3.2 Back-oxidation reactions

Introduction of one-step photocatalysts for overall water splitting combined the H2 evolution and O2 evolution sites on the same catalyst surface. This design of a photocatalytic system that realizes both charge trapping and reduction/oxidation reactions on the same surface not only accelerated the charge recombination but also allowed secondary reactions on these reduction/oxidation centers. When fast removal of the products, i.e., H2 and O2, is not provided and there are no barriers that prevent interaction of these products with highly active sites, the reaction of H2 and O2 on the photocatalyst surface to produce H2O (2H2 + O2 ! H2O) is highly probable. And back-oxidation of the produced H2 is considered to be one of the main reasons for observed low photocatalytic water splitting activity values.

As early as 1985, Sato and coworkers realized the importance of back-oxidation of H2 with O2 to produce H2O. They have realized that the metal-loaded photocatalysts, mainly Pt- or Pd-loaded TiO2, can oxidize H2 with O2 easily under the same photocatalytic water oxidation conditions. They have reported first-order reaction rate constants in the range of 0.23–0.51 h�<sup>1</sup> for Pt, 0.32–1.8 h�<sup>1</sup> for Pd, and 0.2–0.3 h�<sup>1</sup> for Rh, suggesting the least active metal for back-oxidation reaction to be Rh [10]. Later in 2000, Anpo and coworkers investigated back-oxidation reaction on Pt/TiO2 systems under dark conditions and observed increased backoxidation rate with increasing Pt loading (up to 0.1 wt.% [87]). While Pt is active for H2 evolution (Eq. (1)), it is also notoriously active for dark H2–O2 recombination reaction (Eq. (4)) even at room temperature [88]. In order to prevent H2–O2 recombination reaction, the Pt surface is modified with F ions for Pt/TiO2 catalyst, and the reaction rate decreased from 2 to 0.3 h�<sup>1</sup> upon F� modification [89]. The inhibition mechanism is suggested to be due to the occupation of the H2 surface adsorption sites on Pt by F atoms.

explains the significant photocatalytic H2 evolution activity on Rh/Cr2O3-loaded GaN:ZnO (130 � <sup>10</sup>�<sup>12</sup> molecules/s). Lower back-oxidation rate of Rh-loaded GaN: ZnO could be related to the low-oxygen reduction reaction (Eq. 5) activity of Rh

HR-TEM images of GaN:ZnO photodeposited with (A) Rh and (B) Rh/Cr2O3. Reprinted with permission from [55]. Copyright 2007 American Chemical Society. (C) Schematic representation of O2 and H2 evolution reactions with inhibited O2 permeation and O2 reduction reaction on core-shell-type co-catalysts.

Similar selective permeability concept is considered to be the case for Ni/NiO core-shell structures deposited on various photocatalysts such as SrTiO3 or NaTaO3 [34, 57]. In these systems, in addition to the back-oxidation reaction impeding effect of NiO layer on Ni [58], low-oxygen reduction activity of NiOx catalysts when compared to Pt can also be considered to be effective for improved water

Coatings of the whole photocatalyst instead of the co-catalyst by oxyhydroxides

of Ti, Nb, and Ta are reported on Rh-loaded SrTiO3:Sc photocatalyst. Surface nanolayer not only suppressed back-oxidation reactions but also prevented the access of sacrificial agents such as ethanol to the photocatalyst surface, resulting in nearly stoichiometric H2/O2 ratios [95]. Surface nanolayer coatings on the whole photocatalysts have proven to also prevent photodecomposition (N2 evolution)

Prevention of the secondary reactions such as H2 oxidation or O2 reduction reaction to H2O is found to be essential for improving the overall water splitting activity and the apparent quantum yield values (reaching apparent quantum yield value of 69% under irradiation at 365 nm [40]). In addition to the reduced backoxidation rates, complementary measures such as decreasing the charge recombination rates and enhancing the product transfer rates away from the surface (increasing the mass transfer rates) are necessary for increased photocatalytic water

Mass transfer limitations especially in the slurry photocatalytic systems can be

the most overlooked problem in the photocatalytic field. To complete the

of oxynitride photocatalysts while increasing the overall water splitting

O2 þ 4H<sup>þ</sup> þ 4e� ! 2H2O (5)

when compared to Pt [94]:

On the Limits of Photocatalytic Water Splitting DOI: http://dx.doi.org/10.5772/intechopen.89235

splitting activity.

