Investigation of Advanced Oxidation Process in the Presence of TiO₂ Semiconductor as Photocatalyst: Property, Principle, Kinetic Analysis, and Photocatalytic Activity

Abstract

Water pollution is considered a serious threat to human life. An advanced oxidation process in the presence of semiconductor photocatalysts is a popular method for the effective decomposition of organic pollutants from wastewater. TiO₂ nanoparticles are widely used as photocatalysts due to their low cost, chemical stability, environmental compatibility and significant efficiency. The aim of this study is to review the photocatalytic processes and their mechanism, reaction kinetics, optical and electrical properties of semiconductors and unique characteristics of titanium as the most widely used photocatalyst; and to compare the photocatalytic activity between different titania phases (anatase, rutile, and brookite) and between colorful and white TiO₂ nanoparticles. Photocatalytic processes are based on the creation of electron–hole pairs. Therefore, increasing stability and separation of charge carriers could improve the photocatalytic activity. The synthesis method has a significant effect on the intensity of photocatalytic activity. The increase in the density of surface hydroxyls as well as the significant mobility of the electron–hole pairs in the anatase phase increases its photocatalytic activity compared to other phases. Electronic and structural changes lead to the synthesis of colored titania with different photocatalytic properties. Among colored titania materials, black TiO₂ showed promising photocatalytic activity due to the formation of surface defects including oxygen vacancies, increasing the interaction with the light irradiation and the lifetime of photogenerated electron–hole pairs. Among non-metal elements, nitrogen doping could be effectively used to drive visible light-activated TiO₂.

1. Introduction

Water scarcity is known as the greatest threat to natural ecosystems and human health, especially in arid areas of the world. Economic development and population growth have led to an increase in water demand and reduction of water availability consequently [1]. It is estimated that there will be one billion people living in the arid area suffering from absolute water scarcity by 2025. Thus, people living in such areas will be forced into a reduction of water consumption in agricultural sectors and transmitting water to other parts, which could reduce their domestic food production. Organic wastes, which originate from different industrial products such as dyes, plastics, pesticides, and detergents, are toxic pollutants that could lead to serious diseases in humans. Although wastewater treatment has been extensively used for the degradation of organic pollutants, persistent organic pollutants (POPs) are resistant to degradation and could remain in the treated water [2]. In addition, there are different indoor air pollutants, which could result in wide-ranging health problems.

Different methods have been used for the degradation of organic pollutants in water, including sonochemical degradation [3,4], advanced oxidation process (AOP) [5,6,7,8,9,10], adsorption [11,12], micellar-enhanced ultrafiltration (MEUF) [13,14], electrochemical oxidation (EO) [15,16], precipitation [17], coagulation [17,18], biodegradation [19], ion exchange [20,21] and forward/reverse osmosis [22,23]. It is notable that each of these processes has advantages and disadvantages. AOPs are divided into various techniques including photo-Fenton process, heterogeneous photocatalysis, ozonation, Fenton process and H₂O₂ photolysis [24]. In general, AOPs have been proposed for poorly biodegradable organic pollutants [2]. Extremely highly reactive hydroxyl radicals (•OH), which are known as the (secondary) oxidant agents in these processes, are formed by primary oxidants (such as ozone or hydrogen peroxide) and are capable of oxidizing various organic pollutants. The hydroxyl radicals, which are the common aspect of all AOPs, are among the non-selective and powerful oxidants that could react through three mechanisms: the transfer of electrons, the abstraction of hydrogen and the addition of radicals. Thus, they can be potentially used for the degradation of complex chemical structures such as refractory species [25,26]. Although AOPs need input of chemicals and energy [27], they are becoming more efficient processes, e.g., photocatalysis. Around 60% of the expenses of photocatalytic reactors could be allocated to the energy consumption [28]. AOPs have a major advantage, as they are capable of partial or even complete degradation of pollutants. In comparison, coagulation, flocculation and membrane processes concentrate pollutants within one phase or transfer them from one phase to another [29].

Environmental photocatalysis has received remarkable attention since the discovery of the TiO₂ photocatalytic activity in 1972 [30]. The oil crisis was one of the reasons that encouraged research in non-fossil fuels in the early 1970s. Moreover, searching for renewable energy sources is another major driver [31]. After their first observation over water splitting by TiO₂, the photocatalytic reduction of CO₂ by different inorganic photocatalysts was reported by Fujishima et al. in 1979 [32]. SnO_2, TiO₂, and ZnO have been extensively used for photocatalytic decomposition of organic pollutants. Despite its several advantages, the removal efficiency of organic pollutants in the presence of a tin semiconductor is not that promising, limiting its use compared to main semiconductors [33,34,35,36], whereas TiO₂ and ZnO semiconductor nanoparticles are widely used for the photocatalytic removal of organic pollutants. In general, TiO₂ and ZnO might act as electron acceptors/donors when irradiated [37]. Because of its transparency, compatibility with the environment, and suitable band gap, ZnO has attracted the attention of many researchers for photocatalytic activities [38,39]. ZnO has three main crystallite structures including wurtzite, rocksalt, and zinc blend. Noteworthy, wurtzite is its most stable polymorph at ambient temperature and pressure [40]. Although ZnO has shown higher photo-absorption ability than TiO₂, it suffers from photocorrosion while exposed to UV irradiation [10]. Overall, TiO₂ (as an ideal semiconductor) has attracted the attention of many researchers due to its unique properties such as significant physicochemical stability, low cost, non-toxicity, electronic and optical properties, as well as abundance, in various fields such as pigments, catalysts, mineral membranes, dielectric materials and removal of pollutants [41,42]. TiO₂ nanoparticles have shown higher photocatalytic activity than bulk TiO₂ (due to larger surface area). The properties of TiO₂ nanoparticles, including morphology, crystal structure, composition of phases, degree of crystallinity, specific surface area, and band gap are influenced by the synthesis method [43,44,45]. TiO₂ nanoparticles have three major crystal structures including anatase, rutile, and brookite with unique band gap energies of 3.2, 3.0, and 3.1 eV, respectively. Notably, anatase phase with its wider band gap energy than other titania polymorphs has received more attention for photocatalytic activities [44]. The crystal structure of the main phases of titania, i.e., anatase, rutile, and brookite, could be explained by various arrangements of TiO₆ octahedra (Ti⁴⁺ surrounded by six O²⁻). Hence, 3-D assembly of TiO₆ octahedra and different degrees of distortion are differences between these crystal structures. Crustal structures of anatase, rutile, and brookite TiO₂ are exhibited in Figure 1 [46]. Noteworthy, the blue and red balls represent Ti and O atoms, respectively.

Photocatalysis is a branch of research that uses photons’ energy to initiate chemical reactions, which has been inspired by natural photosynthesis [31]. Photocatalytic (PC) and photosynthetic (PS) devices are different technologies that show sensitivity to charge-transfer kinetics, carrier mobility and specific surface area though at varying degrees [47].

From the viewpoint of thermodynamics, chemical reactions are divided into uphill and downhill categories. The schematic of these reactions is illustrated in Figure 2 (the ‘*’ sign could represent the transition state). Uphill reactions that are powered by light could not be considered as photocatalysis [31]. Thermodynamically uphill reactions are nonspontaneous, and the use of a canonical catalyst could not initiate these reactions [31]. Usually, photocatalysis is considered as an appropriate terminology to describe a large number of spontaneous chemical reactions (downhill reactions) that are hindered by high activation energies. Thus, the introduction of light, as a source of energy, could enable these reactions [31,47]. Notably, there is another group of reactions that borrows the photocatalysis term. These reactions that use external potentials, usually, are referred to as photo-electrocatalytic/photo-electrochemical reactions [31]. Unlike photocatalysis, the photo-electrochemical water splitting is a thermodynamically uphill reaction [48,49,50]. Thus, during the process of photocatalytic water splitting, the energy of photons is converted to chemical energy (by using a photocatalytic material) [50].

