Detailed comparison of the Williams–Watts and Cole–Davidson functions
- 1 October 1980
- journal article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 73 (7) , 3348-3357
- https://doi.org/10.1063/1.440530
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.Keywords
This publication has 28 references indexed in Scilit:
- Analysis of Structural Relaxation in Glass Using Rate Heating DataJournal of the American Ceramic Society, 1976
- Light‐Scattering Measurements of Structural Relaxation in Glass by Digital Correlation SpectroscopyJournal of the American Ceramic Society, 1975
- Strain relaxation in glass by optical correlation and pressure jump relaxationJournal of Applied Physics, 1975
- Aspects of the low-frequency dielectric relaxation of supercooled non-associated liquids and other viscous liquidsPublished by Royal Society of Chemistry (RSC) ,1975
- Electrical Relaxation in Na2O·3SiO2 GlassJournal of the American Ceramic Society, 1972
- Dielectric study of the motion of molecules in the supercooled liquid stateFaraday Symposia of the Chemical Society, 1972
- Molecular motion in the supercooled liquid state: Small molecules in slow motionChemical Physics Letters, 1971
- Further considerations of non symmetrical dielectric relaxation behaviour arising from a simple empirical decay functionTransactions of the Faraday Society, 1971
- Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay functionTransactions of the Faraday Society, 1970
- DIELECTRIC RELAXATION IN LIQUIDS: I. THE REPRESENTATION OF RELAXATION BEHAVIORCanadian Journal of Chemistry, 1961