Figure 3.

activity [64, 68].

splitting activity.

185

3.3 Mass transfer limitations

Another modification to the noble metal surfaces is reported by Lercher et al., in which CO is chemisorbed on the Rh co-catalyst for GaN:ZnO semiconductor. Chemisorbed molecular layer of CO suppressed the back-oxidation reaction by selective metal poisoning of the back-oxidation sites by CO. While H2 evolution rates of 28 μmol/h are achieved (75 mg photocatalyst, 300 W Xe lamp [90]), significant CO oxidation to CO2 is also observed.

The back-oxidation reaction-inhibiting effects of the nanolayer coating on noble metals are shown on Rh/Cr2O3-loaded GaN:ZnO photocatalysts. Rh/Cr2O3 coreshell structure [91] is formed by photodeposition of Rh and reduction of CrO4 <sup>2</sup>� by electrons coming from Rh upon radiation, resulting in few nanometer thickness of Cr2O3 layer (2–3 nm, see Figure 3). Hydrated Cr2O3 nanolayer is reported to selectively permeate protons for H2 evolution reaction [92], whereas it hinders O2 permeation from the layer inhibiting O2 reduction reaction (Eq. (5)) on Rh sites [93]. The same effect is also valid for Cr2O3-coated Pt catalyst (GaN:ZnO). Backoxidation rates on Pt-loaded GaN:ZnO photocatalyst decreased significantly from �<sup>105</sup> � <sup>10</sup>�<sup>12</sup> molecules/s to �<sup>8</sup> � <sup>10</sup>�<sup>12</sup> molecules/s, while photocatalytic H2 evolution rate increased from �<sup>5</sup> � <sup>10</sup>�<sup>12</sup> molecules/s to �<sup>30</sup> � <sup>10</sup>�<sup>12</sup> molecules/s upon Cr2O3 coating [93]. Apart from the oxygen-blocking role of the Cr2O3 nanolayer, much lower back-oxidation rate of Rh-loaded GaN:ZnO when compared to Pt-loaded GaN:ZnO (11 � <sup>10</sup>�<sup>12</sup> molecules/s vs. 105 � <sup>10</sup>�<sup>12</sup> molecules/s)

On the Limits of Photocatalytic Water Splitting DOI: http://dx.doi.org/10.5772/intechopen.89235

Figure 3.

These co-catalysts are known to enhance the charge migration from the semiconductor depending on the alignment of the potentials of the semiconductor and the co-catalyst. As these co-catalysts accelerate the desired H2 evolution and O2 evolution reactions, they can also increase the rates of undesired secondary reactions such

Introduction of one-step photocatalysts for overall water splitting combined the H2 evolution and O2 evolution sites on the same catalyst surface. This design of a photocatalytic system that realizes both charge trapping and reduction/oxidation reactions on the same surface not only accelerated the charge recombination but also allowed secondary reactions on these reduction/oxidation centers. When fast removal of the products, i.e., H2 and O2, is not provided and there are no barriers that prevent interaction of these products with highly active sites, the reaction of H2 and O2 on the photocatalyst surface to produce H2O (2H2 + O2 ! H2O) is highly probable. And back-oxidation of the produced H2 is considered to be one of the main reasons for observed low photocatalytic water splitting activity values.

As early as 1985, Sato and coworkers realized the importance of back-oxidation

Another modification to the noble metal surfaces is reported by Lercher et al., in

The back-oxidation reaction-inhibiting effects of the nanolayer coating on noble metals are shown on Rh/Cr2O3-loaded GaN:ZnO photocatalysts. Rh/Cr2O3 coreshell structure [91] is formed by photodeposition of Rh and reduction of CrO4

electrons coming from Rh upon radiation, resulting in few nanometer thickness of Cr2O3 layer (2–3 nm, see Figure 3). Hydrated Cr2O3 nanolayer is reported to selectively permeate protons for H2 evolution reaction [92], whereas it hinders O2 permeation from the layer inhibiting O2 reduction reaction (Eq. (5)) on Rh sites [93]. The same effect is also valid for Cr2O3-coated Pt catalyst (GaN:ZnO). Backoxidation rates on Pt-loaded GaN:ZnO photocatalyst decreased significantly from �<sup>105</sup> � <sup>10</sup>�<sup>12</sup> molecules/s to �<sup>8</sup> � <sup>10</sup>�<sup>12</sup> molecules/s, while photocatalytic H2 evolution rate increased from �<sup>5</sup> � <sup>10</sup>�<sup>12</sup> molecules/s to �<sup>30</sup> � <sup>10</sup>�<sup>12</sup> molecules/s upon Cr2O3 coating [93]. Apart from the oxygen-blocking role of the Cr2O3

nanolayer, much lower back-oxidation rate of Rh-loaded GaN:ZnO when compared to Pt-loaded GaN:ZnO (11 � <sup>10</sup>�<sup>12</sup> molecules/s vs. 105 � <sup>10</sup>�<sup>12</sup> molecules/s)