The fundamental principles of photocatalysis and photocatalytic activity of various kinds of semiconducting materials have been widely evaluated by researchers, especially in recent years. Although this process is well-known as an efficient process for water and wastewater treatment, several key points should be further considered to facilitate the use of this process for practical applications. Firstly, the use of promising photocatalytic materials increasing the proficiency of this process is of high importance. Moreover, the expansion of the scope of reactions should receive more attention. For example, TiO₂ has found applications in building materials (for antifogging and self-cleaning properties) and antibacterial materials since the discovery of its super hydrophilicity [52]. Super hydrophilicity is an effect observed for materials whose surfaces display water contact angles (WCAs) below 10° [53]. Super hydrophilicity and photocatalysis are two simultaneous phenomena occurring upon the illumination of TiO₂ [54]. The attempt to degrade emerging pollutants plays an important role in the development and practical applications of this process. However, broad applications of this process would be unlikely without consideration of an appropriate method of photocatalyst immobilization. Another key point is that 3–6% of the solar spectrum is from the ultraviolet radiation [55], while TiO₂, as the most common photocatalytic material, has negligible visible-light adsorption. Since about 43% of the solar spectrum is allocated to visible light [56], attempts are intensifying currently to drive visible-light activated photocatalysts. In recent years, photocatalytic processes in the presence of semiconductors have attracted the attention of many researchers for the removal and decomposition of organic pollutants. Several factors such as photocatalyst type, structure, synthesis method and doping with metallic or non-metallic elements could affect the efficiency of semiconductors. Therefore, the main goal of this study is to review the kinetics of photocatalytic reactions and specifically clarify the photocatalytic properties of TiO₂ with different phases and colors.

2. Photocatalysis

2.1. Principles

Overall, semiconductor photocatalysis relies on four steps as follows [31]:

• Absorption of photons with equal/larger energy than the bandgap energy of semiconductor under irradiation of light that results in the photogeneration of electron and hole pairs;
• Charge carrier separation;
• Transfer of charge carriers to the surface of semiconducting material;
• Redox reactions initiated by charge carriers.

The photogeneration of electron and hole pairs could be followed by the generation of active species [57,58]. These highly reactive oxygen species (ROSs), including hydroxyl radicals (^•OH), superoxide radical ions (^•O₂⁻), hydrogen peroxide (H₂O₂), hydroperoxy radicals (^•HO₂) and singlet oxygen (¹O₂), are responsible for further reactions [55,59,60,61]. The oxidation potential of hydroxyl radical (Eº(^•OH/H₂O = 2.8 V) is just below that of fluorine [62]. Notably, the photogenerated e⁻/h⁺ pairs could migrate through various pathways, as they could migrate to the surface of the semiconductor material. The electron acceptors (A) such as O₂ could receive the photogenerated electrons, and the photogenerated holes could result in the oxidation of donor species (D) under these circumstances. The redox potential levels of the adsorbed species and the position of conduction band (CB) and valence band (VB) play an important role in the rate and probability of the charge transfer processes for photogenerated e⁻/h⁺ pairs. The more is the lifetime of photogenerated e⁻/h⁺ pairs, the more quantity of ROS should be produced, which leads to the higher efficiency of photodegradation of organic contaminations in air and water. On the other hand, the recombination of photogenerated e⁻/h⁺ pairs, which could happen either at the surface or in the bulk of the semiconductor, prevents electron transfer processes and could result in the emission of light or release of heat [63,64]. To yield the highest photocatalytic activity, the recombination rate of charge carriers should be restricted. For such a purpose, several techniques such as heterojunction formation [65], metal deposition [66], creation of oxygen vacancies [67], and non-metal/metal ion doping [68] have been employed. It is noteworthy that surface reactions take place only if the reduction and oxidation potentials are more positive and negative than CB and VB levels, respectively [69].

The mechanism of an ideal heterogeneous photocatalytic process is based on the Equations (1)–(12) [70,71,72].

Semiconductor + hυ → Semiconductor (h⁺_VB + e⁻_CB)

(1)

h⁺_VB + e⁻_CB → heat

(2)

OH⁻ + h⁺_VB → ^•OH

(3)

H₂O + h⁺_VB → ^•OH + H⁺

(4)

^•OH + ^•OH → H₂O₂

(5)

e⁻ + H⁺ + O₂ → ^•HO₂

(6)

^•HO₂ + ^•HO₂ → O₂ + H₂O₂

(7)

O₂ + e⁻ → •O₂⁻

(8)

•O₂⁻ + H⁺ + ^•HO₂ → O₂ + H₂O₂

(9)

H₂O₂ + e⁻ → ^•OH + OH⁻

(10)

H₂O₂ + ^•OH → H₂O + ^•HO₂

(11)

^•OH + organic substances → intermediate → product

(12)

The photocatalytic process in water could be carried out as follows [30]:

• Transfer of the pollutants from the liquid phase to the surface of catalyst;
• Pollutants adsorption onto the surface of the activated catalyst;
• Photogeneration of ROSs, including ^•OH, followed by pollutants degradation;
• Desorption of intermediates from the surface of catalyst;
• Transferring intermediates into the liquid phase.

Due to the crucial role of surface reactions in the photocatalysis mechanism, the adsorption of reactants on the surface of the semiconducting material is of great importance [31]. For instance, various mechanisms of oxidation have been observed for the degradation of phenol, benzene, and formic acid using TiO₂ [73]. Formic acid could be chemisorbed strongly on titania in water, which leads to direct oxidation by trapping photogenerated holes. In comparison, benzene is physisorbed on titania and has been photo-oxidized by an indirect transfer mechanism. When it comes to phenol, both chemisorption and physisorption processes could take place, and its photooxidation mechanism depends on the solvent used [31]. In addition to the reactants, the relative binding strength of products/intermediates to the surface of photocatalytic material is of high importance. For instance, the photocurrent decrease of WO₃ in HClO₄ has been allocated to the bond of photogenerated species on it, which could hinder the water oxidation of active sites [31]. Another key point is the probable interactions between water and the photocatalysts, which should be considered to determine the mechanism of photocatalytic processes.

2.2. Kinetic Analysis

The classical equation of Langmuir–Hinshelwood (L-H) has been widely used for the kinetic analysis of both liquid-phase and gas-phase photocatalysis [55,74,75,76,77,78]. Using this model, the relationship between the oxidation rate and the concentration of reactant is shown in Equation (13) (when the concentrations of oxygen and water remain constant) [77,78]:

$$\mathrm{r}=-\frac{\mathrm{dD}}{\mathrm{dt}}=\frac{{\mathrm{r}}_{\mathrm{L}}{\mathrm{K}}_{\mathrm{L}}^{\mathrm{app}}\left[\mathrm{D}\right]}{1+{\mathrm{K}}_{\mathrm{L}}^{\mathrm{app}}\left[\mathrm{D}\right]}$$

(13)

where r and [D] are the oxidation rate (mg m⁻³ min⁻¹) and the concentration of reactant (mg m⁻³), respectively [78]. Langmuir–Hinshelwood parameters are ${\mathrm{K}}_{\mathrm{L}}^{\mathrm{app}}$ and r_L that are identified as the apparent Langmuir adsorption constant (m³ min⁻¹) and the apparent L-H rate constant of the reaction, respectively [78,79].

