How a Liquid Becomes a Glass Both on Cooling and on Heating

The onset of structural arrest and glass formation in a concentrated suspension of silica nanoparticles in a water-lutidine binary mixture near its consolute point is studied by exploiting the near-critical fluid degrees of freedom to control the strength of an attraction between particles and multispeckle x-ray photon correlation spectroscopy to determine the particles’ collective dynamics. This model system undergoes a glass transition both on cooling and on heating, and the intermediate liquid realizes unusual logarithmic relaxations. How vitrification occurs for the two different glass transitions is characterized in detail and comparisons are drawn to recent theoretical predictions for glass formation in systems with attractive interactions.

Figure 1

(a) False-color image of the SAXS pattern from concentrated silica spheres in WL, obtained at beam line 8-ID at the Advanced Photon Source (APS) in run A with a 0.15 s exposure. (b) Average SAXS intensity vs wave vector obtained for several temperatures on warming (run A). The lines are the best fits to the model described in the text.

Figure 2

(a) Best-fit values of $u$ for run A (diamonds), B (triangles), and C (circles). The different colors indicate the different phases realized: red corresponds to a RG, blue to a liquid, and green to an AG. The fitted value of $u$ appears constant in the attractive glass, suggesting that no structural evolution occurs in this phase. (b) Phase diagram in the $u-\varphi$ plane. Diamonds, triangles, and circles correspond to data points from runs A, B, and C, respectively. Red, green, and blue symbols correspond to RG, AG, and liquid phases, respectively. Solid lines are schematic phase boundaries, inspired by Refs. 5, 6, 7, 8, with the black circle corresponding to the MCT $A_3$ singularity. The dashed line separates the region of logarithmic relaxations above the line, from the region of stretched exponential relaxations below. Although our particles are subject to gravitational settlement, the volume fraction across the height of the x-ray beam ($20\mu \mathrm{m}$) was approximately constant to within 1%. Usually, the volume fraction also remained constant in time. In run B, however, the volume fraction varied as a result of slow settlement.

Figure 3

$g_1$ versus delay time during run C. For clarity, (a) corresponds to temperatures from $33.000°\mathrm{C}$ to $33.375°\mathrm{C}$ and (b) from $33.390°\mathrm{C}$ to $33.600°\mathrm{C}$. Points are data. Lines correspond to the models discussed in the text.

Figure 4

(a) $f$, (b) $t_0$, and (c) $S$ vs. temperature for run B at $QR=2.28$ (cyan squares), 2.86 (blue diamonds) and 3.70 (orange triangles), and for run C at $QR=1.13$ (red circles), 2.34 (magenta squares), and 2.82 (green diamonds). The solid lines are guides to the eye.