<sup>2</sup>� by

which CO is chemisorbed on the Rh co-catalyst for GaN:ZnO semiconductor. Chemisorbed molecular layer of CO suppressed the back-oxidation reaction by selective metal poisoning of the back-oxidation sites by CO. While H2 evolution rates of 28 μmol/h are achieved (75 mg photocatalyst, 300 W Xe lamp [90]),

photocatalysts, mainly Pt- or Pd-loaded TiO2, can oxidize H2 with O2 easily under the same photocatalytic water oxidation conditions. They have reported first-order reaction rate constants in the range of 0.23–0.51 h�<sup>1</sup> for Pt, 0.32–1.8 h�<sup>1</sup> for Pd, and 0.2–0.3 h�<sup>1</sup> for Rh, suggesting the least active metal for back-oxidation reaction to be Rh [10]. Later in 2000, Anpo and coworkers investigated back-oxidation reaction on Pt/TiO2 systems under dark conditions and observed increased backoxidation rate with increasing Pt loading (up to 0.1 wt.% [87]). While Pt is active for H2 evolution (Eq. (1)), it is also notoriously active for dark H2–O2 recombination reaction (Eq. (4)) even at room temperature [88]. In order to prevent H2–O2 recombination reaction, the Pt surface is modified with F ions for Pt/TiO2 catalyst, and the reaction rate decreased from 2 to 0.3 h�<sup>1</sup> upon F� modification [89]. The inhibition mechanism is suggested to be due to the occupation of the H2 surface

of H2 with O2 to produce H2O. They have realized that the metal-loaded

as hydrogen oxidation or oxygen reduction to water reactions.

3.2 Back-oxidation reactions

Water Chemistry

adsorption sites on Pt by F atoms.

184

significant CO oxidation to CO2 is also observed.

HR-TEM images of GaN:ZnO photodeposited with (A) Rh and (B) Rh/Cr2O3. Reprinted with permission from [55]. Copyright 2007 American Chemical Society. (C) Schematic representation of O2 and H2 evolution reactions with inhibited O2 permeation and O2 reduction reaction on core-shell-type co-catalysts.

explains the significant photocatalytic H2 evolution activity on Rh/Cr2O3-loaded GaN:ZnO (130 � <sup>10</sup>�<sup>12</sup> molecules/s). Lower back-oxidation rate of Rh-loaded GaN: ZnO could be related to the low-oxygen reduction reaction (Eq. 5) activity of Rh when compared to Pt [94]:

$$\text{O}\_2 + 4\text{H}^+ + 4\text{e}^- \to 2\text{H}\_2\text{O} \tag{5}$$

Similar selective permeability concept is considered to be the case for Ni/NiO core-shell structures deposited on various photocatalysts such as SrTiO3 or NaTaO3 [34, 57]. In these systems, in addition to the back-oxidation reaction impeding effect of NiO layer on Ni [58], low-oxygen reduction activity of NiOx catalysts when compared to Pt can also be considered to be effective for improved water splitting activity.

Coatings of the whole photocatalyst instead of the co-catalyst by oxyhydroxides of Ti, Nb, and Ta are reported on Rh-loaded SrTiO3:Sc photocatalyst. Surface nanolayer not only suppressed back-oxidation reactions but also prevented the access of sacrificial agents such as ethanol to the photocatalyst surface, resulting in nearly stoichiometric H2/O2 ratios [95]. Surface nanolayer coatings on the whole photocatalysts have proven to also prevent photodecomposition (N2 evolution) of oxynitride photocatalysts while increasing the overall water splitting activity [64, 68].

Prevention of the secondary reactions such as H2 oxidation or O2 reduction reaction to H2O is found to be essential for improving the overall water splitting activity and the apparent quantum yield values (reaching apparent quantum yield value of 69% under irradiation at 365 nm [40]). In addition to the reduced backoxidation rates, complementary measures such as decreasing the charge recombination rates and enhancing the product transfer rates away from the surface (increasing the mass transfer rates) are necessary for increased photocatalytic water splitting activity.

