A transfer function approach to reaction rate analysis with applications to phase-change materials and devices

Abstract

A very good approximate, closed-form solution to the reaction rate equation with Arrhenius temperature dependence is derived, valid for activation energies E >> kBxT0 (kB is Boltzmann constant and T0 is room temperature) and monotonically decreasing temperatures. This solution is then used to develop a transfer function description of the reaction rate equation, enabling the bandwidth of the reaction rate to be determined and related to the kinetic and thermophysical parameters of the medium. Applications of the transfer function approach to understanding and predicting reaction (i.e. crystallization) rates in phase-change materials and devices are discussed.