Critical Examination of the Calculus Convolution Kinetics: The Influence of Nonstationary Diffusion on Excimer Formation with Dissociation

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Abstract
If time dependent rate coefficients (TDRC) appear in reactions, ordinary rate equations (RE) fail. The calculus convolution kinetics (CK) provides consistent results in these cases, but its appliance is quite unfamiliar. For rate coefficient(s) (RC) that are time‐independent the results of CK are analytically identical with those of RE, though being obtained on a completely different way. – In this paper the failure of the RE method will be briefly demonstrated with an example. Furthermore the concept of CK will be presented in short and applied on excimer formation. On the level of synthesis data a comparison of the result of the rate equations' treatment with √t‐term obtained numerically, the CK result and measuring data will be carried out. For this the time resolved decay curves of “single photon counting” – measurements and synthesis data of both methods convoluted by flash will be graphically laid on top of each other. It turns out that curves from CK represent the measuring graph better than data of the RE calculated with the same parameters. Larger differences appear in the initial part of the curves with both methods. To explain these differences a new mechanism of excimer formation will be brought into discussion, but also the uncompletness of the Smoluchowski approximation for nonstationary diffusion will be taken into account. – The kinetical treatment given below is an example of excited state kinetics [1]; but CK is not limited on this kind of kinetics.