skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Evolution of elliptical SAXS patterns in aligned systems
Small-angle X-ray and neutron scattering (SAXS and SANS) patterns from certain semicrystalline polymers and liquid crystals contain discrete reflections from ordered assemblies and central diffuse scattering (CDS) from uncorrelated structures. Systems with imperfectly ordered lamellar structures aligned by stretching or by a magnetic field produce four distinct SAXS patterns: two-point `banana', four-point pattern, four-point `eyebrow' and four-point `butterfly'. The peak intensities of the reflections lie not on a layer line, or the arc of a circle, but on an elliptical trajectory. Modeling shows that randomly placed lamellar stacks modified by chain slip and stack rotation or interlamellar shear can create these forms. On deformation, the isotropic CDS becomes an equatorial streak with an oval, diamond or two-bladed propeller shape, which can be analyzed by separation into isotropic and oriented components. The streak has elliptical intensity contours, a natural consequence of the imperfect alignment of the elongated scattering objects. Both equatorial streaks and two- and four-point reflections can be fitted in elliptical coordinates with relatively few parameters. Equatorial streaks can be analyzed to obtain the size and orientation of voids, fibrils or surfaces. Analyses of the lamellar reflection yield lamellar spacing, stack orientation (interlamellar shear) angle α and chain slip angle ϕ, as well as the size distribution of the lamellar stacks. Currently available computational tools allow these microstructural parameters to be rapidly refined.  more » « less
Award ID(s):
2118860
PAR ID:
10542077
Author(s) / Creator(s):
;
Editor(s):
Sato, TJ
Publisher / Repository:
International Union of Crystallography
Date Published:
Journal Name:
Journal of Applied Crystallography
Volume:
57
Issue:
4
ISSN:
1600-5767
Page Range / eLocation ID:
1127 to 1136
Subject(s) / Keyword(s):
aligned objects lamellar arrays semicrystalline polymers small-angle X-ray scattering elliptical traces.
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Favorable polymer-substrate interactions induce surface orientation fields in block copolymer (BCP) melts. In linear BCP processed near equilibrium, alignment of domains generally persists for a small number of periods (∼4–6 D 0 ) before randomization of domain orientation. Bottlebrush BCP are an emerging class of materials with distinct chain dynamics stemming from substantial molecular rigidity, enabling rapid assembly at ultrahigh (>100 nm) domain periodicities with strong photonic properties (structural color). This work assesses interface-induced ordering in PS- b -PLA bottle b rush diblock copolymer films during thermal annealing between planar surfaces. To clearly observe the decay in orientational order from surface to bulk, we choose to study micron-scale films spanning greater than 200 lamellar periods. In situ optical microscopy and transmission UV-Vis spectroscopy are used to monitor photonic properties during annealing and paired with ex situ UV-Vis reflection measurement, cross-sectional scanning electron microscopy (SEM), and small-angle X-ray scattering (SAXS) to probe the evolution of domain microstructure. Photonic properties were observed to saturate within minutes of annealing at 150 °C, with distinct variation in transmission response as a function of film thickness. The depth of the highly aligned surface region was found to vary stochastically in the range of 30–100 lamellar periods, with the sharpness of the orientation gradient decreasing substantially with increasing film thickness. This observation suggests a competition between growth of aligned, heterogeneously nucleated, grains at the surface and orientationally isotropic, homogeneously nucleated, grains throughout the bulk. This work demonstrates the high potential of bottlebrush block copolymers in rapid fabrication workflows and provides a point of comparison for future application of directed self-assembly to BBCP ordering. 
