Sensitizer self-quenching reactions

When the rate constants are such that the last term in Eq. (15) is not negligible, determination of the quantum yield of reaction as a function of sensitizer concentration will reveal back transfer this experiment also tests for sensitizer self-quenching (Section III.B). In the most frequently encountered case, forward transfer is much faster than back transfer (i.e., ke k.e) so that this term is small. The dependence of m on sensitizer concentration disappears and Eq. (15) reduces to the usual expression for quantum yield as a function of [A]. 

Notice that this is the same as the mechanism written in Section II except that step (9), self-quenching, has been added. If we assume that the quantum yield of intersystem crossing for the sensitizer is unity and that all the sensitizer triplet is quenched either by the acceptor or by ground state sensitizer, then the following expression for 4>a, the actual quantum yield for reaction of the substrate triplet, can be derived ... 

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