Nonparametric Analysis of Nonexponential Relaxation: Standard and Two-Dimensional Kinetics

When a system’s relaxation is not well described by a single rate constant, the range of results is often restricted before the data are analyzed. This paper presents an alternative, “data-first” approach that avoids these restrictions. The method is nonparametric: no model or fitting function, such as a stretched exponential, is used. At the same time, it avoids the ambiguities in nonparametric approaches that are based on the inverse Laplace transform. Experimental data are initially transformed into a spectral representation, which helps to visualize their important features and limitations. These kinetic spectra are then quantified by “descriptors” that characterize the relaxation mechanism but are insensitive to the details of the data analysis. This method not only treats standard kinetics; it also extends naturally to newer, multidimensional experiments. These ideas are illustrated with one- and two-dimensional data from a recent study of solute rotation in micelles.