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X-ray diffraction
Published in D. Campbell, R.A. Pethrick, J.R. White, Polymer Characterization, 2017
D. Campbell, R.A. Pethrick, J.R. White
If the distortions are such that long range order is destroyed they are described as ‘lattice distortions of the second kind'. This can occur if low angle boundaries are present, producing what is sometimes called a mosaic structure. Lattice distortions of the second kind may well occur in polymers as a result of their chain structure. For example in a highly drawn crystalline fibre the regions between neighbouring crystallites may contain molecules that are highly parallel even though they are not arranged in perfect crystal register. Thus they will possess a certain short range order that would permit each of the chain atoms to be associated with a particular crystal lattice point from which it is displaced. Thus although within such a region there may be some short range order an extended region of this kind would not possess long range order and the intervention of such regions between crystallites, as shown in Fig. 8.8, prevents long range order within the assembly of connected undistorted crystallites. This concept of a structure with short range order that can be associated (locally) with a crystal lattice, yet in which the distortional displacements of the atoms are not on average zero about the lattice points (as required for the preservation of long range order) but are instead accumulative, has been given the name ‘paracrystallinity’.*
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Published in Joseph C. Salamone, Polymeric Materials Encyclopedia, 2020
The size of the hard-segment domains in non-ionic polyurethanes varies with their chemical composition and thermal history. In some of the early work on non-ionic polyurethanes, iodine vapor was used to preferentially stain the hard domains of polyester- and polyether-polyurethanes.71 The hard domains had a diameter of ~ 0.003–0.01μm., smaller than the domain sizes in styrene-butadiene-styrene block copolymers, which had domains of diameter of ~ 0.03- 0.05μm. More recently, polyurethanes made from polypropylene oxide (PPO)/4,4′-diphenylmethane diisocyanate (MDI)/butane 1,4-diol (BD) have been studied.72 The microstructure was consistent with hard domains of some tens of pm in diameter, made up of hard-segment-rich fibrils of ~ 100Å (0.01 pm). Other methods of enhancing contrast in polyurethanes and ionomers include electron etching and the staining of double bonds in hard segments, with osmium tetroxide.73–75 An SEM study of some piperizine-based polyurethanes showed an added complication because of spherulites with a diameter of ~ 5μm in the surface.76 Wide angle electron diffraction (WAXD) has been used to determine the order of crystallinity/paracrystallinity in segmented polyurethanes; references to early works are summarized elsewhere.77 Domain formation in polyesterpolyurethanes revealed domains that were lamellar in shape with an average separation of 0.01–0.025μm.78 Higher spacings were obtained with longer soft segments and higher hard block content. IR spectroscopy has also been used to study the effect of hydrogen bonding, segmental orientation, and phase separation of segmented polyurethanes.77
Microstructural Characterization of Conjugated Organic Semiconductors by X-Ray Scattering
Published in John R. Reynolds, Barry C. Thompson, Terje A. Skotheim, Conjugated Polymers, 2019
Maged Abdelsamie, Michael F. Toney
Regardless of the simplicity of the estimation of the coherence length by Scherrer’s equation, the breadth of diffraction peak has contribution from microstructural features other than crystallites size that need to be decoupled for more accurate crystallite size estimation [27, 28]. Quantitative decoupling of the paracrystalline disorder and crystallite size is well established in inorganic materials but less considered in organic optoelectronic materials, in spite of the strong presence of paracrystallinity in many organic thin films, especially polymers [67, 68]. One method relies on the analysis of the scattering pattern of a diffraction peak and its higher orders where crystallites with no paracrystalline disorder show the same breadth of the diffraction peaks with higher order, as shown in Figure 12.4d (gray line-plot) [28]. On the other hand, crystallites with cumulative disorder exhibit cumulative broadening of the higher-order peaks, see Figure 12.4d (black line-plot). Thus, one methodology for decoupling the disorder effect on broadening, namely Williamson–Hall analysis, depends on plotting the peak breadth (Δq or (Δq/2π)2) versus the order of the diffraction peak (m) [m2 or m4], as represented in Equation (12.9) and shown in the inset of Figure 12.4d [67–71]. The coherence length can be determined from the intercept (m = 0), and slope of the curve is related to the disorder terms and can be used to define the paracrystalline disorder (g), see Equation (12.9), where crystallites with no cumulative disorder (g ≈ 0) show slope approaching ≈ 0, see inset of Figure 12.4d. (false(Δqfalse)hkl2π)2={(1/Lc)2}intercept(m=0)+{false(πgfalse)4dhkl2}slopem4
Molecular packing analysis of the crystal smectic E phase of a benzothieno-benzothiophene derivative by a combined experimental / computational approach
Published in Liquid Crystals, 2021
Sebastian Hofer, Wolfgang Bodlos, Jiří Novák, Alessandro Sanzone, Luca Beverina, Roland Resel
For analysing the films in terms of paracrystallinity, the peaks were fitted with a Gaussian function in both in-plane (qxy) and out-of-plane (qz) directions. For the resulting peak widths ∆qxy and ∆qz a linear regression based on is calculated, where m and dhkl denote the order of the diffraction peak in terms of its Laue index (h, k or l) and the inter-planar spacing of the diffraction peaks, respectively. This allows determining the crystallite size Dhkl and the amount of paracrystallinity g of the sample in two individual directions. No correction for the instrumental peak broadening was used.