Equation (13) can be transformed as Equation (14) [77]:

$$\frac{1}{\mathrm{r}}=\frac{1}{{\mathrm{r}}_{\mathrm{L}}}\left(1+\frac{1}{{\mathrm{K}}_{\mathrm{L}}^{\mathrm{app}}\left[\mathrm{D}\right]}\right)$$

(14)

The time dependence of the concentration of the adsorbed reactant is given in Equation (15) [77]:

$$\frac{\mathrm{d}\left[{\mathrm{D}}_{\mathrm{ad}}\right]}{{\mathrm{d}}_{\mathrm{t}}}={\mathrm{k}}_{\mathrm{a}}\left[\mathrm{D}\right]\left(\left[{\mathrm{S}}_{\mathrm{D}}\right]-\left[{\mathrm{D}}_{\mathrm{ad}}\right]\right)-{\mathrm{k}}_{\mathrm{d}}\left[{\mathrm{D}}_{\mathrm{ad}}\right]-{\mathrm{k}}_{\mathrm{i}}\mathrm{I}\left[{\mathrm{D}}_{\mathrm{ad}}\right]$$

(15)

where [S_D], k_a, k_d, and k_i are the total concentration of the adsorption site for reactant, adsorption rate constant in the dark, desorption rate constant in the dark, and photoinduced desorption rate constant, respectively. There are some concerns for robotic application of L-H model to interpret the kinetic data [73,79]:

• Adsorption–desorption equilibrium of substrate species is not disturbed under illumination (as a pre-assumption);
• Ambiguous photon flow intervention (as an experimental parameter);
• Issues in intervening physical meaning;
• Chemical nature of the semiconductor surface does not change during photocatalysis (as a pre-assumption);
• Disregarding the electronic interaction of surface with substrate species;
• Considering that chemisorption of organic species onto the surface of catalyst is vital for photocatalysis.

The dark Langmuir adsorption constant (K_L) is not the same as ${\mathrm{K}}_{\mathrm{L}}^{\mathrm{app}}$(${\mathrm{usually} \mathrm{K}}_{\mathrm{L}}^{\mathrm{app}}\gg {\mathrm{K}}_{\mathrm{L}}$). It has been shown that ${\mathrm{k}}_{\mathrm{LH}}$ is a function of absorbed light intensity (I^β) where β equals 1.0 (at low absorbed light intensity) or 0.5 (at high absorbed light intensity) [80]. After reevaluation of the semiconductor photo-assisted reactions, another simple mechanism has been suggested as follows [80]:

$$\mathrm{D}\left(\mathrm{liquid}\right)\leftrightarrow \mathrm{D}\left(\mathrm{ads}\right)$$

(16)

$$\mathrm{D}\left(\mathrm{ads}\right)\stackrel{{\mathrm{k}}_{\mathrm{LH}}}{\leftrightarrow }\mathrm{products}$$

(17)

It is assumed that the reaction of a surface hydroxyl radical and the absorbed reactant takes place in the latter step, Equation (17), which results in the formation of products. Based on the relationship between this step and absorbed light intensity (and the incident light intensity, consequently) correlation between ${\mathrm{k}}_{\mathrm{LH}}$ and I^β has been proposed as follows [80]:

$${\mathrm{k}}_{\mathrm{LH}}={\mathsf{\alpha }\mathrm{I}}^{\mathsf{\beta }}$$

(18)

In which α is proportionality constant and β equals 1.0 or 0.5 as discussed above. The surface coverage of the reactant (θ_D) is defined as follows by consideration of a pseudo-steady-state hypothesis [80]:

$${\mathsf{\theta }}_{\mathrm{D}}=\frac{{\mathrm{K}}_{\mathrm{ads}}^{\mathrm{app}}\left[\mathrm{D}\right]}{1+{\mathrm{K}}_{\mathrm{ads}}^{\mathrm{app}}\left[\mathrm{D}\right]}$$

(19)

where ${\mathrm{K}}_{\mathrm{ads}}^{\mathrm{app}}$ is given by Equation (20) as follows [80]:

$${\mathrm{K}}_{\mathrm{ads}}^{\mathrm{app}}=\frac{1}{{\mathrm{K}}_{\mathrm{diss}}^{\mathrm{app}}}=\frac{{\mathrm{k}}_1}{{\mathrm{k}}_{-1}+{\mathsf{\alpha }\mathrm{I}}^{\mathsf{\beta }}}$$

(20)

${\mathrm{K}}_{\mathrm{diss}}^{\mathrm{app}}$ is defined as the apparent dissociation constant. Thus, the oxidation rate, r, is given as follows by considering that $-\mathrm{r}={\mathrm{k}}_{\mathrm{LH}}{\mathsf{\theta }}_{\mathrm{D}}$ [80]:

$$-\mathrm{r}=\frac{{\mathrm{k}}_{\mathrm{LH}}\left[\mathrm{D}\right]}{{\mathrm{K}}_{\mathrm{diss}}^{\mathrm{app}}+\left[\mathrm{D}\right]}$$

(21)

Boulamanti et al. have proposed the following equation by studying the photocatalytic activity of target gas and by considering the effect of water vapor [81]:

$$\mathrm{r}=\mathrm{k}\frac{{\mathrm{K}}_{\mathrm{LH}}\mathrm{D}}{1+{\mathrm{K}}_{\mathrm{LH}}\mathrm{D}+{\mathrm{K}}_{\mathrm{w}}{\mathrm{D}}_{\mathrm{w}}}$$

(22)

where K_w is a Langmuir adsorption constant proportional to the adhered water molecules to the surface of the catalyst, and D_w is the concentration of water in the gas-phase.

3. Band Gap Estimation and Quantum Size Effect

Inorganic/organic semiconductors display various physical properties, and thus can be used for a variety of purposes [82]. The optical properties of semiconducting nanomaterials are their band gap energy (E_g) as well as absorption coefficient (K), potentially. The band gap energy of semiconductors is a crucial characteristic of their electronic structure, which determines their potential applications [83]. Although it could be affected by the synthesis/processing method, the exact determination of its value is a challenge in materials science and engineering. In direct band gap semiconductors, the recombination of e⁻/h⁺ pairs could be radiative, if the VB maximum and CB minimum are aligned in the momentum space, which results in photoluminescence [82]. When it comes to the indirect band gap semiconductors, phonons (lattice vibrations) that are involved in the emission and absorption of light allow the semiconductor to convert the light energy into mechanical (photoacoustic) or thermal (photothermal) responses [82]. When a semiconductor is exposed to photons of energy larger than its band gap, the transfer of electrons from the valence band to the conduction band leads to an abrupt increase in the absorbency of the semiconductor to the wavelength, which corresponds to the band gap energy. The relationship between the incidental photon energy and the absorption coefficient is dependent on the type of band gap (direct or indirect). The electronic properties of semiconductors are usually studied by conversion of DR spectra to pseudo-absorption spectra, $\mathrm{F}\left({\mathrm{R}}_{\infty }\right)$, using the Kubelka–Munk function as follows [83,84]:

$$\mathrm{F}\left({\mathrm{R}}_{\infty }\right)=\frac{\mathrm{K}}{\mathrm{S}}=\frac{{\left(1-{\mathrm{R}}_{\infty }\right)}^2}{2{\mathrm{R}}_{\infty }}$$

(23)

$${\mathrm{R}}_{\infty }=\frac{{\mathrm{R}}_{\mathrm{sample}}}{{\mathrm{R}}_{\mathrm{standard}}}$$

(24)

where $\mathrm{F}\left({\mathrm{R}}_{\infty }\right)$ is the Kubelka–Munk function and ${\mathrm{R}}_{\infty }$ is the diffused reflectance of the non-transparent material with infinite thickness. Thus, the supporting material is not contributed (in the case of semiconductors deposited on a substrate). The $\mathrm{S}$ and $\mathrm{K}$ parameters are the scattering and absorption K-M coefficients, respectively. It is notable that $\mathrm{S}$ does not depend on the wavelength for particles larger than 5 µm. Therefore, S could be considered as a constant and $\mathrm{F}\left({\mathrm{R}}_{\infty }\right)$ could be considered as a pseudo-absorption function, consequently [83]. By far, a combination of absorption-based spectroscopic methods, including diffuse reflectance spectroscopy (DRS) on bulk samples or transmission measurements on thin films and coatings and the Tauc method, is the most common procedure of determination of band gap energy [83]. Since absorption-based spectroscopic methods do not confound bulk properties with surface effects, they are preferable for the measurement of bulk properties [83]. The Tauc method was proposed by Tauc et al. as a method for determination of band gap energy by plotting an optical absorption coefficient against energy while evaluating the electronic and optical properties of amorphous germanium. The strength of optical absorption is dependent on the difference between the energy of photons and the band gap energy as follows [84]:

$${\left(\mathsf{\alpha }\mathrm{h}\mathsf{\nu }\right)}^{\frac{1}{\mathrm{n}}}=\mathrm{A}\left(\mathrm{E}-{\mathrm{E}}_{\mathrm{g}}\right)$$

(25)

where $\mathsf{\nu }$ is the photon/light frequency, $\mathsf{\alpha }$ is the linear absorption coefficient, ${\mathrm{E}}_{\mathrm{g}}$ is the band gap energy, $\mathrm{h}$ is the Planck’s constant, A is a proportionality constant, and n is a constant that depends on the nature of the electronic transition [84]:

• For direct allowed transitions: n = 1/2;
• For indirect allowed transitions: n = 2;
• For direct forbidden transitions: n = 3/2;
• For indirect forbidden transitions: n = 3.

