Properties of Non-Equilibrium States : Dense Colloidal Suspensions under Steady Shearing

Abstract

In this thesis, different properties of colloidal suspensions near the glass transition under shear are analyzed theoretically. This system is in a non-equilibrium stationary state. Focus is put on the fluctuation dissipation theorem (FDT) which connects the response of the slightly perturbed system to the thermal fluctuations of the unperturbed system. It is violated under shear. In computer simulations, a very peculiar violation of the FDT was found for glasses under shear. The equilibrium form of the FDT seems to hold if the temperature is replaced by a different value, the so called effective temperature.We start with the analysis of different non-equilibrium correlation functions, namely the transient, the two-time and the stationary correlator. The difference between these correlators have so far only been studied in simulations and experiments. In chapter 3, the dynamics of a tagged particle in the sheared system is analyzed, e.g. the mean squared displacement.Concerning the FDT under shear, we achieve an approximative connection between the response function and measurable time derivatives of correlation functions and compare our results successfully with the simulations. In the simplest approximation, we find a universal FDT-violation, which is in agreement with the notion of an effective temperature. Corrections depend on the considered variable and hence contradict the notion of an effective temperature. We finish with an illustrative discussion of the FDT-violation and employ a simple toy model to illustrate the studied effects.