Dielectric Relaxation and Molecular Structure. V. Application of the Single Frequency Method to Systems with two Debye Dispersions

There are four Debye equations for dilute solutions which can be used to determine the relaxation time of a polar solute molecule. This paper offers a critical examination of these equations, especially two representative formulas which are mutually independent. If the solute molecule has a non-rigid configuration and has two relaxation times, τ1 and τ2, for overall and internal rotations, respectively, average relaxation times will be obtained from these equations based on measurements at a single frequency. However, the analysis of this paper shows that under a certain condition (if a proper frequency for the measurement and a suitable equation for the calculation are employed) one may make a crude estimate regarding one of the two relaxation times. Further, the ratio of two relaxation times seems to afford a clue for investigating the mechanism of internal rotation. In addition, Cole-Cole dispersion and atomic polarization problems are also discussed.