The ‘$\mathrm{E}$’ term is the incident photon energy and is calculated as follows:

$$\mathrm{E}\left(\mathrm{eV}\right)=\mathrm{h}\mathsf{\nu }=\frac{\mathrm{hC}}{\mathsf{\lambda }\left(\mathrm{nm}\right)}=\frac{1236}{\mathsf{\lambda }\left(\mathrm{nm}\right)}$$

(26)

It is notable that the majority of basic absorption processes are allowed transitions (n = 2 or n = 1/2 for indirect and direct transitions, respectively) [84]. Finally, the graph of ${\left(\mathsf{\alpha }\mathrm{h}\mathsf{\nu }\right)}^{\frac{1}{\mathrm{n}}}$ vs. $\mathrm{h}\mathsf{\nu }$ is plotted, and the band gap energy is easily extrapolated by the interception of the linear region to the X-axis. Usually, different values of n (usually 1, and 1/2) are used to identify the correct type of transition. As an example, the Tauc plot of TiO₂ is shown in Figure 3 [85]. Noteworthy, the straight blue line has been plotted to estimate E_g.

It is notable that the size of particles could change the band gap energy of semiconductors [55,86]. The planetary model of the Bohr hydrogen atom is generally used for description of the movement of the bonded electron–hole pair originated by photoexcitation. The exciton Bohr radius, $a_B$, is used for calculation of the region of delocalization of the electron hole pair as follows [86]:

$$a_B=\frac{{\hslash }^2\epsilon }{e^2} \left[\frac{1}{m_e^{\ast }{m}_O}+\frac{1}{m_h^{\ast }{m}_O}\right]$$

(27)

where $\epsilon$ is the dielectric constant of the semiconductor, e is the charge of an electron, $\hslash$ is the reduced Planck’s constant, $m_e^{\ast }$ is the effective mass of electron, $m_h^{\ast }$ is the effective mass of hole, and $m_O$ is the rest mass of an electron. The steric limitation of photoexcited charges is observed in the bulk of a semiconductor whose nanocrystals are smaller than the region of delocalization of exciton. This could change some characteristic features of semiconductors. However, the degree of changes depends on the ratio of nanoparticle radius, R, and the value of $a_B$. In this case, two different modes could be considered [86]:

$a_B$ ≤ R: There is a weak restriction in this region so that a similar electronic structure is observed for both the bulk crystal and the nanoparticle.

$a_B$ > R: There is a strong quantum confinement in the region so that a radical rearrangement is observed for the electronic structure of semiconductor nanoparticle. For example, energy of the exciton excitation increases. Moreover, discrete electronic levels are provided by gradual change in the energy bands of the semiconductor.

This phenomenon, in which the top of VB and the bottom of CB shift in positive and negative directions, respectively, is called a quantum-size effect and could result in the expansion of band gap energy. The Bohr radius of rutile and anatase TiO₂ is around 0.3 and 2.5 nm, respectively. Thus, interpreting the results by using quantum-size effect needs deep evaluations, in cases such as TiO₂, since synthesis of such a small size might be difficult [55]. It is noteworthy that the band gap energy of semiconducting nanomaterials could be highly dependent on their morphology. For instance, titania particles with nanoburrs or lateral organization could have lower band gap energies [87]. Based on the band gap energy, semiconductors are divided into two major categories: wide band gap semiconductors and narrow band gap semiconductors. Band gap energies of some major semiconductors are illustrated in Figure 4 [88]. Among different photocatalysts, TiO₂ is used as the most common semiconductor for photocatalytic applications and is discussed in the following part.

4. TiO₂

4.1. General Properties and Applications

TiO₂ has found several applications in toothpaste, sunscreens, plastics, printing ink, condensers, paper, electronic components, leather, cosmetics, ceramics, food, and pigmentation since its commercial production [89,90,91]. High refractive indices of anatase and rutile phases, which lead to high reflectivity from surfaces, takes account for its several applications where white coloration is desired [42,92]. Since the discovery of the photocatalytic water splitting on a titanium oxide electrode under UV illumination by Fujishima and Honda, serious efforts have been allocated to the study of its efficiency in photocatalysis, photovoltaics, sensors, and photoelectrochemical applications, which can be generally divided into two discrete categories of environmental and energy [93,94]. TiO₂ is non-toxic and earth abundant, and has high photostability [94,95]. It is the most common semiconducting material used for photocatalytic applications and has been employed as a benchmark photocatalyst in many research works (especially commercial Degussa P-25 powder, which consists of both anatase and rutile phases) [96,97,98]. Although there are various semiconducting materials, an overwhelming majority of researchers (around 60%) have focused on different TiO₂ phases in photocatalytic works during the 2000s [99]. The position of the top valence band of TiO₂ is ca. 3 V vs. NHE (at pH 0). Therefore, the potential of its positive holes is remarkably more positive than oxidation potential of ordinary organic compounds. The valence bands of the majority of metal oxides are composed of the same orbitals (O2p). Thus, most of them possess the same potential of the top valence band and the same oxidation ability is expected for all of them [55]. In addition, the surface chemistry of water and oxygen is fundamental to important processes such as the oxygen reduction reaction (ORR) and photocatalytic water oxidation. These reactions are mediated by photoexcited electrons and holes, respectively. Water oxidation is a hole-mediated process as follows [100]:

2H₂O + 4h⁺→ 4H⁺ + O₂

(28)

The ORR is a process mediated by photoexcited electrons that is followed by reactions with coadsorbed water as follows [100]:

O₂ + e⁻→ (O₂)⁻

(29)

OOH⁻ + e⁻→ OH⁻ + (O_ad)⁻

(30)

(O_ad)⁻ + e⁻ + H₂O → 2OH⁻

(31)

H₂O + OOH⁻→ OH⁻ + H₂O₂

(32)

(O₂)⁻ + e⁻ + H₂O → OH⁻ + OOH⁻

(33)

H₂O₂ + 2e⁻→ 2OH⁻

(34)

Although both the ORR and water oxidation involve the same intermediate species (H₂O₂, OH⁻, or OOH⁻), the identification of the reaction intermediates is not simple (since they are usually short-lived) [100]. To illustrate this point, characteristic times for different photo-reactions in the heterogeneous photocatalysis on TiO₂ are shown in

Table 1. Characteristic times for heterogeneous photocatalysis on TiO₂: where e_cb⁻ is the conduction band electron, h_vb⁺ is the valence band hole, e_tr⁻ is the trapped conduction band electron, >TiOH shows the primary hydrated surface functionality of titania, >Ti^IVOH•+ is the surface-bound hydroxyl radical, >Ti^IIIOH is the surface-trapped conduction band electron, Red is the reductant, and OX is the oxidant [101].

Type of Primary Reaction	Primary Reaction	Characteristic Time (s)
Generation of charge carriers	TiO2 + hυ → ecb− + hvb+	fs
Charge carrier trapping	Hvb+ + > TiIVOH → > {TiIVOH}+	10 ns
Deep trap (irreversible)	ecb− + > TiIV → >TiIII	10 ns
Shallow trap (dynamic equilibrium)	ecb− + > TiIVOH ↔ {>TiIIIOH}	100 ps
Charge carrier recombination	hvb+ + {> TiIIIOH} → >TiIVOH ecb− + > {TiIVOH•}+ → >TiIVOH	10 ns 100 ns
Interfacial charge transfer	{>TiIVOH•}+ + Red → > TiIVOH + Red•+ etr− + OX → TiIVOH + OX•−	100 ns ms

[101].

