Detailed comparison of the WilliamsWatts and ColeDavidson functions
Abstract
The distribution function of relaxation times underlying the nonexponential relaxation function of Williams and Watts is derived and compared with the analogous ColeDavidson distribution function. In order to make the comparison between the two distribution functions, a simple empirical relationship between the ColeDavidson and WilliamsWatts parameters was determined which may be used to compare data analyzed using the two fitting functions. Although the relaxation functions are similar to each other, the distribution functions are quite dissimilar. The ColeDavidson distribution shows a sharp long time cutoff, while the WilliamsWatts distribution decays approximately exponentially at long times. Finally, several useful relations between relaxation and distribution functions are summarized or derived, and the limitations of deriving distribution functions from relaxation functions are discussed.
 Publication:

Journal of Chemical Physics
 Pub Date:
 October 1980
 DOI:
 10.1063/1.440530
 Bibcode:
 1980JChPh..73.3348L
 Keywords:

 77.40.+i