Delayed Response in Tracer Experiments and Fragment-Carrier Approach to Transit Time Distributions in Nonlinear Chemical kinetics

A delayed response tracer experiment is suggested, based on the following constraints: (1) The kinetics of the process can be expressed by local evolution equations without delays, for example by the mass action law. (2) The kinetic isotope effect can be neglected, that is, the rate coefficients for labeled and unlabeled chemicals are the same. (3) The total fluxes of the various chemicals are generally time dependent, but are not modified by the presence of the labeled compounds. (4) The experiment consists in the measurement of the time dependence of the fractions βu, u = 1, 2, . . . of labeled chemicals in the output fluxes as functionals of the time dependence of the fractions αu, u = 1, 2, . . . of labeled chemicals in the input fluxes, which are controlled by the researcher. We show that the output fluxes are related to the input fluxes by a linear delayed superposition theorem: βu(t) = ∑ u′ ∫ χuu′(t, t ′)αu′(t′)dt′, where χuu′(t, t ′), is a delayed susceptibility function, which is related to the probability density of the transit time, that is, the time necessary for a molecular fragment to cross the system. This linear superposition law is not the result of a linearization procedure and holds even if the underlying kinetic equations are highly nonlinear. We establish a relationship between the transit time probability densities and the lifetime distributions of the various species in the system. The law permits extracting information about the mechanism and kinetics of chemical processes from response experiments.