Structure and dynamics of concentrated dispersions of polystyrene latex spheres in glycerol: Static and dynamic x-ray scattering D. Lumma, L. B. Lurio, M. A. Borthwick, P. Falus, and S. G. J. Mochrie* Department of Physics and Center for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 Received 7 February 2000 X-ray photon correlation spectroscopy and small-angle x-ray scattering measurements are applied to char- acterize the dynamics and structure of concentrated suspensions of charge-stabilized polystyrene latex spheres dispersed in glycerol, for volume fractions between 2.7% and 52%. The static structures of the suspensions show essentially hard-sphere behavior. The short-time dynamics shows good agreement with predictions for the wave-vector-dependent collective diffusion coefficient, which are based on a hard-sphere model C. W. J. Beenakker and P. Mazur, Physica A 126, 349 1984. However, the intermediate scattering function is found to violate a scaling behavior found previously for a sterically stabilized hard-sphere suspension P. N. Segre and P. N. Pusey, Phys. Rev. Lett. 77, 771 1996. Our measurements are parametrized in terms of a viscoelas- tic model for the intermediate scattering function W. Hess and R. Klein, Adv. Phys. 32, 173 1983. Within this framework, two relaxation modes are predicted to contribute to the decay of the dynamic structure factor, with mode amplitudes depending on both wave vector and volume fraction. Our measurements indicate that, for particle volume fractions smaller than about 0.30, the intermediate scattering function is well described in terms of single-exponential decays, whereas a double-mode structure becomes apparent for more concentrated systems. PACS numbers: 82.70.Dd, 05.40.-a, 83.10.Pp I. INTRODUCTION Dispersions of spherical particles with effectively hard- sphere interactions are the simplest complex fluids. Indeed, one may hope to build understanding of more complicated soft matter on the behavior of colloidal dispersions. It is therefore notable that after more than 20 years of research 1–4 the dynamics of colloidal particles with hard-sphere interactions are still not fully understood. The ability to pre- pare colloidal suspensions, composed of nearly perfectly spherical, highly monodisperse nanoscale particles dispersed in a liquid 5–7, enables experiments on accurate realiza- tions of hard spheres. Moreover, because colloidal particles are much larger than atoms and molecules, a variety of ex- perimental methods can be applied, which permit detailed studies of the structure and dynamics on the length and time scales relevant to individual particles 8–13. In this article, we present static and dynamic x-ray scat- tering measurements of the structure and dynamics of con- centrated colloidal suspensions of charge-stabilized polysty- rene PS spheres dispersed in glycerol for volume fractions from a few percent up to the crystallization limit. Our goal is to elucidate how particle diffusion is modified as the motions of the particles become increasingly constrained by the pres- ence of neighbors, as necessarily occurs at large volume frac- tions. Insofar as their static structure and phase behavior is concerned, these dispersions show essentially hard-sphere in- teractions. However, their dynamics appear to present sig- nificant differences from the dynamical behavior observed experimentally 8,14 for the prototypical hard-sphere sys- tem of polymethyl methacrylatePMMA spheres, steri- cally stabilized with a grafted layer of polyhydroxy steric acidPHSA, and suspended in decalin/tetralin mixtures 15. Because of the refractive index difference n PS -n Gl be- tween polystyrene ( n PS 1.59) and glycerol ( n Gl 1.47), our suspensions are milky in appearance, as a result of strong multiple scattering of light. Consequently, it would be very difficult to carry out light scattering studies of the dynamic mode structure and static correlations in any of the highly concentrated samples considered, even using the two-color technique 8. Instead, we have applied the emerging tech- nique of x-ray photon correlation spectroscopy XPCS, which employs the principles of dynamic light scattering, but uses x-ray photons from a high-brilliance synchrotron rather than laser light 16–23. To characterize the system’s static structure, simultaneous small-angle x-ray scattering SAXS measurements were performed. Multiple scattering of x rays occurs only for unusually strong scatterers, and was of no concern for the present study. A. Interactions and phase behavior PS spheres in glycerol, a polar solvent, constitute a pro- totypical colloidal system. Their interactions, the so-called Derjaguin-Landau-Verwey-Overbeek DLVO interactions, are representative of a large class of colloids, consisting of a screened electrostatic repulsion between charges at the spheres’ surfaces, plus a longer-ranged, attractive van der Waals component 5–7. Frequently, colloidal particles in- teracting via DLVO interactions are taken to have effectively hard-sphere interactions 10. This hypothesis has found re- cent support in elegant experiments demonstrating that *Present address: Departments of Physics and Applied Physics, Yale University, New Haven, CT 06520. PHYSICAL REVIEW E DECEMBER 2000 VOLUME 62, NUMBER 6 PRE 62 1063-651X/2000/626/825812/$15.00 8258 ©2000 The American Physical Society