Defect Chemistry of Titanium Dioxide. Application of Defect

J. Phys. Chem. C 2008, 112, 5275-5300

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FEATURE ARTICLE Defect Chemistry of Titanium Dioxide. Application of Defect Engineering in Processing of TiO2-Based Photocatalysts† M. K. Nowotny, L. R. Sheppard, T. Bak, and J. Nowotny* Centre for Materials Research in Energy ConVersion, School of Materials Science and Engineering, The UniVersity of New South Wales, Sydney, NSW 2052, Australia ReceiVed: September 11, 2007; In Final Form: December 6, 2007

The present work brings together the concepts of defect chemistry and photoelectrochemistry in order to consider TiO2-based photosensitive oxide semiconductors as photocatalysts for water purification. This paper reports the most recent progress in the defect chemistry of TiO2 and its solid solutions with aliovalent ions forming donors and acceptors. The relationship between the defect-related properties, such as electrical and photocatalytic properties, are outlined. It is shown that reactivity, photoreactivity, and the related charge transfer of photocatalysts based on TiO2 are determined by defect disorder and the related chemical potential of electrons. Therefore, defect chemistry may be used as a framework for the processing of well-defined TiO2-based photocatalysts. The photoreactivity of TiO2 with water and its solutes is considered in terms of the effect of both collective and local properties. The effect of noble metals attached to TiO2 as a separate phase, such as platinum, on photoelectrochemical properties and the related photocatalytic performance of TiO2 is discussed. The key functional properties, which are responsible for the efficient conversion of solar energy into chemical energy (required for water purification), are outlined. The effect of TiO2 doping with aliovalent ions on properties is considered in terms of the doping mechanisms and the related semiconducting properties. It is argued that comparison of the experimental data reported in the literature on the photocatalytic properties of TiO2 dictates the need to establish standards for photocatalysts, which are well-defined. This paper reports the processing conditions of well-defined TiO2. It is argued that knowledge of the mass transport kinetic data, such as chemical and self-diffusion coefficients, is needed for selecting the optimal processing conditions.

1. Introduction Titanium dioxide, TiO2, at present is used mainly as a pigment for toothpastes, paints, plastics, and textiles as well as sunscreen creams. This soon may change because it has been realized that TiO2 has a wide range of potential environmentally friendly applications, such as photocatalytic water purification,1-3 hydrogen generation by water splitting,3-6 and functional coatings for building materials.1 These applications are closely related to the ability of TiO2 to absorb solar energy and its lightinduced reactivity with water.1-10 The latter effect is related to the ability of TiO2 to form reactive agents, such as hydroxyl radicals, which may be used for water decontamination. Therefore, there is a general expectation that TiO2 may be used as a functional material for the conversion of solar energy into chemical energy for the photocatalytic oxidation of water contaminants, such as toxic organic compounds and microorganisms, and the production of an environmentally friendly fuelssolar hydrogen.4-6,11,12 While TiO2 is reactive with water, at the same time it exhibits an outstanding resistance to corrosion and photocorrosion in † This project was performed as part of the UNSW R&D program on solar-hydrogen and photocatalytic water purification. * Corresponding author. E-mail: [email protected]. Phone: +61 2 9385 6459. Fax: +61 2 9385 6467.

aqueous environments. Therefore, the properties of TiO2 are not affected by water. The research on TiO2 photocatalysis aims at the modification of the properties of TiO2 in order to process TiO2-based materials with enhanced functional properties that are required for the above applications. It is a common perception that the key functional property for both applications is electronic structure and, specifically, the band gap.3-6 It has been shown recently, however, that although a suitable value of the band gap is important for light absorption, the reactivity of TiO2 is closely related to several other bulk and surface properties.12 The most recent studies indicate that the properties of TiO2, including its reactivity and photoreactivity, are closely related to its defect disorder.11,12 It has been shown that defect chemistry may be used as a framework for the engineering of the functional properties of TiO2 that are important for its photoreactivity, including electronic structure, charge transport, and surface properties. The purpose of the present work is to bring together the concepts of defect chemistry and photoelectrochemistry to consider the reactivity and photoreactivity of TiO2-based oxide semiconductors and the related charge transfer. The present work considers defect disorder and defect-related properties of TiO2,

10.1021/jp077275m CCC: $40.75 © 2008 American Chemical Society Published on Web 03/18/2008

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M. K. Nowotny is a Senior Research Associate at the UNSW Centre for Materials Research in Energy Conversion. She graduated as a Ph.D. from the UNSW School of Materials Science and Engineering in 2006 with a Ph.D. thesis on semiconducting properties of TiO2. Her research interest includes photocatalysis on oxide semiconductors. She has received the Pfeil Award of the Institute of Materials, Minerals and Mining, London, 2007, for her work on surface properties of zirconia and the A. von Humboldt Fellowship, 2007, to support her work on TiO2 photocatalysis.

L. R. Sheppard is a Senior Research Associate at the UNSW Centre for Materials Research in Energy Conversion. He graduated as a Ph.D. from the UNSW School of Materials Science and Engineering in 2007. His Ph.D. thesis was on mass and charge transport of Nb-doped TiO2. His research interest includes photoelectrochemistry and segregation in oxide semiconductors. He is a recipient of the Tall Poppy Science Award of the Australian Institute of Policy and Science, 2006, and the German Academic Exchange Organisation (DAAD) to support his collaboration with the Hahn-Meitner-Institut.

including charge transport, electronic structure, and charge transfer at the TiO2/H2O interface. The effect of defect disorder on the photoreactivity of TiO2 with water and its organic solutes, and the related charge transfer, is considered in terms of both collective and local properties. The effect of noble metals (such as platinum), attached to TiO2 as a separate phase, on the reactivity and photoreactivity of TiO2 is discussed in terms of both photoelectrochemical cells (PECs) for water splitting and photocatalysts for water purification. The photocatalysts for water purification are considered in terms of a micro-PEC limited to a single TiO2 grain. It is argued that defect chemistry may be applied as a framework for the processing of both welldefined TiO2-based photocatalytic systems as standards for TiO2 photocatalysis and high-performance photocatalysts. The analysis of the defect chemistry of TiO2 will be preceded by a short postulation of the problem that impacts the progress of research on high-performance TiO2-based photocatalysts.

Nowotny et al.

T. Bak is a Senior Research Fellow at the UNSW Centre for Materials Research in Energy Conversion. His research interest includes solid state electrochemistry, defect chemistry and charge transport in oxide semiconductors. His publication record includes 160 refereed papers and three patents. He has received the Pfeil Award of the Institute of Materials, Minerals and Mining, London 2007, for the work on surface properties of zirconia.

J. Nowotny is the Director of the Centre for Materials Research in Energy Conversion, UNSW. He is leading a research program on solarhydrogen and photocatalysis. His research interest includes solid-state electrochemistry and photocatalysis. He has been a visiting Professor at U. of Bordeaux, U. of Grenoble, U. of Nancy, U. of Marseille, U. of Paris-Orsay, Tokyo Institute of Technology, and Max-Planck-Institute for Solid State Research.

2. Postulation of the Problem 2.1. Solar Energy Materials. The need for energy supply is increasing. At the same time, there is an increasingly urgent need to develop energy that is environmentally friendly, relatively cheap, and commonly accessible. Solar energy, which is avaialable in abundance, could and should be used more extensively. It appears that the main reason of the present limitation in the use of solar energy is the high cost of silicon, which is the main solar energy material. Therefore, there is an intensive search for a new generation of photosensitive materials that are needed for high-efficiency solar energy conversion devices. Awareness is growing that metal oxides, and specifically TiO2-based oxide semiconductors, are the most promising materials for harnessing solar energy for a wide range of applications.1-14 This has resulted in intensive research to develop new TiO2-based functional materials, which may be used for the conversion of solar energy into the chemical energy required for the following two applications, which are of importance for humanity: 1. Photocatalysts for water purification (removal of organic contaminants and microorganisms).

Feature Article 2. Photoelectrodes for water splitting into hydrogen and oxygen gases. The first technology aims to address the basic human right to have access to drinking water. Therefore, there is an urgent need to develop a cheap, widely available, and high-performance photocatalyst, which could be used for purification of contaminated water. The second technology aims to use solar energy for the production of environmentally friendly hydrogen fuel. However, despite the increasing amount of reports on research related to the above applications, these technologies have not been commercialized so far. The aim of the present paper is to consider some of the hurdles that should be addressed in the development of TiO2based high-performance photocatalysts. 2.2. Photocatalysis versus Solid-State Chemistry. The main stream of research reports on TiO2 are addressing its photocatalytic properties. The most commonly applied research strategies in the development of TiO2-based photocatalysts and photoelectrodes have been concentrated on the following approaches:7-10 1. Examinations of the effect of crystal structure (anatase vs rutile), microstructure, and surface area on photocatalytic properties, 2. Modifications of commercially available TiO2 specimens (Degussa, Kerr-McGee, Millennium Chemicals), including (a) deposition of small particles of noble metals as electron scavengers, and (b) doping with aliovalent ions. Deposition of Noble Metals. The research aims to enhance photocatalytic performance through optimized scatter of metal islets and the related surface areas. An increasingly clear picture that emerges from that research indicates that although the presence of noble metals results in an enhanced performance the enhancement factor and the related costs are not meeting the commercialization criteria.7 Doping. The aim of doping is to modify the chemical composition. However, the applied doping procedures are not well-defined. In many cases it is even not clear whether doping leads to the formation of a solid solution or a compositie, or both. Another stream of research concerns the solid-state properties of TiO2, addressing the related issues, such as nonstoichiometry and the related defect disorder, the effect of composition on electronic structure, and the determination of mass and charge transport kinetics.15-31 It is important to note that although diffusion has no impact on photocatalytic properties, knowledge of the diffusion data is essential for the processing of welldefined TiO2-based solids. The above two streams of research appear to be remote from each other in terms of concepts and the applied theories. However, the progress of research in TiO2 photocatalysis requires the bringing together these two research areas in order to address the challenges in the development of new TiO2-based solar energy materials, and specifically high-performance photocatalysts. It seems that the progress of research in this area requires the formation multidisciplinary research programs, able to create a “critical mass’’ needed to convert the commercially available TiO2 into a high-performance solar material for a wide range of environmentally friendly applications. The scientific issues, which are specifically urgent to be addressed, are outlined below. 1. Point Defects. The theoretical models frequently suffer from not recognizing that TiO2 involves a wide range of thermodynamically reversible point defects, which play a crucial role in reactivity and photoreactivity.12,15,23 In consequence, the properties of different TiO2 specimens, even if of high purity,

