Clean by Light Irradiation

Practical Applications of Supported TiO2

By Vincenzo Augugliaro, Vittorio Loddo, Giovanni Palmisano, Leonardo Palmisano, Mario Pagliaro

The Royal Society of Chemistry

Copyright © 2010 V. Augugliaro, V. Loddo, M. Pagliaro, G. Palmisano and L. Palmisano
All rights reserved.
ISBN: 978-1-84755-870-1

Contents

Chapter 1 Fundamentals, 1,
Chapter 2 Powders versus Thin Film Preparation, 41,
Chapter 3 Unique Properties of Supported TiO2, 98,
Chapter 4 Photocatalytic Glass, 116,
Chapter 5 TiO2-modified Cement and Ceramics, 144,
Chapter 6 TiO2 on Plastic, Textile, Metal and Paper, 168,
Chapter 7 Devices for Water and Air Purification, 199,
Chapter 8 Standardization, 235,
Subject Index, 262,

CHAPTER 1

Fundamentals

1.1 Working Principles and Thermodynamics of Heterogeneous Photocatalysis

1.1.1 Conductors, Insulators and Semiconductors

The valence bond theory is useful in explaining the structure and the geometry of the molecules but it does not provide direct information on bond energies and fails to explain the magnetic properties of certain substances. The molecular orbitals (MO) theory solves these drawbacks. It is based on the assumption that the electrons of a molecule can be represented by wave functions, ψ, called molecular orbitals, characterized by suitable quantic numbers that determine their form and energy. The combination of two atomic orbitals gives rise to two molecular orbitals, indicated as ψ+ and ψ-. If an electron occupies the ψ+ molecular orbital, a stable bond is formed between two nuclei, and so this is called bonding orbital. Conversely, when an electron occupies the ψ- orbital it is called anti-bonding orbital and the presence of an electron promotes the dissociation of the molecule. Molecular orbitals of a solid consisting of n equal atoms are obtained by means of a linear combination of atomic orbitals. The number of molecular orbitals formed is equal to that of the atomic ones. By increasing the number of atoms the difference between the energetic levels decreases and a continuous band of energy is formed for high values of n.

The width of the various bands and the separation among them depends on the internuclear equilibrium distance between adjacent atoms. If the energetic levels of isolated atoms are not so different, progressive enlargement of the bands may lead to their overlapping by decreasing the internuclear distance. The most external energetic band full of electrons is called the valence band (VB).

The energy band model for electrons can be applied to all crystalline solids and allows one to establish if a substance is a conductive or an insulating material. Indeed, the properties of a solid are determined by the difference in energy between the different bands and the distribution of the electrons contained within each band.

If the valence band is partially filled or it is full and overlapped with a band of higher energy, electrons can move, allowing conduction (conductors), as in the case of metals that have relatively few valence electrons that occupy the lowest levels of the most external band.

In contrast, the valence band is completely filled in ionic or covalent solids but it is separated by a high energy gap from the subsequent empty band. In this situation no electrons can move even if high electric fields are applied and the solid is an insulator. If the forbidden energy gap is not very high, some electrons could pass into the energetic empty band by means of thermal excitation and the material behaves as a weak conductor, i.e., as a semiconductor. The empty band, which allows the movement of the electrons, is called the conduction band (CB).

The energy difference between the lowest conduction band edge and the highest valence band edge is called the band gap (EG). A material is generally considered a semiconductor when EG ≤ 3 eV, whereas it is considered a wide band gap semiconductor when its band gap value ranges between 3 and 4 eV.

Figure 1.1 shows the position of the energy bands of different types of materials.

1.1.2 Properties of Semiconductor Materials

The de Broglie relation associates a wavelength with the electron as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.1)

where p is the momentum and h is the Planck constant. It shows that the wavelength is inversely proportional to the momentum of a particle and that the frequency is directly proportional to the particle’s kinetic energy:

f = E/h (1.2)

The wave number corresponds to the number of repeating units of a propagating wave per unit of space. It is defined as:

[bar.v] = 1/λ (1.3)

In the case of non-dispersive waves the wave number is proportional to the frequency, f:

[bar.v] = f/v (1.4)

where v is the propagation velocity of the wave. For electromagnetic waves propagating in vacuum the following relation is obtained:

[bar.v] = f/c (1.5)

where c is the velocity of light.

