# Nanomaterials in Photocatalysis: An In-Depth Analysis of Their Role in Enhancing Indoor Air Quality
## 4 Photocatalytic Oxidation
### Thermodynamics and Kinetics  
As previously noted, photocatalysts absorb radiation with sufficient energy to excite electrons from the valence band to the conduction band, resulting in the generation of photogenerated electrons in the conduction band and positively charged holes in the valence band. The transfer of holes from the valence band to water molecules is enhanced when the edge of the valence band is more positive than the oxidation potential of water. Similarly, the transfer of electrons from the conduction band to pollutant molecules is facilitated when the edge of the conduction band is more negative than the reduction potential of the pollutant. Pollutants like acetaldehyde and formaldehyde have reduction potentials that are more positive than the conduction band edge of several semiconductors; thus, water molecules also participate in the oxidation process of pollutants due to their low oxidation potential. Additionally, if a pollutant has a more negative reduction potential than that of the reduction product, this leads to increased production of the reduction product [87].  
Kinetically, the degradation of pollutants through photocatalytic oxidation can be described within two steps. In the decay profiles, an initial drop can be observed due to the adsorption and desorption of molecules on the surface of the photocatalyst, followed by a second drop at longer times due to the photocatalytic reactions. The photocatalytic oxidation of a pollutant follows pseudo-first-order kinetics, which can be described by the equation [88]:  
\[\ln\left(\frac{C_{0}}{C_{t}}\right)=k_{d}t\]  
where \(C_{0}\) and \(C_{t}\) are the concentrations of the target pollutant at times \(t=0\) and \(t\) respectively, and \(k_{d}\) is the apparent photocatalytic degradation rate constant.  
Identifying the onset of photocatalysis is not straightforward; it requires consideration of two criteria. First, photocatalysis becomes the predominant process only after the system reaches an initial equilibrium between adsorption and desorption over a certain period. Second, the start of photocatalysis must also take into account the moment when the yield of the product stabilizes, indicating that the photocatalytic degradation of the pollutant is consistent. The photocatalytic process can therefore begin at different times for  
Figure 1: (**A**) photoluminescence spectra of P25 TiO\({}_{2}\) and USPNT [85] and (**B**) Photoluminescence spectra of P25 (a) and Au–TiO\({}_{2}\) containing various amounts of Au (b–d) [86].  
various pollutants. For instance, in a study using Mn/TiO\({}_{2}\) and Co/TiO\({}_{2}\), the initial time of photocatalysis was observed at approximately 120 min, while using Mn/Co/TiO\({}_{2}\), it was observed at 20 min [88].  
The Langmuir-Hinshelwood kinetic model describes heterogeneous photocatalytic reactions. The photocatalytic degradation rate (\(r_{0}\)) of the pollutant can be described by this model with the following equation [89]:  
\[r_{0}=\frac{kKC_{0}}{1+KC_{0}}\]  
where \(k\) is the reaction kinetic constant, and \(K\) is the equilibrium absorption constant.