## 3 Results and Discussion
The observed decreases in band gaps in the case of Cu-modified TiO\({}_{2}\) can be explained by the penetration of the charge state function into the forbidden energy gap, which creates extra energy levels within the band gap. Furthermore, Cu creates a p-type semiconductor; thus, the Fermi energy level shifts from the center of the band gap toward the valence band. Loading of Zr particles into TiO\({}_{2}\) had no significant effect on the composite's band gap at 95% CI as compared to the pure TiO\({}_{2}\) or Cu-modified TiO\({}_{2}\). The comparison of charge carrier lifetimes in Table 2 reveals important effects of TiO\({}_{2}\) modified with Cu as well as with Zr. Charge carrier lifetimes can be deduced from BDS measurements because the charge carrier density affects the thermal diffusivity of the material, which is directly related to the amplitude and phase of the BDS signal. The charge carriers were generated throughout the entire irradiated volume of the sample. The collisions of excited electrons with phonons resulted in energy transfer to the bulk of the material and its heating. These processes are strongly dependent on the band gap of the material but also on its thermal properties. The increase in thermal diffusivity is associated with the decrease in carriers' lifetime as a result of the increase in carriers' concentration according to the relation \(n\propto 1/\tau\)[10; 25], where \(\tau\) is the carrier lifetime and \(n\) is the carriers' concentration. Furthermore, the modification of TiO\({}_{2}\) introduced additional defects within the material, which in turn limited the carriers' lifetime since they act as recombination centers in the band gap. In addition, the decrease in the carriers' lifetime was also a consequence of collisions between the charge carriers, which increase with carriers' concentration. This result confirms the predominance of free carriers' contribution to heat transport. The decrease in carriers' lifetime (95% CI) was observed for both Cu-modified samples. The highest difference, i.e., a 20% decrease in charge carriers' lifetime, was found in the case of TiO\({}_{2}\) modification with 0.05% Cu. Within the determination uncertainty, the loading of TiO\({}_{2}\) with 1% Zr did not result in a change in carriers' lifetime when compared to unmodified TiO\({}_{2}\). More importantly, the presence of 1% Zr in TiO\({}_{2}\) containing 0.05% Cu significantly increased the charge carriers' lifetime as compared to TiO\({}_{2}\)/Cu (0.05%) material and resulted in only a 15% lower charge carrier lifetime as compared to pure TiO\({}_{2}\), which is of high importance for the efficiency of TiO\({}_{2}\)-based materials as photocatalysts. It can be concluded that loading Cu into TiO\({}_{2}\) material is effective for reducing the band gap of the photocatalyst. Unfortunately, at the same time, loading of Cu also reduces the carriers' lifetime. This may have a negative effect on the material's photocatalytic performance but can be compensated by additional Zr loading, which keeps the value of carriers' lifetime nearly the same as in unmodified TiO\({}_{2}\). The carriers' lifetime and the band gap are the factors that determine the photocatalytic activity of the material, which is reflected in the rates of photocatalytic reactions. In this work, we investigated the degradation of 5 mg L\({}^{-1}\) RB19 aqueous solution exposed to illumination by a simulated solar light in the presence of unmodified TiO\({}_{2}\) photocatalyst and TiO\({}_{2}\) photocatalyst materials modified with Cu and/or Zr. In this regard, it is crucial to determine the efficiency of the modified catalysts by studying the photocatalytic reaction rates using a highly sensitive technique. The rate of photocatalytic reaction was monitored using the TLS technique since the LOQs of the UV-Vis (4 mg L\({}^{-1}\)) spectrophotometric technique were not sufficiently low to enable reliable determination of the RB19 concentrations used in this study.