J. Phys. Chem. C, Vol. 112, No. 14, 2008 5277 may differ substantially because of different nonstiochiometries and the related defect disorder. 2. Well-Defined Systems. It becomes increasingly clear that the properties of TiO2 are closely related to defect disorder.15 However, the vast majority of data reported on photocatalytic oxide systems are not well-defined in terms of nonstoichiometry and the related defect disorder. Consequently, the data related to similar systems and properties cannot be compared. Therefore, there is an increasing need to (i) introduce some standards, which are based on well-defined TiO2 and (ii) report the data for TiO2 specimens that are well-defined in terms of the properties that are closely related to their photocatalytic performance. 3. Charge Transfer. The chemical reactivity and photoreactivity of metal oxides are determined by their ability to donate or accept electrons. At the same time, the studies on photocatalysts mainly address the properties that are not directly related to charge transfer, such as structure, phase relations, composition, and surface area. Therefore, there is a need to extend the characterization range into the properties that are related to the charge transfer, such as the chemical potential of electrons. 4. Doping. There is an increasingly urgent need to understand the effect of both the unintentional doping (impurities) and the intentional doping on properties: (a) Impurities. In many instances the effect of impurities on preformance is larger than that of other properties, such as crystal structure, microstructure, and surface area. (b) Procedure. It is essential to assess whether the applied doping procedure results in the formation of solid solutions or composities or both (these phenomena and underlying science are entirely diferent). (c) Oxygen ActiVity. The reported doping procedures suffer from not recognizing that oxygen should also be considered a dopant. It has been established that oxygen activity impacts the mechanisms of doping as well as the resulting properties. There has been an accumulation of reports on the effect of several processing procedures on the properties of TiO2, such as photocatalytic activity.8-10,13,14 However, most of the reported data are not well-defined. Therefore, it is difficult to compare the data even for the same systems, if possible at all. In consequence, the published reports provide an extensive crossreference of each others data; however, these data are incompatible. The reports of Khan et al.13 and Neumann et al.14 on the effect of carbon on properties of TiO2 may serve as an example of incompatible photocatalysts. On one hand, Khan et al.13 reported that the introduction of carbon results in the reduction of the band gap to 2.32 eV, leading in consequence to a substantial increase in the efficiency of water splitting to 8.35 % (from ∼1% for undoped TiO2). The XPS data of Khan have shown that carbon is incorporated into the TiO2 lattice according to a substitutional mechanism. On the other hand, Neumann et al.14 reported that carbon incorporation does not lead to a significant change of the band gap, which is 3.02 and 3.11 eV at 2.98 and 0.42 mol %, respectively, and no oxygen evolution. Most interestingly, Neumann et al.14 have compared their data to those for TiO2 of Degussa P25, rather than to the data of Khan et al.13 Both of these reports represent an outstanding piece of work. At the same time, they represent an outstanding example of the increasingly urgent need to develop well-defined doping procedures. 2.3. Aim. The main objective of the present work is to consider the effect of defect disorder of TiO2 and its solid solutions on properties. The present work also will outline the basis of defect engineering that can be used to convert TiO2 of

5278 J. Phys. Chem. C, Vol. 112, No. 14, 2008 unknown nonstoichiometry into a well-defined TiO2. The real chemical formula of TiO2, which is reflective of its wide range of compositions, will be derived. It will be shown that defect chemistry may be used as a framework for the processing of high-performance TiO2-based oxide systems with controlled properties that are desired to harness solar energy for a wide range of applications. This work does not aim at overviewing the literature reports on photocatalysis (several outstanding overview papers have been published recently1-4,7-10). Instead, an effort will be made to comment on the impact of defect-related properties on the photoreactivity of TiO2 and the related photocatalytic properties. It will be shown that the progress of research on using metal oxides as photocatalysts requires an increase in the present state of understanding on the effect of defect disorder on photocatalytic performance. The theoretical models described in this paper concern TiO2. However, the concept of defect engineering may be applied to other nonstoichiometric oxides as well. 3. Defect Disorder and Electronic Structure of TiO2 3.1. Defect Chemistry. Nonstoichiometric oxides, such as TiO2, may be oxidized or reduced within a single phase leading to the formation or removal of point defects in the crystal lattice, such as15,16 1. Oxygen Vacancies: oxygen ion is missing from its lattice site. 2. Metal Vacancies: metal ion is missing from its lattice site. 3. Metal Interstitials: metal ion is located in an interstitial site. 4. Electrons: the Ti3+ ions in their lattice sites. 5. Electron Holes: the O- ions in their lattice sites. Ionization of ionic defects leads to the formation of electronic defects (electrons and electron holes), which are responsible for the charge transport. It was shown that defect disorder is closely related to reactivity, photoreactivity, and the related charge transfer. Therefore, knowledge of defect disorder is essential to assess the reactivity and photoreactivity. TiO2 is not an exception. Accordingly, defect chemistry may be used as a framework for the processing of TiO2 with enhanced photoreactivity with water and its solutes. In equilibrium, the concentration of thermodynamically reversible defects is a function of temperature and oxygen activity and is independent of the applied experimental procedure. Because the defects in oxide crystals may be considered as a solid solution, the mass action law may be used to describe the related defect equilibria. Quantitative assessment of the effect of defect disorder on properties, such as semiconducting properties, requires knowledge of the related equilibrium constants. These constants may then be used for the derivation of defect disorder diagrams representing the effect of oxygen activity on the concentration of defects. The following sections report the most recent progress in defect chemistry of TiO2, including the contribution made by the authors in derivation of defect disorder diagrams and the determination of defect-related properties of TiO2. It will be shown that the photocatalytic properties of nonstoichiometric compounds, such as TiO2, are dependent on defect disorder in much greater extent than the commonly studied properties, such as crystal structure and surface area. The topical sections will be concluded with the remarks on the impact of specific properties on photocatalysis.

Nowotny et al.

Figure 1. Schematic representation of the defected lattice of TiO2. The symbols are explained in Table 1.

3.2. Undoped TiO2. TiO2 is a nonstoichiometric compound, which has been generally considered as an oxygen-deficient compound, TiO2-x.12-14 This picture has been supported by gravimetric studies.17-23 Therefore, there has been a widespread perception, until very recently, that the predominant defects in TiO2 are oxygen vacancies. Recent studies have shown, however, that strong oxidation of TiO2 (at elevated temperatures) leads to the formation of a metal-deficient oxide.24-31 In this case, TiO2 may be represented by the formula Ti1-xO2 or, more precisely Ti1-xO2-y, where x > y/2. The properties of the metaldeficient TiO2 are determined by titanium vacancies that are formed during a prolonged oxidation leading, in consequence, to p-type properties.28-31 Using Kroeger-Vink notation,32 the formation of defects at elevated temperatures may be described by the following defect equilibria24

1 OO a V••O + 2e′ + O2 2

(1)

2OO + TiTi a Ti••• i + 3e′ + O2

(2)

+ 4e′ + O2 2OO + TiTi a Ti•••• i

(3)

• O2 a 2OO + V′′′′ Ti + 4h

(4)

nil a e′ + h•

(5)

where e′ and h• denote electron and electron hole, respectively. A schematic representation of defected TiO2 is shown in Figure 1. (The classical notation used in Figure 1 is shown in Table 1 vs the Kroeger-Vink notation; the latter has been employed commonly to write defect equilibria.) Defect disorder must satisfy the charge neutrality condition, which requires that the crystal is electrically neutral. Consequently, the concentration of all charged defects must satisfy the following condition

2[V••O] + 3[Ti••• i ]+ • 4[Ti•••• i ] + [D ] + p ) n + [A′] + 4[V′′′′ Ti ] (6)

where n and p denote the concentrations of electrons and electron holes, respectively, and [D•] and [A′] denote the concentrations of singly ionized donor- and acceptor-type foreign ions, respectively. The condition expressed by eq 6 involves both thermodynamically reversible defects (oxygen vacancies, titanium interstitials, titanium vacancies, and electronic defects), of which the concentration depends on oxygen

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J. Phys. Chem. C, Vol. 112, No. 14, 2008 5279 TABLE 1: Notations of the TiO2 Lattice Species Used in Figure 1 along with the Kroeger-Vink Notation32 notation

meaning

Ti4+ Ti Ti3+ Ti

Ti4+ ion in the titanium lattice site Ti3+ ion in the titanium lattice site (quasi-free electron) M5+ cation in the titanium lattice site M3+ cation in the titanium lattice site titanium vacancy Ti3+ ion in the interstitial site Ti4+ ion in the interstitial site M+ cation in the interstitial site O2- ion in the oxygen lattice site oxygen vacancy O- ion in the oxygen lattice site (quasi-free electron hole) A- anion in the oxygen lattice site A3- anion in the oxygen lattice site

M5+ Ti M3+ Ti VTi Ti3+ i Ti4+ i M+ i O2O VO OO Figure 2. Defect diagram based on simplified charge neutrality conditions for pure TiO2. The related oxygen activity ranges and the expressions for the concentrations of defects are in Table 3.

AO A3O

Kroeger-Vink notation TiTi× e′ M•Ti M′Ti V ′′′′ Ti Ti••• i Ti•••• i M•i O× O V•• O h• A•O A′O

the impurities (dopants) may be considered as an effectiVe concentration of acceptors: • A ) 4[V′′′′ Ti ] + [A′] - [D ]

(7)

For pure TiO2, which is is free of both donor- and acceptortype foreign impurities, A may be directly related to the concentration of titanium vacancies:

A ) 4[V′′′′ Ti ]

(8)

According to eqs 1-4, the concentrations of intrinsic defects can be closely related to oxygen activity. Although equilibria eqs 1-3 may be established relatively fast, the formation and the transport of titanium vacancies, represented by eq 4, is extremely slow.28,31 Therefore, the titanium vacancies in eqs 6 and 7 may be assumed as acceptor-type dopants; that is, their concentration remains practically independent of oxygen activity. This is the reason that these defects are treated differently than other types of ionic defects. Therefore, the imposition of the required concentration of defects may be manipulated not only by oxygen activity during processing but also by the kinetic factor (equilibration time). The equilibrium constants for eqs 1-5 may be expressed as follows

K1 ) [V••O]n2 p(O2)(1/2) Figure 3. Defect disorder diagram for pure TiO2 at 1273 K showing the effect of oxygen activity in the concentration of ionic and electronic defects, where |x| is the absolute value of the deviation from stoichiometry.

activity, and also those defects that are thermodynamically irreversible (foreign ions). Although titanium vacancies are thermodynamically reversible (theoretically), these defects are relatively immobile and, therefore, may be considered as quenched in the experimental conditions commonly applied in the determination of defectrelated properties. Hence, in commonly applied experimental conditions titanium vacancies may be considered as acceptortype impurities.28,31 Consequently, both titanium vacancies and

(9)

3 K2 ) [Ti••• i ]n p(O2)

(10)

4 K3 ) [Ti•••• i ]n p(O2)

(11)

4 -1 K4 ) [V′′′′ Ti ] p p(O2)

(12)

Ki ) np

(13)

where square brackets represent the concentration of ionic defects (molar fractions). Transforming eqs 9-13, the concentration of both electronic and ionic defects may be expressed as functions of the p(O2):


Nowotny et al.

