The phase behavior of a model suspension of colloidal polydisperse plateletsis studied using density-functional theory. Platelets are modelled as parallelrectangular prisms of square section $l$ and height $h$, with length and heightdistributions given by different polydispersities $\delta_l$ and $\delta_h$. Weobtain the phase behavior of the model, including nematic, smectic and columnarphases and its dependence with the two polydispersities $\delta_l$ and$\delta_h$. When $\delta_l>\delta_h$ we observe that the smectic phasestabilises first with respect to the columnar. If $\delta_h>\delta_l$ weobserve the opposite behavior. Other more complicated cases occur, e.g. thesmectic stabilises from the nematic first but then exists a first-ordertransition to the columnar phase. Our model assumes plate-rod symmetry, but theregions of stability of smectic and columnar phases are non-symmetric in the$\delta_l-\delta_h$ plane due to the different dimensionality of ordering inthe two phases. Microsegregation effects, i.e. different spatial distributionfor different sizes within the periodic cell, take place in both phases.
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