Phase behaviour, sedimentation and stacking in colloidal mixtures of thick and thin hard rods
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In this thesis we take a look at a binary mixture of thick and thin hard rods using Onsager theory, and look at their high pressure expansion to study the nematic phase more accurately. We will numerically solve the non-linear integral equations leading to the orientation distribution functions of the system for several diameter ratios, concentrations and compositions. Using these solutions, we will draw the phase diagrams summarizing the possible phases of the system, and find isotropic-nematic, nematic-nematic as well as isotropic-isotropic demixing, with corresponding isotropic-nematic-nematic and isotropic-isotropic-nematic triple points. In a few cases, a nematic-nematic or isotropic-isotropic critical point will appear. Then we will look at sedimentation profiles by including the effects of gravity in our calculations, and calculate the paths these mixtures can take in various phase diagrams as function of the height in a test tube. Here we find many configurations of the contents of the test tube, for example an isotropic phase between two nematic phases, and the composition variable of the heavier particles that is not increasing as function of the height. We will summarize these different configurations in a phase stacking diagram, and see that this diagram is not trivial, even for the simple case where there is only isotropic-nematic phase coexistence.