[V••O] ) K1n-2 p(O2)-(1/2)

(14)

-3 p(O2)-1 [Ti••• i ] ) K2n

(15)

[Tii••••] ) K3n-4 p(O2)-1

(16)

p ) Ki n-1

(17)

Knowledge of the equilibrium constants enables the determination of the concentrations of defects. These equilibrium constants have been determined by the authors recently33 by using three independently measured defect-related properties (electrical conductivity,25,28 thermoelectric power,26,28 and thermogravimetry17-23). These constants can be related to the standard-state thermodynamic quantities: entropy ∆S 0 and enthalpy ∆H 0

ln K )

∆S 0 ∆H 0 R RT

(18)

where both ∆S 0 and ∆H 0 are specific material properties. These thermodynamic quantities are listed in Table 2.33 The most commonly applied representation of defect disorder is in the form of defect diagrams, which are based on simplified charge neutrality conditions, valid over narrow regimes of nonstoichiometry. These regimes, the related charge neutralities, and the effect of oxygen activity on the concentrations of specific defects for undoped TiO2 are outlined in Table 3 and represented graphically in Figure 2. Although these diagrams may be used for the verification of defect disorder models,15 they do not inform of defect concentrations. Using the combination of eqs 9-13 and the condition of eq 6, we may describe the concentration of electronic charge carriers by a relationship involving p(O2), equilibrium constants, and the effective concentration of acceptors:33

n5 + An4 - Ki n3 - 2K1 p(O2)-(1/2) n2 3K2 p(O2)-1n - 4K3 p(O2)-1 ) 0 (19) As seen from eq 19, the effect of p(O2) on the concentration of electronic charge carriers depends on a combination of all defects. This equation may be used for the derivation of a defect disorder diagram in the form of the plot of the concentration of the reversible defects as a function of p(O2). Figure 3 shows the defect diagram in terms of the concentration of defects as a function of oxygen activity at 1273 K.33 As seen, the concentration of electronic charge carriers, and the related electrical properties of undoped TiO2, are closely related to oxygen activity, which may be used for the imposition of both n- and p-type properties as well as mixed conduction. In equilibrium, the data represented in the defect disorder diagram (Figure 3) are well-defined by the equilibrium conditions (temperature and oxygen activity). Of course, the changes in the concentrations of defects during cooling to room temperature depend on the applied cooling procedure. In the vicinity of the n-p transition regime, the effect of p(O2) on the concentration of electronic charge carriers may be expressed as follows4

n ) (2K1)(1/3) p(O2)-(1/6)

(21)

The ionic defects are responsible for the formation of donor and acceptor levels in the electronic structure of TiO2. As seen in Figure 4, both oxygen vacancies and titanium interstitials form donor levels34,35 and titanium vacancies form acceptors.36 The effect of these defects on the concentrations of electronic charge carriers depends on the their ionization degree. The concentration values may be assessed from defect disorder diagrams such as that in Figure 3. At this stage, the following points should be made: 1. TiO2 may exhibit both n-type and p-type properties. Its defect disorder and defect-related properties are closely related to oxygen activity in the TiO2 lattice. 2. Titanium vacancies have a strong effect on properties of titanium dioxide. These defects form surface active sites for water splitting.37 Recent studies have shown that nanosize TiO2 exhibits much larger concentrations of these defects than that in the bulk phase.38 3. Defect disorder diagrams may be used for the processing of TiO2 with controlled properties that are desired for specific performance. 3.3. Donor-Doped TiO2. The properties of TiO2 may be modified by the incorporation of foreign ions with a valency that differs from that of the host lattice ions. Such ions form donors or acceptors.15 This section will consider the effect of niobium (donor) on the defect disorder of TiO2. Niobium has been most commonly applied as a donor-type dopant for the modification of the semiconducting properties of TiO2.39-41 The studies of the authors have led to the establishment of the effect of oxygen activity on the mechanism of niobium incorporation into the TiO2 lattice.42-44 At low oxygen activity, niobium incorporation leads to the formation of electrons according to the following reaction:

1 Nb2O5 a 2Nb•Ti + 2e′ + 4OO + O2 2

(22)

The defect disorder in this regime is governed by the following charge compensation:

n ) [Nb•Ti]

(23)

As seen, the concentration of electrons in this regime is determined by the niobium content and is practically independent of p(O2). It was shown that TiO2 in this regime exhibits a quasi-metallic conduction.42,43 The mechanism of niobium incorporation into TiO2 at high oxygen activity is different. In this case, Nb incorporation leads to the formation of ionic defects (titanium vacancies):43

2Nb2O5 a 4Nb•Ti + V′′′′ Ti + 10OO

(24)

In that regime, the defect disorder is governed by the ionic charge compensation:

n ) n0 p(O2)-(1/4) p ) p0 p(O2)(1/4)

where n0 and p0 denote the concentration of electrons and holes in standard conditions. In strongly reduced conditions, when p(O2) < 10-5 Pa, the concentration of electrons is the following function of p(O2):9

(20)

• 4[V′′′′ Ti ] ) [NbTi]

(25)

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TABLE 2: Equilibrium Constants of Defect Reactions for TiO2 (K1, K2, K3, K4, and Ki are Defined in the Text) ∆H 0 [kJ/mol]

equilibrium constant K1 K2 K3 K4 Ki

∆S 0 [J/mol]

specimen

methods

493.1

106.5

undoped TiO2

334.9 879.2 1025.8 354.5 394.5 222.1

49.9 190.8 238.3 -202.1 -378.7 44.6

Nb-doped TiO2 undoped TiO2 undoped TiO2 undoped TiO2 Nb-doped TiO2 undoped TiO2

electrical conductivity thermoelectric power electrical conductivity thermogravimetry thermogravimetry electrical conductivity electrical conductivity electrical conductivity thermoelectric power thermogravimetry

authors Bak et al., 200633 Sheppard et al., 200643 Kofstad, 196717,18 Kofstad, 196717,18 Bak et al., 200633 Sheppard et al.., 200643 Bak et al., 200633

ln K ) (∆S 0/R) - (∆H 0/RT)

TABLE 3: Concentrations of Electronic and Ionic Defect in Undoped TiO2 within the Regimes Corresponding to Different Oxygen Activities and Governed by Simplified Charge Neutrality Conditionsa regime charge neutrality Defects n p [V′′′′ Ti ] [V•• O] [Ti••• i ] a

extremely reduced n)

3[Ti••• i ]

strongly reduced n)

2[V •• O]

(3K2)(1/4) p(O2)-(1/4) Ki(3K2)-(1/4) p(O2)(1/4)

(2K1)(1/3) p(O2)-(1/6) (Ki /(2K1)(1/3)) p(O2)(1/6)

(3K4K2/K4i ) p(O2)0 (K1/(3K2)(1/2)) p(O2)0 (K2/27)(1/4) p(O2)-(1/4)

((2K1)(4/3) K4/K4i ) p(O2)(1/3) (K1/4)(1/3) p(O2)-(1/6) (K2/2K1) p(O2)-(1/2)

reduced [V •• O]

oxidized [V •• O]

) 2[V′′′′ Ti ]

(K4i K1/(2K4))(1/6) p(O2)-(1/4) (2K4K2i /K1)(1/6) p(O2)(1/4) (K21K4/(4K4i ))(1/3) p(O2)0 (2K21K4/K4i )(1/3) p(O2)0 (2K22K4/K1)(1/2) p(O2)-(1/4)

strongly oxidized p ) 4[V′′′′ Ti ]

) 2[V′′′′ Ti ]

(K4i K1/(2K4))(1/6) p(O2)-(1/4) (2K4K2i /K1)(1/6) p(O2)(1/4) (K21K4/(4K4i ))(1/3) p(O2)0 (2K21K4/K4i )(1/3) p(O2)0 (2K22K4/K1)(1/2) p(O2)-(1/4)

(Ki/(4K4)) p(O2)-(1/5) (4K4)(1/5) p(O2)(1/5) (K4/256)(1/5) p(O2)(1/5) (K14K4(2/5)/K2i ) p(O2)(1/10) (K2(4K4)(3/5)/K3i ) p(O2)-(2/5)

Equilibrium constants: K1, K2, K4, and Ki are defined by eqs 9, 10, 12, and 13, respectively

p ) Ki

Figure 4. Band model of TiO2 showing the energy levels of intrinsic lattice defects.24-26,33

Therefore

( )

[Nb•Ti] n ) Ki 4K4

( ) [Cr′Ti] 2K1

(1/2)

p(O2)(1/4)

The above relationship has been verified experimentally by Carpentier et al.45 by using measurements of electrical conductivity. These data will be discussed later. 3.5. Chemical Formula Representing the Defected TiO2. The derived defect disorder models indicate that the TiO2 lattice involves a number of species, which may be grouped according to their location in the lattice, including43 • The titanium sublattice, A Ti • Interstitial sites, Bi • The oxygen sublattice, CO Accordingly, the lattice of TiO2 may be represented by the following general formula

A TiBiCO

(1/4)

p(O2)

-(1/4)

(26)

As seen, the concentration of electrons in this case changes with the slope of log n versus log p(O2) equal to -1/4. The effect of niobium on the electrical properties of TiO2 is closely related to the oxygen activity. The above relationships will be considered below in terms of the effect of Nb on electrical conductivity.43 3.4. Acceptor-Doped TiO2. Chromium has been commonly used as an acceptor-type dopant of TiO2.15 Its incorporation into the TiO2 lattice at low oxygen activity may be represented by the following reaction

Cr2O3 a 2Cr′Ti + 3OO + V••O

(27)

where the charge neutrality requires that

[Cr′Ti] ) 2[V••O]

(28)

Therefore, the concentration of electron holes for Cr-doped TiO2 is the following function of p(O2):

(29)

(30)

where A Ti, Bi, and CO are the integral parts (modules) of the TiO2 lattice. These modules may be expressed by the following specific formulas:

A Ti ) [(TiTi4+)a(TiTi3+)b(MTi5+)c(MTi3+)d(VTi)f] (31) Bi ) [(Tii3+)g(Tii4+)h(Mi+)j]

(32)

CO ) [(OO2-)k (VO)l (OO-)m(AO-)o(AO3-)r]

(33)

The notation used in describing the species in eqs 31-33 is outlined in Table 1 along with the Kroeger-Vink notation.32 According to this notation, the indexes a, b, c, d, f, g, h, j, k, l, m, o, and r correspond to the amount of the related lattice species that are expressed in molar ratio. Although the concentrations of the lattice species are interdependent, a wide range of their combinations may be imposed in a controlled manner by appropriate processing conditions at elevated temperatures. The resulting properties are then determined by (i) oxygen activity in the gas phase and (ii) the con-


Nowotny et al.

