Anisotropic Pair Correlations and Structure Factors of Confined Hard-Sphere Fluids: An Experimental and Theoretical Study

We address the fundamental question: how are pair correlations and structure factors of hard-sphere fluids affected by confinement between hard planar walls at close distance? For this purpose, we combine x-ray scattering from colloid-filled nanofluidic channel arrays and first-principles inhomogeneous liquid-state theory within the anisotropic Percus-Yevick approximation. The experimental and theoretical data are in remarkable agreement at the pair-correlation level, providing the first quantitative experimental verification of the theoretically predicted confinement-induced anisotropy of the pair-correlation functions for the fluid. The description of confined fluids at this level provides, in the general case, important insights into the mechanisms of particle-particle interactions in dense fluids under confinement.

Figure 1

Experimental (solid lines) and theoretical (dashed lines) local volume fractions $C(z)$ across the confining channel. The channel widths are, from top to bottom, $w\approx 2.45\sigma$, $2.65\sigma$, $2.90\sigma$, and $3.10\sigma$, and the profiles are vertically offset by multiples of 0.5 for clarity. The nearly vertical lines in the experimental data depict the confining walls.

Figure 2

Experimental (top) and theoretical (bottom) anisotropic structure factors $S(q_{\perp },q_{\parallel })$. The channel widths are, from left to right, $w\approx 2.45\sigma$, $2.65\sigma$, $2.90\sigma$, and $3.10\sigma$. The feature at $q_{\parallel }=0$ in the experimental data is diffraction from the fluid-filled nanofluidic channel array, which was used to obtain the density profiles shown in Fig. 1.