Some phenomenological relaxation rate equations based on Bose–Einstein similar kinetics
作者:
Michael J. Kuba´t,
Jan‐Fredrik Jansson,
Mats Delin,
Josef Kuba´t,
Rodney W. Rychwalski,
Sven Uggla,
期刊:
Journal of Applied Physics
(AIP Available online 1992)
卷期:
Volume 72,
issue 11
页码: 5179-5186
ISSN:0021-8979
年代: 1992
DOI:10.1063/1.351998
出版商: AIP
数据来源: AIP
摘要:
The possibility of describing transient phenomena associated with flow and consolidation of solids, such as stress relaxation or physical aging, in terms of a kinetic mechanism comprising spontaneous and induced events is discussed. The starting point is the differential equationdn˙/dt=−an˙[1−(b/a)n˙], withndenoting the number of relaxed entities andn˙=dn/dt(a,bare constants,tis time), yielding ann˙(t) function reminiscent of a Bose–Einstein distribution. The correspondingn(t) relation describes the linear variation ofnwith log t, and the exponential dependence ofn˙ onn, as often found experimentally. Replacingn˙ in the starting equation by the relative raten˙/nyields a power‐law‐typen˙(n) dependence. A further modification, where the induction termn˙/nis not linear but raised to a power ≳1, finally produces a generalized version of the stretched exponential. When interpreted formally in terms of a spectrum of relaxation times &tgr;, all three equations produce response functions with discrete &tgr; distributions, provideda≠0.
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