Hierarchical Dynamics and Time-Length Scale Superposition in Glassy Suspensions of Ultra-Low Crosslinked Microgels
We employ small-angle X-ray and dynamic light scattering to investigate the microscopic structure and dynamics of dense suspensions of ultra-low crosslinked (ULC) poly(N-isopropylacrylamide) (PNIPAM) microgels. By probing the supercooled and glassy regimes, we characterize the relationship between structure and dynamics as a function of effective volume fraction $\phi$ and probed length scale. We demonstrate that ULC microgels act as fragile glass formers whose dynamics are governed solely by $\phi$. In contrast, the microscopic structure depends on the specific combination of microgel number density and swelling state that define $\phi$. We identify an anomalous glassy regime where relaxation times are orders of magnitude faster than predicted by supercooled extrapolations, and show that in this regime dynamics are partly accelerated by laser light absorption. Finally, we show that the microscopic relaxation time measured for different $\phi$'s and at various scattering vectors may be rationalized by a ``time-length scale superposition principle'' analogous to the time-temperature superposition used to scale onto a master curve rheology or dielectric relaxation data of molecular systems. Remarkably, we find that the resulting master curve also applies to a different microgel system [V. Nigro \textit{et al.}, Macromolecules \textbf{53}, 1596 (2020)], suggesting a general dynamical behavior of polymeric particles.