The percolation threshold for polydisperse systems of (i) isotropically oriented, and (ii) perfectly aligned, circular disks is calculated within an analogy to a lattice model. Our results are expressed in terms of moments of the distribution function over the disk radii, and they closely resemble findings obtained from an integral equation approach. The threshold is found to be quite sensitive to polydispersity in the disk radii and, for monodisperse systems, to approach a plateau for large values of the aspect ratio (thickness to diameter ratio). A similar plateau is found for disks with perfectly nematic orientational order, for which the percolation threshold always exceeds that for identical systems of disks that are oriented isotropically.
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