Transit Time Distributions, Linear Response, and Extracting Kinetic Information from Experimental Data

4 Transit Time Distributions, Linear Response, and Extracting Kinetic Information from Experimental Data 

In order to extract kinetic information from tracer experiments, we express the response theorem (12.82) in terms of the probability density (0 t) (eq. (12.91)). We have 

We consider two different types of response experiments (1) transient experiments, for which the excitation functions / (t) have the form of a unitary impulse or of a Heaviside step function (2) frequency response experiments, for which the excitation functions a / (t) are periodic. 

An example of the first type of transient response experiment consists in the generation 

We notice that, in order to evaluate the probability density cpuuo (9, t), it is necessary to carry out many response experiments, for which the excitation of the system takes place at different initial times to = t K t — The method simplifies considerably if the system is operated in a stationary regime. In this case, owing to the property of temporal invariance, we have 

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