Therefore, one of the probable reasons for high photocatalytic activity of TiO₂ could be its high reduction potential that is responsible for the injection of photogenerated electrons into the molecular O₂ on its surface [55]. Notably, equal numbers of positive holes and electrons must be consumed for completion of photocatalytic reactions. Thus, positive holes cannot be used for oxidation reactions, despite of their high potentials, unless the photogenerated electrons are consumed simultaneously. Most other metal oxides have high oxidation ability; however, their low reduction ability may result in their lower photocatalytic activity compared with TiO₂ [55].

4.2. Optical and Electrical Properties of TiO₂

In general, rutile TiO₂ is more anisotropic than anatase TiO₂ in the range from infrared to visible spectra. On the other hand, an important anisotropy is observed for anatase phase in the band gap region [102]. Since titania is known as an n-type semiconductor, donor-type defects (e.g., titanium interstitials and oxygen vacancies) are responsible for its conductivity [103]. The excessive electrons in the solid, introduced by oxygen vacancies, could enhance the electrical conductivity [102]. However, oxidized titania may show p-type properties as a result of concurrent presence of acceptor-type defects including titanium vacancies. Ti_1−xO₂ or TiO_2+x could be applied, instead of TiO₂, where titanium vacancies could make a remarkable contribution to the defect disorder (under prolonged oxidation conditions) [103]. Doping is an efficient method that could be used to form both n-type and p-type titania. For example, manganese-doped TiO₂ has shown p-type electrical conduction [104,105]. In addition to manganese, iron, nickel, chromium and cobalt could act as electron acceptors. Thus, Fe-doped [106,107], Ni-doped [108], Cr-doped [109,110,111] and Co-doped [112,113] TiO₂ could show p-type electrical conduction. The ratio between the concentration of metal dopants and that of oxygen vacancies could be crucial to the reduction or augment of the electrical conductivity. In addition to the concentration of oxygen vacancies, their contribution should also be taken into account for evaluation of the electrical conductivity [102]. On the other hand, niobium and tantalum could act as electron donors. Therefore, W-doped [114], Ta-doped [115], and Nb-doped [116,117] TiO₂ could show n-type electrical conduction.

Various non-metal elements including N, P, S, B, and I have been extensively employed to drive visible-light-activated TiO₂. Among those, N-doping has received remarkable attention as a method efficiently used for driving visible-light activated TiO₂ [118,119,120,121,122]. It has been shown that nitrogen-doping could remarkably reduce the formation energy of oxygen vacancies as confirmed by DFT calculations. Thus, N-doped TiO₂ can take advantage of the presence of oxygen vacancies (especially on its surface) [123]. By far, various methods have been used for the synthesis of N-doped TiO₂ including sputtering, sol-gel, chemical vapor deposition, decomposition of nitrogen-containing metal-organic precursors, spray pyrolysis, pulsed laser deposition, combustion reaction, high-energy milling, and implantation. Schematic illustrations of models for doping of different nitrogen species including substitutional N-doping, interstitial N-doping, substitutional NO-doping, substitutional NO₂-doping, and interstitial NO-doping are shown in Figure 5.

Thus, nitrogen doping into a TiO₂ lattice structure could be either interstitial or substitutional. Peng et al. synthesized both interstitial and substitutional N-doped TiO₂ for photocatalytic degradation of methyl orange and phenol. They suggested that although both interstitial and substitutional nitrogen doping could drive visible-light activated TiO₂, interstitial N-doped TiO₂ could show a higher photocatalytic activity than that of substitutional N-doped TiO₂ [125]. Zeng et al. compared the photocatalytic activity of visible-light activated interstitial and substitutional N-doped TiO₂ toward degradation of benzene under the same conditions (similar grain size, crystallinity, and specific surface area of the as-prepared samples) [126]. Unlike Peng et al., they concluded that substitutional N-doped TiO₂ could show higher photocatalytic activity than that of interstitial N-doped TiO₂. Lower recombination rate of the photogenerated e⁻/h⁺ pairs and higher proportion of surface hydroxyl groups have accounted for the higher photocatalytic activity of substitutional N-doped TiO₂. The higher photocatalytic activity of interstitial N-doped TiO₂ than that of substitutional N-doped TiO₂, as reported by Peng et al. [125], could originate from different methods used by Peng et al. for the synthesis of interstitial and substitutional N-doped TiO₂ [126]. It should be noted that the photocatalytic activity of semiconductors could be highly influenced by their grain/particle size [127,128,129], specific surface area [130,131,132], and crystallinity/polymorph [133,134,135]. Of note, nitrogen doping could be achieved through simultaneous interstitial and substitutional doping as confirmed by XPS analysis [136]. In substitutional doping, either oxygen atoms or titanium atoms can be substituted by nitrogen atoms. Therefore, TiO_2−xN_x (titanium oxynitride) and Ti_1-yO_2−xN_x+y are the results of the substitution of oxygen atoms and substitution of both oxygen and titanium atoms by nitrogen atoms, respectively. As suggested by Peng et al., Ti_1−yO_2−xN_x+y could be formed at high concentrations of nitrogen (as high as 21 mol%) [137]. Valentin et al. suggested that nitrogen doping is likely accompanied by the formation of oxygen vacancies. Besides, they proposed that the abundance of nitrogen-doping species is dependent on the preparation conditions including the annealing temperature and the oxygen concentration (in the atmosphere) [138]. As for the substitutional N-doped TiO₂ (N-Ti-O and Ti-O-N), localized N 2p states (slightly above the VB of pure TiO₂) could be responsible for the visible-light response [139]. Migration of photo-excited electrons from VB to the N 2p states could reduce the band gap energy of TiO₂ [136]. Notably, NO bond with π-character that generates new localized states (slightly above the VB of pure TiO₂) accounts for the visible-light response of interstitial N-doped TiO₂ [139]. Valentin et al. suggested that the highest localized states for the interstitial and substitutional nitrogen species are 0.73 and 0.14 eV above the top of the valence band, respectively [140]. Not only could interstitial and substitutional nitrogen doping increase the visible-light harvest, but it could also intensify the absorption of UV-light, which originates from the appearance of defect energy levels in the band gap [126].

It has been shown that the photocatalytic efficiency of titania could be strongly correlated to its (micro) structure and semiconducting properties [103,141]. Additionally, the electrical properties of titania nanostructures depend on the crystallographic directions [102]. It is why the evaluation of the electrical properties of TiO₂ is of high importance for photocatalytic applications, as shown in

Table 2. Comparison of the crystal structural, optical and electrical properties for TiO₂ nanostructures. Adapted with permission from Ref. [102]. Copyright 2018, Royal Society of Chemistry. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence (https://creativecommons.org/licenses/by-nc/3.0/) (Accessed on 1 December 2022).

Properties	TiO2 Nanostructures
	Rutile	Anatase	Brookite
Crystal Structure	Tetragonal	Tetragonal	Orthorhombic
Lattice constant (A)	a = 4.5936 c =2.9587	a = 3.784 c = 9.515	a = 9.184 b = 5.447 c = 5.154
Molecule (cell)	2	2	4
Volume/molecule (A˚3)	31.21	34.061	32.172
Density (g cm−3)	4.13	3.79	3.99
Ti–O bond length (${\mathrm{A}}^{°}$)	1.949 (4) 1.980 (2)	1.937 (4) 1.965 (2)	1.87–2.04
O–Ti–O bond angle	$\begin{array}{c}{81.2}^{°}\\ {90}^{°}\end{array}$	$\begin{array}{c}{77.7}^{°}\\ {92.6}^{°}\end{array}$	$77-{105}^{°}$
Band gap at 10 K	3.051 eV	3.46 eV
Static dielectric constant (ε0, in MHz range)	173	48
High frequency dielectric constant, ${\epsilon }_{\infty }$ ($\lambda =600 \mathrm{nm}$)	8.35	6.25

.

