## 1 Introduction  
Nowadays, water pollution is a big concern for many countries in the world. contaminant substances in wastewater might include recalcitrant organic compounds and/or metals which require breakthrough technology for treatment and purification processes. One of the technologies of high interest is photocatalysis, which is based on energy absorption of UV radiation from sunlight that in turn activates a photocatalyst to degrade the contaminant. One of the most promising photocatalysts in terms of reaction efficiency, in many environmental and energy applications, is titanium dioxide (TiO\({}_{2}\)). It is chemically stable and therefore almost inert to the environment and humans, abundant and inexpensive. Furthermore, it has a high ability to break molecular bonds, leading to their degradation. TiO\({}_{2}\) in the form of nanoparticles is especially very attractive because it is more reactive than its bulk form as a result of the smaller particle sizes and thus larger surface area. Unfortunately, the activation of TiO\({}_{2}\) occurs mainly due to UV irradiation, which represents only around 5% of the solar light spectrum, thus providing relatively low photocatalytic efficiency. This is a result of the large band gap (-3.2 eV) as well as the rapid recombination of the photogenerated electron-hole pairs. To increase its efficiency and enable activation also by visible light from solar radiation, TiO\({}_{2}\) must be modified by loading N, C, S, another semiconductor, dyes or metal particles (e.g., Cu or Zr) to reduce its band gap and, consequently, electron-hole recombination rates. The modification includes doping, decoration and structural modification of TiO\({}_{2}\) particles to enhance its photoactivity [1; 2; 3; 4; 5]. A common approach to evaluate the capability of photocatalysts to act under visible light is by determining the apparent band gap of the material. This is usually performed using a UV-Vis spectrophotometer to record the sample's absorption spectra over a chosen wavelength range. After plotting the graph of (\(\alpha lv\))\({}^{\mathrm{n}}\) as a function of photon energy hv (named a Tauc plot), it is possible to determine the values of band gaps as the intercept of extrapolation of the linear parts of the graphs to the abscissa axis, for which \(\alpha lv\) = 0. Parameters \(\alpha\), \(h\), \(v\) and \(n\) represent, respectively, an energy-dependent absorption coefficient, the Planck constant, the photon's frequency and the factor depending on the nature of the electron transition, which is equal to 1/2 or 2 for the direct and indirect transition band gaps, respectively. Such a method does not provide sufficient sensitivity in case the samples are weakly absorbing. Another factor that determines the material's photocatalytic activity is the carrier lifetime of photogenerated electron-hole pairs that tend to recombine at different defects (e.g., interstitial atoms, vacancies and grain boundaries), which decreases materials' photocatalytic activity but can be overcome by eliminating all the internal defects. Nanopowders are rich in defects because of their size and have many particle boundaries. Furthermore, the distance from bulk to surface is shorter compared to larger particles, causing faster migration and trapping of the charge carriers. This leads to low carrier mobility and reduces the lifetimes of photogenerated charge carriers. Nevertheless, in combination with a high surface area, it can result in enhancement of the overall photocatalytic activity since the photocatalytic reaction takes place on the surface of the material, and thus, particles with smaller sizes provide more reactive sites. Furthermore, the migration of photogenerated electron-hole pairs occurs through shorter distances, which reduces the carrier quenching rate. It is also important that the diffusion length of photogenerated electron-hole pairs should be longer than the material particle size.