    more » « less
  2. Semicrystalline polymers exhibit different re-organization behaviors during heating depending on crystal growth methods. Upon heating, solution-grown crystals (SGCs) undergo lamellar doubling while melt-grown crystals (MGCs) show a gradual increase in lamellar thickness. However, the molecular-level mechanisms driving these distinct reorganization processes remain unresolved. In this study, we investigate the morphological development, crystalline chain dynamics, chain packing, and chain-folding structures of poly (L-Lactic Acid) in both SGCs and MGCs upon heating by using solid-state NMR spectroscopy and in-situ Small Angle X-ray Scattering (SAXS). By comparing the hierarchical semicrystalline structures and crystalline chain dynamics in SGCs and MGCs, it is found that the chain-folding structure and the presence or absence of entanglements are key factors influencing the thermal stability and different reorganization mechanisms of mobile polymer crystals. 
    more » « less
  3. Adding crowding agents such as polyethylene glycol (PEG) to lyotropic chromonic liquid crystals (LCLCs) formed by water dispersions of materials such as disodium cromoglicate (DSCG) leads to a phase separation of the isotropic phase and the ordered phase. This behavior resembles nanoscale condensation of DNAs but occurs at the microscale. The structure of condensed chromonic regions in crowded dispersions is not yet fully understood, in particular, it is not clear whether the condensed domains are in the nematic (N) or the columnar (C) state. In this study, we report on small angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS) measurements of mixtures of aqueous solutions of DSCG with PEG and compare results to measurements of aqueous solutions of pure DSCG. X-ray measurements demonstrate that addition of PEG to DSCG in the N phase triggers appearance of the C phase that coexists with the isotropic (I) phase. Within the coexisting region, the lateral distance between the columns of the chromonic aggregates decreases as the temperature is increased. 
    more » « less
  4. ABSTRACT Soft materials with unique nanostructures such as lamellar, hexagonal, and cubic morphologies can replicate complex structures that have potential in various fields, including biomedical and industrial applications. However, a key challenge in advancing the broader applications of 3D printing for these nanostructured soft materials is insufficient mechanical properties that hinder their printability and compromise structural stability in the final product. In this study, the suitability of a fatty acid‐based lamellar gel is evaluated for direct extrusion‐based 3D printing. The lamellar gel with varying water content is integrated with a photocurable hydrogel to preserve the shape and stability of the final prints. Complex 2D and 3D design patterns are used to assess extrusion behavior, structural stability, and print precision under varying pressures. Small‐angle X‐ray Scattering (SAXS) measurements reveal the formation of lamellar nanostructures and confirm their retention after photocuring in various gels. Rheological analysis confirms that these gels exhibit key properties suitable for extrusion‐based 3D printing, such as shear‐thinning behavior. Additionally, tensile testing is conducted to evaluate the mechanical properties across cured print samples. This study underscores the potential of nanostructured gels as a robust and versatile platform, facilitating the development of materials engineered for various applications. 
    more » « less
  5. Abstract This study presents an improved approach to common‐conversion point stacking of converted body waves that incorporates scattering kernels, accurate and efficient measurement of stack uncertainties, and an alternative method for estimating free surface seismic velocities. To better separate waveforms into thePandSVcomponents to calculate receiver functions, we developed an alternative method to measure near‐surface compressional and shear wave velocities from particle motions. To more accurately reflect converted phase scattering kernels in the common‐conversion point stack, we defined new weighting functions to project receiver function amplitudes only to locations where sensitivities to horizontal discontinuities are high. To better quantify stack uncertainties, we derived an expression for the standard deviation of the stack amplitude that is more efficient than bootstrapping and can be used for any problem requiring the standard deviation of a weighted average. We tested these improved methods onSpphase data from the Anatolian region, using multiple band‐pass filters to image velocity gradients of varying depth extents. Common conversion point stacks of 23,787Spreceiver functions demonstrate that the new weighting functions produce clearer and more continuous mantle phases, compared to previous approaches. The stacks reveal a positive velocity gradient at 80–150 km depth that is consistent with the base of an asthenospheric low‐velocity layer. This feature is particularly strong in stacks of longer period data, indicating it represents a gradual velocity gradient. At shorter periods, a lithosphere‐asthenosphere boundary phase is observed at 60–90 km depth, marking the top of the low‐velocity layer. 
    more » « less