Shear moduli of two dimensional colloidal mixtures


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SEYBOLDT, Rabea, 2011. Shear moduli of two dimensional colloidal mixtures

@mastersthesis{Seyboldt2011Shear-14626, title={Shear moduli of two dimensional colloidal mixtures}, year={2011}, author={Seyboldt, Rabea} }

2011-11-09T08:19:21Z In this thesis a Mode Coupling Theory (MCT) equation is derived that calculates the shear<br />modulus for multi-component colloidal mixtures in two-dimensional systems in linear approximation.<br />With this equation, the plateau shear modulus G∞ is calculated for two two-dimensional<br />systems at the glass transition: for a binary mixture of hard spheres and for a binary mixture<br />of dipolar particles.<br /><br />The results for the shear modulus are compared with a three-dimensional system of hard<br />spheres using data by Götze and Voigtmann. The plateau shear modulus has about the size<br />G<sub>∞</sub>/(nkT) ≈ 20 and a variation of ±10 for all systems. Here n denotes the total number density.<br /><br />We find that for all systems (the dipolar, the two-dimensional and the three-dimensional<br />hard sphere system) the critical surface (φc resp. Γ<sub>c</sub>) and G<sub>∞</sub> have maxima in the region of<br />large differences in the size of the particles and large concentration of the smaller particles.<br /><br />We disagree with the common explanation of depletion attraction for this effect but show<br />that the maxima in the plateau shear modulus are produced by the big particles and the<br />force of the small ones on them.<br />With exception of the region of these maxima, all systems show a lowering of G∞ through<br />mixing. This can be compared to the effect of plasticizing for polymers.<br />The glass transition surface shows that for all systems the liquid is stabilized, but for the<br />hard sphere systems there exists a threshold for the size ratio of the particles. Above that<br />the glass is stabilized. This threshold is lower for the two-dimensional system.<br />For the dipolar system there exist experimental values for the system developed by König<br />et al. A comparison shows a good agreement of the plateau shear modulus. The transition<br />parameter Γc is overestimated by MCT by a factor two, as has been found for other systems.<br /><br />A perturbational method, where the shear moduli of the particles are calculated separately<br />as would be done for a monodisperse system and then added up, shows good qualitative<br />and mostly even quantitative agreements with the two-component calculation, although the<br />maximum in the region of large differences in the size of the particles and large concentration<br />of the smaller particles is overestimated.<br />Overall MCT seems to yield good results for the systems studied here. Only close to<br />the boundaries some small-scale crystallizing is visible in the particle plots of the dipolar<br />system. Shear moduli of two dimensional colloidal mixtures 2011-11-09T08:19:21Z Seyboldt, Rabea Seyboldt, Rabea deposit-license 2011 eng

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