Figure 5. Effect of oxygen activity on the electrical conductivity for high-purity TiO2 single crystal.25

Figure 7. Effect of oxygen activity on the electrical conductivity for Nb-doped43 and Cr-doped TiO245 along with the data for high-purity TiO2 single crystal at 1273 K.25 Figure 6. Diagram showing the individual electrical conductivity components related to electrons (σn), electron holes (σp) and ions (σi) for high-purity TiO2 single crystal.25

tent of foreign ions forming donors and acceptors. Each combination, however, requires that the following conditions are satisfied: • The sum of concentrations of all species in the titanium sublattice must be equal to unity:

a+b+c+d+f)1

(34)

• The sum of concentration of all species in the oxygen sublattice must be equal to two:

k+l+m+o+r)2

(35)

• The lattice charge neutrality condition requires that the charges associated with all lattice species are fully compensated electrically: 4a + 3b + 5c + 3d + 3g + 4h + j ) 2k + m + o + 3r

(36)

The defects indexed by f and l are not involved in the condition of eq 36 because they are electrically neutral. The diagram in Figure 3 also shows the effective deviation from stoichiometry, x, which according to the present nomenclature may be defined as follows:

x)

2(g + h - f) + l 1+g+h-f

(37)

The concept of “defect engineering’’ for the processing of TiO2based systems with desired properties is based on eqs 9-17. The derived defect disorder diagrams and the determined defectrelated properties may be used to describe the effect of oxygen activity on properties of TiO2 in terms of the indices of the real chemical formula represented by eqs 30-33. 3.6. Concluding Remarks. The formula TiO2 is not reflective of the complex composition of this nonstoichiometric compound that involves a wide range of ionic and electronic point defects that impact its properties. The real chemical formula of TiO2 may be derived from defect disorder diagrams. The concept of defect engineering is based on the imposition of desired properties by controlled combination of the concentrations of lattice species, which are a function of the following variables: 1. Temperature 2. Oxygen activity 3. Concentration of aliovalent ions The reactivity and photoreactivity of TiO2-based oxide semiconductors and the related photocatalytic properties are closely related to their electroactivity, which is determined by defect disorder. Therefore, the derived defect disorder diagrams may be used for an assesment of the electroactivity and prediction of optimized processing conditions.

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Figure 8. Arrhenius plot of the mobility terms for electronic charge carriers for high-purity TiO2 single crystal (SC) and high-purity polycrystalline TiO2 (PC).46

The aliovalent ions incorporated into the TiO2 lattice (deliberately and incidentally) have a substantial impact on the semiconducting properties. Correct understanding of the effect of doping imposes the following requirements: 1. Basic characterization of undoped TiO2 specimens should include the determination of impurities. 2. The formation of TiO2-based solid solutions leads to a welldefined system when the doping procedure is well-defined in terms of (i) oxygen activity, (ii) time of processing, and (iii) cooling procedure. Therefore, it is essential to verify the effect of doping procedure on the distribution of dopants within the specimen, including the formation of intergranular precipitates. 4. Electrical Properties

σ ) σ0n p(O2)-(1/4) + σ0p p(O2)(1/4) + σi

4.1. Electrical Conductivity. Charge transport may be assessed by the measurements of electrical conductivity, which involves the components related to both electrons and electron holes25,26,29

σ ) enµn + epµp

(38)

where e is elementary charge, µ is mobility, and the subscripts n and p correspond to specific charge carriers. For amphoteric oxides, such as TiO2, the electrical conductivity in the n-p transition regime involves the components related to both charge carriers25,26

σ ) σ0n p(O2)-(1/4) + σ0p p(O2)(1/4)

(39)

where σ0n and σ0p are the electrical conductivity components related to electrons and holes in standard conditions. However, in strongly reduced conditions the electical conductivity exhibits the dependence, which is consistent with eq 21:25,29

σ ) σ0n p(O2)-(1/6)

been verified against well-defined experimental data of electrical conductivity for high-purity TiO2 single crystal (TiO2-SC), which are shown in Figure 525 and also for high-purity polycrystalline TiO2 (TiO2-PC).31 As seen, the electrical conductivity of reduced TiO2 is consistent with eq 40. The difference between the electrical conductivity for TiO2-SC and TiO2-PC allows us to assess the local semiconducting properties of the grain boundaries.46 It was shown that the electrical conductivity at elevated temperatures include a substantial contribution from the ionic conductivity component, σi, which cannot be ignored, especially in the n-p transition regime. Therefore

(40)

The defect disorder models represented by eqs 20 and 21 have

(41)

The individual electrical conductivity components outlined in eq 41, that were determined from the experimental data shown in Figure 5, are shown in Figure 6. The defect disorder models for Nb-TiO2 and Cr-TiO2, outlined by eqs 26 and 29, have also been verified by the measurements of the electrical conductivity42,45 (Figure 7). This figure indicates the following: 1. Niobium results in a substantial increase of the electrical conductivity. The effect depends on oxygen activity. 2. Chromium results in a small decrease of the electrical conductivity in the n-type regime. At the same time, Cr (5 atom %) leads to a shift of the n-p transition regime, at 1273 K, from p(O2) ) ∼8.3 × 103 Pa for undoped TiO2 to p(O2) ) ∼300 Pa for Cr-doped TiO2. 4.2. Mobility of Electronic Charge Carriers. The use of eq 38 in the verification of the defect disorder model requires knowledge of the mobility terms. These terms have been determined by using the concentration terms derived from defect disorder diagrams33 and well-defined experimental data of the electrical conductivity for high-purity TiO2 single crystal (TiO2SC):25


Nowotny et al.

Eg ) E0g - βT

(44)

where β is the temperature coefficient. According to Becker and Frederikse,48 the component E0g may be determined from the minimum value of electrical conductivity, σmin corresponding to the n-p transition measured as a function of p(O2)

σmin ) 2e(µnµp NnNp)(1/2) exp

() ( ) E0g β exp 2k 2kT

(45)

where Nn and Np are the density of states for electrons and electron holes, respectively, and k is the Boltzmann constant. The determination of the factor β is complicated (both β and Eg may be determined from the Jonker analysis (performed at several temperatures) that is based on the isothermal plot of S versus log σ.49 The plot of σmin as a function of 1/T for undoped TiO2 single crystal at elevated temperatures leads to the following band gap (Figure 10):25

Eg ) 3.16 ( 0.02 [eV]

Figure 9. Effect of oxygen activity on the electrical conductivity (upper part) and thermoelectric power (lower part) for high-purity TiO2 single crystal at 1073 K.25

µn(TiO2-SC) ) (6.7 ( 0.3)‚10-6 [m2V-1s-1]

(

µp(TiO2-SC) ) (1.5 ( 0.7)‚10-1 exp -

)

94 ( 4[kJ/mol] RT [m2V-1s-1] (42)

As seen, the transport of electrons and holes is consistent with the band model and the hopping model, respectively. The transport in polycrystalline TiO2 (TiO2-PC) is similar; however, the absolute values of the mobility terms are different:

(

4.4. Effect of Cooling. The processing procedures, aiming at the imposition of controlled oxygen activity, take place at elevated temperatures at which the gas/solid kinetics is relatively fast.25,29 However, the performance of TiO2 as a photelectrode and a photocatalyst takes place at room temperature. The effects during cooling may be considered in the following terms:15 1. The changes of the concentration of ionic defects, which are electrically charged, and the related formation term, ∆Hf. 2. The changes of the mobility term, ∆Hm. 3. The changes of the ionization degree of ionic defects. The effect of cooling on the electrical conductivity of oxide semiconductors is represented schematically in Figure 11. As seen, the activation energy of the electrical conductivity at higher temperatures (above the TC level) involves both ∆Hm and ∆Hf terms. Then15

(

)

2 ∆H - ∆Hm mσ f σ ) const exp RT

(47)

where mσ is the slope of the following dependence:

1 ∂ log σ ) mσ ∂ log p(O2)

(48)

Below a certain critical temperature, TC, the activation energy is determined by the ∆Hm term:

µn(TiO2-PC) ) (9.0 ( 1.3)‚10-6 [m2V-1s-1] µp(TiO2-PC) ) (3.9 ( 10.1)‚10-2 × exp -

(46)

)

84 ( 13[kJ/mol] RT [m2V-1s-1] (43)

The mobility data are shown in Figure 8. As seen, the charge transport mechanisms of electrons and electron holes for both TiO2-SC and TiO2-PC are the same. An important issue in the assessment of the effect of oxygen activity on the semiconducting properties of TiO2 is the determination of the n-p transition point. The related p(O2) corresponding either to the minimum of electrical conductivity or the zero value of thermoelectric power is shown in Figure 9.25,26 4.3. Band Gap. The band gap, Eg, is the following function of temperature47,48

σ ) const exp

( ) ∆Hm RT

(49)

The model represented by eq 47 is valid when 1. The electrical conductivity during cooling corresponds to equilibrium. 2. The ionization degree of ionic defects remains unchanged. The changes of the electrical conductivity during the dynamic cooling (100 K/h) for both undoped and Nb-doped TiO2 are shown in Figure 12.50 As seen, the enthalpy term ∆Hm for undoped (TC ) ∼1000 K) and Nb-doped TiO2 (TC ) ∼500 K) is 1.7 kJ/mol and 0.7 kJ/mol, respectively. It appears, however, that the temperature dependence during the dynamic cooling that is shown in Figure 12 (Eσ ) 49.2 kJ/ mol) differs from that in equilibrium (Eσ ) 125 kJ/mol).25

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Figure 11. Schematic representation of the log σ vs 1/T slope in equilibrium (above TC) and below equilibrium (below TC).15

Figure 10. Effect of oxygen activity on the electrical conductivity within the n-p transition regime for high-purity TiO2 single crystal at 1198 K (a) and the Arrhenius plot of the minimum of the electrical conductivity data showing the band gap (b).25

Therefore, the latter one is appropriate for the determination of the formation term, which for undoped TiO2 is ∆Hf ) 246.6 kJ/mol at mσ ) 4.25 For Nb-doped TiO2 at (T > ∼800 K), the temperature dependence of the conductivity assumes a negative value, which has been considered in terms of metallic-type conduction.42 As also seen, the character of the conductivity temperature dependence in the range of 500-800 K is complex.50 4.5. Concluding Remarks. Electrical conductivity is a very sensitive defect-related property. Although its physical meaning is complex, the measurements of electrical conductivity may be applied for in situ monitoring of its defect disorder during processing at elevated temperatures, during cooling, and also during performance. The data on the effect of oxygen activity on the electrical conductivity may be used for the verification of defect disorder models and the determination of the band gap. Simultaneous measurements of electrical conductivity and thermoelectric power allow the determination of both the concentration and mobility terms for electronic charge carriers.54 5. Collective and Local Factors in Reactivity and Photoreactivity of TiO2 The prerequisite of the reactions between TiO2 and water or its solutes is the adsorption of the reacting species on the TiO2 surface. The reactivity is determined by the ability of TiO2 to donate or accept electrons and the chemical affinity or ionization potential of the adsorbed species. There has been a general

perception that the reactivity of TiO2 (with water and its organic solutes) is closely related to collective properties of TiO2. So far, little is known about the effect of local surface properties, which are related to the presence of point defects, on reactivity. 5.1. Collective Factor. The collective factor is related to collective properties in a macroscale, which are representative of the entire bulk phase or its surface layer as a continuum. An important collective factor, controlling the reactivity of oxide semiconductors and their ability for charge transfer, is the chemical potential of electrons or holes, which is related to their activities: 0 µn,p ) µn,p + RT ln an,p

(50)

At low concentration, when electrons can be considered as an idal solid solution in the lattice, the activity term can be treated as equal to concentration, which may be determined from defect diagrams (see Figure 3). There is a general perception that the charge transfer within a TiO2-based photoelectrochemical cell (PEC) is determined by the electron energy levels of the electrodes and the electrochemical couples H+/H2 and O2/H2O, forming the electrochemical chain.51,52 In analogy, the collective properties that are expected to control the reactivity of TiO2 with organic molecules dissolved in water may be considered in terms of the chemical potential of the electronic charge carriers and the ionization potential (or electronic affinity) of the adsorbed organic molecules. 5.2. Local Factor. Although the collective factor is the driving force of the charge transfer within the PEC, it has been shown recently that the mechanism of photoreactivity of the TiO2 surface, and the related charge transfer, must be considered in terms of both the collective factor and a local factor.37 The local factor is related to local interactions at an atomic scale between the adsorbed molecules and surface-active sites formed by individual surface defects. Not all surface sites have


Nowotny et al.

