Scavenger kinetics and the laplace transform relationship. 1. Homogeneous systems

The use of a Laplace transform (LT) relationship to link time dependent kinetics and scavenger yields in homogeneous systems is examined theoretically. It is shown analytically that the connection is strictly valid only for a single pair of reactants and for first order reactions. The accuracy of the LT method is tested for multiparticle systems. For small numbers of reactive particles the true decay kinetics are compared with the inverse Laplace transform (ILT) of the scavenger yield, and the scavenged yield is compared with the LT of the kinetics. The extent of the discrepancies found depends upon the rate constants for the various possible combination reactions. The smaller the rate constant for the combination of like particles relative to the recombination of unlike particles, the more accurate the decay kinetics are described by the LT relationship. When only unlike recombinations occur the agreement is excellent. In single species systems, where only like species can combine, there is considerable disagreement: In particular the ILT kinetics show an unrealistic minimum for systems initially containing an odd number of reactants.