Nowadays, increasing awareness of environment and fossil fuels protection stimulates intensive research on clean and renewable sources of energy. Production of hydrogen from water through solar-driven splitting reactions is one of the most promising approaches in the field of photoelectrochemistry (PEC). In this work we have fabricated well-aligned, highly-ordered, smooth-mouth TiO₂ nanotube arrays (TNAs) in a two-step anodization process of titanium foil, which were then used as photoelectrodes for PEC water splitting. It demonstrates for the first time correspondence between non-linear component characteristics of multiscale rough surface and crystalline structure of annealed TNAs measured at various fabrication stages and their photoelectrochemical response. The as-anodized TNAs with isotropic surface (deduced from AFM and SEM images) and largest figure of merit (according to their PEC performance) were annealed at 450 °C in air. Scale-invariant descriptors of the surface structure of the deposits involved: fractal dimension, corner frequency, roughness, size of nanostructures and their dominant habits. Moreover, X-ray diffraction data processed using the Rietveld method confirmed co-existence of various oxides, for example: TiO₂ in the form of anatase, TiO and Ti₃O₅ phases in the TNAs under study pointing that previous well-established mechanisms of the TNA growth were to certain degree incomplete.

Density function theory calculations were carried out to clarify storage states of Lithium (Li) ions in graphene clusters. The adsorption energy, spin polarization, charge distribution, electronic gap, surface curvature, and dipole momentum were calculated for each cluster. Li-ion adsorbed graphene, doped by one Li atom is spin polarized, so there would be different gaps for different spin polarization in electrons. Calculation results demonstrated that a smaller cluster between each two larger clusters is preferable, because it could improve graphene Li-ion batteries; consequently, the most proper graphene anode structure has been proposed.