#### 3.3 Mass transfer limitations

Mass transfer limitations especially in the slurry photocatalytic systems can be the most overlooked problem in the photocatalytic field. To complete the

photocatalytic reaction cycle, adsorption of the reactants, reduction/oxidation of the reactants, desorption of the products, and transfer of the products from the photocatalyst surface to the gas phase need to be realized. When the rates of the mass transfer of the products from the surface are slower than the reduction/ oxidation rates, produced H2 and O2 would stay longer on the surface, resulting in promotion of back-oxidation reactions. Moreover, when the mass transfer rates are slower than the reaction kinetics, the apparent H2 and O2 evolution rates in the gas phase will be limited by the mass transfer rates.

weight and liquid volumes (keeping the catalyst concentration constant). H2 evolution rates on an hour basis (μmol H2/h) are found the same regardless of the liquid volume (or catalyst weight) above 62.5 ml (Figure 4b) as the H2 evolution rate per gram and hour basis decreased as liquid volume increased. Similar H2 evolution rates regardless of the catalyst weight indicate significant mass transfer limitations

Mass transfer limitations for different photocatalytic reaction systems are analyzed by different groups. For immobilized photocatalyst systems, the importance of internal mass transfer resistance is emphasized [97]. In another investigation, severe mass transfer limitations are observed in the product separator (liquid–gas interface) for a fluidized bed/separator system, in which modification of the liquid–

To prevent mass transfer limitations in the photocatalytic tests and to report actual kinetic rates; stirring rates, liquid levels, and mass transfer areas should be designed carefully. To design these parameters, approximate mass transfer rates should be known. Here, we present a sample calculation for H2 mass transfer rate in a slurry reactor containing 0.5 g TiO2 photocatalyst having a surface area of 40 m2

Mass transfer resistances in a gas–liquid–solid multiphase photocatalytic systems involve the internal mass transfer, mass transfer from the solid catalyst particles to liquid (Eq. 6), transfer from the liquid bulk to the liquid interface (Eq. 7), and transfer from the liquid–gas interface to the gas phase (Eq. 8). Photocatalysts such as perovskites and TiO2 are known to be nonporous (unless mesoporous versions are prepared on purpose [99, 100]) and have surface area values between 5 and

/g. For nonporous photocatalysts, the internal mass transfer limitations can be

rH2,<sup>S</sup> ¼ ksaSð Þ CS � CL (6)

rH2,<sup>L</sup> ¼ kLaLð Þ CL � CL,<sup>i</sup> (7) rH2,<sup>G</sup> ¼ kGaGð Þ CG,<sup>i</sup> � CG (8)

(9)

<sup>¼</sup> <sup>2</sup> <sup>þ</sup> <sup>0</sup>:52 Re <sup>0</sup>:<sup>52</sup>Sc<sup>1</sup>=<sup>3</sup> (10)

agitated glass reactor having 200 ml liquid volume and a tank diameter of 7 cm.

discarded (Eq. 9). Hence, the H2 mass transfer rate equation will have a form containing the mass transfer resistances from the solid–liquid and liquid–gas inter-

> rH<sup>2</sup> <sup>¼</sup> CH2,<sup>s</sup> � HCH2,<sup>g</sup> 1 ksaS <sup>þ</sup> <sup>1</sup>

number calculation to consider the effect of solid particle size [101]:

Sh <sup>¼</sup> ksdp DH<sup>2</sup>�H2<sup>O</sup>

The mass transfer limitations coming from the solid–liquid and liquid–gas interfaces may play important role depending on the photocatalytic reactor type. The most often used photocatalytic reactor systems such as slurry reactors have solid– liquid and liquid–gas phase interfaces that suspend its catalysts by agitation using an impeller or a magnetic stirrer. The convection mass transfer coefficient for solid– liquid interface of such a system could be estimated using Eq. 10 suggested by Armenante and Kirwan for agitated tanks using Kolmogorov's theory for Reynold's

where ks is the convection mass transfer coefficient from solid to liquid in (m/s), dp is the particle diameter in (m), DH<sup>2</sup>�H2<sup>O</sup> is the diffusion coefficient of H2 in liquid

/s), and Sc is the Schmidt number. A rough estimation for ks for such

kLaL <sup>þ</sup> <sup>H</sup> kGaG /g inside an

gas surface area enhanced the H2 evolution rates by 350% [98].

in the liquid–gas interface.