2H2O + VTi f (2H2O - VTi)

(51)

2. The transfer of electron holes to the adsorbed water species resulting in the formation of an active complex * (2H2O - VTi) f (2H2O2 + - V′′′′ Ti )

(52)

where (2H2O2 + - V′′′′ Ti)* is a metastable surface active complex formed of a water molecule and the titanium vacancy and V′′′′ Ti represents the Ti vacancy with the associated O- ions. 3. Decomposition of the active complex into gaseous oxygen and hydrogen ions: * + (2H2O2 + - V′′′′ Ti ) f O2 + 4H + V′′′′ Ti

(53)

The transfer of electron hole, localized on the lattice O- ions, to the adsorbed water species is represented in Figure 13. 4. Light-induced ionization over the band gap, leading to the formation of electron-hole pairs, may be represented by the following reaction: × • O× O + TiTi + hν f OO + Ti′Ti

(54)

5. Reactivation of the surface sites: × 4O•O + V′′′′ Ti f 4OO + VTi

Figure 12. Arrhenius plot of the electrical conductivity for high-purity undoped TiO2 and Nb-doped TiO2 during cooling from 1273 to 300 K in the gas phase of controlled composition.50

the same ability for the charge transfer. Recent studies have shown that titanium vacancies at the outermost surface layer, and the associated electron holes, are the favorable active surface sites that allow effective charge transfer between the H2O molecule and the TiO2 surface. The proposed reactivity model, involving the reaction between the H2O molecule and the TiO2 surface site, leading to the formation of an active complex, may be considered in terms of the following steps:37 1. Adsorption of a water molecule on the specific surface active site (VTi), which exhibits strong electron affinity (the ability to donate electron holes):

(55)

A schematic representation of the energy diagram for the reaction of water splitting is shown in Figure 14. In analogy, oxygen vacancies and the associated trivalent titanium ions may be considered as the local active sites for the formation of chemisorbed oxygen species, which are important in photocatalytic water purification.2 The related reactivity model is represented in Figure 15. 5.3. Concluding Remarks. The development of highperformance photocatalysts for water splitting and water purification requires that both collective and local factors are taken into account. The latter factor is determined by defect disorder of the outermost surface layer. Consequently, knowledge of the surface versus bulk defect disorder is essential for the processing of TiO2 with enhanced photocatalytic performance. 6. Reactivity between TiO2 and Oxygen Changes to the oxygen activity in the gas phase results in the imposition of a new gas/solid equilibrium. At lower temperatures, when lattice transport is quenched, the changes in gas-phase composition lead to changes in chemisorption equilibria. Then oxygen activity of the oxide lattice is indepen-

Figure 13. Model representing the formation of the surface active complex, involving the water molecule and the titanium vacancy, resulting in multielectron charge transfer and water splitting.37

Feature Article


Figure 14. Energy path for photocatalytic water splitting in the presence and absence of surface active sites (dashed and solid lines, respectively).37

form of doubly ionized atomic species, which are formed according to eq 58. This claim, however, is in conflict with the energy-related data indicating that these species may only be stable within the crystal field, that is, after its incorporation into the oxide lattice.60

Figure 15. Model representing the surface active sites for oxygen chemisorption on undoped TiO2.37

dent of the gas-phase composition. However, the imposition of a new gas phase at elevated temperatures results in the propagation of the newly imposed oxygen activity into the bulk phase. The bulk equilibration kinetics is determined by the chemical diffusion coefficient, which is the rate constant of the diffusion of defects under a chemical potential gradient.53 6.1. Oxygen Chemisorption. Oxygen chemisorption on oxide semiconductors may be considered in terms of the following equilbria:54,55

O2 + e′ a O2-

(56)

O2- + e′ a 2O-

(57)

O- + e′ a O2-

(58)

Equation 56 represents the formation of singly ionized molecular species, which is considered as a weak type of oxygen chemisorption. In dark conditions, these species have a tendency to be transformed to singly ionized atomic species, represented by eq 57, which is a strong form of oxygen chemisorption. The imposition of light leads to the transition of these species back to the singly ionized molecular species, which are formed as a result of a leftward shift of equilibrium (eq 57).56-58 According to Henrich and Cox,59 oxygen may also be chemisorbed in the

The charge transfer related to the reactivity of TiO2 with oxygen was studied by work function (WF) measurements by Bourasseau et al.56-58 and Nowotny et al.61 As seen in Figure 16, oxidation of TiO2 at 298 K (initially equilibrated at p(O2) ) 10 Pa, T ) 1173 K) results in the following effects:61 1. Rapid WF increase (∼0.38 eV) that is related to the formation of chemisorbed species (O2- and O-). 2. Slow WF increase (∼0.22 eV) that is related to oxygen incorporation. The subsequent reduction results in WF decrease by only ∼0.05 eV, indicating that only a part of chemisorbed species, related to the weak form of chemisorption (O2-), are desorbed. 6.2. Lattice Diffusion. When TiO2 reacts with oxygen at elevated temperatures then oxidation and reduction results in shifts of defect equilibria, which are represented by eqs 1-5. The defects are formed or removed at the gas/solid interface. The newly imposed defects then diffuse into the bulk phase leading to the imposition of a new equilibrium state. The related mass transport may be considered in terms of two kinetic regimes:27,28 1. Kinetic Regime I. This regime corresponds to the transport of fast defects (in this case mainly trivalent titanium interstitials) that exhibit high diffusion rates. 2. Kinetic Regime II. The kinetics in this regime is determined by the diffusion rate of titanium vacancies, which is exceptionally slow (it takes 3-4 months at 1323 K to impose an equilibrium concentration of titanium vacancies in a TiO2 disk that is 1 mm thick). The effects of isothermal oxidation at 1323 K on electrical conductivity, thermoelectric power, and the related concentration


Nowotny et al.

Figure 16. Work function changes during oxidation and reduction for undoped TiO2 at 298 K after preliminary standardization at 1173 K.61

of defects during Kinetic Regime I (the left-hand side) and Kinetic Regime II (the right-hand side) are shown in Figure 17.24 As seen, these data are consistent with n-type properties in close vicinity to the n-p transition. These data also indicate that 1. The electrical properties in Kinetic Regime I are determined by the change in the concentration of trivalent titanium interstitials. 2. Oxidation in Kinetic Regime II is rate-controlled by the changes in the concentration of titanium vacancies. The chemical diffusion data for TiO2 single crystal and polycrystalline specimens are shown in Figure 18. As seen, the diffusion data are different for TiO2-PC and TiO2-SC, indicating that the effect of grain boundaries on the transport of defects is substantial.62 As also seen, the mass transport for Nb-doped BaTiO3, which is controlled by titanium vacancies as well,63 is even slower than that for TiO2. The diffusion data in Figure 18 may be used to predict the time required to achieve a uniform imposition of oxygen activity over the specimen. The electrical conductivity and thermopower data determined in Kinetic Regimes I and II have been used for the determination of the concentration of titanium vacancies, which are shown in Figure 19 by curves 1 and 2, respectively.33 6.3. Concluding Remarks. The reactivity between TiO2 and oxygen results in changes in chemisorption equilibria (at low and moderate temperatures) and defect equilibria (at elevated temperatures). The first process leads to changes in the concentration of chemisorbed species, while the bulk is quenched. The latter process leads to changes in the bulk oxygen content, the chemical potential of electrons, and the ability of TiO2 for charge transfer. 7. Effect of Doping 7.1. General Comments. Doping has been commonly applied in the modification of TiO2 properties, including photocatalytic properties. It appears, however, that the term “doping’’ has been used to consider a wide range of processes leading to different doping mechnisms and resulting in different changes of proper

Figure 17. Changes of the electrical conductivity and thermoelectric power for high-purity TiO2 single crystal at 1323 K during oxidation within short times (Kinetic Regime I), left, and during prolonged oxidation (Kinetic Regime II), right28 (a), along with the changes of centration for selected point defects (b).

ties. In consequence, it is difficult to compare the reported doping-related effects, if possible at all, because the reported data are frequently not well-defined and not compatible.

Feature Article

Figure 18. Chemical diffusion coefficient for both high-purity TiO2 single crystal and high-purity polycrystalline TiO227 in the Kinetic Regimes I and II (explained in the text) along with the data for Nbdoped BaTiO3.63

Figure 19. Arrhenius plot of the concentration of titanium vacancies in high-purity TiO2 single crystal in equilibrium (curve 1) and in Kinetic Regime I (curve 2).33

The reported effects of doping with aliovalent ions include both cations and anions: 1. Cations.43,64-70 In most cases doping aims at the incorporation into the TiO2 lattice of cations with a valency larger or lower than that of Ti4+ leading to the formation of donors, such as Nb and Ta, and acceptors, such as Cr and Fe, respectively.


Figure 20. Possible doping mechanisms of polycrystalline TiO2, involving (a) deposition of isolated islets on the surface, (b) spread of the dopants on the surface and within grain boundaries, (c) filling of grain boundaries leading to limited diffusion profile, (d) limited bulk transport leading to the formation of a concentration gradient, and (e) homogeneous distribution of the dopant within the specimen.

