constant within the margin of uncertainty over the assessed range of f meso. This is reflected by the large uncertainties of C2 and C1, and the values of R2 ≈ 0 (nos. 6 and 8, Table 2). A systematic, nonlinear increase of Lb by a factor of 2 is observed from f meso = 0.64 to f meso = 1.00 (no. 7, Table 2). From f meso = 0.54, we obtained diffractograms that appeared to be from amorphous phases at first sight (Figure 6). However, they differed from the amorphous background patterns, the diffractograms of iso-PHB, or those reported for predominantly syndiotactic PHB (crystal structure shorthand: syn-PHB).14,30 Microscopy. Optical Microscopy. Under crossed polarizers, the numbers of objects per area that showed birefringence increased with f meso. The observed particle sizes E
DOI: 10.1021/acs.macromol.8b01047 Macromolecules XXXX, XXX, XXX−XXX
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Figure 7. Transmission light micrographs with crossed polarizers and compensator showing objects found in sheets of PHB cast from chloroform solution for (a) f meso = 0.54, (b) f meso = 0.75, and (c) f meso = 1.00.
Figure 8. Low-voltage transmission electron micrographs of PHB with f meso = 0.54, deposited from chloroform solution, and showing (a) branched and (b) linear structures. Arrows in (b) denote evenly spaced structural features. At the white arrows, the features are not apparent.
perpendicular to their long axis, a helical folding pattern might be assumed. We interpret the intensely dark node at the center of the chain in Figure 8b to be a loop of the chain over itself. Infrared Spectroscopy. The obtained infrared spectra match those reported in the literature.3 The difference spectra with regard to the completely isotactic PHB, used to determine the boundaries of the IR regions I−IV, match those observed by Zhang et al.31 In range II, no systematic change in absorbed intensity with f meso was detected; instead, the broad absorbance band within this range shifted to lower wavenumbers with increasing crystallinity. In the ranges III and IV, changes in the relative intensities with f meso were detected. The calculated index of crystallinity Ic, its subindices Ic,III and Ic,IV (not presented for brevity), and the shift of the carbonyl peak kCO show a clear correlation with changing f meso (Figure 9). The fitting parameters for Ic,III, Ic,IV, and Ic (nos. 9−11 in Table 2, respectively) show that while Ic,IV has the strongest absolute correlation with changing f meso, it does not have the lowest relative uncertainty, nor the highest coefficient of determination. Ic,III fares even worse in both regards. However, when combining the two via eq 7, Ic is obtained. The relative uncertainties of its polynomial fit coefficients are lower than for either of its constituents, and it has a coefficient of determination R 2 > 0.9. For k CO ( f meso ), the relative uncertainties of the coefficients, as well as R2, are between those of Ic,III and Ic,IV. The change in kCO was expectedly robust against changes of the integration borders, as long as the absorption peak was entirely contained. Since the aim of IR spectroscopy was to assess whether it can serve as a quantitative measure of fc, we prepared plots of
Figure 9. Values of the qualitative index Ic (triangles and solid line) and positions of the characteristic carbon−oxygen absorption bands kCO (circles and dashed line), as determined from infrared spectroscopy with changing f meso together with their second-order polynomial fits (nos. 11 and 12, Table 2).
the three IR-based Ic, as well as of kCO, over fc (Figure 10). We plotted the values of those samples for which both XRD and IR had been performed. However, since we had obtained polynomial fits of fc(f meso), and of Ic(f meso) and kCO(f meso) for larger sets of samples each, we drew the correlations between the fitted functions for the entire sets as solid lines. We fitted the plotted data points with linear functions, shown as dashed lines (nos. 13−16, Table 2). Data Fitting. Depending on the fitting purpose, parameters were set to 0 (Table 2). We chose the coefficients to be not redundant, i.e., using either X0 or C0 to move the fit curve in direction of f meso. Values of R2 → 0, per definition, reflect that the variance of the fit residuals approaches the variance of the data around its mean. This is the case if the fitted function does not describe the correlation well, but also if two parameters are not correlated, as for example in the case of (a, b, c)( f meso), Figure 4, and La,c(f meso), Figure 5.