On the Limits of Photocatalytic Water Splitting DOI: http://dx.doi.org/10.5772/intechopen.89235

50 m<sup>2</sup>

water (m<sup>2</sup>

187

system can be found in Table 5.

faces as seen in Eq. 8:

Experimental evidence for mass transfer limitations in agitated systems is presented in a previous publication [96]. In a batch slurry reactor, where the catalyst particles are suspended via agitation, observed H2 evolution rates for UVirradiated Pt/TiO2 photocatalyst showed improvement with increasing stirring rates up to 900 rpm (Figure 4a). This improvement is a direct indication of mass transfer limitations on the solid–liquid and gas–liquid interfaces as the turbulence in the liquid and therefore boundary layers are affected by increasing stirring rates. In another experiment, the effect of liquid volume is investigated by varying catalyst

#### Figure 4.

(a) Effect of stirring rate on photocatalytic hydrogen evolution with methanol as sacrificial agent, with 0.5 wt% Pt/TiO2, 250 ml deionized water, 2 ml methanol, (■) 900 rpm and (●) 350 rpm. (b) Observed hydrogen evolution rates in the gas phase with changing liquid volume, CH3OH/H2O:1/125 (v/v) and Ccatalyst: 1 g/L for each case. Adapted from [96].

On the Limits of Photocatalytic Water Splitting DOI: http://dx.doi.org/10.5772/intechopen.89235

photocatalytic reaction cycle, adsorption of the reactants, reduction/oxidation of the reactants, desorption of the products, and transfer of the products from the photocatalyst surface to the gas phase need to be realized. When the rates of the mass transfer of the products from the surface are slower than the reduction/ oxidation rates, produced H2 and O2 would stay longer on the surface, resulting in promotion of back-oxidation reactions. Moreover, when the mass transfer rates are slower than the reaction kinetics, the apparent H2 and O2 evolution rates in the gas

Experimental evidence for mass transfer limitations in agitated systems is presented in a previous publication [96]. In a batch slurry reactor, where the catalyst particles are suspended via agitation, observed H2 evolution rates for UVirradiated Pt/TiO2 photocatalyst showed improvement with increasing stirring rates up to 900 rpm (Figure 4a). This improvement is a direct indication of mass transfer limitations on the solid–liquid and gas–liquid interfaces as the turbulence in the liquid and therefore boundary layers are affected by increasing stirring rates. In another experiment, the effect of liquid volume is investigated by varying catalyst

(a) Effect of stirring rate on photocatalytic hydrogen evolution with methanol as sacrificial agent, with 0.5 wt% Pt/TiO2, 250 ml deionized water, 2 ml methanol, (■) 900 rpm and (●) 350 rpm. (b) Observed hydrogen evolution rates in the gas phase with changing liquid volume, CH3OH/H2O:1/125 (v/v) and Ccatalyst: 1 g/L for

phase will be limited by the mass transfer rates.

Water Chemistry

Figure 4.

186

each case. Adapted from [96].

weight and liquid volumes (keeping the catalyst concentration constant). H2 evolution rates on an hour basis (μmol H2/h) are found the same regardless of the liquid volume (or catalyst weight) above 62.5 ml (Figure 4b) as the H2 evolution rate per gram and hour basis decreased as liquid volume increased. Similar H2 evolution rates regardless of the catalyst weight indicate significant mass transfer limitations in the liquid–gas interface.

Mass transfer limitations for different photocatalytic reaction systems are analyzed by different groups. For immobilized photocatalyst systems, the importance of internal mass transfer resistance is emphasized [97]. In another investigation, severe mass transfer limitations are observed in the product separator (liquid–gas interface) for a fluidized bed/separator system, in which modification of the liquid– gas surface area enhanced the H2 evolution rates by 350% [98].

To prevent mass transfer limitations in the photocatalytic tests and to report actual kinetic rates; stirring rates, liquid levels, and mass transfer areas should be designed carefully. To design these parameters, approximate mass transfer rates should be known. Here, we present a sample calculation for H2 mass transfer rate in a slurry reactor containing 0.5 g TiO2 photocatalyst having a surface area of 40 m2 /g inside an agitated glass reactor having 200 ml liquid volume and a tank diameter of 7 cm.

