By H. Mauser and G. Gauglitz (Eds.)
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Extra resources for Photokinetics: Theoretical Fundamentals and Applications
Example text
1 Photophysics 11 means the molecule marked as A* in the following and in the figure is 'hot' in comparison to its environment. For this reason it equilibrates its 'temperature' in a short time in the condensed phase. It deactivates without radiation to the lowest vibrational state of the actual electronic state (marked in Fig. 1 as te). By isoelectronic internal conversion (ic) it can pass over to a very high vibrational state of the next lower electronic energy state. These deactivations normally take place until the molecule has reached the vibrational ground state of the first excited electronic state Si.
2 - 1 1 1 0 0 V = 0 - 1 0 1 1 This demonstrates clearly that in general matrices v**^ and v% respectively, are singular. In consequence the changes in concentrations are according to eq. 4) (Aa^ (-1 0^ 1 -1 A6 Ac = 1 0 0 1 \Ad ^Ae, . 0 ij In the chosen example the concentrations of two components a and b suffice to describe the progress of the reaction. The vector Aa" can be reduced and the equation above is written as Aa^ -1 0 Ab, 1 -1 V-'^2, By inversion of the reduced stoichiometric matrix the relationship can be rearranged to an equation according to eq.
The first element is the degree of advancement of this reaction X\, The last element is determined by the derivative of this degree of advancement with respect to time used in eq. 3). A simple example is the reaction A + B~>C + D according to eq. 3): B - 1 ~1 D 1 1 Degrees of advancement are formal quantities. However, their use allows us to obtain equations with mass balance by combination of eq. 2). g. taking A,). One obtains accordingly Aa, = VjX or jc = v, Aa,. Thus, the use of the degree of advancement simplifies the equation and the number of components to be monitored during the reaction to one.