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DISCUSSION Controlling Crystalline Fractions via Tacticities. We found that fc is unambiguously correlated to f meso (Figure 3). While degrees of crystallinity in PHB depend on its short-term F
DOI: 10.1021/acs.macromol.8b01047 Macromolecules XXXX, XXX, XXX−XXX
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negligible within the considered scattering angles: 2θ = 35° corresponds to a scattering vector of 3.9 nm−1, only above which these effects should require attention. Diffractograms obtained from purely crystalline PHB by subtracting fitted amorphous patterns were reasonable matches with calculated diffraction patterns, allowing for variations in directional crystal dimensions, texture, and lattice parameters (Figure 11). Since the calculated patterns intersect the measured diffractograms at about 2θ = 11°, the angular region 10° < 2θ < 12° is indeed suitable to match amorphous patterns. As pointed out above, the increasing differences between the calculated and measured curves below 2θ = 10° are due to divergent-beam and increased-area background scattering. These intensities had been removed from the amorphous phase patterns during background subtraction. The presented diffractograms also show the origin of the systematic error incurred when fitting polynomial functions to the minima between reflexes: They do not approach I = 0 at any point 2θ > 12°. Thus, fitting a polynomial background function to local minima of X-ray diffractograms leads to understated values of fc, with fc → 0 for f meso → 0.5. Instead, by fitting recorded amorphous phase patterns, we determined that fc → 0.5 for f meso → 0.5. The shape of the amorphous background pattern is, as expected, with highest intensity values in the range of 10° < 2θ < 20°. They correspond, via Bragg’s equation, to measures of 0.88 nm > d > 0.44 nm, larger than interatomic distances, but matching interchain distances in iso-PHB.23 The average interchain distances in amorphous PHB can be expected to be of the same order; oscillations around which determine the broadness of the amorphous pattern.27 Because of the lack of long-range order, no higher-angle diffraction intensities, which would result from higher Miller index lattice planes, are observed. Our amorphous patterns also match those from weakly crystallized blends32 and copolymers3 of PHB and polyhydroxyvalerate. As Vonk pointed out, “the separation of the crystalline peaks from the background of amorphous scattering [...] requires knowledge of the shape of the diffraction curve of the amorphous phase in those regions where the crystalline peaks are superimposed.”28 Any function curve substituting for this knowledge is based on the assumption that in the “intervals [used for the determination of the fit parameters,] crystalline peaks are entirely absent.”28 Consequently, Vonk also demonstrated that regions containing overlapping crystalline
Figure 10. Plots of four different infrared spectroscopy-based measures of fc in PHB. Triangles: main index Ic. Downward-pointing triangles and squares: subindices Ic,III and Ic,IV (eq 7). Circles: kCO. Solid lines: plots calculated from polynomial fits (Table 2) from full data sets: Ic (no. 11), Ic,III (no. 9), Ic,IV (no. 10), and kCO (no. 12), each over fc (no. 2). Dashed lines: linear direct fits of reduced data sets (nos. 13−16, Table 2).
