Flexopolydispersity of Nematic Liquid Crystals*

Flexopolydispersity is the coupling of gradients in the director field \textbf{n}(\textbf{r}) of a nematic phase made from a polydisperse mixture of anisotropic particles in solution to the spatial change in variables describing the local mean particle shape, size, and concentration: In solutions of sufficiently polydisperse plates this coupling can lead to a nematic phase with a ``blue-phase'' like array of +1 defect lines. Such a structure has been observed in the lyotropic nematic phase of solutions of graphene oxide sheets.