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Detailed comparison of the Williams–Watts and Cole–Davidson functions
Abstract
The distribution function of relaxation times underlying the nonexponential relaxation function of Williams and Watts is derived and compared with the analogous Cole–Davidson distribution function. In order to make the comparison between the two distribution functions, a simple empirical relationship between the Cole–Davidson and Williams–Watts 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 Cole–Davidson distribution shows a sharp long time cutoff, while the Williams–Watts 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.
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Cites
Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics
Cole, K. S., & Cole, R. H. (1941) · The Journal of Chemical Physics · doi:10.1063/1.1750906 · Cited by 10,152
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Metadata
- Authors
- Lindsey, C. P., & Patterson, G. D.
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 1980-10-01
- Volume
- 73
- Issue
- 7
- Pages
- 3348-3357
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W2091570098
- Cited by
- 1,022
- References
- 1
- FWCI
- 6.62
- Type
- journal article
- Language
- en
- Open access
- closed
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