The wave vector is a vector related to a wave and its amplitude is equal to the wave number while its direction is that of the propagation of the wave:

[bar.k] = 2π/λ (1.6)

Therefore, the electron momentum can be expressed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.7)

where [??] is the reduced Plank constant also known as the Dirac’s constant ([??] = h/2π).

The electron energy is therefore:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.8)

where the coefficient m is the inertial mass of the wave-particle. As m varies with the wave vector, it is called effective mass, m*, defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.9)

A semiconductor is called a direct band gap semiconductor if the energy of the top of the valence band lies below the minimum energy of the conduction band without a change in momentum, whereas it is called an indirect band gap semiconductor if the minimum energy in the conduction band is shifted by a difference in momentum (Figure 1.2).

The probability f(E) that an energetic level of a solid is occupied by electrons can be determined by the Fermi–Dirac distribution function. It applies to fermions (particles with half-integer spin, including electrons, photons and neutrons, which must obey the Pauli exclusion principle) and states that a given allowed level of energy E is function of temperature and of the Fermi level, E0F according to the equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.10)

where kB is the Boltzmann constant. The level E0F represents the probability of 50% of finding an electron in it. For intrinsic semiconductors and for insulating materials, E0F falls inside the energetic gap and its value depends on the effective mass of electrons present at the end of the conduction band (m*e), on the effective mass of electrons at the beginning of the valence band (m*h), and on the amplitude of the band gap (EG) according to the following equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.11)

The value of E0F is equivalent to the electrochemical potential of the electron, i.e., it can be considered as the work necessary to transport an electron from an infinite distance to the semiconductor.

Figure 1.3 shows that the Fermi–Dirac distribution is a step function at T = 0 K. It has the value of 1 and 0 for energies below and above the Fermi level, respectively. As the temperature increases above T = 0 K, the distribution of electrons in a material changes. At T > 0 K the probability that energy levels above E0F are occupied, and similarly energy levels below E0F are empty, is not zero. Moreover, the probability that an energy level above E0F is occupied increases with temperature (distribution sigmoidal in shape) because some electrons begin to be thermally excited to energy levels above the chemical potential, µ(E0F). To understand the meaning of the chemical potential some considerations are presented here.

In determining the surface composition it is important to consider the thermodynamics of surfaces. The surface contribution to the free energy, G, of a solid is always positive. To create a new surface, it is necessary to perform a work on the system, which is employed to break bonds between the surface atoms. The work required to increase the surface area by dA, by means of a reversible path, at constant temperature and pressure, depends on the surface tension γ according to the following relation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.12)

For a single-component system, it is possible to express g as a function of the surface free energy per unit area, GS, as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.13)

where GS represents the work (per unit surface) done to form a new surface dA and the second term of the right-hand side is the work done in stretching a preexistent surface to increase it by dA. In this last case the number of surface atoms is fixed, whereas the state of strain of the surface changes. If the surface is unstrained, the second term of the right-hand side of Equation (1.13) is zero and g is equal to the surface free energy:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.14)

For a multicomponent system the Gibbs equation can be written as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.15)

were SS is the surface entropy, µi the chemical potential of species i, and Γi is the number of moles of component i per unit surface (nSi/A) in excess with respect to those that would be present if the system was homogeneous from bulk up to the surface.

The chemical potential can be expressed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.16)

where µ0i is the standard chemical potential of the pure component i.

By substituting Equation (1.16) in Equation (1.15), at constant temperature, the following relation is obtained:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.17)

From Equation (1.17) it is possible to determine the excess concentration of a component by taking the derivative of the surface tension with respect to its concentration in the bulk.

Equation (1.17) states that if the surface tension decreases by increasing the bulk concentration of a component, the component will have a greater surface concentration (Γi>0). Moreover, the component with the lowest surface tension will form a surface layer (if the temperature is high enough to allow its diffusion).

Owing to the difficulty in measuring the surface tension of the solids, the above equations allow us to determine the surface composition only qualitatively; to obtain more precise data it is necessary to apply statistic thermodynamics and experimental techniques.

Some types of impurities and imperfections may drastically affect the electric properties of a semiconductor. In fact the conductivity of a semiconductor can be significantly increased by adding foreign atoms in the lattice (doping) that make electrons available in the conduction band and holes available in the valence band. For example, silicon has a crystal structure similar to that of diamond (Figure 1.4) and each silicon atom forms four covalent bonds with four nearest atoms, corresponding to a chemical valence equal to four. The addition of atoms, for instance arsenic, phosphorous or antimony, having one valence electron more will lead to an excess of positive charge (Figure 1.5a), due to the transfer of an electron from the foreign atom to the conduction band (donor doping).

