Limitations on distinguishing between representations of relaxation data over narrow frequency ranges

In this article, we examine the ability to distinguish between relaxation functions with data over a limited range of frequency. It is demonstrated that over these limited frequency ranges under a variety of conditions, the Cole–Cole equation can be used to fit data generated by the Havriliak–Negami equation. These results show that discerning between several very different broad relaxation functions fit to data obtained over narrow time or frequency ranges is nearly impossible within experimental accuracy. Therefore, the uniqueness of the fit parameters, and hence the ability to verify model predictions, is brought into question. Furthermore, as this conclusion is drawn from comparison of exact functions that experience no dispersion overlaps or instrumental systematic errors that can mask exact fits, the true situation with experimental data is even worse. The same conclusion can be applied to time domain data.