Mass transfer resistances in a gas–liquid–solid multiphase photocatalytic systems involve the internal mass transfer, mass transfer from the solid catalyst particles to liquid (Eq. 6), transfer from the liquid bulk to the liquid interface (Eq. 7), and transfer from the liquid–gas interface to the gas phase (Eq. 8). Photocatalysts such as perovskites and TiO2 are known to be nonporous (unless mesoporous versions are prepared on purpose [99, 100]) and have surface area values between 5 and 50 m<sup>2</sup> /g. For nonporous photocatalysts, the internal mass transfer limitations can be discarded (Eq. 9). Hence, the H2 mass transfer rate equation will have a form containing the mass transfer resistances from the solid–liquid and liquid–gas interfaces as seen in Eq. 8:

$$r\_{H2,S} = k\_s a\_S (C\_S - C\_L) \tag{6}$$

$$r\_{H2,L} = k\_L a\_L (\mathbf{C}\_L - \mathbf{C}\_{L,i}) \tag{7}$$

$$r\_{H2,G} = k\_G a\_G (\mathcal{C}\_{G,i} - \mathcal{C}\_G) \tag{8}$$

$$r\_{H2} = \frac{\mathbf{C}\_{H2,\mathfrak{s}} - H\mathbf{C}\_{H2,\mathbf{g}}}{\left(\frac{1}{k\_{\rm idS}} + \frac{1}{k\_{\rm LaL}} + \frac{H}{k\_{\rm GaG}}\right)}\tag{9}$$

The mass transfer limitations coming from the solid–liquid and liquid–gas interfaces may play important role depending on the photocatalytic reactor type. The most often used photocatalytic reactor systems such as slurry reactors have solid– liquid and liquid–gas phase interfaces that suspend its catalysts by agitation using an impeller or a magnetic stirrer. The convection mass transfer coefficient for solid– liquid interface of such a system could be estimated using Eq. 10 suggested by Armenante and Kirwan for agitated tanks using Kolmogorov's theory for Reynold's number calculation to consider the effect of solid particle size [101]:

$$\text{Sh} = \frac{k\_\text{s} d\_p}{D\_{H2-H2O}} = 2 + 0.52 \,\text{Re}^{0.52} \text{Sc}^{1/3} \tag{10}$$

where ks is the convection mass transfer coefficient from solid to liquid in (m/s), dp is the particle diameter in (m), DH<sup>2</sup>�H2<sup>O</sup> is the diffusion coefficient of H2 in liquid water (m<sup>2</sup> /s), and Sc is the Schmidt number. A rough estimation for ks for such system can be found in Table 5.

The creation of air/inert bubbles in the continuous phase (water) due to agitation could be considered as the transfer mechanism of produced H2 from the liquid phase to the gas phase. In such systems, comparing the mass transfer resistance from liquid to interface and interface to gas, it can be assumed that nearly all of the mass transfer resistance comes from the liquid side of the interface [102], leaving Eq. 9 as Eq. 11:

$$r\_{H2} = \frac{\mathbf{C}\_{H2, \mathbf{r}} - \mathbf{C}\_{H2, Li}}{\left(\frac{1}{k\_{\rm \alpha S}} + \frac{1}{k\_{\rm \alpha L}}\right)}\tag{11}$$

are calculated in the range of �200–8000 μmol/h (see Figure 5) for a surface H2 adsorption capacity range of 50–400 μmol/g (H2 chemisorption on 0.1% Pt/TiO2 is reported to be �400 μmol/g at room temperature [104]) and gas holdup ratio

found to be close to the calculated mass transfer rates here (see Table 1).

Parameter Unit Value Bubble size, db μm 700 Density of water, ρ<sup>L</sup> kg/m3 997 at 25°C Density of air, ρ<sup>G</sup> kg/m3 1.18 at 25°C Viscosity of water, <sup>μ</sup><sup>L</sup> Pa s <sup>890</sup> � <sup>10</sup>�<sup>6</sup> at 25°C

Convection mass transfer coefficient for liquid, kL m/s 2.5 � <sup>10</sup>�<sup>4</sup>

db ¼

should be improved for better photocatalytic efficiencies.

