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Liquids are condensed matter in which atoms are strongly correlated in position and momentum. The atomic pair density function (PDF) is used often in describing such correlation. However, elucidation of many properties requires higher degrees of correlation than the pair correlation. For instance, viscosity depends upon the stress correlations in space and time. In this paper, we examine the cross correlation between the stress correlation at the atomic level and the PDF for two-dimensional liquids. We introduce the concept of the stress-resolved pair distribution function (SRPDF) that uses the sign of atomic-level stress as a selection rule to include particles from density correlations. The connection between SRPDFs and stress correlation function is explained through an approximation in which the shear stress is replaced by a pseudospin. We further assess the possibility of interpreting the long-range stress correlation as a consequence of short-range Ising-like pseudospin interactions. [ABSTRACT FROM AUTHOR]

In this paper we demonstrate the presence of anisotropic stress correlations in the simulated two-dimensional liquids. Whereas the temporal correlation of macroscopic shear stress is known to contribute to viscosity via the Green-Kubo formula, the general question regarding angular dependence of the spatial correlation among atomiclevel stresses in liquids without external shear has not been explored. We observed the apparent anisotropicity with well-defined symmetry which can be explained in terms of the elastic continuum theory by Eshelby. In addition, we found that the shear stress correlation is screened compared to the prediction by the elastic continuum theory, and the screening length depends on temperature and follows the power law, suggesting divergence around the glass transition temperature. The success of the Eshelby theory to explain the anisotropy of the stress correlations justifies the idea that the mismatch between the atom and its nearest neighbor cage produces the atomic-level stress as well as the long-range stress fields. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]