Partial photochemical quantum yields

As for thermal reactions complex photoreactions can be the result of more than one step of the reaction. By analogy one can correlate a partial photochemical quantum yield to each of the partial steps of the reaction 

is the amount of light absorbed by this reactant which starts the photoreaction (see also Section 1.4.2). 

Under these conditions n is the number of reactants which start any photoreaction and n is the total number of all reactants, is the number of photoreactions, sr - s the number of thermal reactions to which the Bodenstein hypothesis (see Section 2.1.3.2) cannot be applied. 

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G. Gauglitz, R. Goes, W. Stoob, and R. Raue, Determination of partial photochemical quantum yields of reversible photoisomerizations ofstilbene-1 derivatives, Z. Naturforsch. 40a, 317-323 (1984). 

The change in concentration of reactants is at the centre of interest in photokinetics as well as the determination of these partial photochemical quantum yields. The time laws cannot be integrated in a closed form. Therefore to avoid the problems with solving these differential equations, the integrals are numerically calculated - a procedure named formal integration. This method also turns out to be advantageous in thermal and photochemical examinations. 

The number of such reactions is large. The differential equations for the changes of the concentrations with time can be given in general. In the following example a consecutive reaction which contains two photoisomerisation steps (forward, backward) is followed by a consecutive thermal step. This reaction can be chosen to demonstrate the consequence of the definition of partial photochemical quantum yields (see Section 2.1.2.2), the linear dependencies, and the influence of the thermal reaction ... 

Conclusion (a) Photochemical steps of reaction include many thermal degradation processes, which do not need to be considered in the rate law, if the Bodenstein hypothesis is valid, (b) The mechanism has to be reduced as far as possible to avoid linear dependencies, (c) Thermal and photochemical reactions can be treated in principle by the same formalism. Rate constants times concentrations have to be substituted by the product of the partial photochemical quantum yield times the amount of light absorbed, which contains the concentration of the reactant which starts the photoreaction. 

Based on the fundamental considerations in Sections 1.3 and 1.4, the principle of quantum yield was introduced in Section 2.1.2 to allow a treatment of photochemical reactions in a way comparable to thermal reactions. The difference from thermal reactions has been demonstrated by taking account of the photophysical steps in Sections 2.1.3.3 and 2.1.4.3. These have to be considered in detail to find out whether the partial photochemical quantum yield depends on the intensity of the irradiation source or even on concentrations. Furthermore the definitions derived in Chapter 2.1 and summarised in Table 2.2 are used. In particular the definitions for the degrees of advancement for partial steps in general x, for photophysical steps in special x-, and for linearly independent steps x of the reaction procedure have to be remembered. 

It is assumed that the partial photochemical quantum yields and

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In Chapters 2 and 3 partial photochemical quantum yields have been introduced as parameters which give information on photochemical reactions. According to eqs. (2.12) and (2.14) they depend on the change in concentration of the reactant which undergoes the photoreaction and on the light absorbed by this reactant. For this reason an essential of any photochemical examination is the determination of this amount of light absorbed. Two principles are known ... 

This equation can be integrated. The slope of the diagram ln[/(J (r) — Ia(s)] versus t gives, using eq. (5.143), the partial photochemical quantum yield of the second step... 

This partial photochemical quantum yield of the second step can only be determined if the molar absorption coefficient of the reactant B is known. Another possibility of evaluation is to take the integrated eq. (S.142) in its exponential form and to calculate by curve fitting procedures (py and (p with known and using... 

Neglecting the photo-degradation processes in laser dyes the partial photochemical quantum yields of stilbene-1 derivatives have been determined by evaluation procedures as given above [93]. In Section 4.3.2 a microprocessor controlled device is described [176], which allows convenient measurement of the data. Even an optical multi-channel analyser can be used [175]. 

The defined parameters correlate with the partial photochemical quantum yields according to... 

Fig. 5.49. Determination of the partial photochemical quantum yield of the primary photodegradation step of umbeliiferone using the fluorescent intensity corrected by absorbance at...

In Section 5.6.1.1 quantitative results for the partial photochemical quantum yields of the photoreaction of stilbene-1 were given. A photoisomerisation was assumed to be the mechanism as a first step. This proposal is supported by a reaction chromatogram of the photodegradation reaction of this laser dye. The two parts of the diagram (see Fig. 5.58) prove a photo-reversible isomerisation as a first step [190]. This information was used for the evaluation mentioned. 

However, model reactions can demcxistrate that the interferometric measurement in combination with application of the Kramer-Kronig relationship [S] allows calculation of the abscnbance-time curves and the determination of the partial photochemical quantum yield. Thus, the method makes it pos-sibile to monitor photoreactions in a solid matrix. As an application the quantum yield of the photoreaction of a 7,7a-dihydrobenzofuran derivative to the (Z)-fulgide is obtained as =0.03 [201]. 

Approximate partial photochemical quantum yields for the photoreaction of the fulgide in the polymer liquid crystal at 100°C irradiation at 365 nm [196]... 

Since the determination of absorption coefficients is in only 10-23 fxm thick layers, only relative concentrations can be determined, given in Fig. 5.72. Accordingly the partial photochemical quantum yields can only be approximated. Their values in Table 5.9 demonstrate that the absorption coefficients are determined to be too small. However, their values relatively fit to the data obtained in stirred solutions. These results prove the ability of the formalism presented in this book to treat photokinetic data even under extreme conditions. 

After derivation of the principles of kinetic examinations and especially the fundamentals of photokinetics in this final chapter a large number of examples have been discussed based on the equations derived in Chapters 2 and 3. These examples cover a wide field of types of photochemical reactions that take place in various applications. By use of different types of equipment, it was demonstrated how relevant data can be obtained during the reaction. This knowledge was applied to calculate reaction constants as partial photochemical quantum yields or at least the data for a turn over, if the spectroscopic or other characteristics of the compounds involved in the reaction are not known in detail. 

In consequence the partial photochemical quantum yields are represented by... 

The different coefflcients allow us to calculate the partial photochemical quantum yields knowing the absorption coefficients. Using the absorption coefficients for the three reactants at the wavelength of irradiation (313 nm) =15900, = 1320 l mol" cm the three quantum yields are obtained as... 

These methods offer the chance to determine the partial photochemical quantum yields of each step in a multi-step reaction procedure. By way of this quantity, the influence of changed reaction conditions or substitution of the compound in question can be determined quantitatively. By considering the principles and the methods mentioned, it will be possible to reduce the number of experiments to optimise photo-degradation processes or the photostability of products. Both applications are of immense interest in the optimal system for reversible storage of information or to increase photostability of laser dyes. The same is valid for all photochemical processes run in industry or even in laboratories in research groups. 

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