The mesopores in silica fibers run in a circular direction around the axis(see Figure), as demonstrated here by examining the optical properties and electron microscopy images of mesoporous silica fibers grown by slow acid synthesis. These fibers are a unique example of a material that is highly ordered on the nanometer scale, but where the ordering does not lead to translational invariance in all three dimensions.
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Marlow et al. (2000) studied this question.