Kinetics of anisotropic ordering in Laponite dispersions induced by a water-air interface

In this work, we report the kinetics of ordering occurring at the water-air interface of Laponite dispersions. Propagation of such ordering into the bulk and its relaxation dynamics were systematically studied through light scattering measurements. Depolarization ratio $D_p$, which accounted for the optical anisotropy, was measured as a function of depth from the interface and aging of the samples. The extent of spatial ordering was found to be several decades larger than the typical particle size. Spatial ordering originated from the interface and percolated into the bulk with aging time $t_w$. Growth in $D_p$ with waiting time was found to follow power-law behavior given as $D_p\sim t_w^n$, with $n$ increasing from 0.1 to 4 as one moved away from the interface into the bulk. $D_p$ decreased exponentially with depth $h$ given as $D_p\sim e^{-(h/h_0)}$, where $h_0$ is the decay length, increasing from 0.4 to 0.75 mm with aging time. Dynamic structure factor measurements performed on the samples at various aging times, depths, and temperatures yielded two distinct relaxation times: one fast mode followed by a slow mode. The fast mode remained invariant while slow mode relaxation time followed an exponential decay with depth. This study indicated that the arrested phase nucleated from the interface and propagated into the bulk, which was not observed when the surface was insulated with a layer of hydrophobic liquid. Dilution of the concentrated samples destroyed the aforesaid ordering and made the dispersion homogeneous implying the ordered state was a glass.

Figure 1

Schematic illustration of the setup used to study the height dependent growth of anisotropy in the system. The sample holder, micrometer screw jack, and the sample are shown in the inset.

Figure 2

Variation of depolarization ratio $D_p$ as a function of depth from water-air interface of the sample at different aging times. Panels (a) and (b) depict data for 3$\%$ and 1.5$\%$ (w/v) dispersions, respectively. The data in (a) were least-squares fitted to the exponential decay given by Eq. (3) (with χ${}^2$ $=$ 0.99), and the decay lengths are plotted as a function of waiting time shown in the inset. The arrow divides the exponential fitting and the constant values. The size of the symbol represents the error in the measurement.

Figure 3

Time dependent evolution of $D_p$ at various depths of 3$\%$ (w/v) Laponite dispersion. These data were least-squares fitted to the power-law relations given by Eq. (4). Inset shows the variation of power-law exponent with depth from interface.

Figure 4

Effect of covering the surface of the Laponite dispersion with hydrophobic solvent layers. $D_p$ is shown as function of depth at different aging times; (a) water-hexanol and (b) water-octanol interface.

Figure 5

Depolarization ratio shown as a function of depth of the sample at different temperatures as indicated against each curve. This data was least-squares fitted to the exponential relation given by Eq. (3). Inset shows the variation of $h_0$ as the function of temperature. The solid curves represent the least square fitting to Eq. (5).

Figure 6

Evolution of the dynamic structure factors, $g_1^{VV}(q,t)$ (left panel) and $g_1^{VH}(q,t)$ (right panel), at different depths at 25 °C. The arrows indicate increasing depths starting from 0.63 to 4.5 mm. Solid lines represent the fitting curve to Eq. (6).

Figure 7

Characteristic slow mode relaxation time plotted as a function of depth for polarized and depolarized components at different temperatures as indicated. The exponential decay lengths are indicated for each curve.

Figure 8

(a) The characteristic slow mode relaxation time with the depth of the sample at two different temperatures, 25 °C and 35 °C, in the depolarized mode dynamic structure factor, $g_1^{VH}(q,t)$. The exponential decay lengths are indicated for each curve. (b) Depth dependent evolution of β for polarized and depolarized modes at 25 °C.

Figure 9

Depolarization ratio plotted as the function of slow mode relaxation time determined from polarized mode dynamic structure factor, $g_1^{VV}(q,t)$ (left panel), and depolarized mode dynamic structure factor, $g_1^{VH}(q,t)$ (right panel). The power-law exponents are indicated for each curve.