Introduction

H. Mauser, †; G. Gauglitz    Eberhard-Karls-Universität Tübingen Institut für Physikalische und Theorestische Chemie Tübingen, Germany

1.1 GENERAL CONSIDERATIONS

The study of photochemical kinetics is a very important approach for elucidating reaction mechanisms and determining the quantitative parameters characteristic for the progress of the photochemical reaction. Since the excitation of electronically excited states can be achieved more selectively than by thermal pathways, irradiation allows reactions to be guided into specific reaction channels. Solvent interaction, matrices, and variation in chemical derivatisation will influence this reaction coordinate.

The intention of classical photochemistry was to determine a turnover at an empirical level. However, detailed kinetic examination supplies data beyond such procedures. The determination of the dependence of rates of reaction on the experimental conditions mentioned induced developments in the fields of solar energy storage, information recording, photobiology, understanding of environmental problems, and optimisation of industrial chemical production.

Understanding of mechanistic studies requires fundamental knowledge on

• creation and properties of radiation and its interaction with matter,

• structure and properties of excited states,

• photophysical reaction channels, and

• subsequent degradation and relaxation processes.

All these aspects are frequently treated in textbooks on physical chemistry or photochemistry. Modem equipment allows the monitoring of reaction down to the time domain of femtoseconds. Thus, application of such time resolved methods allows the determination of intermediates and sometimes even the characterisation of transition states. By these means, in many cases the mechanism of elementary reactions can be determined as in the case of examinations of thermal reactions.

However, in thermal kinetics the description of reaction progress by rate laws, rate constants, and thermodynamic data usually avoids the quantitative specification of the different elementary steps of the overall reaction. These examinations give rise to rate equations according to the order of the reaction which are used to argue about mechanisms and support the information obtained by flash spectroscopy. This formal approach requires experimental data, measuring the concentrations of the components resolved in time during the reaction procedure at a high level of quality. Modem analytical methods can supply such data. In principle UV/vis spectroscopy is favoured as it is fast, photometrically very exact, and relatively inexpensive.

Rate constants are determined by variation of experimental conditions and chemical composition of the reaction mixture. Data are measured by application of a variety of modem analytical methods. Modem numerical approaches of curve fitting and/or solution of differential equations are applied. Results and consequences influence chemical reaction engineering as well as production costs. Many books cover these formal thermal kinetics in detail, but most are restricted to simple mechanisms. In contrast, analogous treatments of photochemical reactions are restricted to publications of special reactions and examinations. Therefore this book aims to supply an overall treatment of formal photokinetics beyond the scope of normal books on kinetics.

In principle the approach in photokinetics can be compared to the handling of thermal reactions:

• a model of the mechanism of the reaction is stated,

• the differential equations are set up,

• an analytical numerical solution is tried,

• the kinetics are measured,

• changes in concentration of the reactants are calculated,

• mathematical tools of parametrisation, iteration, or direct determination of coefficients (rate constants) are applied, and

• the steps of the thermal reaction procedure together with rate constants are obtained for further interpretation.

Unfortunately a general transfer of this well established procedure in the quantification of thermal reactions is not possible directly to photokinetics. In photokinetics even the simplest pseudo first order reaction cannot be described by a differential equation in a closed form. The amount of light absorbed during the reaction has to be taken into account in addition to a quantity comparable to the rate constant. This amount of light absorbed changes during the reaction because of a change in concentration of the component starting the step of the photoreaction. Thus, the proportionality constant in the rate law, set up in analogy to thermal kinetics, includes a coefficient dependent on irradiation time. The problem can be demonstrated for the simple reaction

→B,

which can be described in the case of a thermal reaction as

˙=−ka,

where a is the actual concentration of reactant A (measured with time), k is the rate constant, and ˙ is the rate (change of A per time). The comparable rate law for the photochemical reaction is given by

˙=−φIA=−φIεA'aFt

where φ is the photochemical quantum yield (a constant, if correctly defined), ε'Α is the molar absorption coefficient of reactant A at the wavelength of irradiation λ', I is the incident intensity, and IA is the amount of light absorbed by the component A starting the photoreaction. The factor F represents the fraction of absorption by this component A in the overall absorption of the reaction mixture. Since during the reaction the concentration of A changes, IA (and F) is not constant. Frequently this problem is solved by working at total absorption of the solution or using just initial slopes of the concentration time curves. All these approaches do not allow a general treatment and are approximations to reality. Their quality depends very much on the conditions under which the reaction is examined.

This book derives a concise treatment of both thermal and photochemical reactions by use of generalised differential equations, their set-up in matrix notation, and their solution by a formalism using numerical integration. This approach might be surprising at first glance. However, the reader will realise that there are quite a few good reasons to do so beyond the argument that didactics of thermal reactions are more easily to handle than those of photokinetics. This generalised approach allows treatment of thermal and photochemical reactions quite equivalently:

• Many photochemical reactions are superimposed on thermal backward reactions or other thermal reaction steps. Using the same formalism these mechanisms can be handled in a uniform approach.

• Photoreactions are treated as pseudo first order kinetics. As demonstrated in Section 2.1.3.3, besides the photochemical step, a variety of photophysical steps such as radiationless transitions are included in the mechanism. Excited states are intermediates. The considerations typical in thermal kinetics as, for example, Bodenstein’s hypothesis, can also be applied to these steps. Thus an overall treatment of the total mechanism becomes possible.

• If constant intensity of irradiation with time is assumed, only the photokinetic factor F has to be included in the time variable. It depends on the progress of the reaction normally, as stated above depending on the absorption of the sample. Then the product of irradiation intensity and photochemical quantum yield forms a constant equivalent to the rate constant of thermal reactions. The dependent variable is a product of the factor F and the irradiation time t combined as a variable Θ. This introduction of a transformation in the time axis allows formal kinetics to be applied to thermal and photochemical reactions as well. It even allows the handling of solutions which cannot be homogenised, or solid samples in which the concentration varies locally because of decreasing irradiation intensity in the direction of irradiation by the turnover of the reactants.

• As in thermal kinetics, the changes in concentration are usually monitored in photokinetics by spectroscopic measurements. Under these conditions, a distinction between different mechanisms is not possible for many reactions. Just the number of spectroscopically linear independent steps of reaction can be determined (see Chapter 4).

• An essential approach is the so-called partial (differential) photochemical quantum yield, which is time independent and refers to a specific step of the photochemical reaction. It can...