NOVELTY - An electrochemical anodization method (M1) for producing a nanostructure array having single and/or multipodal nanotubes involves: providing a substrate capable of undergoing anodization, an electrolytic solution for receiving the substrate, and units for restricting the mobility of ions in the electrolytic solution; and anodizing the substrate to produce single and/or multipodal nanotubes.    USE - As electrochemical anodization method for producing a nanostructure array having single or multipodal nanotubes, or complex hierarchical structures (claimed), where the nanostructure array having single or multipodal nanotubes, or complex hierarchical structures are used in a variety of applications such as gas sensors, photocatalysts and scaffolds for excitonic solar cells, drug eluting coatings for medical implants, solid-phase microextraction (SPME) fibers and stem cell differentiation.    ADVANTAGE - The method provides controllable and reproducible method of producing nanotubes and nanostructure arrays having more complex topology (e.g. multipodal nanostructure). The method is capable of restricting or constraining the transport/movement of ions through the electrolytic solution (i.e. more onerous ion travel). The foregoing hindrance of mass ion transport can further prevent possible dissipation of ion gradients within the electrolytic solution, thereby preserving the scarcity of certain ions at different areas along the nanostructure during its formation.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) an electrochemical anodization method for producing a nanostructure array having complex hierarchical structure, involving either a) providing a titanium substrate capable of undergoing anodization, b) providing an electrolytic solution for receiving the substrate comprising mixture of solvent having a viscosity of at least 32 cP, fluoride-bearing species, where the concentration of the fluoride-bearing species is less than 0.5%, and de-ionized water, and c) anodizing the substrate at a voltage of 120-150V for at least 40 hours; or a1) providing a titanium substrate capable of undergoing anodization, where the substrate comprises pre-existing nanostructures, b1) providing an electrolytic solution for receiving the substrate comprising a mixture of a solvent having a viscosity of 3-1000 cP, a fluoride-bearing species, where the concentration of the fluoride bearing species is less than 0.5%, and de-ionized water, c1) anodizing the substrate in a first step at a voltage of 10V, d1) rinsing the nanostructure array, and e1) anodizing the substrate in at least one subsequent step at a voltage of at least 35V; and    (2) a nanostructure array comprising several oriented, tapered nanostructures, where some or all of the nanostructures can be at least bipodal.