Colloidal Glass Transition Observed in Confinement

We study a colloidal suspension confined between two quasiparallel walls as a model system for glass transitions in confined geometries. The suspension is a mixture of two particle sizes to prevent wall-induced crystallization. We use confocal microscopy to directly observe the motion of colloidal particles. This motion is slower in confinement, thus producing glassy behavior in a sample which is a liquid in an unconfined geometry. For higher volume fraction samples (closer to the glass transition), the onset of confinement effects occurs at larger length scales.

Figure 1

Mean square displacements. (a) Data for sample $A$, showing motion parallel to the walls, for thicknesses $H=\mathrm{\text{bulk}}$, 16.28, 11.06, 9.41, and $6.92\mu \mathrm{m}$ (from top to bottom). The dashed line has a slope of 1 and indicates the expected motion for a very dilute bulk suspension of particles with radius $a_{\mathrm{small}}$. (b) Similar to (a) but for motion perpendicular to the walls. Data are ordered by thickness as $\Delta t\to \infty$, as in (a).

Figure 2

(a) Particle number density $n_{\mathrm{small}}(z)$ as a function of distance $z$ across the sample cell. Additional particles are stuck to the walls of the sample cell (not shown in the plot) which have centers located at $z=0.00\mu \mathrm{m}$ and $z=H=11.06\mu \mathrm{m}$. These data correspond to the middle curve in Fig. 1a, that is, a sample with moderately slowed dynamics. (b) Mean square displacement parallel to the walls ($x$) and perpendicular to the walls ($z$), as a function of $z$. The displacements are calculated using $\Delta t=100\mathrm{s}$. The vertical dotted lines indicate the positions of the peaks from (a). Data shown are from sample $A$ ($\varphi \approx 0.42$).

Figure 3

Value of $⟨\Delta x^2⟩$ at $\Delta t=100\mathrm{s}$, as a function of thickness $H$, for samples with $\varphi$ as indicated. The open circles correspond to sample $A$ with $N_{\mathrm{small}}/N_{\mathrm{large}}=3.5$, while the solid symbols correspond to samples $B–D$ with $N_{\mathrm{small}}/N_{\mathrm{large}}=3.0$. The lines are drawn to guide the eye. The plateau for each data set indicates behavior corresponding to the bulk, whereas the downturn at low $H$ gives an idea of the length scale at which confinement becomes important.