If the foreign atom, for instance boron, gallium, indium, has one valence electron less it can accept one electron from the valence band (acceptor doping) (Figure 1.5b). In the first case (Figure 1.5a) an energetic level close to the conduction band is introduced; consequently, electrons can pass more easily in it. In this case the solid is called an “n” type semiconductor and the Fermi level will be close to the conduction band (Figure 1.6b). In the second case an energetic level close to the valence band is formed, in which electrons can be promoted with the formation of holes. Here, the semiconductor is of “p” type and its Fermi level will be close to the valence band (Figure 1.6c).

The notion of energetic levels of electrons in solids can be extended to the case of an electrolytic solution containing a redox system. The occupied electronic levels correspond to the energetic states of the reduced species whereas the unoccupied ones correspond to the energetic states of the oxidized species. The Fermi level of the redox couple, EF,redox, corresponds to the electrochemical potential of electrons in the redox system and it is equivalent to the reduction potential, V0. To correlate the energetic levels of a semiconductor to those of a redox couple in an electrolyte, two different scales can be used. The first is expressed in eV, and the other in V (Figure 1.7a). The two scales differ because in solid-state physics zero is the level of an electron in a vacuum, whereas in electrochemistry the reference is the potential of the normal hydrogen electrode (NHE). The two scales can be correlated using the potential of NHE, which is equal to –4.5 eV when it is referred to that of the electron in vacuum.

If a semiconductor is placed in contact with a solution containing a redox couple, equilibrium is reached when the Fermi levels of both phases become equal. This occurs by means of an electron exchange from solid and electrolyte, which leads to the generation of a charge inside the semiconductor. This charge is distributed in a spatial charge region near the surface, in which the values of holes and electrons concentrations also differ considerably from those inside the semiconductor. Figure 1.7(a) shows schematically the energetic levels of a “n” type semiconductor and a redox electrolyte before contact. In particular, as the energy of the Fermi level is higher than that of the electrolyte, equilibrium is reached by electron transfer from the semiconductor to the solution. The electric field produced by this transfer is represented by the upward band bending (Figure 1.7b). Owing to the presence of the field, holes in excess generated in the spatial charge region move toward the semiconductor surface, whereas electrons in excess migrate from the surface to the bulk of the solid. Figure 1.8 shows the contact between a redox electrolyte and a “p” type semiconductor. In this case transfer of electrons occurs from the electrolyte to the semiconductor and the band bending is downward.

If the potential of the electrode changes due to an anodic or cathodic polarization, a shift of the Fermi level of the semiconductor with respect to that of the solution occurs with an opposite curvature of the bands (Figure 1.9).

For a particular value of the electrode potential, the charge excess disappears and the bands become flat from the bulk to the surface of the semiconductor. The corresponding potential is called the flat band potential, VFB, and the determination of this potential allows us to calculate the values of the energy of the conduction and the valence bands.

When a semiconductor is irradiated by radiation of suitable energy – equal to or higher than that of the band gap, EG – electrons can be promoted from the valence band to the conduction band. Figure 1.10 shows the scheme of electron–hole pair formation due to the absorption of a photon by the semiconductor.

The existence of an electric field in the spatial charge region allows the separation of the photogenerated pairs. In the case of “n” type semiconductors, electrons migrate toward the bulk whereas holes move to the surface (Figure 1.10a). In the case of “p” semiconductors, holes move toward the bulk whereas electrons move to the surface (Figure 1.10b).

Photoproduced holes and electrons, during their migration in opposite directions, can (i) recombine and dissipate their energy as either electromagnetic radiation (photon emission) or more simply as heat, or (ii) react with electron-acceptor or electron-donor species present at the semiconductor–electrolyte interface, thereby reducing or oxidizing them, respectively.

(Continues…)Excerpted from Clean by Light Irradiation by Vincenzo Augugliaro, Vittorio Loddo, Giovanni Palmisano, Leonardo Palmisano, Mario Pagliaro. Copyright © 2010 V. Augugliaro, V. Loddo, M. Pagliaro, G. Palmisano and L. Palmisano. Excerpted by permission of The Royal Society of Chemistry.
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