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Title: A Tribute To Marian Smoluchowski's Legacy On Soft Grains Assembly And Hydrogel Formation
Authors: Gadomski, Adam
Kruszewska, Natalia
Beldowski, Piotr
Lent, Bogdan
Ausloos, Marcel
First Published: 1-May-2018
Presented at: XXX Marian Smoluchowski Symposium on Statistical Physics On the Uniformity of Laws of Nature, Kraków, Poland, September 3–8, 2017
Publisher: Jagiellonian University Press
Citation: Acta Physica Polonica B, 2018, 49 (5) XXX Marian Smoluchowski Symposium on Statistical Physics On the Uniformity of Laws of Nature, pp. 993-1005
Abstract: The paper compares the statistical description of physical-metallurgical processes and ceramic-polycrystalline evolutions, termed the normal grain growth (NGG), as adopted to soft- and chemically-reactive grains, with a Smoluchowski’s population-constant kernel cluster–cluster aggregation (CCA) model, concerning irreversible chemical reaction kinetics. The former aiming at comprehending, in a semi-quantitative way, the volumeconservative (pressure-drifted) grain-growth process which we propose to adopt for hydrogel systems at quite a low temperature (near a gel point). It has been noticed that by identifying the mean cluster size hki from the Smoluchowski CCA description with the mean cluster radius’ size RD, from the NGG approach of proximate grains, one is able to embark on equivalence of both frameworks, but only under certain conditions. For great enough, close-packed clusters, the equivalence can be obtained by rearranging the time domain with rescaled time variable, where the scaling function originates from the dispersive (long-tail, or fractal) kinetics, with a single exponent equal to d + 1 (in d-dimensional (Euclidean) space). This can be of interest for experimenters, working in the field of thermoresponsive gels formation, where crystalline structural predispositions overwhelm. The interest can likely be extended to some dispersive-viscoelastic, typically neurophysical, and in particular cognition involving systems.
DOI Link: 10.5506/APhysPolB.49.993
ISSN: 0587-4254
eISSN: 1509-5770
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © the authors, 2018. This is an open-access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Appears in Collections:Published Articles, School of Management

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