<sup>b</sup> ð Þ ρL�ρ<sup>G</sup> g μLDH<sup>2</sup>�H2<sup>O</sup>

Diffusion coefficient of H2 in water m<sup>2</sup>

kLaL m<sup>3</sup>

The H2 concentration on the solid surface and the gas–liquid contact area are not easy to estimate. However, for the limited gas–liquid area, the photocatalytic reaction rates above the calculated mass transfer rate will be suppressed due to the limiting mass transfer rates. Therefore, special care must be given for the UVirradiated photocatalytic systems, in which observed H2 and O2 evolution rates are

These studies show that for each type of photocatalytic system that contains limited gas–liquid contact area or immobilized photocatalyst, mass transfer limitations should not be underestimated, and not only the materials but also the systems

5.97 � <sup>10</sup><sup>5</sup>

Convection mass transfer coefficient calculation for liquid–gas transfer and parameters used in the calculation.

Calculated H2 mass transfer rate values (μmol H2/h) for gas holdup values of 0.001 and 0.005 and H2 adsorption capacity values in the range of 50–400 μmol/g. The liquid volume is taken as 200 ml and catalyst

DH<sup>2</sup>�H2<sup>O</sup> <sup>¼</sup> <sup>2</sup> <sup>þ</sup> <sup>0</sup>:31Ra<sup>1</sup>=<sup>3</sup> 28.1

/s 6.3 � <sup>10</sup>�<sup>9</sup> at 25°C

/s 2.2 � <sup>10</sup>�<sup>6</sup>

m<sup>2</sup> 0.008 (gas holdup, ϕ, assumed to be 0.005)

between 0.001 and 0.005.

On the Limits of Photocatalytic Water Splitting DOI: http://dx.doi.org/10.5772/intechopen.89235

Raleigh number Ra <sup>¼</sup> <sup>d</sup><sup>3</sup>

db VL where ϕ ¼ VG

6ϕ

Table 6.

Figure 5.

189

weight is taken as 0.5 g.

Sherwood number, Sh <sup>¼</sup> kLdb

Liquid–gas bubble contact area, aL <sup>¼</sup> <sup>6</sup>VG

=VL

The liquid side mass transfer coefficient for such a system could then be calculated using Calderbank and Moo-Young correlation for rising small bubbles of gas in continuous liquid phase (Eq. 12) [103]:

$$\text{Sh} = \frac{k\_L d\_b}{D\_{H2-H2O}} = 2 + 0.31 Ra^{1/3} \text{ where } Ra = \frac{d\_b^3 (\rho\_L - \rho\_G) \text{g}}{\mu\_L D\_{H2-H2O}} \tag{12}$$

The first term on Eq. 12 is the molecular diffusion term, whereas the second term is for the rise of the bubbles due to gravitational forces independent of the agitation. With estimations on the bubble size and gas holdup of such a system (given in Table 6), the mass transfer coefficient and kLaL term are calculated to be 2.5 � <sup>10</sup>�<sup>4</sup> m/s and 2.2 � <sup>10</sup>�<sup>6</sup> <sup>m</sup><sup>3</sup> /s, rendering liquid–gas mass transfer resistance way more important than solid–liquid resistance.

The overall mass transfer coefficient and the mass transfer rate from solid to the gas phase can be calculated with the estimated ksaS and kLaL values. As the concentration of H2 in the gas phase will be negligible (CG�0), the liquid phase interface can also be assumed to be equal to zero (CH2,Li�0) with negligible gas phase resistance. Therefore, from Eq. 11, the rate of H2 mass transfer can be calculated by assuming H2 concentration at the catalyst surface and the gas holdup ratio in the liquid. The rate of H2 mass transfer values for 200 ml of water and 0.5 g of catalyst


#### Table 5.

Convection mass transfer coefficient calculation for solid–liquid transfer and parameters used in the calculation.

### On the Limits of Photocatalytic Water Splitting DOI: http://dx.doi.org/10.5772/intechopen.89235

The creation of air/inert bubbles in the continuous phase (water) due to agitation could be considered as the transfer mechanism of produced H2 from the liquid phase to the gas phase. In such systems, comparing the mass transfer resistance from liquid to interface and interface to gas, it can be assumed that nearly all of the mass transfer resistance comes from the liquid side of the interface [102], leaving

> rH<sup>2</sup> <sup>¼</sup> CH2,<sup>s</sup> � CH2,Li 1 ksaS <sup>þ</sup> <sup>1</sup> kLaL

The liquid side mass transfer coefficient for such a system could then be calculated using Calderbank and Moo-Young correlation for rising small bubbles of gas in

<sup>¼</sup> <sup>2</sup> <sup>þ</sup> <sup>0</sup>:31Ra<sup>1</sup>=<sup>3</sup> where Ra <sup>¼</sup> <sup>d</sup><sup>3</sup>