thermal history,14 the correlation nos. 1 and 2 (Table 2) allow tuning the crystallinities in the long term steady state via the processing conditions, as discussed in the section Controlling Tacticities through Processing Conditions. Bloembergen et al. found that the nonlinear progression of crystallization in PHB is such that one can safely place the boundary to a steady state at 24 h.3 Instead of performing laborious and error-prone full profile fits, we found that it suffices to identify an angular range where diffractograms are composed only of scattering from the amorphous phase and the tail-end intensities from the next closest Bragg reflex. The range 10° < 2θ < 12° was chosen, since to lower angles increased background scattering, due to beam divergence and increasing illuminated areas, was observed, while at higher angles, multiple broad Bragg reflexes overlapped. Our approach substitutes calculated background patterns for measured ones and omits the effects of thermal vibrations considered by Ruland,27 since we deemed them
Figure 11. Comparison of diffractograms from purely crystalline PHB, obtained by subtracting the fitted amorphous patterns from Figure 1 (solid lines) and calculated with changing peak full widths at half-maximum (fwhm, dashed lines) for (a) f meso = 0.64, 2θ(fwhm) = 1.5° and (b) f meso = 1.00, 2θ(fwhm) = 1.0°. G
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Macromolecules diffraction peaks are not suitable for fitting. In the case of PHB with crystallites sized in the 10 nm regime, the only diffraction vector that is practically free of intensity from crystalline reflexes is below 1.1 nm−1, corresponding to 2θ = 10° with copper Kα radiation. Therefore, fitting recorded or calculated amorphous phase patterns to diffractograms from partially crystalline samples is the only sensible manner of quantifying the atom fraction of molecules in nanocrystalline arrangements. Regardless, the function fitting approach has been widely applied, either implicitly3,14 or explicitly stated.20,26 The reported values of fc match those obtained by the alternative function fitting in this work (Figure 3). On the other hand, optical microscopy, in particular of f meso = 1.00 (Figure 7c), supports the significantly higher values of fc obtained by the pattern fitting approach. That these values of fc are more credible is further underlined by their narrow distribution around the fit curve, as opposed to the larger scattering of values from function fitting (Figure 3). Using Infrared Spectroscopy To Trace Crystalline Fractions. Out of the four different indices, which were assessed as facile alternatives to XRD, we deem Ic to provide the best measure of fc. Figure 10 shows that a linear fit to Ic( fc) provides a measure that has the lowest relative uncertainties with regard to slope C1 and position C0, namely 0.06 and 0.04, respectively. It also shows the highest coefficient of determination and deviates at maximum by 0.1 from the polynomial correlation, which was calculated from the full data sets via fit nos. 2 and 11. Crucially, the integrals over range I, used to normalize spectra for the determination of Ic,III and Ic,IV via eqs 5 and 6, cancel out, allowing the calculation of Ic via eq 7 from unmodified spectra. Another advantage of using IR spectroscopy to trace fc is the amount of sample material required to obtain a reliable signal, which is on the order of micrograms compared to milligrams, required for XRD. The special merit of the second-best measure, kCO, lies in the facile and robust manner by which it is determined. This intensity-weighted mean carbonyl band position also requires no normalization of the patterns and will work regardless of the applied units (absorbance, optical depth, reflectance, or transmittance). However, it incurs a larger random error, as can be observed from the data points which are scattered around the fit line. The shifts of the band constituting the carbonyl region were observed by Iriondo et al.15,16 and Zhang et al.31 The latter conducted a detailed investigation of the constituents of this composite band: The sub-bands at 1747 and 1739 cm−1 arise from the amorphous conformation, while those at 1731 and 1722 cm−1 stem from crystalline antiparallel 21 helix chains. These findings provide the basis for the shift of the sum peak kCO to lower wavenumbers with increasing fc, shown in Figure 10, which we traced via a facile approach without the need to fit a model. Bloembergen et al. also observed the changes in kCO and the intensities of the IR ranges III and IV (Table 1).3 They used single maximum absorbance values for indexation instead of integrals over the surrounding regions. Similar to our approach, they normalized the absorbances to crystallinity-insensitive CH vibrations. While we opted for range I (Table 1), Bloembergen et al. chose the frequency 1382 cm−1 for normalization. Expectedly, very similar results were obtained, with smaller uncertainties being incurred by our integrating approach at the expense of increased computation effort. The values of CI
