Probing dynamical disorder kinetics with chemical relaxation techniques

Abstract

A number of theoretical models describing non-exponential kinetic behavior in complex media exist. It is often difficult to discriminate between these models on the basis of their ability to provide good statistical fits to experimental data. In this work the use of chemical relaxation techniques to discrminate non-exponential models is explored. A class of simple dynamical disorder models is considered and it is shown that relaxation techniques can be used to distinguish these models from structural disorder models. In these dynamical disorder models the activation energy of the chemical process is assumed to be linearly related to a fluctuating thermodynamic variable of the system. These fluctuations alter the rate constant for the chemical process and, therefore, the integrated rate expression must be averaged to obtain the macroscopic law. Highly accurate approximations can be derived for the model using a cumulant expansion. For irreversible chemical processes, the systems' response to an external periodic perturbation is derived. This response can be used to separate parameters related to the internal fluctuations from those related to the chemical process. For chemical relaxations about equilibrium (reversible dynamical processes), it is shown that double pulse perturbations can be used to distinguish general classes of structural disorder models from dynamical disorder models. Experimental design strategies for discriminating non-exponential models are also discussed.