2. Anions:13,14,71-76 a) Fluorine. The doping of TiO2 with fluorine may be achieved through the addition of NaF to TiO2 water suspension.75,76 It was observed that F-TiO2 exhibits enhanced photocatalytic activity. b) Nitrogen. The reported TiO2 doping procedures with nitrogen include (i) sputtering,71 (ii) annealing (in N-containing gas phase),71 (iii) sol-gel technique,72 and (iv) implantation.66 The latter process leads to the destruction of the lattice and, therefore, subsequent annealing is required. c) Carbon. Doping with carbon may be achieved by exposing the TiO2 to the flame of natural gas13 and via alternative processing routes.14 7.2. Doping Mechanisms. A wide range of doping mechanisms have been reported. Some of them are represented schematically in Figure 20. As seen, these mechanisms lead to different distributions of dopants and result in entirely different effects on properties. Therefore, comparisons of the effect of doping on properties is possible only when the mechanisms of doping are identical. The first mechanism represents surface coverage with small islets (Figure 20a). The effect of this kind of doping on properties depends on the surface coverage, the size of particles, and the nature of the interface formed between these particles


Nowotny et al.

Figure 21. Electronic structure of TiO2 showing energy levels of different ions, according to Mizushima et al.64

and the TiO2 grain. This form of doping was reported in the studies of the effect of WO3 on the properties of the WO3 /TiO2 system.77,78 The second mechanism (Figure 20b) represents the dopant spread over the surface and along the grain boundaries, thus forming a thin oxide layer. This kind of doping may lead to the blockage of the entire surface of TiO2 with the dopant. The third mechanism (Figure 20c) involves the grain boundary penetration of the dopant by grain boundary diffusion (that is faster than bulk diffusion). This doping, which may occur at elevated temperatures (required for the transport of the dopant along the grain boundaries), leads to the following effects: 1. Limited bulk diffusion leading to the formation of a diffusion gradient of the dopant in the vicinity of grain boundaries. 2. Imposition of surface linear defects that are formed by intersections of grain boundaries with the external surface. Figure 20d represents the limited diffusion penetration of the dopants into the grains, resulting in the formation of a solid solution and a compositional gradient. Although this kind of doping leads to changes of semiconducting properties, these changes are not well-defined because of the unknown effect of dopant concentration gradients. However, when the system is brought into the gas/solid equilibrium, then the dopant is distributed homogeneously within the grains (Figure 20e). This system is well-defined and may be assessed in terms of defect chemistry. At this point, the following comments should be made: 1) Effect of Doping. The incorporation of aliovalent ions into the TiO2 lattice results in the formation of donor- and acceptortype levels. The energy levels of several transition-metal ions in TiO2 are shown in Figure 21.64 2) Kinetics. The distribution of dopants within the specimen is rate-controlled by diffusion in the TiO2 lattice. Therefore, knowledge of the related diffusion data is essential to predict the conditions of the doping procedure (time and temperature). Figure 22 shows the diffusion data for several cations in TiO2.79-88

Figure 22. Self-diffusion coefficient of aliovalent ions in TiO2.79-82,84

3) Effect of Oxygen ActiVity. The effect of aliovalent ions on properties is well-defined when oxygen activity within the specimen is well-defined. Consequently, a) The distribution of oxygen activity within the specimen requires knowledge of the chemical diffusion coefficient.53 As seen in Figure 23, the chemical diffusion coefficient for TiO2 is very sensitive to oxygen activity27 b) The chemical diffusion coeficient, which may be considered as the rate constant of the gas/solid equilibration, is related to the transport of all defects leading to a decrease of the chemical potential gradient.15 The kinetics of the gas/solid equilibration for the TiO2-O2 system are shown in Figure 17. 4. Effect on Band Gap. Doping results in changes of electronic structure, leading to the formation of donor and acceptor levels as is shown in Figure 21.64 In certain cases, doping leads to the formation of mid-gap bands resulting, in consequence, in the reduction of the effective band gap required for light-induced ionization. The following effects have been reported:

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Figure 24. Effect of molibdenum and chromium ions on band gap according to Wilke and Breuer.86

Figure 23. Effect of oxygen activity on the chemical diffusion coefficient for high-purity TiO2 single crystal.27

(a) Asahi et al.71 have reported that the band gap reduction may be achieved by lifting the valence band energy through mixing of 2p states of oxygen and s states of dopants. They observed that N-doping results in the reduction of the band gap from 3 to 2.4 eV. A similar effect was reported by Kudo et al.85 (b) Wilke and Breuer86 have shown that the incorporation of chromium and molybdenum results in the reduction of the band gap to 2 and 2.8 eV, respectively (Figure 24). (c) Khan et al.13 have reported that exposure of the TiO2 surface to a flame of natural gas results in the reduction of the band gap of TiO2 to ∼2.3 eV. This effect was considered in terms of carbon incorporation. (d) Liu et al.72 reported the effect of nitrogen on the reduction of the band gap of TiO2 in terms of the shift of optical absorption edge (Figure 25) and its impact on the inactivation of E.coli bacteria and decolorisation of acid orange. 5. Effect of Impurities. The properties of different TiO2 specimens may be compared only when the effect of impurities may be ignored (or is comparable). Even minor additions of aliovalent ions added unintentionally may have a substantial effect on properties.87 Therefore, the characterization of photocatalysts must be accompanied by the impurity analysis. 6. Segregation. The chemical composition of the surface differs from that of the bulk phase because of the effect of segregation.54,55 This is considered below. 7.3. Concluding Remarks. The data on the effect of doping on photocatalytic properties may be compared only when the

Figure 25. Effect of N-doping on the reflectance spectra of TiO2 according to Liu et al.72

applied doping procedures are well-defined and compatible. This requires the following issues to be addressed: 1. Selection of doping conditions (temperature and time) should be based on the knowledge of the diffusion data. 2. The procedure of doping is well-defined when leading to the formation of a solid solution, which is equilibrated in the gas phase of controlled oxygen activity. 3. When doping aims at the imposition of concentration gradients, the doping process leads to reproducible effects only when the applied doping procedure is reproducible. 4. Doping frequently leads to to the formation of precipitates of other phases. Their properties may differ entirely from a solid solution. Therefore, correct assessment of the effect of doping requires that their presence, if any, is identified. 8. Segregation 8.1. Effect on Surface and Near-Surface Properties. The properties of the bulk may differ substantially from those of the surface in terms of chemical composition and structure because of the effect of segregation.54,55 It is, therefore, essential that the effect of segregation on properties is understood properly. It is important to recognize that the performance of photocatalysts cannot be considered solely in terms of bulk properties. Moreover, photocatalytic properties of TiO2 are determined principally by the properties of the surface for the following reasons:


Nowotny et al.

Figure 27. Surface vs bulk composition of Nb-doped TiO2.132

Figure 26. Schematic representation of the segregation-induced enrichment of the surface layer.

1. The considerations of photocatalytic processes must take into account the effect of segregation on surface structure and associated surface phenomena.87 2. Solar energy is absorbed mainly by the surface layer (within the surface layer of ∼1 µm thickness) rather than the bulk phase. 3. The difference in the chemical composition between the surface layer and the bulk phase leads to the formation of a chemical potential barrier.54,55 The related electric field may reach substantial values (∼105V/cm). Therefore, segregation may be used as a technology for the imposition of a chemically induced electric field, which has an effect on charge separation.87,88 Although knowledge of segregation in metal oxides is still limited, it is apparent that the segregation-induced chemical and resultant electrical potential barrier leads to the formation of substantial electric fields in the surface layer.88 Figure 26 represents schematically the segregation-induced concentration gradient and the equations describing the relationships between chemical concentration (c) and the related electrochemical gradients, including electrical potential (Ψ), chemical potential (µ), electrochemical potential (η), and charge distribution (F(x)). The effect of segregation on bulk versus surface composition of Nb-doped TiO2 is shown in Figure 27. The recent studies of the authors have determined the effect of both temperature and oxygen activity on the segregation-induced concentration profile of niobium in TiO2.89 These effects may be used for engineering the near-surface electric fields required for charge separation. Segregation may also be used to modify the flat-band potential, FBP (the potential to be imposed over the electrode/electrolyte interface in order to make the bands flat).90,91 Specifically, the process of water photoelectrolysis may take place when the flatband potential is higher than the redox potential of the H+/H2 couple.90 Figure 28 shows the flat-band potential of several oxide materials versus the band gap compared to the vacuum level

Figure 28. Flat band potential of different oxide semiconductors vs band gap energy.92

and the normal hydrogen electrode (NHE).92 It has been a common perception that FBP is a material-related property. 8.2. Concluding Remarks. The defect disorder of the surface layer may differ substantially from that of the bulk because of the effect of segregation. The segregation-induced gradients may have either beneficial or detrimental effects on the performance of TiO2-based photocatalysts. Therefore, it is important that the segregation-induced effects are well-defined. Moreover, segregation may be used as a technology for the imposition of desired surface and near-surface properties including the FBP. 9. Light Absorption 9.1. Effect of Electronic Structure. The concept of heterogeneous photocatalysis is based on the ability of photocatalysts to absorb light energy, which is then converted into the chemical energy that is required to decompose toxic contaminants into harmless products. The light-induced electrons and electron holes may lead to enhanced reactivity, if they are effectively separated (to supress recombination). The effect of light on the electroactivity may be considered in terms of the splitting of the Fermi energy, EF, into two quasi-Fermi energy levels related to electrons, (EF)n, and holes, (EF)p.93 A schematic representation of the effect of light on the Fermi energy is in Figure 29. As seen, the effect of light on EF for electrons for n-type semiconductors, such as n-type TiO2, is very small. However, the effect on minority charge carriers (holes) is substantial. Therefore, the photon-induced ionization results

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Figure 29. Light-induced split of the Fermi energy into the quasiFermi energy related to electrons, (EF)n, and electron holes, (EF)p.93

for conversion. In practice, the photons that may be used for conversion must have an energy larger than 1.23 eV because of the energy losses related to polarization and recombination.87,90,91 Therefore, the energy of photons that are available for conversion must be larger than ∼1.8 eV. As seen in Figure 30, the amount of solar energy absorbed by TiO2, which is available for conversion, represented by the integral J4, is only a very small part of the entire solar energy spectrum (Eg ) 3 eV).25 Therefore, there have been efforts to reduce the band gap of TiO2 from 3 to 2 eV in order to increase the amount of absorbed energy, which is represented by the integrals J3 + J4. This may be achieved, for example, through the imposition of mid-gap bands, 9.2. Concluding Remarks. Although optimization of the band gap energy is important to maximize the amount of solar energy available for light absorption, it is essential to note that the efficient conversion of solar energy into the chemical energy for the photocatalytic process requires that we also address other functional properties that are considered below. 10. The TiO2-Pt System

Figure 30. Number of photons vs photon energy for the solar spectrum.90

in a substantial increase of the oxidation potential of electron holes. The light-induced electrons and holes are then available for a photocatalytic reaction. However, because their lifetime is limited to nanoseconds,3 the light-induced charge carriers may be used effectively only within this time limit. Consequently, the photoreactivity is more effective when the light-induced charge carriers are separated effectively, transported to the cathodic and anodic sites, and then used in appropriate reactions leading to their effective removal from these sites. The band gap is the key functional property of TiO2 as a photocatalyst because it has a critical impact on the energy conversion of photons. Only photons of energy equal to, or larger than, the band gap may be absorbed and used for conversion. The flux of absorbed photons of energy equal to or larger than Ei is

