Shear moduli of two dimensional colloidal mixtures

In this thesis a Mode Coupling Theory (MCT) equation is derived that calculates the shear modulus for multi-component colloidal mixtures in two-dimensional systems in linear approximation. With this equation, the plateau shear modulus G∞ is calculated for two two-dimensional systems at the glass transition: for a binary mixture of hard spheres and for a binary mixture of dipolar particles. The results for the shear modulus are compared with a three-dimensional system of hard spheres using data by Götze and Voigtmann. The plateau shear modulus has about the size G∞ nkBT ≈ 20 and a variation of ±10 for all systems. Here n denotes the total number density. We find that for all systems (the dipolar, the two-dimensional and the three-dimensional hard sphere system) the critical surface (φc resp. Γc) and G∞ have maxima in the region of large differences in the size of the particles and large concentration of the smaller particles. We disagree with the common explanation of depletion attraction for this effect but show that the maxima in the plateau shear modulus are produced by the big particles and the force of the small ones on them. With exception of the region of these maxima, all systems show a lowering of G∞ through mixing. This can be compared to the effect of plasticizing for polymers. The glass transition surface shows that for all systems the liquid is stabilized, but for the hard sphere systems there exists a threshold for the size ratio of the particles. Above that the glass is stabilized. This threshold is lower for the two-dimensional system. For the dipolar system there exist experimental values for the system developed by König et al. A comparison shows a good agreement of the plateau shear modulus. The transition parameter Γc is overestimated by MCT by a factor two, as has been found for other systems. A perturbational method, where the shear moduli of the particles are calculated separately as would be done for a monodisperse system and then added up, shows good qualitative and mostly even quantitative agreements with the two-component calculation, although the maximum in the region of large differences in the size of the particles and large concentration of the smaller particles is overestimated. Overall MCT seems to yield good results for the systems studied here. Only close to the boundaries some small-scale crystallizing is visible in the particle plots of the dipolar system.