X-ray photon correlation spectroscopy during homogenous shear flow

Abstract

We report x-ray photon correlation spectroscopy measurements of advective and diffusive dynamics in a dispersion of colloidal particles subjected to homogeneous shear flow in a rotating-disk shear cell. Intensity autocorrelation functions from scattering data collected using homodyne detection respond to the variation in velocity across the scattering volume when the scattering vector has a component parallel to the flow direction. Theoretical expressions for the impact of homogenous shear flow on the correlation function provide a quantitative prediction of the dependence of correlation functions on the scattering vector and shear rate. Under most circumstances, the applied shear deformation dominates the decay of the intensity correlation function. When scattering data are collected perpendicular to the flow direction, it is possible to measure the diffusive dynamics of the particles free from effects of the superimposed shear flow; however, this approach only works below some upper shear rate limit, beyond which data are affected either by shear effects (caused by the finite width of the detector) or by particle transit through the scattering volume.

Echoes in x-ray speckles track nanometer-scale plastic events in colloidal gels under shear

“…As illustrated schematically in Fig. 3, the change in strain between extrema leads to gradients in the particle displacements that alter the speckle pattern completely [38,39] even for modest values of strain. Thus, g 2 (q,t) ≈ 1 at t = (n + 1/2)T , where n is an integer.…”

Recent developments in polymer applications of synchrotron small‐angle X‐ray scattering

“…For microrheology, XPCS measurements have been conducted on opaque polymeric solutions (1–20 wt%) using colloidal silica as a ‘marker’ . Very recently, in situ XPCS measurements have been conducted for a dispersion of colloidal particles subjected to homogeneous shear flow in a rotating‐disc shear cell . The dynamics of polymer chains near the free surface of a polymer film in the melt have also been studied by conducting grazing‐incidence XPCS using gold nanoparticles as a ‘marker’, which are dispersed in the polymer melt …”

Brownian and advective dynamics in microflow studied by coherent X-ray scattering experiments

“…Angled brackets denote a time average, q is the momentum transfer, t a chosen time point and a time shift relative to t. The auto-correlation functions in laminar flow depend on three independent effects: (a) the intrinsic particle dynamics of the sample system, in our case the diffusive motion of the scattering objects due to Brownian motion, (b) the advective transit time of the colloids moving through the scattering volume and (c) a shear-induced oscillatory decorrelation depending on the velocity gradient of the particles (Fuller et al, 1980;Busch et al, 2008;Fluerasu et al, 2008;Burghardt et al, 2012). As the velocity difference between particles depends on the flow profile and flow direction, the correlation functions depend on the scattering geometry of the experiment and can be separated perpendicular and parallel to the (main) flow direction with…”

“…X-rays can probe a large range of momentum transfers q and have a large penetration depth, which allows for probing a wide range of length scales and to analyze samples which are optically opaque (Leheny, 2012;Shpyrko, 2014). XPCS has been used for studying the dynamics of colloidal (Dierker et al, 1995;Burghardt et al, 2012;Westermeier et al, 2016), polymeric (Falus et al, 2005) and soft hybrid systems (Carnis et al, 2014;Herná ndez et al, 2015). Pioneering experiments on XPCS in flowing liquid samples have been performed by Fluerasu et al (Fluerasu et al, , 2010Busch et al, 2008), studying the laminar flow in tube-like flow cells.…”