Confinement-induced liquid ordering investigated by x-ray phase retrieval

Using synchrotron x-ray diffraction, we have determined the ensemble-averaged density profile of colloidal fluids within confining channels of different widths. We observe an oscillatory ordering-disordering behavior of the colloidal particles as a function of the channel width, while the colloidal solution remains in the liquid state. This phenomenon has been suggested by surface force studies of hard-sphere fluids and also theoretically predicted, but here we see it by direct measurements of the structure for comparable systems.

Figure 1

(Color online) Oscillatory ordering. Schematic of the structural force as a function of surface separation (top panel), with the corresponding arrangement of the fluid particles (center panel) and density profile (bottom panel).

Figure 2

(Color online) Experimental setup. The x-ray beam impinges under normal incidence onto the sample chip on which several different microfluidic arrays were prepared. The sample chip is covered with a glass plate to avoid evaporation. The diffracted intensity is recorded with a high-resolution microstrip detector. The inset shows a SEM image of a microfluidic array.

Figure 3

(Color online) Experimental data. Retrieved (green line) and measured (blue dots) intensities on a logarithmic scale for 100 diffraction orders of a grating with $1.25\mu \mathrm{m}$ period and $615\mathrm{nm}$ channel width.

Figure 4

(Color online) Phase profiles of charged silica colloids (left) and hard-sphere-like colloids (right) in the same microfluidic arrays. The profiles are offset vertically for clarity. The determined channel widths are shown for each profile. As we interpret oscillations as being caused by layering, i.e., increased concentration, we have highlighted these using spheres with the diameter of the colloid particles drawn to scale.

Figure 5

(Color online) Volume fraction of colloidal particles. The silica concentration inside the microfluidic channels is shown as a contour plot for several channel widths for charged silica colloids (top) and hard sphere like colloids (bottom). The excluded volume effect of 0% volume fraction directly at the confining walls as well as pronounced increases due to the confinement are clearly visible. The dark red outer region is the area of the confining silicon walls.