There is provided a method of making a hollow fiber having improved resistance to microfracture formation at a fiber-matrix interface. The method includes mixing in a first solvent a plurality of nanostructures, one or more first polymers, and a fugitive polymer which is dissociable from the nanostructures and the one or more first polymers, to form an inner-volume portion mixture. The method further includes mixing in a second solvent one or more second polymers to form an outer-volume portion mixture, spinning the inner-volume portion mixture and the outer-volume portion mixture and extracting the fugitive polymer from the inner-volume portion mixture to form a precursor fiber, heating the precursor fiber to oxidize the precursor fiber and to change a molecular-bond structure of the precursor fiber, and obtaining a hollow fiber with the inner-volume portion having the nanostructures and the first polymers, and with the outer-volume portion having the second polymers.