Kinetic analysis of photoinduced reactions at the water semiconductor interface
Introduction
The photocatalysed conversion of organic species under aerobic conditions has been deeply investigated from basic, mechanistic and practical points of view due to the great potential of the process for pollutant abatement and waste treatment [1]. The basic mechanism was treated in a number of papers [2]. Following the light absorption primary excited species are formed which can either recombine or migrate to the surface of the semiconductor, where several redox reactions may take place. The organic substrate reacts with formed active species (oxidant or reducing) depending on its initial oxidation state and the nature of substituents [3], forming radicals and other species that are further oxidized or reduced. Several complex networks of reaction have been reported on the basis of detailed chemical analyses of the time evolution of substrate and formed intermediates or by-products [4], [5], [6], [7].
In photocatalytic processes the degradation rate depends, no matter what the mechanism of degradation is, upon the photon absorption rate. In practical systems the distribution of radiation intensities inside the reactor space is highly non-uniform. Its dependence on reactor geometry, and, for slurries, on the relative contributions of absorption and scattering was deeply investigated [8]. The solution of the integro-differential equation that results is not a simple task even for a simple geometry. Equations more manageable may be forecast for thin films. Given the spectral volumetric absorption, the absorption and scattering coefficients, and the distribution function for photon scattering, the incident radiation at any point inside the reactor space can be obtained [8]. The last is directly related to the local photon absorption rate. The photocatalytic degradation rate could be calculated, provided that a chemical kinetic model relating primary chemical events with absorbed photon rate is available.
Owing to the complex network of reactions, even for a chosen substrate it is difficult to develop a model for the dependence of the degradation rate on the experimental parameters for the whole treatment time. All the possible formed species must be identified, their kinetic constants for reaction either with photogenerated species or with other active species (radicals, other intermediates) have to be measured (by independent degradation experiments) or estimated. Since this is a heavy (and perhaps useless) task, kinetic modeling of the photocatalytic process is usually restricted to the analysis of the initial rate of degradation. This is the product of the initial slope and the initial substrate concentration in an experiment in which the variation of the substrate concentration is measured as a function of time. The extrapolation of the rate to time = 0 avoids the possible interference from by-products, both for the kinetic aspect (avoiding the growing complexity of the system as the degradation time increases), and for the possibility that formed species are physisorbed or chemisorbed [9], eventually reducing the possibility of formation of active species, or, in extreme cases, blocking or poisoning surface sites.
However, even under the reduced complexity deriving from the initial rate simplification, the interpretation of the rates obtained in photocatalytic experiments is still under debate. An attempt to model the initial steps of the photocatalytic process and to analytically solve the resulting kinetic system is presented. Attention was paid to obtain equations with physical meaning and reduced complexity. Several possible kinetic models have been explored.
Section snippets
The kinetic of photocatalyzed transformation
The common shape observed for the initial rate of degradation ro as a function of the substrate or catalyst concentration is an increasing function tending to a limiting value (zero order rate), as if the rate would be determined by the adsorption properties of the substrate on the catalyst surface. This was historically, but even now interpreted in terms of the Langmuir–Hinshelwood two-parameter equation either invoking physical reasons or simplicity [10], [11].
LH equation (
Results
The differential kinetic system that can be derived from reactions 2 is not solvable, even under steady illumination, unless numerically with a huge number of parameters. The hypothesis of the steady state can be applied to transient species (e.g. differential equations = 0). Nevertheless, the resulting system has no analytical solution. Its numerical solutions give the dependence of the rate as a function of {Red1} and {Ox2} similar to that reported below (see Fig. 1). Because the number of
Conclusions
The present kinetic analysis lead to manageable analytical solutions for the dependence of the rate on operational parameters. From a mechanistic point of view, it has been concluded that, when a maximum is observed for the rate as a function of substrate concentration, the reaction of Ox2 with Ox1 is not predominant. On the contrary, when a maximum is not observed, the reaction (3i) may be important, or the conditions of the photocatalytic systems are close to that reported in Fig. 1 top (i.e.
Acknowledgements
This work was supported by EEC program SOLARDETOX under contract BRPR-CT97-0424 (DG12-GZMM) and by MURST research program under contract with Tecnoparco ValBasento.
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