• No se han encontrado resultados

Criterios de optimalidad

Fundamento matem´ atico de la optimizaci´ on

3.8. Criterios de optimalidad

2.3.1 Titanium Dioxide: TiO2

Since the discovery of TiO2’s capability for water-splitting and the photocatalytic

degradation of organic compounds, there has been an extensive research on a variety of semiconductors for environmental and energy applications.12 TiO

2 has been the

most important semiconductor material that has been studied over the years due to its band gap structure, high stability and low cost.52 In addition, TiO2 can be synthesized

in different structural forms including nanoparticles,53 thin films54 and nanorods/nanotubes.55,56 A number of production methods have been studied to synthesize these different structures such as sol-gel, chemical vapour deposition, hydrothermal synthesis, pulsed laser deposition, sputtering and anodisation. The growth mechanism and correspondingly physical, chemical and optical properties differ in each of the production methods.

The crystal structure of TiO2 consists of 3 forms: namely, anatese, rutile and brookite

(Figure 2.27).57 Rutile has a tetragonal structure with lattice constants of a = 0.4584

and c = 0.2953nm. Anatese also has a tetragonal structure with lattice constants of a = 0.3733 and c = 0.937nm. Brookite has a rhombohedral with a = 0.5436, b = 0.9166, c = 0.513558. Rutile is regarded as the most thermodynamically stable phase whereas anatase and brookite are metastable.59

34

Due to the differences between the three crystal phases, such as band structures and crystal growth orientations, the photocatalytic activities of each phase has been found to vary. In general, anatase is reported to have the highest photocatalytic performance and although a general consensus has not been held in this respect, some explanations have been suggested. Anatase has a larger band gap (~3.2eV) compared to rutile (~3.0eV) and brookite (~3.1eV).60 Although this decreases the amount of light absorbed, the valence band is at a higher energy level, that is, closer to oxidation potentials of adsorbed molecules resulting in more effective oxidation reactions.61 Morever, photoexcited electrons and holes have longer lifetimes within the anatase structure which is related to its indirect band structure. Recombination is more difficult in indirect band gap semiconductors as indirect transitions needed for electrons and holes to meet require more energy. Finally, it has been reported that, the charge carrier mobility of the photoexcited electrons and holes are higher in anatase compared to rutile and brookite and they manage to reach to the surface within their lifetime.61 Therefore, with delayed recombination and more suitable band structure compared to rutile and brookite, anatase has the highest photocatalytic performance among the three TiO2 crystal structures.62 The photoreactivity of

certain facets of TiO2 crystal differs from each other due to their surface

Figure 2.27 Crystal structures of TiO2: (a) anatese, (b) rutile and (c) brookite 57

anatese rutile brookite

35

chemistry.{001} facet of anatase TiO2 and (110) plane of rutile have been reported to

be most photoreactive among the other facets.63,64 Therefore, facet engineering has been studied to grow the crystals at such certain directions and planes during the synthesis of TiO2.65

Although TiO2 is the most commonly used photocatalyst due to its superior

properties such as high chemical stability, the material still exhibits low efficiency for water-splitting under solar energy. The main reason for this is that TiO2 has a

large band gap energy (~3.2eV); therefore, it can only use UV light. Since UV light is only 5% of the total solar energy, the efficiency of solar hydrogen production is limited.14 It is important that a photocatalyst also utilises visible light which compromises 50% of solar energy.11 One other disadvantage of TiO

2 is the short

lifetime of photoexcited carriers.13 The photogenerated electrons may recombine with holes at lower energy states. Efficient charge separation before recombination is essential. There has been extensive research on the modification of TiO2 to resolve

these problems.

2.3.2. Bismuth Ferrite: BiFeO3

Ferroelectric materials hold some interesting promise in photocatalytic and photovoltaic applications due to their materials properties associated with carrier separation and chemical stability under illumination in aqueous environments.15,16 Among ferroelectric photocatalysts such as BaTiO3 (3.2eV) and LiNbO3 (4.7eV)

with large band gaps, BiFeO3 (BFO) stands out as a visible light driven photoactive

material due to its narrow band gap (2.0-2.2eV).17 BiFeO3 has been investigated

extensively for its structural, optical and electrical properties to understand its complex structure induced by its varying band positions, indirect/direct band gap characteristics and type of conductivity.66,67,68,69

36

BiFeO3’s phase at room temperature is R3c with a perovskite-type unit cell (Figure

2.28).70 The valence band of BiFeO3 is composed of O 2p states mixed with Fe 3d

and Bi 6p states whereas Fe 3d state dominates the formation of conduction band hybridised with Bi 5p states in the region.71

The hybridisation between the orbital states and the valence state of Fe, which depends on oxygen vacancies and stoichiometry, can introduce a momentum or a shift to the energy level of conduction and valence band. Therefore, a wide range of band gap, from 2.0eV to 2.8eV, has been reported for BiFeO3 thin films where

indirect/direct band gap characteristics have been both observed with small phonon participation. Density functional theory (DFT) has been the most commonly studied computational method using local spin density approximation (LSDA) to calculate the density of states of local orbitals in BiFeO3 and correspondingly map the band

levels.71,72 The classical Tauc approach from experimental UV-vis spectroscopy supports computational values whereas Neaton et al. has calculated an indirect band gap of approximately 1.9eV using the LSDA+U approximation.73 Clark has estimated a value of 2.8eV with direct band gap characteristics.74 Ihlefeld et al. has also estimated a direct band gap of 2.77eV since the Tauc plot lacked characteristic shape when plotted for (αhv)1/2, therefore suggesting an indirect band gap.67

37

BiFeO3’s type of conductivity depends on the intrinsic defects of the crystal structure.

The bonding between the three elements and vacancies result in a variation in density of states, hence, band structures. Both p and n type conductivity have been reported for BiFeO3 depending on its element deficiencies. BiFeO3 grown in reducing

conditions with oxygen vacancies has n-type conductivity whereas Bi and Fe vacancies result in p-type conductivity. 75,76,74 Maso and West studied conductivity of

Bi deficient Ca doped BiFeO3 under different processing conditions and found that

the changing processing atmosphere from N2 to air or O2 increased the p-type

conductivity.77

However, BiFeO3 has inherent disadvantages for water splitting and photocatalysis

applications. One main drawback is the high leakage current which affects the dielectric and ferroelectric properties. This is due to varying valence state of Fe (from Fe3+ to Fe2+).78 One other drawback is its low conductivity as a result of defects and grain boundaries. This influences photovoltaic and photocatalytic performances where efficient charge transport is essential.79 Photoelectrocatalysis reports for BiFeO3 thin films or particles mostly include half reactions of water

splitting, that is, the photo-oxidation of water to evaluate oxygen gas. The studies for H2 evolution by BFO are however limited. The limitation for hydrogen production by

BiFeO3 is attributed to the band positions as the conduction band of BiFeO3 is below

the hydrogen reduction potential. Modifications on BiFeO3 such as metal deposition

or coupling with another semiconductor have also been reported to enhance the photocatalytic activity.80,81,82

38