Interacting Colloidal Systems, Gels, Glasses

This chapter addresses scattering from suspensions of interacting colloids at finite concentrations, from both a theoretical and an experimental perspective. We start in Section 2 by describing the main effective interactions arising in colloidal systems: excluded volume effects as in hard particle suspensions, electrostatic contributions due to charge dissociation and release of counter-ions, and depletion interactions. We then discuss in Section 3 the Ornstein–Zernike equation, which allows one to calculate the radial distribution function and static structure factor directly from the interaction potential, by using a so-called closure relation. After introducing the most popular closures, we examine their predictions for the equation of state and the problem of thermodynamic consistency. We then briefly tackle the extension of the treatment to mixtures and polydisperse particles. Next, in Section 4 we introduce the ideal Mode-Coupling Theory of the glass transition, a microscopic theory that allows one to predict dynamics solely from the knowledge of the structure. In Section 5, we discuss the main experimental challenges that arise in scattering studies of non-ergodic systems, for which the usual time average performed in experiments does not yield the desired ensemble average. Various schemes proposed for collecting ensemble-averaged data are presented, including multi-speckle methods that allow for time- and space-resolved dynamic light scattering. In Section 6, we illustrate the concepts presented in the first part of the chapter by presenting some key experimental results for colloidal glasses and gels. We start by discussing repulsive hard and soft glasses. Then, we focus on short-ranged attractive colloids and discuss them in the context of attractive glasses as well as gels, highlighting the comparison between theoretical predictions and experimental results. In the final section, we draw some conclusions and make remarks for future work.