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This talk highlights a proof-of-concept that demonstrates the ability to calculate high-resolution Fourier transforms. These can be combined with multi-scale modeling to simulate scattering over a wide range, from small-angle scattering to XRD and PDF.
The preprint documenting this is available on the ArXiv here:
https://doi.org/10.48550/arXiv.2303.13435
The Jupyter notebook, VASP calculation details and MOUSE measured scattering patterns are available from this Zenodo repository: https://dx.doi.org/10.5281/zenodo.7764045
## Summary:
This notebook and associated datasets (including VASP details) accompany a manuscript available on the ArXiv (https://doi.org/10.48550/arXiv.2303.13435) and hopefully soon in a journal as short communication as well. Most of the details needed to understand this notebook are explained in that paper with the same title as above. For convenience, the abstract is repeated here:
## Paper abstract:
We demonstrate a strategy for simulating wide-range X-ray scattering patterns, which spans the small- and wide scattering angles as well as the scattering angles typically used for Pair Distribution Function (PDF) analysis. Such simulated patterns can be used to test holistic analysis models, and, since the diffraction intensity is presented coupled to the scattering intensity, may offer a novel pathway for determining the degree of crystallinity.
The ``Ultima Ratio'' strategy is demonstrated on a 64-nm Metal Organic Framework (MOF) particle, calculated from $Q<0.01$\,$\mathrm{nm}^{-1}$ up to $Q\approx150$\,$\mathrm{nm}^{-1}$, with a resolution of 0.16\,\AA. The computations exploit a modified 3D Fast Fourier Transform (3D-FFT), whose modifications enable the transformations of matrices at least up to $8000^3$ voxels in size. Multiple of these modified 3D-FFTs are combined to improve the low-$Q$ behaviour.
The resulting curve is compared to a wide-range scattering pattern measured on a polydisperse MOF powder.
While computationally intensive, the approach is expected to be useful for simulating scattering from a wide range of realistic, complex structures, from (poly-)crystalline particles to hierarchical, multicomponent structures such as viruses and catalysts.
We demonstrate a strategy for simulating wide-range X-ray scattering patterns, which spans the small- and wide scattering angles as well as the scattering angles typically used for Pair Distribution Function (PDF) analysis. Such simulated patterns can be used to test holistic analysis models, and, since the diffraction intensity is on the same scale as the scattering intensity, may offer a novel pathway for determining the degree of crystallinity.
The "Ultima Ratio" strategy is demonstrated on a 64-nm Metal Organic Framework (MOF) particle, calculated from Q < 0.01 1/nm up to Q < 150 1/nm, with a resolution of 0.16 Angstrom. The computations exploit a modified 3D Fast Fourier Transform (3D-FFT), whose modifications enable the transformations of matrices at least up to 8000^3 voxels in size. Multiple of these modified 3D-FFTs are combined to improve the low-Q behaviour. The resulting curve is compared to a wide-range scattering pattern measured on a polydisperse MOF powder. While computationally intensive, the approach is expected to be useful for simulating scattering from a wide range of realistic, complex structures, from (poly-)crystalline particles to hierarchical, multicomponent structures such as viruses and catalysts.
A versatile software package in the form of a Python extension, named CDEF (computing Debye’s scattering formula for extraordinary form factors), is proposed to calculate approximate scattering profiles of arbitrarily shaped nanoparticles for small-angle X-ray scattering (SAXS). CDEF generates a quasi-randomly distributed point cloud in the desired particle shape and then applies the open-source software DEBYER for efficient evaluation of Debye’s scattering formula to calculate the SAXS pattern (https://github.com/j-from-b/CDEF). If self-correlation of the scattering signal is not omitted, the quasi-random distribution provides faster convergence compared with a true-random distribution of the scatterers, especially at higher momentum transfer. The usage of the software is demonstrated for the evaluation of scattering data of Au nanocubes with rounded edges, which were measured at the four-crystal monochromator beamline of PTB at the synchrotron radiation facility BESSY II in Berlin. The implementation is fast enough to run on a single desktop computer and perform model fits within minutes. The accuracy of the method was analyzed by comparison with analytically known form factors and verified with another implementation, the SPONGE, based on a similar principle with fewer approximations. Additionally, the SPONGE coupled to McSAS3 allows one to retrieve information on the uncertainty of the size distribution using a Monte Carlo uncertainty estimation algorithm.
The SPONGE
(2020)
Supramolecular copolymerization driven by integrative self-sorting of hydrogen-bonded rosettes
(2020)
Molecular recognition to preorganize noncovalently polymerizable supramolecular complexes is a characteristic process of natural supramolecular polymers, and such recognition processes allow for dynamic self-alteration, yielding complex polymer systems with extraordinarily high efficiency in their targeted function. We herein show an example of such molecular recognition-controlled kinetic assembly/disassembly processes within artificial supramolecular polymer systems using six-membered hydrogen-bonded supramolecular complexes (rosettes). Electron-rich and poor monomers are prepared that kinetically coassemble through a temperature-controlled protocol into amorphous coaggregates comprising a diverse mixture of rosettes. Over days, the electrostatic interaction between two monomers induces an integrative self-sorting of rosettes. While the electron-rich monomer inherently forms toroidal homopolymers, the additional electrostatic interaction that can also guide rosette association allows helicoidal growth of supramolecular copolymers that are comprised of an alternating array of two monomers. Upon heating, the helicoidal copolymers undergo a catastrophic transition into amorphous coaggregates via entropy-driven randomization of the monomers in the rosette.