Diameter and Elasticity Governing the Relaxation of Soft‑Nanoparticle Melts

Acting as soft-nanoparticles, series of microgels are microemulsion polymerized and investigated for their dynamics in the melt state. Each series is kept at the same average number of repeating units between crosslinking points, in short, the crosslinking degree. The relaxation time increases at the 30th power of their diameters or 10th power of their molecular weights or volume and then diverges upon approaching the critical diameter. Our proposed equation describes their relaxation time as a function of diameter and crosslinking degree and unifies both our and literature data. Soft-nanoparticles larger than the critical diameter cannot relax in the melt state within the experimental limits. This may serve as the boundary between thermal molecular or macromolecular domains and the athermal colloidal domain. This critical diameter obeys 1/3 power of the crosslinking degree. This agrees with the Hertzian contact model and the stress originates from elastic deformation. This scaling also implies that the boundary is where SNPs contain a constant number of crosslinking points, around 200. Our equation foresees that for the same molecular weight while changing the topology from linear chains to more and more elastic soft-nanoparticles the relaxation time should first decrease and then increase to infinity. The initial decrease is more dramatic for lower molecular weights.