Glass transition of soft colloids

We explore the glassy dynamics of soft colloids using microgels and charged particles interacting by steric and screened Coulomb interactions, respectively. In the supercooled regime, the structural relaxation time ${\tau }_{\alpha }$ of both systems grows steeply with volume fraction, reminiscent of the behavior of colloidal hard spheres. Computer simulations confirm that the growth of ${\tau }_{\alpha }$ on approaching the glass transition is independent of particle softness. By contrast, softness becomes relevant at very large packing fractions when the system falls out of equilibrium. In this nonequilibrium regime, ${\tau }_{\alpha }$ depends surprisingly weakly on packing fraction, and time correlation functions exhibit a compressed exponential decay consistent with stress-driven relaxation. The transition to this novel regime coincides with the onset of an anomalous decrease in local order with increasing density typical of ultrasoft systems. We propose that these peculiar dynamics results from the combination of the nonequilibrium aging dynamics expected in the glassy state and the tendency of colloids interacting through soft potentials to refluidize at high packing fractions.

Figure 1

(a) Representative flow curves of PNiPAM suspensions with stars, squares, and circles respectively, corresponding to regimes I, II, and III described in the text. The lines are Herschel-Bulkley fits. (b) Representative correlation functions of PNiPAM suspensions with symbols chosen as in (a).

Figure 2

(a) and (b) Volume fraction dependence of the relaxation time (scaled by its dilute limit ${\tau }_0$), (c) and (d) the stretching exponent of the scattering function, and (e) and (f) the height of the first peak of the structure factor. The left column is data for PNiPAM, and the right column is data for Ludox. The dashed lines in (a)–(f) are guides to the eye, and the vertical lines indicate the approximate boundaries between the different dynamical regimes.

Figure 3

Rescaled relaxation time versus volume fraction rescaled by the operational glass transition ${\phi }_g$. The solid symbols are experiments on soft particles (PNiPAM and Ludox) and polymethylmethacrylate (PMMA) hard spheres (data taken from Ref. [8]). The open symbols: simulations of harmonic spheres whose adimensional softness $\tilde{\epsilon }$ is varied from the hard to the ultrasoft limit. The line is a fit to data in regime II according to ${\tau }_{\alpha }\sim exp[A/({\phi }_0-\phi )]$ with ${\phi }_0=(1.04\pm 0.05){\phi }_g$.

Figure 4

(a) Temporal fluctuations of the dynamics at a fixed time lag $\tau \approx {\tau }_{\alpha }$ for a PNiPAM sample with $\phi =0.851$ (data are offset vertically for clarity). The two curves are measured simultaneously in two independent sample chambers in the setup sketched in panel (b) and display uncorrelated fluctuations. (c) Maximum of the dynamical susceptibility $\chi \left({\tau }_{\alpha }\right)$ as a function of $\phi$ for the PNiPAM samples. (d) Age dependence of the dynamics for representative PNiPAM samples. From bottom to top, $\phi =0.743$, 0.818, 0.835, 1.012, 1.091, and 0.906. The line shows ${\tau }_{\alpha }=t_w$: In all cases, we access the ${\tau }_{\alpha }<t_w$ regime where the structural relaxation and aging timescales are well separated.