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Anisotropy Factors in Small-Angle Scattering for Dilute Rigid-Rod Suspensions



Jack Rooks, Peter H. Gilbert, Lionel Porcar, Yun Liu, Paul Butler


Alignment of anisotropic particles along specific orientations influences the mechanical and rheological properties of a material. Small-angle scattering techniques are widely used to probe this alignment through analysis of anisotropic two-dimensional scattering intensity patterns. Alignment factor is the simplest and most common quantitative parameter for describing scattering anisotropy, especially in systems containing rod-like particles. There are several methods for calculating this factor. However, there has been no systematic study comparing these methods, while evaluating the limitations imposed by nonidealities from instrumentation or polydisperse morphology. We examine three of the most common methods for calculating an alignment factor and evaluate their effectiveness for describing orientation of a theoretical cylinder. We find that the theoretical range of zero to one for alignment factor is only available at certain values of scattering vector, . Our analysis details recommendations for -range selection and data binning, as these influence calculation. Theoretical results are supported by experimental small-angle neutron scattering data for a wormlike micelle solution undergoing shear, where different calculation methods yield distinct quantifications of anisotropy.
Journal of Applied Crystallography


small-angle scattering, alignment factor, anisotropy, orientation


Rooks, J. , Gilbert, P. , Porcar, L. , Liu, Y. and Butler, P. (2023), Anisotropy Factors in Small-Angle Scattering for Dilute Rigid-Rod Suspensions, Journal of Applied Crystallography, [online], (Accessed July 13, 2024)


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Created June 1, 2023, Updated January 23, 2024