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We study the influence of a magnetic field on the biaxial nematic phase of board-like goethite colloids both experimentally and theoretically. Using synchrotron small angle X-ray scattering techniques we find that applying a magnetic field along the main director of the biaxial nematic phase leads to a clear decrease in biaxiality with increasing magnetic field strength. Above a certain magnetic field strength the biaxiality is completely suppressed and the biaxial nematic phase transforms into an ordinary prolate uniaxial nematic phase. In order to interpret the physical mechanism behind this phenomenon, we develop a mean-field theory for the liquid crystal phase behaviour of the suspension. Within this theory the magnetic properties of the particles are modelled by taking into account the effect of both the permanent and the induced magnetic dipoles. The resulting phase diagrams support our experimental findings of the field-induced biaxial nematic to prolate uniaxial nematic transition. They additionally predict that for more plate-like particles, which initially would only display oblate nematic ordering of the shortest axis, the rare biaxial phase can be induced by applying a magnetic field with a carefully chosen field strength, a parameter which can be easily tuned.

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Using microradian x-ray scattering and polarized light microscopy the rich liquid crystalline phase behaviour of a polydisperse system of chromium-modified goethite particles has been studied for five years. We observe that the particles stay highly mobile over years and the rich phase behaviour keeps developing in novel and even surprising ways. While in many other colloidal systems particle size polydispersity suppresses the formation of ordered phases, goethite particles form multiple coexisting ordered phases. The particle polydispersity problem is then solved by particle exchange between coexisting phases. One usually expects that a less ordered phase (e.g., nematic) is formed first while crystallization of the smectic and columnar crystals might take a longer time. For goethite particles we find the opposite, i.e. the nematic phase grows over years at the expense of a better ordered smectic phase. Moreover, SAXS patterns revealed peak splitting for both the smectic and the columnar phase, meaning that the system displays fractionated crystallization. We further discovered that the centred rectangular columnar phase spontaneously forms out of the simple rectangular columnar phase. The reverse transition is observed as well. We explain the ease of these martensitic transitions by showing how slight rotation and translation of the particles triggers the transition.

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