“Confinement” and “quantization|” are two closely related definition: If a particles is
“confined” then its energy is “quantized”, and vice versa. According to the dictionary, to
“confine” mean to “restrict within limits” to “enclose”, and even to “imprison”. A typical example, illustrating the relation between confinement and quantization, is the restriction of the motion of a particle by enclosing it within an infinite potential well of size LA. This simple constraint results in the well-known quantized energy spectrum
2
Here is the wave number and is the free electron mass. To have an idea about the characteristic energy scales involved and their dependence on the confinement length , the energy for electrons confined by an infinite potential well with size 1Å, 1nm, and
1 u m are given in Table 1-2.
kn m
LA
En
This is the quantum confinement that is observed as blue shift in absorption spectra with a decrease of particle size.[69] As the size is reduced to approach the exciton Bohr radius, there is a drastic change in the electronic structure and physical properties, such as a shift to higher energy, the development of discrete feature in the spectra, and
concentration of the oscillator strength into just a few transitions. The electron states in the limiting three-dimensional confinement lead to molecular orbitals (strong
confinement). The electronic states of a quantum dot are better described with a linear combination of atomic orbitals than bulk Bloch functions in momentum space.[70]
The quantum confinement not only causes the increase of the energy gap (blue shift of the absorption edge) and the splitting of the electronic states, but also changes the
densities of state and the exciton oscillator strength.[70] It was revealed that many of the differences between the electronic behaviors of the bulk and the quantum-confined low-dimensional semiconductors are due to their difference densities of state. [65, 71-73]
Figure 1-8 shows variation of states of electrons with increase the quantization dimension
in quantum structure.
1-4-3 TiO
2
1-4-3-1 Introduction of TiO
2Nanocrystalline titania has been thoroughly studied for applications including
photocatalysis,[74] solar energy harvesting,[75-76] biological coatings,[77] and sensors.
Titania has a high refractive index, 2.4-2.9 depending on the phase,[78] which may be important for photonic band gap (PBG) materials and other photonic applications.
Recently, photocatalysis and photovoltaic application are more attracted by scientists.
The process of photocatalysis is relatively simple. Light energy from ultraviolet
radiation (light) in the form of photons, below 390nm, excites the electrons on the surface of titanium atoms suspended in the contaminated water, moving them from the valence band to the conductance band. Photoexcitation always requires photons of below 390nm.
The result of this energy change is the formation of holes in the surface of the titanium atom, and free electrons, which are now available to form hydroxide (_OH), or other radicals, which can oxidize organic chemicals, or reduce metal species. There are currently two methods that can be used to perform TiO2 photocatalysis: slurry and fixed phase reactors. In the slurry phase, TiO2 powder is added to the waste stream and exposed to ultraviolet light. The light can come from sunlight or lamps. In the fixed phase, the TiO2 is annealed to the surface of a supporting plate such as microporous titania ceramics.
These can actually be used for liquid and gas streams. The ceramic titanium dioxide nanoparticles are deposited as a porous film on a glass tube or used as a particle aggregate in a packed bed reactor. Ultraviolet light is then used to activate these semiconducting metal oxide particles. Presently phototaclysts are being used in air pollution. Water pollution is an area of increasing interest for the use of photocatalytic degradation. The reason for the interest in UV activated oxidation of organic pollutants is the possibility of complete destruction of the pollutants in one step (Konstantinou,
Albanis et al., 2003). The end result being lower costs for the cleansing of the pollutants.
In the photovoltaic application, the dye-sensitized cells, light absorption occurs in a monolayer of dye at the interface between a transparent oxide electron conductor (usually TiO2) and a transparent electrolyte. A general consensus is that electrons move through TiO2 by diffusion rather than drift. In the standard electrolytes, electron diffusion in TiO2 is the limiting charge-transport rate as opposed to ion diffusion in the electrolyte.
Furthermore, there are a large number of trap sites in or at the surface of the TiO2, and the concentration of trapped electrons is higher than that of conduction-band electrons.
Recently, a well-dispersed TiO2 nanostructure material with low polydispersity and high purity is needed for photovoltaic application.
1-4-3-2 Crystal phase of TiO
2Titanium dioxide (titania) is found in many mineral forms. It is the fourth most
abundant metallic mineral in the earth’s crust. It is readily available, and inexpensive to get from the earth. There are four polymorphs of titanium dioxide (TiO2) found in nature: rutile (tetragonal), anatase (tetragonal), brookite (orthorhombic), and TiO2 (B) (monoclinic). Rutile is a common mineral found in various igneous, metamorphic, and, due to its relative resistance to weathering, sedimentary rocks. [79] Anatase is mostly found in sediments and hydrothermal veins, and is a common weathering product of perovskite or other Ti-rich minerals. [79-80] Brookite is rare, but is found most often in hydrothermal zones associated with contact metamorphism. [79] TiO2 (B) has been described recently in weathering rims on tektites [81] and perovskite, [82] and as lamellae in anatase from hydrothermal veins. [80] Rutile, anatase, and brookite have all been found coexisting.[82] The various structure polymorphs of TiO2 was shown in Figure 1-9.
The structure of two kinds of rutile crystal surfaces is illustrated in the Figure 1-10.
One half of the Ti cations on the perfect (110) surface are fivefold coordinated, with the remaining half being sixfold coordinated, as in the bulk. As for Ti, there are two kinds of oxygen having different coordination numbers on (110) surface. The first one is threefold coordinated oxygen as in the bulk and another is twofold coordinated oxygen which is higher in position. The twofold coordinated oxygen is protruding from the crystal surface as shown in the figure, therefore the oxygen is called bridging site oxygen. The bridging site oxygen exists on (110) surfaces but not on (001) surfaces. It is well known that the bridging site oxygen is more reactive than usual threefold coordinated oxygen. It is reasonable to consider that the dissociative water adsorption occurs more likely on the bridging oxygen site.[83] That means the growth rate under the face would be faster.
The needle-like crystallites of rutile and anatase produced with lower growth rates were elongated along the c axis. It is well known that surfaces of rutile and anatase single crystals have the different wettability depending on the crystal plane. The (0 0 l) planes of rutile and anatase, which are perpendicular to the c axis, are comparatively inert in the absence of more reactive bridging site oxygens. Other crystal planes having bridging site oxygens, which are parallel to the c axis, are relatively hydrophilic. Crystal growth perpendicular to the c axis was suppressed because co-existing species, such as urea, fluoride, and sulfate anions, were selectively adsorbed on more hydrophilic surfaces parallel to the c axis of the crystallites. The higher growth rate in the [0 0 1] direction caused a needle-shaped crystallite elongated along the c axis.