Kinetics Of Photochemical Processes

The second principle of photochemistry, that absorption is a one-photon process, taken together with quantum theory, requires that each quantum that is absorbed bring about a change (excitation) in that one molecule. In essence, this may be considered to be a "bimolecular" process involving interaction of one photon and one molecule. What happens to the excitation energy, however, depends on the amount of energy absorbed and the nature of the excited molecule. For example, the excited molecule can "lose" all or part of its excitation energy by transferring energy to another species via a non-reactive collision (colljsjonal quenchjng), or it can emit energy in the form of a photon of light (-fluorescence or phosphorescence). Or, the excited molecule may undergo chemical processes (jsomerize, djssocjate, jonjze, etc.), undergo chemical reactions with other species, or transfer its energy by collision to another molecule that ultimately results in a chemical transformation (sensj-tjzatjon). Thus, the overall number of molecules reacting chemically as a result of this absorption of a single photon may be virtually any value ranging from zero to a very large number (> 106). This latter is interpreted as arising from subsequent thermal chain reactions. We will encounter various reactions representing these physical and chemical processes in subsequent chapters.

The efficiency of a photochemical reaction is the quantum yjeld. The overall quantum yield of a substance J, which may be a specific reactant or a stable product, is simply the total number of the specific reactant molecules lost or stable product molecules formed for each photon absorbed. Thus, for the generalized reaction (4-15):

number of A molecules reacted =-

number of photons absorbed number of moles of A reacted number of einsteins absorbed and number of C molecules produced

number of photons absorbed number of moles of C produced number of einsteins absorbed

Since rA is the rate that A reacts, rc is the rate that C is produced, and Ia by definition is the rate of light absorption, it follows that

Ia Ia

This overall quantum yield represents the overall efficiency of the reaction initiated by the absorption of light, which does not have to be absorbed explicitly by a reactant molecule. As already pointed out, however, the initial excitation act of absorption of a photon of light by a molecule X,

may be followed by a variety of physical and chemical primary processes (fluorescence, deactivation, sensitization, etc.) involving the excited molecule X*. (Subsequent thermal chemical and physical reactions are considered secondary processes.) We can define a primary quantum yield ^ as the fraction of X* molecules undergoing a specific (ith) primary process. Thus, for fluorescence, f, in which light is emitted by an excited molecule,

^ number of X* molecules emitting light (4 32)

number of photons absorbed by X

fluorescence rate if

rate of light absorption 7a Thus, in general, for the ith primary process the rate n is r = Va (4-34)

The symbol hv above the arrow in reaction (4-31) indicates that this is the light-absorbing reaction. Although this symbol should be used only for the kinetically simple light-absorbing step, it is often used even in the overall stoichiometric equation to signify a light-initiated reaction in which the overall mechanism consists of a complete set of primary and secondary processes. Since the energy of an absorbed photon has to go somewhere, to the extent that light absorption is a "one-for-one" event (the second principle of photochemistry), the maximum value for a single individual primary quantum yield is unity and the sum of all of the primary quantum yields for both physical and chemical processes must be unity:

where the summation includes all i modes of disappearance of the photoex-cited species, including direct chemical reaction.

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