The photokinetic factor

A very simple derivation of the amount of light absorbed is possible using Lambert-Beer s law in solution given by 

Because monochromatic radiation is a prerequisite to apply this law, only this type of irradiation can be used in photokinetics. The part of radiation lost within the reaction vessel can be determined as the difference between incident 1(f)) and outgoing 1(d) radiation per square area 

Obviously this quantity exhibits units in moles per area and time as irra-diance does. Taking into account that absorption of radiation is related to a volume element, the relationship /,bs( /.A,) has to be divided by the path-length of this volume element d. Thus, finally, by use of eq. (1.38) the following relationship is given for the amount of light absorbed per irradiated volume of the reaction vessel and by reactant A and per second of irradiation  

Substituting the sum in the exponent by eq. (1.38), the amount of irradiation absorbed by that reactant starting the photoreaction (reactant A is assumed) can be written as 

This quantity appears in most of the photokinetic equations. Part of it was named the photokinetic factor. This factor can be defined using different absorption coefficients. 

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Here c > = R2/(k 4 kR2) is the photochemical product formation yield. Note that the absorbance and e values are those at the exciting wavelength. In contrast to the case of photo deracemization, in photodestruction reactions the absorbance [and consequently the photokinetic factor F, Eq. (12)] is not constant therefore the integral... 

A successful approximation for Eq. (8) is the introduction of total (complete) absorption. Under such conditions, the photokinetic factor F t) is replaced by A, and Eq. (8) reduces to... 

A different approximation is based on the use of very dilute solutions in which the absorbance is smaller than 0.02 units (A <0.02). In this case, the photokinetic factor is considered constant as an expansion into series. Accordingly, the factor exhibits a value of 2.303, and the rate depends on the concentration in a similar way as observed in first-order (thermal) reactions. Assuming a partial absorption during the photoreaction and taking into account that the photoproducts will also absorb at the actinic wavelength, the photokinetic equations become more complicated. There are a large number of such different equations, each tailored to a specific problem, as demonstrated in the various examples in the following sections. 

Either 1 /(I qF ) (constant temperature and variable incident photon flux) or baIF (variable temperature and constant incident photon flux) can be used as the variable constraint. The photokinetic factor F must be measured for each of the photostationary states. It should be noted, however, that the relationship in Eq. (A2.1) comprises four unknown quantities (eg, eB, AB, and < >Ba) and cannot be analyzed directly as the numerical values of the slope p and the intercept i with the y axis produce values for only two unknown parameters (Figure A2). hi Section A2.2, we show how this can be resolved. 

Derivation of photochemical equations can become easier using the Napierian molar absorption coefficient. This is discussed in detail in Section 5.1.2.2. The result is the photokinetic factor given by... 

As demonstrated the Jacobi matrices are more complex in the case of photokinetics, since instead of the rate constant the quantum yield together with the photokinetic factor and the absorption coefficient have to be taken. Furthermore all the photochemical steps are accompanied by photophysical steps. Tliese problems are dealt with in the next chapter. 

The integrals (3.43) and (3.44) can be simplified, if in a sensitised photoreaction just the sensitiser A absorbs the incident light. In this case the photokinetic factor (for its derivation and its meaning see Section 1.4.4), given by eq. (1.41) is constant... 

Most integrals cannot be solved in a closed form because of the time dependence of the photokinetic factor (except at specific reaction conditions). Therefore the integrals have to be solved numerically. When the solution cannot be homogenised during the photoreaction by stirring (viscous media) dependencies on time and position have to be taken into account. 

In contrast to thermal kinetics the photokinetic equations given above cannot be solved in a closed form, since the photokinetic factor depends on the absorbance of the solution itself and is consequently dependent on time. In the literature approximations either with respect to total absorbance or to very dilute solutions are used. The consequences are discussed in detail in Section 3.3.3. Using the conditions... 

An approximation using the photokinetic factor given by eq. (3.69) supplies an even better evaluation using azobenzene as an actinometric system. Using a linear interpolation between two points of measurement at time ti and 2 the photokinetic factor according to eq. (5.108) can be approximated within this time domain as... 

A different approach to overcome the change in the photokinetic factor during the progress in the photoreaction is reported elsewhere [169], By variation of the intensity of irradiation in such a way that the change in the photokinetic factor is compensated by this change, in eq. (5.107) the factor... 

To reduce the dependence on the geometric properties in fluorescence spectroscopy usually very dilute solutions are used. The photokinetic factor F(t) is approximated according to eq. (5.111). Under these conditions neither the change in absorbance at the wavelengths of irradiation E nor changes in the factors r(E ) and r(E ) have to be taken into account. Thus eq. (5.136) can be rewritten as... 

In Section 5.5.3, a more sophisticated method has been given to correct measured fluorescence intensities influenced by the change in the photokinetic factor during the photoreaction. By these means the photochemical quantum yields of a large variety of laser dyes can be determined using the corrections according to eq. (5.157). Some structures of dyes used are... 

As derived in Chapter 3.4 the photokinetic factor depends on the volume... 

In the case of a photoreaction the photokinetic factor has to be included. Various evaluations are possible according to Figs. S.18-S.20, the simplest one being the use of formal integration like... 

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