determined by Bloembergen et al. correspond conceptually to 1/Ic,IV in our work. Notably, they applied the function fitting approach to determine degrees of crystallinity via XRD, leading to lower values of fc and therefore to different fitting coefficients. Zhang et al. traced the intensity changes in the regions we designated III and IV in great detail as a function of crystallization time, confirming the relative intensity changes utilized by Bloembergen et al.3 and this study. By multiplying Ic,IV with Ic,III, we obtained the improved index Ic; as pointed out above, this made normalization redundant. We chose Ic to have an inverse proportionality to the true crystallinity for a trivial reason: Plotting it together with kCO as in Figure 9 illustrates their close correlation; naturally, 1/Ic can be applied with the same quality. Controlling Microstructures via Tacticities. The correlations of La,b,c with f meso are in agreement with the widely accepted model for crystallization of iso-PHB,33−35 in which the repeating units in direction c are adjacent molecular chain elements, while those in direction a are from intramolecular chain segments folded onto one another. In direction b, intra- or intermolecular folded sheets, themselves extending in directions a and c, are stacked together. The corresponding lamellar structure with uniform c-directional thicknesses of about 5 nm, cited in the literature,7,33,34 confirms the value determined for Lc, suggesting that La and Lb are quantitatively correct as well. It is notable that Marchessault et al. found the thicknesses of the lamellae to be capped at 5 nm regardless of molecular mass.35 Two observations from Figure 5 fit the prediction that the lattice direction a of iso-PHB is the folding direction: First, La(f meso) remains roughly constant. We expect the average number of folds to be directly correlated to the molecular lengths of PHB, which were quite uniform for all samples. Second, the values of La show a greater variance than Lc, pointing to more relaxed physical boundaries on these dimensions than those in direction c. Considering the model for the crystalline arrangement in direction b, it is conclusive that this stacking arrangement has the weakest interactions and thus is reduced in dimension first, especially when intermolecular groups are involved. Polar groups in iso-PHB are mainly arranged in the a,c plane,24 implying a relatively lower interaction strength in direction b. Indeed, Marchessault et al. reviewed that crystal growth in isoPHB occurs first in direction a and then in b and that, vice versa, a prominent mechanism for enzyme attack is the “edge attack” acting on direction b.34 In mixed iso- and syn-PHB, the alternating meso- and racemic diads would then effectively disrupt growth in direction b. Ellar et al. conducted a thorough assessment of the morphologies of biological granules of iso-PHB.2 By acetone swelling, they could show that they are polycrystalline and consist of “fibrils 100 to 150 Å wide” with “large number[s] of ribbon-like structures with a height of 50 Å” and that the “flexibility of the fibrils” allows for short crystals in the c direction.2 These measurements and observations match those presented in Figure 5. They also match our observations by optical microscopy, where micrometer-sized particles were observed (Figure 7). From the color patterns arising from birefrigence-derived Δλ, we observed that the distances over which the crystalline phases are aligned become smaller with increasing f meso. We tentatively attribute this to crystal growth dynamics, where lowered f meso leads to slower and more H
DOI: 10.1021/acs.macromol.8b01047 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules
alternating syndio- and iso-stereoblocks/-stereosequences.”22 These proposals by Vagin et al. are supported by the reported values of f mm = 0.33, f rr = 0.35, and f rm,mr = 0.16, meaning higher proportions of both iso- and syndiotactic groups than in the sample with f meso = 0.54, assessed in this work. It also supports the hypothesis put forward in the section Proposed Structure of Equally Meso- and Syndiotactic PHB, namely, that for f meso ≈ 0.5 the formation of three-dimensional crystals is effectively hindered by randomly alternating meso- and racemo diads. It is possible to predict and tune f meso for any 0 < f R < 1 with high precision. Using the fitting parameter nos. 1 and 2 (Table 2), one can directly tailor fc via the input parameter f R for any nonselective catalyst. For example, to achieve fc = 0.7 ± 0.2 via f meso = 0.75 ± 0.02, it suffices to include the racemic enantiomer with an amount and certainty of f R = 0.90 ± 0.05.