The overall mass transfer coefficient and the mass transfer rate from solid to the gas phase can be calculated with the estimated ksaS and kLaL values. As the concentration of H2 in the gas phase will be negligible (CG�0), the liquid phase interface can also be assumed to be equal to zero (CH2,Li�0) with negligible gas phase resistance. Therefore, from Eq. 11, the rate of H2 mass transfer can be calculated by assuming H2 concentration at the catalyst surface and the gas holdup ratio in the liquid. The rate of H2 mass transfer values for 200 ml of water and 0.5 g of catalyst

Parameter Unit Value Particle size, dp μm 1 Density of water, ρ<sup>L</sup> kg/m<sup>3</sup> 997 at 25°C Viscosity of water, <sup>μ</sup><sup>L</sup> Pa s <sup>890</sup> � <sup>10</sup>�<sup>6</sup> at 25°C

mass of liquid <sup>m</sup><sup>2</sup>

Convection mass transfer coefficient for solid, ks m/s 0.015

Convection mass transfer coefficient calculation for solid–liquid transfer and parameters used in the

141

0.033

DH<sup>2</sup>�H2<sup>O</sup> <sup>¼</sup> <sup>2</sup> <sup>þ</sup> <sup>0</sup>:52 Re <sup>0</sup>:<sup>52</sup>Sc<sup>1</sup>=<sup>3</sup> 2.46

The first term on Eq. 12 is the molecular diffusion term, whereas the second term is for the rise of the bubbles due to gravitational forces independent of the agitation. With estimations on the bubble size and gas holdup of such a system (given in Table 6), the mass transfer coefficient and kLaL term are calculated to be

(11)

<sup>b</sup>ð Þ ρ<sup>L</sup> � ρ<sup>G</sup> g μLDH<sup>2</sup>�H2<sup>O</sup>

/s, rendering liquid–gas mass transfer resistance

/s 8.93 � <sup>10</sup>�<sup>7</sup>

/s<sup>3</sup> 25 for 5 W stirrer, 200 g solution

/s 6.30\*10�<sup>9</sup> at 25 °C

/s 0.31

(12)

Eq. 9 as Eq. 11:

Water Chemistry

continuous liquid phase (Eq. 12) [103]:

Sh <sup>¼</sup> kLdb DH<sup>2</sup>�H2<sup>O</sup>

2.5 � <sup>10</sup>�<sup>4</sup> m/s and 2.2 � <sup>10</sup>�<sup>6</sup> <sup>m</sup><sup>3</sup>

Schmidt number Sc ¼ <sup>ν</sup>

Energy density, <sup>ε</sup> <sup>¼</sup> Power

Reynold's number Re ¼ <sup>ε</sup>1=<sup>3</sup>dp

Sherwood number, Sh <sup>¼</sup> ksdp

Table 5.

188

calculation.

way more important than solid–liquid resistance.

Kinematic viscosity, ν m<sup>2</sup>

4=3 =ν

Diffusion coefficient of H2 in water m<sup>2</sup>

ksaS m<sup>3</sup>

=DH<sup>2</sup>�H2<sup>O</sup> are calculated in the range of �200–8000 μmol/h (see Figure 5) for a surface H2 adsorption capacity range of 50–400 μmol/g (H2 chemisorption on 0.1% Pt/TiO2 is reported to be �400 μmol/g at room temperature [104]) and gas holdup ratio between 0.001 and 0.005.

The H2 concentration on the solid surface and the gas–liquid contact area are not easy to estimate. However, for the limited gas–liquid area, the photocatalytic reaction rates above the calculated mass transfer rate will be suppressed due to the limiting mass transfer rates. Therefore, special care must be given for the UVirradiated photocatalytic systems, in which observed H2 and O2 evolution rates are found to be close to the calculated mass transfer rates here (see Table 1).

These studies show that for each type of photocatalytic system that contains limited gas–liquid contact area or immobilized photocatalyst, mass transfer limitations should not be underestimated, and not only the materials but also the systems should be improved for better photocatalytic efficiencies.


#### Table 6.

Convection mass transfer coefficient calculation for liquid–gas transfer and parameters used in the calculation.

#### Figure 5.

Calculated H2 mass transfer rate values (μmol H2/h) for gas holdup values of 0.001 and 0.005 and H2 adsorption capacity values in the range of 50–400 μmol/g. The liquid volume is taken as 200 ml and catalyst weight is taken as 0.5 g.
