Modelling of high-symmetry nanoscale particles by small-angle scattering

Abstract

A versatile procedure to build high‐symmetry objects and to calculate their corresponding small‐angle scattering intensity is presented. Starting from a set of vertex positions, available from a large and extensible database, it is possible to build several types of bodies using spherical subunits. A fast implementation, based on the Debye formula using a histogram of distance, is then used to compute the theoretical scattering intensity. Since the model is built from the definition of a small set of parameters, it is possible to perform an optimization of structural parameters against experimental data. Finally, affine size polydispersities can be easily included by the rescaling of the histogram of the positions used in the calculations. Several examples of the calculations are presented, demonstrating the method and its applicability.

Calculation of Small-Angle Scattering Patterns

“…The calculation of the scattering intensity was performed using the optimized Debye equation in a slightly different implementation in order to include different contrasts and demonstrate the potential use of this approach. In the figure of the original article is possible see that the histogram approach also permits an easy computation of affine polydispersities [8,73].…”

“…If the subunits in the model are randomly distributed, the intensity calculation can be again optimized, dividing the histogram into blocks. So, the computational time cost decreases to O[n/num blocks ], where num blocks is the number of blocks [8,72,73].…”

“…Therefore, the obtained results can be affected by the experimental technique itself [7]. Scattering/diffraction methods, on the other hand, can be used for systems directly in solution or in the amorphous matrix, with minimum interaction of the radiation with the matter [7,8]. These methods, namely, small-angle scattering (SAS) either with neutrons (SANS) or X-rays (SAXS), static light scattering (SAS), etc., can provide useful information about the structure of the investigated system.…”

“…These methods, namely, small-angle scattering (SAS) either with neutrons (SANS) or X-rays (SAXS), static light scattering (SAS), etc., can provide useful information about the structure of the investigated system. However, scattering methods give information in the Fourier space (reciprocal space/scattering space) which can difficult its interpretation and modeling [8][9][10].…”

SAXSEV 2.1 cross-platform application for data analysis of small-angle X-ray scattering from polydisperse systems

“…Благодаря прогрессу в приборостроении значительно улучшилось качество экспериментальных данных, современные вычислительные средства позволили оперировать большими объемами данных, и существенно возросли возможности извлечения структурной информации из профиля МУРР [4][5][6][7]. В частности, заметно расширился круг моделей оди-ночных рассеивателей, для которых разработаны как аналитические, так и вычислительные процедуры нахождения форм-факторов [6,8,9].…”