The impact of hierarchically constrained dynamics with a finite mean of cluster sizes on relaxation properties

Journal Article · Wed May 15 00:00:00 EDT 2013 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2013.01.012· OSTI ID:22220714

Weron, Karina ^[1]; Jurlewicz, Agnieszka ^[2]; Patyk, Michał ^[1]; Stanislavsky, Aleksander ^[3]

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1. Institute of Physics, Wrocław University of Technology, Wyb. Wyspiańkiego 27, 50-370 Wrocław (Poland)
2. Institute of Mathematics and Computer Science, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław (Poland)
3. Institute of Radio Astronomy, Ukrainian National Academy of Sciences, 4 Chervonopraporna St., 61002 Kharkov (Ukraine)

In this paper, a stochastic scenario of relaxation underlying the generalization (Kahlau et al., 2010) [15] of the Cole–Davidson (CD) and Kohlrausch–Williams–Watts (KWW) functions is proposed. As it has been shown (Kahlau et al., 2010) [15], the new three-parameter time-domain fitting function provides a very flexible description of the dielectric spectroscopy data for viscous glass-forming liquids. In relation to that result we discuss a hierarchically-constrained model yielding the proposed relaxation fitting function. Within the “exponentially decaying relaxation contributions” framework we show origins of the high-frequency (short-time, respectively) fractional power law, i.e., the characteristic feature of the new, as well as, of both CD and KWW response functions. We also bring into light a reason for which their common behavior in the opposite frequency limit is linear on external field frequency. Finally, we relate the new relaxation pattern (Kahlau et al., 2010) [15] with the Generalized Gamma (GG) survival probability of an imposed, non-equilibrium initial state in a relaxing system. -- Highlights: ► Combine the empirical Kohlrausch–Williams–Watts and Cole–Davidson laws of relaxation. ► Establish a microscopic stochastic scenario explaining the generalized law. ► Derive a frequency-domain relaxation function fitting the dielectric spectroscopy data. ► Find the low- and high-frequency properties for the relaxation pattern.

• OSTI ID: 22220714
• Journal Information: Annals of Physics (New York), Vol. 332; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIELECTRIC MATERIALS
EQUILIBRIUM
GLASS
LIQUIDS
RELAXATION
RESPONSE FUNCTIONS
SPECTROSCOPY
STATISTICAL MECHANICS
STOCHASTIC PROCESSES
VISIBLE RADIATION