When defects are electrically charged, defect disorder could largely affect the electrical properties. There are several reports on the investigation of the electrical properties of rutile TiO₂ at high temperatures and in nanocrystalline form [142,143,144,145,146]. Although evaluation of the electrical properties of anatase TiO₂ is of interest, several experimental problems, owing to its grain growth and partial phase transformation into rutile at elevated temperatures, has prevented its widespread studies [141]. The electrical properties of oxide semiconductors including titania are generally temperature dependent. This dependency is generally considered by the activation energy of electrical conductivity [103,147]. It is notable that the oxygen partial pressure could play a crucial role in the activation energy of electrical conductivity of single-crystal (SC) and polycrystalline (PC) TiO₂ [147]. The electrical conductivity of metals and n-type semiconductors including TiO₂ is the reciprocal of their resistivity and could be expressed as follows [147,148]:

$$\sigma =\frac{1}{\rho }=en{\mu }_n$$

(35)

in which σ is the electrical conductivity, $\rho$ is the resistivity, n is the concentration of electrons, µ_n is the mobility of electrons, and e is the elementary charge [147]. Based on the four probe method, sample dimensions are required to determine the resistivity and/or electrical conductivity as follows [148]:

$$\mathsf{\rho }=\mathrm{R}\frac{\mathrm{L}}{\mathrm{A}}$$

(36)

where R, A, and L are resistance, surface area of the cross section, and distance between voltage electrodes, respectively [148]. The mobility is defined as follows [149]:

$${\mathsf{\mu }}_{\mathrm{n}}=\frac{\mathsf{\nu }}{\mathsf{\epsilon }}$$

(37)

The mobility is usually determined by scattering with photons (in an intrinsic semiconductor). The mobility’s of electrons (µ_n) for some semiconductors such as Si, Ge, GaAs, GaN, InSb, InAs, InP, and ZnO are 1300, 4500, 8800, 300, 77,000, 33,000, 4600, and 230 cm²/Vs, respectively, and the mobilities of holes (µ_p) for the same semiconductors are 500, 3500, 400, 180, 750, 460, 150, and 8 cm²/Vs, respectively. Usually, semiconductors possess a much higher mobility than that of metals including Cu (i.e., 35 cm²/Vs) [149]. In the case of TiO₂, the slope of log σ versus log p (O₂), which is dependent on the oxygen activity, is −1/6 and −1/4 in highly reduced conditions (p(O₂) < 10⁻⁵ Pa) and in oxidized conditions (p(O₂) > 10 Pa), respectively (at elevated temperatures).

4.3. Promising Phases of TiO₂ for Photocatalytic Applications

Titanium dioxide, which is an n-type semiconductor owing to the presence of oxygen vacancies, crystalizes naturally in three major different phases including anatase (tetragonal), brookite (orthorhombic) and rutile (tetragonal). Among all TiO₂ polymorphs, anatase and rutile phases are generally used in photocatalytic applications [150]. However, brookite TiO₂ could also find applications in photocatalysis [151,152,153,154]. It has shown a higher photocatalytic activity than that of rutile TiO₂ in some cases. For instance, hydrothermally synthesized brookite TiO₂ has exhibited superior photocatalytic activity than that of hydrothermally synthesized rutile TiO₂ in degradation of some hazardous pharmaceuticals (ibuprofen, diatrizoic acid, and cinnamic acid) and phenol as model organic pollutant. The higher efficiency of the brookite phase (in this case study) has been devoted to the existence of highly active species, superoxide radicals and valence band holes, in the photocatalytic treatment [155]. In another study, titania nanoparticles (including pure anatase, anatase-rich, pure brookite, and brookite-rich phases) have been synthesized by Kandiel et al. for photocatalytic purposes.

Interestingly, higher photocatalytic activity was observed by using as-prepared brookite titania nanoparticles compared with as-prepared anatase TiO₂ nanoparticles. The surface area of the latter has been three times higher than that of the former. The higher photocatalytic efficiency of brookite titania nanoparticles for methanol photooxidation has been devoted to their higher crystallinity and/or to the cathodic shift of the CB of brookite TiO₂ compared with that of anatase TiO₂, which could facilitate the transfer of interfacial electrons to the molecular oxygen [156]. Although anatase and rutile TiO₂ are the most common titania polymorphs used for photocatalytic applications, it has been shown that brookite TiO₂ could exhibit markedly high photocatalytic activity, even higher than the anatase phase, in some cases (e.g., for degradation of ibuprofen, cinnamic acid, and phenol, and photooxidation of methanol) [152,156]. However, brookite titania has not received great attention due to some limitations such as its difficult synthesis procedure to generate high purities [157]. Of note, rutile TiO₂ is thermodynamically stable at ambient conditions [156] while anatase is a meta-stable phase. The band gap energy of rutile phase is lower than that of the anatase phase with the band gap energy of ~3.2 eV [158]. The phase transition between titania polymorphs depends on several factors. For instance, particle size, surface area, heating rate, particle shape (aspect ratio), volume of sample, atmosphere, measurement technique, soaking time, nature of sample container, and impurities are among various factors that affect the phase transformation of undoped anatase to rutile TiO₂ [92]. The transition of anatase to rutile is a reconstructive process in which the Ti-O bonds are ruptured. Afterwards, a structural rearrangement and formation of new Ti-O bonds occur which result in the formation of rutile phase. It is worth mentioning that the phase transformation of anatase to rutile is a nucleation and growth process [92]. However, it has been shown that this transition is limited by nucleation stage and not by growth. It should be considered that when it comes to the phase transition of nanocrystalline anatase, both surface and interface nucleation processes could be observed though at varying rates. The experiments have confirmed that interface nucleation is more rapid than surface nucleation [159]. Usually, rutile phase nucleates at (112) twin interfaces, in pure anatase, because of similar structure of these sites to rutile phase [92]. Upon heating, both meta-stable brookite and anatase phases could transform to rutile phase, irreversibly, though at different temperatures [92,158,160]. Notably, this transformation could take place at different temperatures and various attempts have been made to promote/inhibit it [92]. When it comes to the pure synthetic TiO₂, it could occur between 600–700 °C [160]. According to the report of Wu et al. [161], the effect of temperature on the phase stability and crystallite size of TiO₂ is shown in Figure 6.

As evident, an increase in the temperature could result in an increase in the crystallite size of both anatase and rutile TiO₂ (though at different degrees). Although the transformation of anatase to rutile has been widely studied, the transformation of brookite to anatase or vice versa is a bit controversial. The transformation of anatase to rutile could be carried out either directly or indirectly. However, some reports suggest that the brookite phase transforms to the anatase phase at first. Then, anatase TiO₂ transforms to rutile TiO₂. On the other hand, there are some reports suggesting that the anatase phase transforms to the brookite and/or rutile phases prior to the transformation of brookite to rutile [156].

Accordingly, the anatase and brookite phases are not stable at large crystallite sizes. In another words, the most thermodynamically stable phases of TiO₂ are rutile, brookite, and anatase, respectively (by increasing the crystallite sizes). Thermodynamic studies have also confirmed the higher stability of the rutile phase than the anatase phase at all positive temperatures and pressures. The results are shown in Figure 7.

Bulk and/or surface doping of TiO₂ could affect the stability of anatase and rutile phases and change the temperature of the transition of anatase to rutile, which has been explained by a ceased crystal growth as the result of the formation of Ti-O-M bonds. For instance, doping with metal cations including Nd [162], La [163], Ni [164], Si, W, Cr [165], Al, Nb, Ga, and Ta [166] could retard the grain/particle growth of anatase and rutile phases and delays the transition of anatase to rutile. The addition of molybdenum and tungsten could completely eliminate the anatase phase at temperatures between 680 and 830 °C, respectively [102]. Doping with V, Ag, Mn [165], Zn, Fe and Cu [166] could generally promote this transformation. However, there are some dual behaviors which should be considered. For example, Wang et al. have reported the acceleration of anatase to rutile phase transition for Nb-doped TiO₂. It is while a depression effect has been observed on the grains growth of anatase for Nb-doped TiO₂ [165]. Using cationic/anionic dopants [167] and non-metal dopants, including carbon [168], nitrogen [169], fluorine [170,171] and chlorine [171] could affect the phase transformation of titania. Unlike interstitial atoms that could increase the strain energy that must be overcome and the bonds that must be broken, the creation of oxygen vacancies, originated from the incorporation of ions with relatively small ionic radius and lower valence than that of Ti⁴⁺, could facilitate the phase transformation by reduction of the strain energy needed for the rearrangement of the Ti-O octahedra. The rate of the transition of anatase to rutile strongly depends on the incorporated dopants [172].

