Capillary Filling of Anodized Alumina Nanopore Arrays

The filling behavior of a room temperature solvent, perfluoromethylcyclohexane, in approximately 20 nm nanoporous alumina membranes was investigated in situ with small angle x-ray scattering. Adsorption in the pores was controlled reversibly by varying the chemical potential between the sample and a liquid reservoir via a thermal offset, $\Delta T$. The system exhibited a pronounced hysteretic capillary filling transition as liquid was condensed into the nanopores. These results are compared with Kelvin-Cohan theory, with a modified Derjaguin approximation, as well as with predictions by Cole and Saam.

Figure 1

(a) SEM image shows well ordered hexagonal packing of alumina nanopores. Reprinted with permission from our previously published work [4]. Copyright by the American Physical Society. (b) SEM of the fractured edge of the membrane showing the parallel packing of the nanopore channels (seen as vertical lines) normal to the membrane surface.

Figure 2

SAXS Geometry: (a) Spectrometer setup: A triple-bounce monochromator ($M$) selects Cu $K_{\alpha 1}$ radiation with high angular resolution in the horizontal plane. An identical triple-bounce analyzer crystal (A) is used after the sample, before the detector (D). (b) Alumina pores are tilted, ${\psi }_s=8.5°$, in the $y\mathrm{\text{−}}z$ plane away from the parallel condition to take advantage of the enhanced horizontal resolution. Scattered intensity is measured as a function of $2\theta$ in the $x\mathrm{\text{−}}z$ plane. (c)(1) Conformal pore filling with film thickness, $d$. (c)(2) Partially filled (metastable condition) pore with meniscus during desorption.

Figure 3

Volume fraction as a function of $\Delta T$. Adsorption (○) and desorption (●) data are shown with arrows indicating the measurement direction. The horizontal axis scale is split ($//$) in order to fit data at high $\Delta T$. A vertical line represents the Kelvin transition, $\Delta T=1.9\pm 0.2\mathrm{K}$. The solid curve is a fit of the pretransition filling within the Derjaguin approximation. Horizontal dashed lines indicate the critical and metastable volume fractions, $V_c$ and $V_m$ respectively. Inset: The $⟨10⟩$ diffraction peak for various $\Delta T$ (symbols ▪, □, ▴, ▵ correspond to $\Delta T$ of 9.9 K, 2.5 K, 2.0 K, and 1.3 K, respectively) during the absorption cycle. The arrow indicates the intensity decrease with decreasing $\Delta T$.