anisotropic growth. This matches observations from PHB with f meso → 0.54 (see next section). Proposed Structure of Equally Meso- and Syndiotactic PHB. The following observations were made with regard to PHB with f meso = 0.54: (1) Diffractograms, obtained from steady-state bulk volumes of the sample (Figure 6), differ intriguingly from the amorphous background patterns obtained by rapidly casting thin films of PHB. (2) PHB has been reported (but not been systematically delimited) to crystallize as syn-PHB for f meso ≤ 0.3814,20 and as iso-PHB for f meso ≥ 0.64 (Figure 1). (3) The material showed no birefringence, save for few randomly distributed crystallites (Figure 7a). (4) LVTEM showedpossibly helically substructuredlinear structures with thicknesses of 15 nm, in either overlapping or stretched states (Figure 8). (5) The development of the crystallite dimensions of the iso-PHB unit cell extrapolates, via the fitting parameter no. 6, to La = 15.3 nm and via no. 7 to Lb = 14.5 nm for f meso = 0.5. Abe et al. reported on a diffractogram obtained from f meso = 0.46. The sample was described as atactic and amorphous; however, the pattern itself was not presented.20 We propose, as the most likely explanation, that the diffractogram in Figure 6 is derived from a partially crystalline material with crystallites, extending by 15 nm in directions a and b, possibly with helical chain arrangement. A point in support of this proposal is provided by the similarity of Figure 6 with diffraction patterns from helical molecules, such as isolated triple-helical collagen36−38 or double-helical desoxyribonucleic acid,39,40 where the “equatorial” reflex, i.e., perpendicular to the fiber axes, occurring below 2θ = 10° for copper Kα radiation, is unpronounced. It is not unlikely that the unit cell of these elongated crystals bears semblance to that of iso-PHB, which contains helical symmetries: In Figure 6, scattered intensities are only observed above 2θ = 14°. In iso-PHB, the only reflex occurring below this scattering angle arises from the (020) plane at 2θ = 13.5°. Small dimensions of the crystals in this direction would lead, for orthorhombic unit cells, to broadened reflexes in directions containing the reciprocal space index k, in Miller notation (hkl). This relation can be observed when comparing Figure 1b to Figure 1a. To exclude a misinterpretation, we also tested whether the pattern in Figure 6 could perform as an amorphous background, which it could not; i.e., the resultant purely crystalline patterns from iso-PHB could not be fitted. Controlling Tacticities through Processing Conditions. The fitting curve shown in Figure 2a (no. 1 in Table 2) indicates that the catalyst used in this work is nonselective toward R- or S-monomers: At each polymerization step, the probability of including either an R- or S-monomer is then 0.5. The four possible permutations are SS, SR, RS, and RR, each of which has the same probability of occurring and two of which are meso diads. Similarly, the fractions of triads in the products follows their statistical probability for a randomly polymerizing catalyst: rr, mr, and rm each consists of two sets of combinations of R and S, each containing one R or one S. If the polymerizing sequence is irrelevant, all are equally probable. On the other hand, mm consists of one set RRR and one set SSS. The probability of obtaining the former approaches 1 for f R → 1. Conclusively, no diffractograms showing reflexes from both iso- and syn-PHB, as reported by Vagin et al., were recorded.22 These mixed diffractograms were put forward as possibly arising from fractions that either “are blends or are composed of PHB macromolecules built by
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OUTLOOK We calculated values differing by factors of more than 2 for the atom fraction of crystalline fc phase by fitting recorded amorphous phase patterns or polynomial functions. It is therefore indicated to reconsider and confirm values obtained by the latter method. Setting the fraction of R-monomer educts was found to be a practical means of tailoring the geometries of crystallites in the iso-PHB lattice, obtained for 0.8 < f R < 0.2, which requires f meso ≥ 0.64. We would expect the same to hold true for synPHB from f meso ≤ 0.38, obtainable with tin-based catalysts.14 With knowledge of the strongly anisotropic crystallite shapes after aging to complete crystallization, tailoring the directional properties of dynamically shaped PHB, i.e., via texturing, is proposed for future works. By assessing samples with differing preparation methods and molecular masses, the wider applicability of the infrared spectroscopy-based indices for the crystalline atom fraction as efficient tools for reliable and rapid determinations of fc might be shown. Finally, gaining more insight into the morphologies of PHB in the range 0.38 < f meso < 0.64 is deemed most interesting; our results suggest that almost linear crystals, i.e., with one highly pronounced lattice orientation, possibly helical in shape, are formed.
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AUTHOR INFORMATION
Corresponding Author
*(D.V.O.) E-mail
[email protected]; Ph +49 (0) 9421 187452; Fax +49 (0)9421 187130. ORCID
Cordt Zollfrank: 0000-0002-2717-4161 Daniel Van Opdenbosch: 0000-0001-8497-0108 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the Bavarian State Ministry of the Environment and Consumer Protection for funding our work through the BayBiotech grant TLK01U-69042.
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