J)

∫E∞ N(E) dE

(59)

i

where J is the flux of photons in s-1 m-2, N(E) is the distribution of photons with respect to their energy, and E is the energy of photons. Figure 30 illustrates the solar energy spectrum,90 which depicts the segments related to photon fluxes corresponding to different energy ranges. The lowest theoretical limit for the band gap of a PEC’s photoanode is determined by the energy required to split the water molecule (E ) 1.23 eV). Accordingly, the photon flux represented by the integral of J1 is not available

10.1. Work Function. Platinum has been commonly applied in photoelectrochemical and photocatalytic studies either as an electrical lead or as a contact/electrode. Platinum has also been applied as a catalytically active agent, which removes the photoinduced electrons from TiO2 and provides them to the reacting molecules. Therefore, there has been an accumulation of data on the Pt-TiO2 system and the related charge transfer, which is closely related to the work function of the individual phases of TiO2 and Pt. The work function, WF, is defined as the energy required to remove an electron from the Fermi energy level of the surface to the vacuum level.55,88 The WF of semiconductors involves the following components

ΦTiO2 ) Φin + Φs + χ

(60)

where Φin is internal WF, Φs is the WF component related to band bending, and χ is the external WF. According to Fomenko,94 Meming,95 Kohl et al.,96 and Kung et al.,97 the WF values of TiO2 and platinum remain in the following ranges:

2.9 eV < ΦTiO2 < 3.2 eV 5.12 eV < ΦPt < 5.93 eV

(61)

These WF values are averaged from several reports and crystallographic planes (it will be shown below that even specific planes exhibit a WF heterogeneity). Although the difference between the lower and the upper WF values reported in the literature depends on the specific surface preparation conditions, there is a clear difference in the magnitude of the WF for these two phases. Consequently

ΦPt > ΦTiO2

(62)

The band model of the phases of TiO2 and Pt, both before and after contact, is shown in Figure 31. As seen in Figure 31a, the Fermi energy of platinum is lower than that of TiO2. The difference between the WF of the two phases is the driving force of the charge transfer. When these phases enter in a galvanic contact, then electrons are transferred from the phase of the higher EF (TiO2) to the phase of the lower EF (Pt), leading, in consequence, to an upward bending of the TiO2 bands as is


Nowotny et al.

Figure 32. Contact potential difference (eCPD ) ΦTiO2 - ΦAu) vs photon energy for undoped TiO2.98

Figure 31. Band model of both TiO2 and Pt before contact (a) and after galvanic contact (b) showing the formation of the contact potential difference.

shown in Figure 31b. The charge transfer results in the formation of an electrical barrier preventing further charge transfer. This electrical barrier is termed the contact potential difference (CPD), which is equal to the difference of WFs of both phases:

1 CPD ) (ΦPt - ΦTiO2) e

(63)

The TiO2/Pt couple, both before and after the contact (Figure 31), is representative of the TiO2-based photocatalyst formed of a TiO2 grain, which is decorated with small islet of platinum deposited on its surface. Therefore, the difference between the WF results in the driving force for the transfer of electrons from TiO2 to Pt. The light-induced WF data are especially useful in the determination of the effect of light on photoreactivity. The effect of photon energy on the CPD between TiO2 and gold (known as surface photovoltage spectroscopy, SPS) over the photon energy in the range 0.4 eV < hν < 4.5 eV (in air) is shown in Figure 32.98 As seen, the increase of photon energy above the absorption edge (3 eV) results in the following three regimes: 1. Conversion of the singly ionized atomic adsorbed oxygen species into molecular species. This process leads to a WF decrease. 2. Oxygen chemisorption in the form of singly ionized molecular species, leading to a WF increase. 3. Oxygen desorption, leading to a WF decrease. 10.2. Reactivity. There is a general perception that noble metals are not reactive. There has been, however, an accumulation of data indicating that noble metals react with TiO2 and oxygen.99-101 The following effects have been reported:

1. Platinum and gold react with oxygen in air and water leading to the formation of thin layers of PtO2 and Au2O, respectively.100-103 2. The studies of both Pt/TiO2 and Au/TiO2 systems indicate that both platinum and gold react with TiO2.99-101 3. The reactivity of the noble metals with TiO2 lead to deterioration of the photocatalytic activity.99,104 The observed reactivity of TiO2 with noble metals is consistent with the studies by the authors on the reactivity between platinum and yttria-stabilized ZrO2 (YSZ).103 It has also been shown that platinum reacts with YSZ at elevated temperatures in air, resulting in the formation of the oxide phases containg Pt, Zr, Y, and O.103 It has been documented that the reaction product spreads over the YSZ surface, which ultimately is covered with a thin layer. Because TiO2 is much more reactive than YSZ, one may expect that the deterioration of the photocatalytic activity observed over prolonged periods of time99,104 is due to the blockage of the TiO2 surface with the reaction products between TiO2 and noble metals. Schematic representation of the reactivity between platinum and TiO2 is shown in Figure 33. 10.3. Concluding Remarks. The charge transfer between two solids, including Pt and TiO2, is determined by their WFs. Although the WF of platinum is substantially larger that that of TiO2, the WF values of different specimens may vary widely because of chemisorption and the surface state. Platinum is reactive with both oxygen and TiO2, leading to the formation of a PtO2 layer and a PtxTiyOz compound. This reactivity is responsible for the deterioration of photocatalytic activity. 11. Photoelectrochemical Properties of the Pt-TiO2 System 11.1. Photoelectrochemical Cell. Fujishima and Honda5 have shown that water may be split into oxygen and hydrogen by using solar energy as the sole driving force of the process. The energy diagram of a PEC for water splitting, involving a TiO2 photoanode and Pt as a cathode, is shown in Figure 34. Its performance may be represented by the following reactions at the photoanode (TiO2) and cathode (Pt), respectively:

2H2O + hν f 4H+ + O2 + 4e′ 4H+ + 4e′ f 2H2

(64)

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J. Phys. Chem. C, Vol. 112, No. 14, 2008 5295 induced quasi-Fermi energy for holes results in the ionization of titanium vacancies, which are the surface active sites for water splitting.37 It has been shown that the processing of high-performance TiO2 requires us to address the following functional properties: 11,115

Figure 33. Schematic representation of the reactivity within the Pt/ TiO2 system in air, involving (a) oxidation of Pt spherical islets resulting in the formation of a PtO2 later, (b) initial stage of the reactivity of PtO2 with TiO2, (c) advanced stage of the reactivity of PtO2 with TiO2 leading to the formation of TixPtyOz, and (d) spread of the reactivity product TixPtyOz leading to surface coverage.

Figure 34. Energy diagram of the photoelectrochemical cell (PEC) formed of TiO2-based photoanode and Pt-based cathode, showing the charge transfer within the PEC during water splitting.

Following the discovery of Fujishima and Honda,5 intensive studies aimed at increasing the energy conversion efficiency (ECE) of solar energy into chemical energy.105-115 Most of these studies are based on the PEC formed of platinum and TiO2. The theoretical background of photoelectrochemical water splitting has been established by Gerischer,93,116 Bockris et al.,117-119 and Chandra.120 As seen in Figure 34, the light-

1. Band Gap. There is a need to reduce the band gap from ∼3 to ∼2 eV. The latter value is a compromise between the minimum energy required for water splitting (1.23 eV) and the energy losses. 2. Charge Separation. The energy losses due to charge recombination may be reduced by the imposition of a chemically induced electric field. 3. Charge Transport. High charge transport is required for a high-performance PEC. This may be achieved through the reduction of the electrical resistance. 4. Surface Reactions. Efficient reactivity between the adsorbed water molecules requires the presence of surface active sites.37 These sites may be considered in terms of either (i) point defects in the outermost surface layer or (ii) traces of another phase deposited on the TiO2 surface, such as Pt. 11.2. Photocatalysts. There is a close analogy between the TiO2-Pt-based PECs for water splitting and the photocatalytic system formed of TiO2 and platinum islets. The main difference between the two consists of cell dimensions. The electrodes in the PECs are separated; therefore, the reaction products, hydrogen and oxygen gases, can be collected independently. The photocatalysts, however, may be considered as a microsized PEC, where both electrodes are located within a single grain. These electrodes are connected (i) internally through the Pt/ TiO2 interface and (ii) externally through the aqueous electrolyte. The best analogue of the PEC shown in Figure 34 is a photocatalyst formed of a TiO2 grain and platinum islets deposited on its surface. Then the surfaces of the TiO2 grain and Pt act as photoanode and cathode, respectively. There has been an accumulation of reports on the effect of loading with noble metals, including Pt,99,121-126 Au,100,104,127 Pd,122,126 Ag,128,129 and Ir104 on the photocatalytic properties of TiO2. In most cases, however, the applied loading procedures results in the formation of systems that are not well-defined. Hiehata et al.130 reported the effect of small Pt islets deposited on the TiO2 surface on the local WF (Figure 35). As seen, the lateral WF changes are consistent with the WF values of platinum and TiO2 for these two phases.94-97 Although the basic concept of the charge transport within the PEC may also be applied for photocatalysts, the reaction mechanisms and the end products in both cases are different. At this point, it is essential to indicate the following: 1. The impressive amount of data reported so far indicate that Pt is not a promising candidate for the formation of cathodic sites of commercial photocatalysts because of its cost and corrosion.102 2. There is an increasingly urgent need to search for an alternative cathodic agent that exhibits performance superior to Pt and other noble metals. The effect of light on the reactivity at the anodic sites may be considered in terms of the reaction between the excess of light-induced holes and water leading to the formation of OH* radicals and hydrogen ions

H2O + h• f H+ + OH*

(65)

where OH* is the reactive hydroxyl radical, which plays an important role in both water purification and water splitting.


Nowotny et al.

