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

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.