Thermal History Asymmetry and Dissipation in Dense Colloidal Microgel Glasses

TL;DR

The paper investigates how dense, thermoresponsive PNIPAM microgel suspensions exhibit Kovacs-like memory in their viscoelastic response under temperature ramps across the volume phase transition. By performing oscillatory rheology with controlled heating and cooling ramps at varying rates and packing fractions, the authors quantify path dependence using an asymmetry parameter $ riangle A$ and identify energy-dissipation peaks in the loss modulus $G''$ that align with microgel rearrangement events. They reveal an inverse relationship between $ riangle A$ and $G''$ peak heights, showing that stronger dissipative rearrangements can erase memory effects, particularly at faster ramps or higher confinement, and that behavior evolves as the system nears or passes the VPTT. These findings illuminate how external driving can tune non-equilibrium relaxation pathways in soft glassy matter, with implications for programmable memory in soft robotics and responsive biomaterials, and underscore the role of dissipation in navigating complex energy landscapes.

Abstract

Microstructurally arrested matter, from molecular glasses to soft glassy materials, can retain a memory of their thermal or mechanical (shear) histories. Their history-dependent and nonlinear microstructural recoveries have been studied within the Kovacs framework. Here, we applied the temperature ramps of varying magnitudes to dense colloidal suspensions of thermoresponsive, deformable and compressible microgel particles should serve as an effective strategy to probe the nonlinear path-dependent structural recovery of these systems. We synthesised Poly (N-isopropyl acrylamide) (PNIPAM) microgel particles using the free radical precipitation polymerisation method. Using oscillatory rheology, we studied the relaxations of the viscoelastic moduli of dense PNIPAM suspensions that were heated and cooled at various temperature ramp rates. Path-dependent structural recovery was quantified by studying the asymmetric approach of the suspension elastic modulus toward the target temperature during the heating and cooling temperature ramps. The loss modulus peaks, observed at the times of initiation and termination of the temperature ramps, were understood to arise from energy dissipation due to microgel rearrangement events. The heights of the peaks were found to be inversely correlated with the asymmetry in the elastic response. Our work highlights the important role of energy dissipation through microgel rearrangements in eliminating path-dependent asymmetries in the storage moduli of dense PNIPAM suspensions subjected to thermal shocks. By tuning the applied temperature ramp rate and particle packing density, therefore, asymmetric storage modulus relaxations in dense systems can be modulated via adjustments of the accessible free volume.

Figures (6)

• Figure 1: (a) Temperature-dependent average hydrodynamic diameters, $\langle d_H \rangle$, of PNIPAM particles in aqueous suspension. (b) Temperature-dependent effective volume fractions, $\phi_{eff}$(T), of a dense aqueous suspension of PNIPAM particles, prepared at $\phi_{eff} =$ 1.6 at 25$^{\circ}$C (indicated by the vertical green dashed line). The insets from left to right display schematic illustrations of self-assembled microgel particles at temperatures below, near and above the VPTT.
• Figure 2: (a) Schematic of the experimental protocol used for heating and cooling ramp experiments. (b) displays temperature profiles applied during representative heating (15$^{\circ}$C to 20$^{\circ}$C) and cooling (25$^{\circ}$C to 20$^{\circ}$C) ramp experiments at ramp rates of 1$^{\circ}$C/min and 20$^{\circ}$C/min. (c) and (d) respectively show the time-dependent responses of the storage modulus, G$^\prime$, of an aqueous PNIPAM suspension of effective volume fraction, $\phi_{eff}$ =1.6 at 25$^{\circ}$C, during heating and cooling temperature ramps applied at rates 1$^{\circ}$C/min and 20$^{\circ}$C/min. Insets in figures (c) and (d) illustrate the areas enclosed by the storage modulus-time plots (shaded in grey) during the heating and cooling ramp experiments, $A_{Heating}$ and $A_{Cooling}$, respectively. (e) and (f) respectively show the loss modulus, G$^\prime$$^\prime$, responses measured simultaneously in the heating and cooling temperature ramp experiments. T$^H_1$ and T$^H_2$ refer to the loss modulus peaks around the temperatures $T_1$ and $T_2$ during the heating experiment, while T$^C_3$ and T$^C_2$ indicate the peaks around the temperatures $T_3$ and $T_2$ during the cooling experiment. In all the experiments, the temperature gradient, $\Delta$T, was kept fixed at 5$^\circ\text{C}$.
• Figure 3: (a) Asymmetry of approach, $\Delta$A, of the storage modulus, G$^\prime$, towards $T_{2}^{\circ}$C. The data was acquired for an aqueous PNIPAM suspension of $\phi_{eff}$ =1.6 at 25$^{\circ}$C, at different heating and cooling ramp rates. (b) Asymmetry of approach of G$^\prime$ towards $T_{2}^{\circ}$C for heating and cooling experiments, applied at a fixed ramp rate of 20${^{\circ}}$C/min, in suspensions prepared at different effective volume fractions, $\phi_{eff}$, at 25$^{\circ}$C. The dashed black lines in both plots represent $\Delta$A = 1. The error bars denote standard deviations estimated from three independent measurements. The insets in (a) and (b) display raw storage moduli data for different temperature ramp rates and $\phi_{eff}$, respectively.
• Figure 4: Insets show the temporal changes in rate of change of effective volume fraction with time, $\frac{d\phi_{\textit{eff}}{(T)}}{dt}$, during heating (15$^{\circ}$C to 20$^{\circ}$C) and cooling (25$^{\circ}$C to 20$^{\circ}$C) ramps at a representative ramp rate of 1$^{\circ}$C/min. The green and blue shaded regions indicate the areas enclosed by the $\frac{d\phi_{\textit{eff}}{(T)}}{dt}$-time curves during heating and cooling processes, respectively. The main figure displays the asymmetric approach of $\frac{d\phi_{\textit{eff}}{(T)}}{dt}$, $\Delta A_{\frac{d\phi_{\textit{eff}}{(T)}}{dt}}$, towards the target temperature under heating and cooling temperature ramps, applied at rates between 1$^{\circ}$C/min and 25$^{\circ}$C/min.
• Figure 5: (a) Loss modulus, G$^{\prime\prime}$, peak heights when a PNIPAM suspension of effective volume fraction 1.6 at 25$^\circ$C was heated from 15$^\circ$C to 20$^\circ$C at different temperature ramp rates. The inset shows the raw loss modulus data during heating ramp experiments. (b) G$^{\prime\prime}$ peak heights when the suspension was cooled from 25$^\circ$C to 20$^\circ$C at the same applied ramp rates. The inset shows the corresponding raw loss modulus data. Loss modulus, G$^{\prime\prime}$, peak heights for different effective PNIPAM volume fractions (c) during heating and (d) cooling temperature ramps. Experiments in (c) and (d) were performed at a constant temperature ramp rate of 20$^\circ$C/min. The insets in (c) and (d) show raw loss modulus data during heating and cooling, respectively. T$^H_1$ and T$^H_2$ in (a) and (c) respectively represent the observed loss modulus peak heights at the blueinitiation and termination of the heating ramp, while T$^C_3$ and T$^C_2$ in (b) and (d) respectively represent the loss modulus peak heights at the initiation and termination of the cooling ramp. The error bars were calculated from three independent measurements.