Homodyne and heterodyne X-ray photon correlation spectroscopy: latex particles and elastomers

Abstract

In a coherent X-ray small-angle experiment, heterodyning between the scattering amplitudes of two samples is obtained by stacking a static reference and a fluctuating sample. Results of homodyne and heterodyne measurements are compared in the case of 98 nm diameter latex particles in glycerol. The method is also used for the study of the slow relaxation process of carbon-blackfilled ethylene-propylene elastomers corresponding to the relaxation of the carbon black skeleton after a 100% elongation. On the scale of the 10 mm coherent beam, heterodyning is used to separate fluctuations from long-term flowing of the sample. We show that this flow can be observed for about 10 h, with velocities of the order of nanometres per second. Random fluctuations are dominant in the speckle changes only for large q values (q > 2 Â 10 À2 Å À1 ) and after a long relaxation time.

Jamming in Filled Polymer Systems

“…It also led to two important observations: (i) the relaxation time τ scales as q −1 ; and (ii) the intensity correlation functions g 2 are better fitted by a compressed exponential function g 2 = 1 + β exp [−2( τ / τ 0 ) µ ] with µ = 1.5 than by a usual exponential function. The same features were found for jammed systems20 which allows us to conclude that there is an intrinsic similarity between them and filled elastomers 28, 29…”

XPCS Investigation of the Dynamics of Filler Particles in Stretched Filled Elastomers

“…The second reason for carrying out a new series of HD-XPCS measurements is the similarity of some of our results on filled elastomers [refs , and unpublished results] with those reported on jammed systems. Robertson and Wang , gave experimental evidence suggesting the existence of an analogy between dynamic strain-induced nonlinearity in the modulus of filled rubbers, the physics of the glass transition of glass-forming materials, and the jamming transition of vibrated granular materials.…”

“…Even for length scales accessible to light scattering, it can be used for opaque samples. A few years ago, we developed a heterodyne technique (HD-XPCS) for XPCS measurements , which yields information about the phase shift in the scattering signal. This allows us to measure the velocity of filler particles during the relaxation after an initial tensile deformation of un-cross- and cross-linked carbon black filled elastomers.…”

Rheo-XPCS

“…developed heterodyne methods for XPCS in which the scattering from a static pack of dry silica nanoparticles immediately upstream of the sample produced a scattering pattern that served as the reference, and they demonstrated this approach in experiments on dilute suspensions of diffusing colloids and on filled elastomers [34,35]. Recently, such a heterodyne configuration has also been used to measure the velocities of tracer nanoparticles in pressuredriven microfluidic flow [36].…”