4.4. Photocatalytic Activity of Anatase Titania Compared with Its Other Polymorphs

It is generally believed that among the anatase, rutile, and brookite phases, the anatase phase is responsible for photocatalytic reactions. There are some statements that a pure rutile phase could not have any photocatalytic activity at all. However, some believe that it could possess photocatalytic activity, which depends on the nature of the organic reactant, preparation method of the photocatalyst and the nature of the precursor materials [150]. Considering pure phases, the anatase phase could provide higher photocatalytic activity than rutile TiO₂ [46,98]. The higher photocatalytic activity of anatase phase than other polymorphs could be attributed to its higher mobility of charge pairs and density of surface hydroxyl [46]. Notably, discrepancy with the recombination kinetics of e⁻/h⁺ pairs might also play an important role in the superior photocatalytic efficiency of anatase phase as photoluminescence (PL) studies for anatase TiO₂ have clarified its lower recombination rate of charge carriers than that of rutile phase under similar condition [173]. Brookite and rutile TiO₂ are direct band gap semiconductors, while anatase TiO₂ belongs to the category of indirect band gap semiconductors [174]. For indirect band gap semiconductors, the electronic transition from the VB to the CB is electrical dipole forbidden. Under these circumstances, the transition results in the change of both momentum and energy of the photogenerated e⁻/h⁺ pairs (transition is phonon assisted). On the other hand, the valence band to the conduction band electronic transition is electrical dipole allowed for direct band gap semiconductors. Due to the momentum change, the electronic absorption/emission of indirect band gap semiconductors is weaker than that of direct band gap semiconductors [175]. Thus, direct band gap semiconductors, such as rutile TiO₂, have more efficient absorption of solar energy than indirect ones (such as anatase TiO₂) [174,175]. However, a longer diffusion length as well as lifetime of photogenerated e⁻/h⁺ pairs could result in better photocatalytic performance of anatase TiO₂ than its rutile phase [174]. In addition, it has been reported that the anatase phase is more active than the rutile phase in absorption of hydroxyl groups and water [150] that could play an important role in photocatalysis. A schematic of recombination processes of photoexcited e⁻/h⁺ pairs within anatase TiO₂ (indirect gap) and rutile TiO₂ (direct gap) is shown in Figure 8 [174].

In addition to the band gap nature, the diffusion of free charge carriers is of remarkable importance. To achieve appropriate photocatalytic efficiency, the photoexcited e⁻/h⁺ pairs should migrate to the active sites where they are used prior to the recombination process. In this context, the diffusion of photogenerated e⁻/h⁺ pairs is strongly linked to their mobility, which is in turn related to their effective mass. The ratio of the effective mass of electrons to effective mass of holes is used to predict the stability of photogenerated e⁻/h⁺ pairs with respect to their recombination. In this case, a larger effective mass difference could enhance the photocatalytic activity as the result of the reduction of the e⁻/h⁺ pair recombination [176]. In general, the transfer rate of photoexcited e⁻/h⁺ pairs that affects the quantum efficiency of photocatalysts could be assessed by the effective mass of electrons and holes [174].

As evident, there is an inverse relationship between the transfer rate of photoexcited e⁻/h⁺ pairs and the effective mass of charge carriers. To sum up, the smaller the effective mass of charge carriers, the faster the transfer rate of charge carriers. Anatase TiO₂ has a lighter average effective mass of photoexcited e⁻/h⁺ pairs than that of both the brookite and rutile phases, which leads to the faster migration of e⁻/h⁺ pairs from bulk titania to its surface. This results in its lower recombination rate of photoexcited e⁻/h⁺ pairs [174]. It should be noted that there is not yet consensus on the reasons for higher photocatalytic activity of the anatase phase than that of the rutile and brookite phases [177]. It is worth mentioning that there are various factors, including method of synthesis, concentration of defects, purity of phases, surface crystallographic orientation, particle size, dopants, specific surface area, and its crystal structure (type of polymorph), that could remarkably affect the photocatalytic activity of TiO₂ [46,98].

4.5. Colorful TiO₂ versus White TiO₂

Recently, colored titania materials such as green, red, yellow, blue, brown and grey of various shades have been developed. The colorful titania could be synthesized by electronic and structural changes such as the incorporation of Ti-OH and Ti-H species, formation of oxygen vacancies, formation of disordered surface layers, reduction of Ti⁴⁺ to Ti³⁺, narrowed band gap energy, and the modified electron density [178]. These could result in the synthesis of green, red, black, and grey materials [179]. Black TiO₂, synthesized by Chen et al. using high pressure hydrogenation, has shown a largely narrowed band gap energy (for massive visible light absorption) and an enhanced photocatalytic activity. Since then, it has received remarkable attention in visible light utilization. Notably, the optical absorption of black titania could be extended to the IR region (approximately 1150 nm) [178]. The importance of black titania has resulted in its various applications in photocatalytic water splitting, photoelectron chemical water splitting, photocatalysis, fuel cells, Li-ion batteries, Na-ion batteries, Al-ion batteries, surface enhanced Raman active scattering substrate, supercapacitors, cancer photothermal therapy, solar desalination, microwave absorption, field emission, and dye sensitized solar cells (DSSC) [180,181]. Various methods, such as low pressure hydrogen treatment, high pressure hydrogen treatment, argon treatment, hydrogen–nitrogen treatment, hydrogen–argon treatment, hydrogen–plasma treatment, chemical oxidation, chemical reduction, electrochemical reduction, pulsed laser ablation, and hydroxylation, have been used to synthesize black titania nanomaterials [180].

Black titania, synthesized by hydrogenation, was firstly used for photocatalytic degradation of methylene blue and phenol [182]. Since then, photodegradation of methylene blue, as a model of organic pollutants, has been studied by many researchers using this polymorph of titania [182,183,184]. It is worth mentioning that black TiO₂ has shown a higher photocatalytic activity than that of white TiO₂ in several cases [184,185].

It has been stated that the formation of some surface defects, including oxygen vacancies and/or Ti³⁺ oxidation states, and disordered layers in the surface of highly crystalline TiO₂, could increase the interaction to the light irradiation and the lifetime of photogenerated electron/hole pairs [184]. However, Ti³⁺ ions have not been observed in some samples of black TiO₂. Thus, oxygen vacancies could be known as the main factor responsible for black coloration of titania [186]. The superior photocatalytic activity and/or photo electrochemical properties of black TiO₂ than pristine TiO₂ or P25 have also been reported by other researchers some of which are given in

Table 3. Superior photocatalytic and photoelectrochemical properties of black TiO₂ than white TiO₂ in some case studies.

