## 3 Results and Discussion
[39] who reported that photocatalytic activity of TiO\({}_{2}\) was enhanced with an increasing of percentage weight of anatase whereas the brookite phase was decreased. The anatase phase provides the highest photocatalytic activity compared to the rutile and brookite phases because anatase phase is an indirect band gap structure while the rutile and brookite phases appear to be the direct band gap one. Indirect band gap structure shows longer lifetime of electron and hole (e\({}^{-}\)-h\({}^{+}\)) pairs separation than direct band gap. Moreover, the anatase phase shows the highest photocatalytic activity because of the smallest particle size and the lightest effective mass of e\({}^{-}\)-h\({}^{+}\) pairs which provides the fastest charge transfer to surface of TiO\({}_{2}\) leading to the lowest e\({}^{-}\)-h\({}^{+}\) recombination [40]. Charge transfer in the different band alignments at the interfaces of TiO\({}_{2}\) shows high efficiency of charge separation for high photocatalytic activity under UV light conditions. The charge transfer mechanism of different phase combinations is proposed in Figure 6b-d. The mechanism of charge transfer of the mixture of anatase and brookite phases of TiO\({}_{2}\)-300 and TiO\({}_{2}\)-400 is shown in Figure 6b. Conduction band (CB) level can be determined from the vacuum level by using electron affinity (EA). Electron affinity of the anatase phase (EA\({}_{\text{A}}\) = 4.94 eV) is higher than that of the brookite phase (EA\({}_{\text{B}}\) = 4.15 eV). Valence band (VB) can be determined by considering energy band gap (E\({}_{\text{g}}\)) (E\({}_{\text{g}}\) of anatase = 3.51 eV and E\({}_{\text{g}}\) of brookite = 3.36 eV) [41]. CB of brookite is higher than that of anatase where electrons can transfer from brookite to anatase whereas the hole conversely transfers from anatase to brookite. With increasing calcination temperature from 400 \({}^{\circ}\)C to 600 \({}^{\circ}\)C, the kinetic constant was increased from \(3.87\times 10^{-2}\) to \(9.46\times 10^{-2}\) h\({}^{-1}\). The proposed charge transfer pathway in three phases of TiO\({}_{2}\)-500 and TiO\({}_{2}\)-600 is illustrated in Figure 6c. Electron affinity of brookite, rutile, and anatase (EA\({}_{\text{B}}\), EA\({}_{\text{R}}\), and EA\({}_{\text{A}}\)) are 4.15, 4.73, and 4.94 eV, respectively [39]. Due to the lowest energy of EA\({}_{\text{B}}\), the CB of brookite is the highest level compared to those of rutile and anatase phases. Electrons can transfer from brookite to rutile and anatase between interfaces while holes transfer in the opposite direction. The mixture of three phases consists of higher interfaces than two phases leading to a longer lifetime of charge transfer and a reduction of charge recombination. Therefore, the mixture of three phases including anatase, rutile, and brookite showed higher photocatalytic activity than two phases of anatase and brookite [16; 17; 42]. TiO\({}_{2}\)-600 showed higher photocatalytic activity than TiO\({}_{2}\)-500 because TiO\({}_{2}\)-600 consisted of higher weight percentage of anatase phase (42%wt.) than TiO\({}_{2}\)-500 (33%wt.). With increasing calcination temperature from 600 \({}^{\circ}\)C to 700 \({}^{\circ}\)C, the kinetic constant was decreased from \(9.46\times 10^{-2}\) to \(6.67\times 10^{-2}\) h\({}^{-1}\). It is interesting to note that even though the anatase phase was increased from 42%wt. (TiO\({}_{2}\)-600) to 53%wt. (TiO\({}_{2}\)-650),the kinetic constant was decreased from \(9.46\times 10^{-2}\) to \(7.73\times 10^{-2}\) h\({}^{-1}\). It was noticed that the crystallite size of anatase and rutile was increased from 600 \({}^{\circ}\)C to 650 \({}^{\circ}\)C as shown in Table 1. This can lead to the lower surface area of TiO\({}_{2}\)-650 compared to that of TiO\({}_{2}\)-600. Therefore, it is the dominance of crystallite size for the decrease of photocatalytic activity between TiO\({}_{2}\)-600 and TiO\({}_{2}\)-700 over the phase. The charge transfer mechanism of the mixture of anatase and rutile phases is shown in Figure 6d.