Hierarchical Dynamics and Time-Length Scale Superposition in Glassy Suspensions of Ultra-Low Crosslinked Microgels

TL;DR

This paper investigates how ultra-low crosslinked PNIPAM microgels slow down as they approach a glass transition, combining SAXS and dynamic light scattering to map structure and dynamics as a function of the effective volume fraction $φ$. They show that microscopic dynamics are governed by $φ$—consistent with fragile glass behavior described by a Vogel–Fulcher–Tammann–type law—while static structure depends separately on density and swelling state, revealing a regime where structural correlations melt as concentration increases. A central contribution is the emergence of a time–length-scale master curve that collapses $τ_α(q,φ)$ across scattering vectors and samples via a two-process interpretation that couples collective density relaxation and localized polymer-chain motion, with a universal form $\tilde{τ}_α/τ^* = 1/[(q/q^*)^a + (q/q^*)^b]$. The master curve’s applicability to a different microgel system (Nigro et al., 2020) suggests broad relevance for polymeric soft particles, though laser-induced local heating can partially accelerate dynamics in the glassy regime. Overall, the work advances understanding of soft colloid glasses and introduces a framework for universal dynamical scaling in polymeric microgels, with implications for designing responsive soft materials.

Abstract

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 $φ$ and probed length scale. We demonstrate that ULC microgels act as fragile glass formers whose dynamics are governed solely by $φ$. In contrast, the microscopic structure depends on the specific combination of microgel number density and swelling state that define $φ$. 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 $φ$'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.

Figures (19)

• Figure 1: Intensity autocorrelation functions $g_2(\tau)-1$ measured in the COLIS setup for an ULC2 sample at fixed $c=0.034$, for various $T$ as shown by the labels. The corresponding $\varphi$ increase from 0.875 to 1.29 as $T$ decreases. Panels a)-c) show data acquired simultaneously for three scattering vectors, indicated above each panel. The lines are KWW fits to the data, see Eq. \ref{['eq:KWW']}.
• Figure 2: Normalized relaxation time $\tau_{\alpha}/\tau_0$ and stretching exponent $\beta$ (a) and b), respectively) as a function of $\varphi$, measured at $q=22.1~\mu \mathrm{m}^{-1}$ for both ULC1 and ULC2. The data labels in c) apply to all panels and indicate how $\varphi$ was changed (by varying either $c$ or $T$) and whether a shutter was used to reduce sample illumination. Solid lines in panel a) are VFT fits, Eq. \ref{['eq:VFT']}, for data in the range $6.5 \leq \tau_{\alpha}/\tau_0 \leq 28043$ and $42.9 \leq \tau_{\alpha}/\tau_0 \leq 41147$ for ULC1 and ULC2, respectively. In panel c), rescaled variables that linearize the VFT law are used to compare data from this work and for silica nanoparticles (Ludox) and crosslinked microgels (CM) philippe2018glass, and colloidal hard spheres (HS) brambilla_probing_2009. $A$ and $B$ are nearly the same for ULC1 and ULC2 (see text), but differ for the other samples. Semitransparent symbols were not included in the VFT fit.
• Figure 3: Kratky plot, $I(q)q^2$vs$q$, for concentrated ULC1 suspensions at three fixed microgel concentrations $c$ and various $T$ as indicated by the labels (a-c), and at fixed $T=20^{\circ}$C and various $c$ (d).
• Figure 4: a) Peak position $q_{max}$ and b) height of the first peak in function of microgel concentration c[wt/wt] and 2 different temperatures as indicated in the panel
• Figure 5: Effect of reducing the average illumination power on the dynamics of the ULC2 microgels, for various $T$. For the measurements with a shutter, the incident beam is blocked $92\%$ of the time, corresponding to an effective reduction of the power on the sample of a factor of 12.5. Inset: relative change of the relaxation time measured with and without the shutter, as a function of temperature.