Determining paracrystallinity in mixed-tacticity polyhydroxybutyrates

Abstract

Recently, the authors reported on the development of crystallinity in mixed-tacticity polyhydroxybutyrates. Comparable values reported in the literature vary depending on the manner of determination, the discrepancies being partially attributable to scattering from paracrystalline portions of the material. These portions can be qualified by peak profile fitting or quantified by allocation of scattered X-ray intensities. However, the latter requires a good quality of the former, which in turn must additionally account for peak broadening inherent in the measurement setup, and due to limited crystallite sizes and the possible presence of microstrain. Since broadening due to microstrain and paracrystalline order both scale with scattering vector, they are easily confounded. In this work, a method to directionally discern these two influences on the peak shape in a Rietveld refinement is presented. Allocating intensities to amorphous, bulk and paracrystalline portions with changing tactic disturbance provided internal validations of the obtained directional numbers. In addition, the correlation between obtained thermal factors and Young's moduli, determined in earlier work, is discussed.

Keywords: Rietveld refinement; mixed tacticity; paracrystallinity; polyhydroxybutyrates; thermal factors.

Figure 1

Recorded diffractograms (black solid curves), as deconvolved into amorphous background (grey solid curves), scattering from bulk crystals (dashed curves) and paracrystalline scattering (dotted curves) of samples with (a) f _meso = 0.54, (b) f _meso = 0.64 and (c) f _meso = 1.00, together with the refinement residuals (thin curves at negative values). In (a), scattering from non-amorphous phases is 0.

Figure 2

Cumulative integrated ratios for the total non-amorphous (black solid curves), amorphous (grey solid curves), bulk crystalline (dashed curves) and paracrystalline (dotted curves) intensities of samples with (a) f _meso = 0.64 and (b) f _meso = 1.00. For f _meso = 0.54, the amorphous ratio is 1.

Figure 3

Crystalline phase fractions determined for mixed-tacticity polyhydroxy­butyrate: total non-amorphous (squares and solid lines), bulk crystalline (circles and dashed lines) and paracrystalline (upward triangles and dotted lines). The fit to previously reported values of crystallinity is given by the bold dotted curve (Haslböck et al., 2018 ▸). The green solid and red dashed curves denote previously determined progressions of the exponential decay coefficients of the iso- and atactic polymer sequence length histograms, inverted, scaled and shifted simultaneously (Haslböck et al., 2019 ▸).

Figure 4

Plot of the displacement factors for the non-amorphous fractions: total (squares and solid lines), thermal (circles and dashed lines) and paracrystalline (triangles and dotted lines). The previously reported values of E for the entire material are given by the dotted curve (Haslböck et al., 2019 ▸).

Figure 5

Plots of (a) the average lattice parameters (red circles and dashed lines), (green upward triangles and dotted lines) and (blue downward triangles and dash–dotted lines), and (b) the density of the bulk crystalline phase.

Figure 6

Plots of the determined disorder (a) magnitude and (b) indicator, for the directions of a (red circles and dashed lines), b (green upward triangles and dotted lines) and c (blue downward triangles and dash–dotted lines). The black line in (a) marks the progression of the total paracrystalline order magnitude v _pc.

Figure 7

Plot of the correlations between the paracrystalline content (black upward triangles and dotted lines) and v _pc via equation (9) (full black lines with shaded uncertainties).

Figure 8

Unit cell of α-PHB viewed in lattice direction a with two exemplary exchanges of groups to obtain the S enantiomer, marked with red arrows.