Synthesis Method	Light Source	Improvement of Photocatalytic Activity	Improvement of Photoelectrochemical Properties	References
Melted aluminum reduction of pristine anodized and air-annealed TiO2 nanotube arrays	The simulated sunlight (intensity of 100 mW cm−2)	-	Approximately 5 times higher than pristine TiO2 nanotube arrays	[187]
Electrospinning process	A 150 W xenon lamp	-	Approximately a 10-fold increase compared with pristine TiO2 nanofibers	[188]
In situ plasma hydration of TiO2 thin films	A 150 W xenon lamp (intensity of 100 mW cm−2)	-	Approximately 2.5 times higher than pristine TiO2 thin films	[189]
Electrochemical reductive doping	UV source: A UV lamp (intensity of 5.8 mW cm−2) Visible-light source: A xenon lamp (intensity of 100 mW cm−2)	-	Approximately 2.2 times higher than pristine anodic TiO2 nanotubes (under both UV and simulated solar irradiation)	[190]
Using Ti2O3 as precursor for preparing Ti3+ self-doped TiO2 nanowires	A 20 W UV lamp	Approximately 7.5 times higher than pure TiO2 (P25) in photodegradation of methyl orange	-	[191]
hydrogen plasma assisted chemical vapour deposition	A 50 W simulated solar light source	Complete photodegradation of rhodamine B after approximately 30 min against partial photodegradation of rhodamine B even after 50 min for pure TiO2	-	[192]
Annealing the TiO2 nanobelts in hydrogen atmosphere	UV source: A 350 W mercury lamp Visible-light source: A 300 W xenon arc lamp	UV illumination: An approximate increase of 24% compared with pristine TiO2 nanobelts in decomposing methyl orange Visible light irradiation: An approximate increase of 17% compared with pristine TiO2 nanobelts in decomposing methyl orange	-	[193]
Annealing the TiO2 nanobelts in hydrogen atmosphere	A 300 W xenon arc lamp	-	Approximately 9.2 times higher than pristine TiO2 nanobelts	[193]

.

Oxygen vacancies are among the most important/common point defects originated by removal of some neutral oxygen atoms from the lattice structure of metal oxides including TiO₂ [194]. However, the major defect could become tetravalent titanium interstitials under extremely reduced conditions that are experimentally difficult to achieve [103]. In general, the driving force for the creation of vacancies is minimizing the Helmholtz free energy to establish thermodynamic equilibrium at a specific temperature. Cations and anions are two different types of vacancy defects in ionic crystals that lead to the formation of localized energy levels over the VB maximum and below the CB minimum, respectively [194]. The formation of oxygen vacancies could result in the development of Ti³⁺ species (by filling the empty states of titanium ions using excesses electrons originated from removal of oxygen atoms) [195,196] and the formation of shallow donor states under the CB of titania originating from Ti 3d orbits [195]. Owing to the higher active surface area of nanomaterials than that of bulk materials, a higher number of oxygen vacancies could be stimulated in the surface and subsurface regions of nanostructured titania than bulk titania. In addition, titania nanocrystals have less formation energy of oxygen vacancies than their bulk counterpart, which is why the creation of oxygen vacancies and evaluation of their effect in TiO₂ nanomaterials have received greater attention. Oxygen vacancies possess the minimum formation energy among the defects that could act as donors. Therefore, they have received great attention in defining chemical and physical properties of materials (including superconductivity, ferromagnetism, photocatalysis, resistive switching, phase transitions, redox activity, piezoelectric response, and photoelectrochemical performance) [194]. Hydrogen thermal treatment, high energy particle bombardment, doping of metal or non-metal ions, thermal treatment under oxygen depleted conditions, and some special reaction conditions are common methods used for development of TiO₂ with oxygen vacancies [195]. Thermal treatment under oxygen deficient conditions could be considered as an efficient method for creation of oxygen vacancies in TiO₂-based nanomaterials [194]. This process is performed at elevated temperatures, usually > 400 °C, in vacuum or pure Ar, He, and N₂ gas atmosphere [195].

The decrease of oxygen pressure results in an increase of the concentration of oxygen vacancies; hence, thermal treatment of titania under oxygen deficient conditions could facilitate the creation of oxygen vacancies. Therefore, the exposure of titania to air leads to the gradual removal of oxygen vacancies [195]. Doping with accept-type foreign ions, including Fe and Zn, could stabilize the as-formed oxygen vacancies [95,195]. Oxygen vacancies on anatase phase and rutile phase have been widely studied since they could be engineered/generated at mild conditions [196]. The calculation of the formation energy of oxygen vacancies has confirmed that creation of oxygen vacancies at the top surface of anatase (101) and (001) planes is more probable than other planes (because of their lower formation energies of vacancies). In comparison, rutile (110) planes have lower vacancy formation energy than that of other rutile crystalline planes [194]. Oxygen vacancies are capable of introducing localized states into the band gap structure (instead of the change of positions of valence band and conduction band). The driving force for development of these localized states is the Madelung potential of highly ionic crystal [195]. Transition of electrons from the oxygen vacancies to the valence band and/or from the valence band to the oxygen vacancies leads to infrared- and visible-light absorption [185,186]. Additionally, they act as potential shallow traps for significant improvement of the efficiency of electron–hole separation [184,186]. The energy level position of oxygen vacancies, which form a donor level under the conduction band of TiO₂, is from 0.75 to 1.18 eV [185,186,195]. It is worth mentioning that experimental and theoretical studies show that the excess electrons, originated from the formation of the oxygen vacancies, could affect the reactivity and surface absorption of important adsorbents including H₂O and O₂ on titania. These are some reasons why development of TiO₂ with the desired amount of oxygen vacancies is of great importance [195].

In addition to black TiO₂, other colored titania materials (including red, green, blue, yellow, and various shades of grey titania) have also found applications in photocatalysis and photoelectrochemical water splitting due to their specific features. For instance, Liu et al. have synthesized anatase titania microspheres with an interstitial B^σ+ (σ ≤ 3) gradient shell, red TiO₂, that are capable of absorbing the full visible light spectrum. UV-visible absorption of the white TiO₂ and these red TiO₂ microspheres are compared in Figure 9 (black and red graphs, respectively) [197]. Noteworthy, the colorful region represents the visible light spectrum ranged from 400 to 700 nm.

As evident, red titania microspheres possess much higher photo absorption ability than white titania in the visible light range. These microspheres have provided a gradient of absorption band gap energy from 1.94 eV (on their surface) to 3.22 eV (in their core) [179,197]. It has also been reported that red anatase TiO₂-based materials could show an unusual visible-light absorption that is representative of new types of visible light absorption bands of titania [198]. Thus, red titania-based photoanodes could be used for photoelectrochemical water splitting under visible-light irradiation [197,198]. Some other colorful titania-based photoanodes, including blue TiO₂, could be inactive in photoelectrochemical water oxidation under visible-light irradiation [198].

5. Conclusions and Perspectives

The application of TiO₂ semiconductor nanoparticles for the photocatalytic decomposition of pollutants in wastewater has been considered in this study. Considering that TiO₂ has three different structures (anatase, rutile and brookite), their stability and photocatalytic efficiency were compared. It should be noted that the band gap energy of these three crystal structures is different. In addition to the effect of band gap energy, the photocatalytic activity is influenced by the degree of stability and separation of the produced electron–hole pairs which could be dependent on the mobility as well as the mass ratio of the electron to the hole. Among the existing phases, the rutile phase has relatively high stability at different temperatures and pressures. The photocatalytic activity of titanium depends on its structure and morphology. Investigations show that the photocatalytic activity of anatase phase is higher than that of rutile and brookite. Although some studies indicate that the rutile phase does not have any photocatalytic activity, studies show that the rutile phase can be used for photocatalytic processes, which depends on the structure of the pollutant, the preparation method, and the precursor material of the photocatalyst. In general, the photocatalytic activity depends on the stability of the produced electron–hole pairs. Increasing the stability and separation of the created charges leads to a decrease in their recombination and an increase in the photocatalytic efficiency. Studies show that the photocatalytic activity of titania is also dependent on its color. Electronic and structural changes such as the combination of Ti-OH and Ti-H species, the formation of oxygen vacancies, the formation of irregular surface layers, and the reduction of Ti⁴⁺ to Ti³⁺ are among the effective factors in the formation of colored titania. Black titania has a largely narrowed band gap energy which leads to the enhancement of photocatalytic activity.

Due to their stability and adverse effects on human health and environment, the application of colorful TiO₂ in the degradation of persistent organic pollutants is worth studying. It should be noted that photocatalysis cannot find practical applications without immobilization of catalysts, due to the several issues encountered by using nanoparticles including agglomeration and difficulty of recovery. Moreover, immobilization could facilitate the application of photoelectrocatalysis with its superior efficiency than custom photocatalysis. Hence, the application of surface engineering methods in the deposition of colorful TiO₂ films for photocatalytic degradation of persistent organic pollutants is of high importance in future studies.