Dynamic Light Scattering (DLS) with visible coherent light is a well established technique used to investigate the static and dynamic properties of colloidal suspensions. It is however subject to two main limitations. One is the occurrence of multiple scattering in opaque systems (e.g. concentrated colloidal suspensions) which considerably complicates the interpretation of the experiments. The other is that using visible light prevents the dynamics to be traced on length scales smaller than about 2000 Å. Both limitations can be surmounted by X-ray photon correlation spectroscopy (XPCS) with the coherent X-ray beam available from beamline ID10A. We have used XPCS to measure the short time diffusion coefficient D(Q) of charge-stabilised colloidal silica in concentrated suspensions up to their solidification point [1]. The free particle diffusion coefficient Do was determined by DLS and XPCS in dilute samples. The static structure factor S(Q) was measured by small-angle X-ray scattering (SAXS). Figure 96 shows S(QR) and the normalised inverse diffusion coefficient Do/D(QR) as a function of QR for a suspension containing 15 vol% of colloidal particles with radius R = 555 Å. Multiple scattering of visible light in dense suspensions can be suppressed by carefully matching the refractive indices of the solvent and the particles leading to identical DLS and XPCS spectra [2]. DLS data taken under such conditions are shown for comparison in Figure 96 (closed squares) illustrating also the limitation of DLS to the low Q regime. The static structure factor shows a pronounced peak that deviates in both position and amplitude from the calculated structure factor for a suspension of hard spheres (dashed line): it thus underlines the charge-stabilised character of the system. The normalised inverse diffusion coefficient Do/D(QR) peaks at QR = 2.5 corresponding to a minimum in the diffusion coefficient. This slowing-down occurs at the maximum of the static structure factor S(QR), showing that the most likely density fluctuations decay the slowest. It is apparent from Figure 96 that Do/D(QR) mimics the behaviour of S(QR) but is not identical. This indicates that indirect, hydrodynamic interactions are relevant for the system. These interactions can be quantified by extracting the hydrodynamic function H(QR) = S(QR) / (Do/D(QR)) from the data. These functions, shown for three different volume concentrations in Figure 97, are asymmetric and skewed towards the high Q side, indicating that the long-wavelength modes are damped more strongly than the short-wavelength ones. Furthermore, H(QR) < 1 and decreases with increasing volume concentration. This is expected if hydrodynamic interactions act as additional "friction" that further slows down the dynamics. This is typically observed in sterically stabilised (hard-sphere) colloidal suspensions but is in contradiction to theory and previous DLS work in moderately concentrated ( 10 vol%), highly-charged colloidal silica suspensions, where speed-up effects (H(QR) > 1) were reported. The results also illustrate that the hydrodynamic interactions in colloidal suspensions can be determined over the relevant wave-vector range, and are free from any modelling of the static or dynamic properties thanks to the availability of coherent X-ray beams.

Principal Publications and Authors
[1] G. Grübel (a), D.L. Abernathy (a), D.O. Riese (b), W.L. Vos (b), G.H. Wegdam (b), J. Appl. Cryst., 33, 424 (2000).
[2] D.O. Riese (b), W.L. Vos (b), G.H. Wegdam (b), F.J. Poelwijk (b), D.L. Abernathy (a), G. Grübel (a), Phys. Rev. E, 61, 1676 (2000).

(a) ESRF
(b) Van der Waals-Zeeman Institute, University of Amsterdam (The Netherlands)