A Tribute to Marian Smoluchowski’s Legacy on Soft Grains Assembly and Hydrogel Formation

摘要

The paper compares the statistical description of physical-metallurgicalprocesses and ceramic-polycrystalline evolutions, termed the normal graingrowth (NGG), as adopted to soft- and chemically-reactive grains, witha Smoluchowski’s population-constant kernel cluster–cluster aggregation(CCA) model, concerning irreversible chemical reaction kinetics. The formeraiming at comprehending, in a semi-quantitative way, the volumeconservative(pressure-drifted) grain-growth process which we propose toadopt 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 theSmoluchowski CCA description with the mean cluster radius’ size RD, fromthe NGG approach of proximate grains, one is able to embark on equivalenceof both frameworks, but only under certain conditions. For greatenough, close-packed clusters, the equivalence can be obtained by rearrangingthe 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.