# A tribute to Marian Smoluchowski's legacy on soft grains assembly and hydrogel formation

Source: [A tribute to Marian Smoluchowski's legacy on soft grains assembly and hydrogel formation](<https://www.sota2.com/research/paper/68fa38201e209131ce8b7b60>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T22:46:26.319Z

Authors: Adam Gadomski, Natalia Kruszewska, Piotr Be{\\l}dowski, Bogdan Lent, Marcel Ausloos

Published: 2018-06-27T08:45:55.000Z

## 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 volume-conservative (pressure-drifted) grain-growth process which we propose to adopt for hydrogel systems at quite low temperature (near a gel point). It has been noticed, that by identifying the mean cluster size $\<k\>$ from the Smoluchowski CCA description with the mean cluster radius' size $R\_D$, 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1807.10353>)

[PDF](<https://arxiv.org/pdf/1807.10353.pdf>)