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A Tribute To Marian Smoluchowski's Legacy On Soft Grains Assembly And Hydrogel Formation

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journal contribution
posted on 2018-12-14, 16:29 authored by Adam Gadomski, Natalia Kruszewska, Piotr Beldowski, Bogdan Lent, Marcel Ausloos
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.

History

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

Author affiliation

/Organisation/COLLEGE OF SOCIAL SCIENCES, ARTS AND HUMANITIES/School of Business

Source

XXX Marian Smoluchowski Symposium on Statistical Physics On the Uniformity of Laws of Nature, Kraków, Poland, September 3–8, 2017

Version

  • VoR (Version of Record)

Published in

Acta Physica Polonica B

Publisher

Jagiellonian University Press

issn

0587-4254

eissn

1509-5770

Copyright date

2018

Available date

2018-12-14

Publisher version

http://www.actaphys.uj.edu.pl/acta_physica_polonica_b?show_last=true

Language

en

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