Reconstruction of three-dimensional anisotropic structure from small-angle scattering experiments
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- National Center for Theoretical Sciences, Hsinchu (Taiwan). Physics Division; Univ. of Tennessee and Oak Ridge National Laboratory, Oak Ridge, TN (United States). Shull Wollan Center; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Biology and Soft Matter Division
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Science (CNMS)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Biology and Soft Matter Division
- Institut Laue-Langevin (France)
- Univ. of Tennessee and Oak Ridge National Laboratory, Oak Ridge, TN (United States). Shull Wollan Center; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Biology and Soft Matter Division
When subjected to flow, the structures of many soft-matter systems become anisotropic due to the symmetry breaking of the spatial arrangements of constituent particles at the microscopic level. At present, it is common practice to use various small-angle scattering techniques to explore flow-induced microstructural distortion. However, there has not been a thorough discussion in the literature on how a three-dimensional anisotropic structure can be faithfully reconstructed from two-dimensional small-angle scattering spectra. Here, in this work, we address this issue rigorously from a mathematical perspective by using real spherical harmonic expansion analysis. We first show that, except for cases in which mechanical perturbation is sufficiently small, the existing small-angle scattering techniques generally do not provide complete information on structural distortion. This limitation is caused by the linear dependence of certain real spherical harmonic basis vectors on the flow-vorticity and flow-velocity gradient planes in the Couette shear cell. To circumvent the constraint imposed by this geometry, an alternative approach is proposed in which a parallel sliding plate shear cell is used with a central rotary axis along the flow direction. Finally, from the calculation of rotation of the reference frame, we demonstrate the feasibility of this experimental implementation for a fully resolved three-dimensional anisotropic structure via a case study of sheared polymers.
- Research Organization:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
- Grant/Contract Number:
- AC05-00OR22725
- OSTI ID:
- 1423001
- Alternate ID(s):
- OSTI ID: 1377129
- Journal Information:
- Physical Review. E, Vol. 96, Issue 2; ISSN 2470-0045
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
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