Charge Carriers in Commercial Photocatalysts: Fractal Kinetics and Effect of „Inert“ Additives
Detlef Bahnemann,1,2, * Fabian Sieland,1 Jenny Schneider1
1Institut für Technische Chemie, Leibniz Universität Hannover, Callinstr. 5, 30167 Hannover,
2Laboratory „Photoactive Nanocomposite Materials“, Saint-Petersburg State University,
Ulyanovskaya str. 1, Peterhof, Saint-Petersburg, 198504 Russia
Charge carrier recombination kinetics of commercial TiO2 powder samples were analyzed in the time domain ranging from 50 ns to 1 ms. The transient reflectance signals of the charge carriers observed by laser flash photolysis spectroscopy do not fit to simple second order kinetics as expected for the recombination of trapped electrons and holes. The deviation from second order reaction dynamics could rather be explained by the segregation of charge carriers and the fractal dimension of the semiconductor agglomerates. According to the fractal reaction kinetics, a time dependent rate coefficient kf has been employed instead of the second order rate constant k2, where the fractal parameter h describes the dimension of the system. This model could successfully be used to describe charge carrier signals in all observed time domains. Moreover, the model was compared with concepts proposing that the charge carrier signals decay following a power-law. The benefits of the fractal model proposed here include the possibility to describe and analyze influences of the morphology on the fractal parameter h and its applicability over a broad range of time domains and excitation energies. 
The effects of the particle size distribution on the charge carrier dynamics and the photocatalytic activity of mixed titanium dioxide (TiO2) powder samples were also investigated in this work. Instead of the synthesis of the small semiconductor particles, the binary particle size distributions of the powders were obtained by mixing commercially available TiO2 powders with different particle sizes. The effects of the particle size on the acetaldehyde degradation could be explained by the formation of agglomerates, which reduce the available surface area of smaller particles. The fast oxidation of acetaldehyde on the surface of TiO2 by direct hole transfer was further independent of the observed charge carrier lifetimes on the microsecond time scale. The photocatalytic NO degradation, on the other hand, increased for samples containing larger amounts of small particles. The corresponding photonic efficiencies correlated well with the charge carrier lifetimes determined by the timeresolved studies. Hence, it was concluded that a long charge carrier lifetime generally leads to higher fractional conversions of NO. The employed fractal fit function was proved to be beneficial for the kinetic analysis of charge carrier recombination in TiO2, in direct comparison with a second order fit function. 
Building materials employing TiO2 as photocatalyst usually contain several additives. The interplay of the additives and the photocatalytic NO degradation has been rarely investigated, although it is of utmost importance for the design of new highly active materials. Hence, in the present study the effects of such additives (BaSO4, CaCO3, and Na2CO3) on the photocatalytic activity and on the charge carrier dynamics have been evaluated. Overall, the obtained apparent quantum yields of the samples correlated well with the charge carrier concentration. Moreover, BaSO4 has proven its chemically inert character. However, the optical properties of the powder samples containing BaSO4 lead to relatively high photonic efficiencies even with low TiO2 content. TiO2-BaSO4 samples with only 25% TiO2 showed nearly the same quantum yield for the NO degradation as the pure photocatalyst. The reason for the high photocatalytic activity is the strong absorption of UV-light caused by the scattering inside the powder samples. The charge carrier kinetics of TiO2 after the addition of Na2CO3 and CaCO3 revealed two different chemical effects of the additives. Na2CO3 reduced the apparent quantum yield of the TiO2 samples due to the fast recombination of charge carriers (identified by a fractal kinetics fit). On the other hand, the presence of CaCO3 had a beneficial influence on the stabilization of trapped charge carriers in TiO2. 
1. F. Sieland, J. Schneider, D. W. Bahnemann, “Fractal Charge Carrier Kinetics in TiO2”, J. Phys. Chem. C 121 (2017) 24282-24291
2. F. Sieland, J. Schneider, D. W. Bahnemann, “Photocatalytic Activity and Charge Carrier Dynamics of TiO2 Powders with a Binary Particle Size Distribution”, Phys. Chem. Chem. Phys. 20 (2018) 8119-8132
3. F. Sieland, N. A.-T. Duong, J. Schneider, D. W. Bahnemann, “Influence of Inorganic Additives on the Photocatalytic Removal of Nitric Oxide and on the Charge Carrier Dynamics of TiO2 Powders”, J. Photochem. Photobiol. A: Chem. in press (2018)
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