Figure 36. Work function map for the surface of InP showing the areas of different work function values according to Ismail et al.132

Figure 35. Work function changes along the TiO2 surface covered with small platinum particles according to Hiehata et al.130

The most important reactive agent for the cathode is oxygen. Therefore, the reactivity of the cathode may be considered in terms of the reduction of oxygen, which has been commonly considered as the most important primary reaction step leading to the removal of electrons from the surface of photocatalysts and resulting in the formation of superoxide species.131 These species then react with protons forming hydroperoxide radical HO2/:9

O2- + H+ f HO2/

(66)

Alternatively, cathodic oxidation may be represented by the following reaction:

O2 + 2e′ + 2H+ f H2O2

(67)

The species HO2/ and H2O2 then react with organic molecules leading ultimately to their oxidation and the formation of stable molecules. For n-type semiconductors, such as TiO2, the light-induced photo-oxidation potential, which is related to electron holes, is much stronger than the reduction potential.93 Therefore, in order to avoid an accumulation of less-reactive electrons at the cathode and to prevent the energy losses due to polarization and recombination, electrons must be scavenged from that site effectively. This may be achieved either by the imposition of Pt, forming active cathodic sites, or by addition of oxidation agents, such as H2O2. An efficient photocatalytic process requires that both cathodic and anodic reactions take place with the same rate leading to efficient removal of excess charge carriers at both anodic and cathodic sites. This is the case even for a single-phase photocatalyst, such as TiO2, which exhibits uniform properties in the bulk phase. Its surface, however, is strongly inhomogenous in terms of the local WF and the ability of the local sites to accept or donate electrons. Ismail et al.132 have shown that WF is a local property of a specific surface site, which may change along the surface. Figure

Figure 37. Model of a micro-photoelectrochemical cell involving both cathodic and anodic sites: (a) TiO2-based cell involving Pt active sites (organic water solutes are represented by CH3OH), (b) general model representing the surface charge required for charge separation and the related charge transfer.

36 represents the image of the WF for InP showing that WF exhibits changes by ∼0.5 eV within a 1 mm distance. These data indicate that the charge transfers within a photocatalytic system should satisfy the charge neutrality condition, which requires that cathodic and anodic currents must be identical. In summary, the cathodic and anodic reactions may be considered in terms of the following alternative approaches: 1. In the case of a homogenous phase, such as TiO2, the cathodic and anodic sites are formed either by the areas of low and high WF, respectively, or donor and acceptor sites, respectively. In this case, however, the charge transfer is rate controlled by the cathodic reaction. 2. The catalytic process may be enhanced substantially by covering the TiO2 surface with small islets of another phase forming cathodic sites. These islets may act as scavengers of electrons when their WF is larger than that of TiO2.

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Figure 38. Electrochemical chain for the the micro-photoelectrochemical cell shown in Figure 37.

A general model of the light-induced excitation in a semiconducting photocatalyst, the related charge transfer, and the favorable band bending is shown in Figure 37b. As seen, the anodic sites exhibit a negative surface charge leading to upright band bending. Alternatively, the cathodic sites exhibit a positive surface charge leading to downward band bending. These sites are formed on the surface areas that exhibit high and low WF, respectively. The related electrochemical chain is shown in Figure 38. Although there is a close analogy between the PEC for water splitting and the microscale PEC, which is contained to a single TiO2 grain, these two cases are essentially different in terms of the kinetics of the anodic processes: 1. The performance of PEC for water splitting is ratecontrolled by oxygen removal from the anode. 2. The performance of photocatalysts is rate-controlled by the supply of oxygen to the anodic sites. 11.3. Concluding Remarks. The studies on the processing of a TiO2 photocatalyst loaded with platinum (and other noble metals) have been focused on controlling the dispersion of Pt on the TiO2 grains. Despite the fact that in most cases Pt results in an enhanced performance, which is consistent with basic theoretical models, the performance level is below the commercial requirements. Moreover, because of cost-related reasons there is a need to replace the Pt/TiO2 system with an alternative system. 12. Standards As outlined in Sections 2 and 7, the data reported on TiO2based photocatalysts are frequently not well-defined in terms of their processing conditions and the related properties. Therefore, the data related to similar effects, such as the effect of specific dopants on photocatalytic activity, are not compatible. Consequently, there is an increasingly urgent need to introduce some standards which are well defined. There have been efforts to develop standards under the auspices of the International Organization for Standardization;133 so far, however, these standards have not been implemented. It is essential that the standards are well-defined in terms of their solid-state chemistryrelated properties, which have an impact on photocatalytic properties, such as 1. Structure 2. Microstructure (surface area, grain size, density, porosity) 3. Processing conditions: (a) Temperature and time of annealing (b) Oxygen activity of the gas phase during the annealing (c) Conditions of cooling 4. Composition (a) Nonstoichiometry

(b) Impurity level (c) Dopant level and its distribution 5. Defect-related properties, such as electrical conductivity 6. Surface properties 7. Photocatalytic activity in selected reactions The development of standards, which should be well-defined solids, will require the bringing together the concepts of photocatalysis with the concepts of solid-state chemistry. An important issue in the assessment of photocatalytic performance is the knowledge of the electronic mechanism of photocatalytic reactions. Such information is essential for the selection of the processing conditions of photocatalysts with enhanced performance. For example, the enhancement of an acceptor-type photocatalytic reaction may require an increase of the chemical potential of electrons at the surface of the photocatalyst. 13. Summary and General Conclusions The photocatalytic properties of oxide semiconductors in general, and TiO2-based oxides in particular, are closely related to their defect disorder. It has been shown that enhancement of the photocatalytic performance for TiO2-based photocatalysts may be achieved through optimization of a number of functional properties, including11 1. Electronic structure. This property, specifically the band gap width, is essential for the amount of light absorption that is available for conversion. 2. Charge transport. The performance of photocatalysts requires efficient charge transport. This property is closely related to defect disorder and the related concentration of electronic charge carriers. 3. Surface properties. These include the collective factor, that is related to the chemical potential of electrons, and the local factor, which is related to the population of the surface active sites. Both factors are closely related to defect disorder. 4. Near-surface properties. The energy losses related to recombination of the light-induced charge carriers may be reduced by the imposition of an electric field in the near-surface layer leading to charge separation. Such a field may be imposed by controlling the following surface phenomena: (a) Chemisorption. Changes in the amount of chemisorbed species and the related surface and space charge (b) Segregation. Imposition of segregation-induced chemical potential gradient (c) Diffusion. Imposition of diffusion controlled chemical potential gradient There is no simple relationship between the above functional properties and the efficiency of the conversion of solar energy into the chemical energy related to the photocatalytic perfor-

5298 J. Phys. Chem. C, Vol. 112, No. 14, 2008 mance. The modification procedures frequently lead to conflicting effects. For example, the procedures aiming at an increase of the efficiency through the reduction of the band gap may result, at the same time, in increased energy losses related to charge transport. Owing to the complex relationship between the functional properties outlined above, a multivariant approach is required in the development of a photocatalyst with enhanced performance. Therefore, the enhancement of the photocatalyst performance may be achieved through optimization of the variables outlined above. It has been shown that TiO2 exibits a complex defect disorder, involving a number of intrinsic point defects, which are thermodynamically reversible, as well as extrinsic defects. Its properties may be enhanced through the imposition of an optimized combination of the individual lattice species. The present work outlines the basic concept of defect engineering in the processing of high-performance photocatalysts for water purification and photoelectrodes for water splitting. It has been shown that oxygen activity is the key property, which is closely related to defect disorder of TiO2 and the related properties. Therefore, controlled properties of TiO2 may be achieved through the imposition of controlled oxygen activity and the concentration of aliovalent ions. Depending on oxygen activity, these properties may vary substantially ranging between n-type quasi-metallic conductors and p-type semiconductors.12 It was shown that the effect of the incorporated aliovalent ions on properties are determined by the oxygen activity. Therefore, the key element in defect engineering is to control the oxygen activity in all stages of the processing. It is essential to recognize that so called doping process, applied in the modification of chemical composition of metal oxides, should be considered in terms of the following procedures: 1. Doping with oxygen. This leads to the imposition of controlled oxygen activity and the related concentration of thermodynamically reversible defects. The effect of oxygen doping on properties is substantial and must not be ignored. 2. Incorporation of aliovalent ions (cations and anions). The incorporation mechanism and the related effects of these ions on semiconducting properties are determined by oxygen activity. Therefore, the doped specimen is well defined only when the oxygen activity during the doping process is known. It is argued that the progress of research on TiO2 photocatalysis requires the determination of well-defined data for welldefined systems, which may be used as standards. Therefore, the introduction of such standards should be considered as the issue of paramount importance. Nomenclature Glossary a A A′ c CPD Dchem D• e e′ EC EF ∆EF

Activity Effective concentration of acceptors [atomic ratio] Singly ionized acceptor-type foreign ion Chemical concentration [atomic ratio] Contact potential difference [V] Chemical diffusion coefficient [m2 s-1] Singly ionized donor-type foreign ion Elementary charge [1.602 × 10-19C] Quasi-free electron Energy of the bottom of the conduction band [eV] Fermi energy [eV] Change in Fermi energy after irradiation [eV]

Nowotny et al. (EF)n (EF)p Eg EV E(H+/H2) E(O2/ H2O) Eσ F h h• ∆Hf ∆Hm j J k m mσ n N(E) Nn Np p p0 p(O2) PEC R S SPS T TiO2-PC TiO2-SC WF x z β η Θ µ σ ν F(x) Ψ χ Φ ΦS

Light-induced quasi-Fermi energy associated with electrons [eV] Light-induced quasi-Fermi energy associated with electron holes [eV] Band gap [eV] Energy of the top of the valence band [eV] Energy level of the redox couple H+/H2 [eV] Energy level of the redox couple O2/H2O [eV] Activation energy of electrical conductivity [kJ/mol] Electric field [V/m] Planck constant [6.626 × 10-34J‚s] Quasi-free electron hole Activation enthalpy of defects formation [kJ/mol] Activation enthalpy of defects motion [kJ/mol] Current density [A/m2] Light flux [lm] Boltzmann constant [1.3807‚10-23 J/K] Mass of electron [kg] Parameter related to defect disorder (reciprocal of the p(O2) exponent of electrical conductivity) Concentration of electrons [m-3] Distribution of photons with respect to energy [s-1 m-2 eV-1] Density of states in the conducting band [m-3] Density of states in the valence band [m-3] Concentration of electron holes [m-3] Concentration of electron holes before irradiation [m-3] Oxygen activity [Pa] Photoelectrochemical cell Universal gas constant [8.3144 J‚mol-1 K-1] Thermoelectric power [V/K] Surface photoelectron spectroscopy Absolute temperature [K] Polycrystalline titanium dioxide Single-crystal titanium dioxide Work function [eV] Distance [m] Valence Temperature coefficient of the band gap [eV/K] Dielectric constant Electrochemical potential [eV] Surface coverage [ratio] Chemical potential [eV] Electrical conductivity [Ω-1m-1] Frequency of light [Hz] Charge distribution [C/m] Electrical potential [V] External work function [eV] Work function [eV] Work function component related to surface charge [eV]

Acknowledgment. The present work was supported by the Australian Research Council, Mailmasters Pty Ltd., Brickworks Pty Ltd., Avtronics (Australia) Pty Ltd., and RJ Horton Solutions. Thanks are due to Professor Horst Kisch for his constructive criticism on the first draft of the present work. References and Notes (1) Fujishima, A.; Hashimoto, K.; Watanabe, T. TiO2 Photocatalysis. Fundamentals and Applications; BKC, Inc.: Tokyo, 1999; pp 14-176.

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Defect Chemistry of Titanium Dioxide. Application of Defect

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