Abstract
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. 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. 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.
| Original language | English |
|---|---|
| Article number | 022612 |
| Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
| Volume | 96 |
| Issue number | 2 |
| DOIs | |
| State | Published - Aug 28 2017 |
Funding
This work was sponsored by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division. This research at the Spallation Neutron Source and the Center for Nanophase Materials Sciences of Oak Ridge National Laboratory was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. Y.Y.W. gratefully acknowledges the support by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT Battelle, LLC, for the U.S. Department of Energy. G.R.H. acknowledges the support from the National Center for Theoretical Sciences, Ministry of Science and Technology in Taiwan (Project No. MOST 106-2119-M-007-019), and the Schull Wollan Center during his visit to Oak Ridge National Laboratory.