The use of optical micro- and nanofibers has become commonplace in the areas of atom trapping using neutral atoms and, perhaps more relevantly, the optical trapping and propulsion of micro- and nanoscale particles. It has been shown that such fibers can be used to manipulate and trap silica and polystyrene particles in the 1-3 pm range using either the fundamental or higher order modes of the fibers, with the propulsion of smaller particle sizes also possible through the use of metallic and/or high index materials. We previously proposed using a focused ion beam nanostructured tapered optical fiber for improved atom trapping geometries; here, we present the details of how these nanostructured optical fibers can be used as a platform for submicron particle trapping. The optical fibers are tapered to approximately 1.2 pm waist diameters, using a custom-built, heat-and-pull fiber rig prior to processing using a focused ion beam. Slots of approximately 300 nm in width and 10-20 pm in length are milled clean though the waist regions of the tapered optical fibers. High fiber transmissions (> 80%) over a broad range of wavelengths (700-1100 nm) are observed. We present simulation results for the trapping of submicron particles and experimental results on the trapping of 200 nm particles. This work demonstrates even further the functionality of optical micro- and nanofibers as trapping devices across a range of regimes.