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

F Livet,M Sutton,F Ehrburger-Dolle,E Geissler,F Bley,I Morfin

doi:10.1107/s0021889807003561

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-black-filled ethylene–propylene elastomers corresponding to the relaxation of the carbon black skeleton after a 100% elongation. On the scale of the 10 µm 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 × 10−2 Å−1) and after a long relaxation time.

Highlights

Since the pioneering work of Sutton et al (1991), X-ray photon correlation spectroscopy (XPCS) has become a well established technique, and it provides a very good method for the study of fluctuations in soft condensed matter systems
The method is 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
In the case studied here, this long-term relaxation corresponds to the reconstruction of the carbon black network after a large deformation, and new experiments have to be carried out with well controlled stress and strain

Summary

Introduction

Since the pioneering work of Sutton et al (1991), X-ray photon correlation spectroscopy (XPCS) has become a well established technique, and it provides a very good method for the study of fluctuations in soft condensed matter systems (cf. references [9]–[18] in Falus et al, 2004). The main advantages of this method are that it opens up the possibility of measurements at large q values [q 1⁄4 ð4=Þ sin >0:01 A À1, where is the X-ray wavelength and 2 is the detection angle] and allows the study of systems which are optically opaque, like carbon-black-filled elastomers Another characteristic of coherent X-ray beams is in their small size. For practical experiments, ’ 10 mrad, primarily because the CCD detectors used (Livet et al, 2000) have a 20 mm resolution with a sample-to-detector distance of the order of 2 m This means that ’ 10 mm, and that the irradiated surface is at least two orders of magnitude smaller than in light scattering (obviously, a laser beam can be focused to a size smaller than 10 mm, but its divergence due to diffraction gives an effective beam size of about 100 mm for a sample of a thickness in the millimetre range). We demonstrate the technique by studying the Brownian motion of latex spheres in glycerol and by performing velocity measurements in a model rubber system of ethylene–propylene elastomers filled with carbon black particles

Homodyne and heterodyne correlations in a latex suspension

Livet et al Homodyne and heterodyne X-ray intensity fluctuations s39

Relaxation of filled polymers

Conclusion

Findings

Livet et al Homodyne and heterodyne X-ray intensity fluctuations s41