Liquids on Topologically Nanopatterned Surfaces Oleg Gang, 1,2, * ,† Kyle J. Alvine, 3 Masafumi Fukuto, 3 Peter S. Pershan, 3, * ,‡ Charles T. Black, 4 and Benjamin M. Ocko 1, * ,x 1 Department of Physics, Brookhaven National Laboratory, Upton, New York 11973, USA 2 Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA 3 DEAS, Harvard University, Cambridge, Massachusetts 02138, USA 4 IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA (Received 4 February 2005; published 16 November 2005) We report here surface x-ray scattering studies of the adsorption of simple hydrocarbon liquid films on nanostructured surfaces—silicon patterned by an array of nanocavities. Two different regimes, filling and growing, are observed for the wetting film evolution as a function of the chemical potential offset from the bulk liquid-vapor coexistence. The strong influence of geometrical effects is manifested by a dependence of liquid adsorption in the nanocavities that is stronger than the van der Waals behavior 1=3 for flat surfaces. The observed dependence is, however, much weaker than predicted for the infinitely deep parabolic cavities, suggesting that the finite-size effects contribute significantly to the observed adsorption behavior. DOI: 10.1103/PhysRevLett.95.217801 PACS numbers: 68.15.+e, 61.30.Hn, 68.03.Fg, 68.08.Bc The behavior of liquids on laterally heterogeneous sur- faces has recently attracted much theoretical attention [1– 4] due to its relevance to the basic properties of liquids that are confined to nanoscale structures [5,6]. Related phe- nomena such as the effect of nanoroughness on wetting [7] and the crossover to capillary filling [8] have impact on emerging applications, including nanofluidic devices [9], nanotemplating [10], and surface rheology [11]. For ho- mogeneous flat surfaces, the microscopic development of liquid wetting films is dictated by the details of the inter- molecular interactions [12,13]. The power-law form d / often successfully describes the dependence of film thickness d on the chemical potential offset from the bulk liquid-vapor equilibrium. For flat surfaces and van der Waals (vdW) forces the exponent 1=3 [14]. Much more complex behavior is found for random rough or self-affine surfaces [15,16], due to the contribution of the microscopic local curvature [17]. However, for well- defined surface topologies, recent theoretical studies pre- dict a power-law form dependence for liquid adsorption with 1=3. The direct correspondence between the wetting exponent and the shape of surface structures can be established theoretically for a variety of geometries [18– 21]. On the other hand, experimental constraints have limited the verification of these predictions to isolated submicron drops [22] and micron-sized surface topo- graphical features [23,24], and the majority of the pre- dicted phenomena on the nanoscale has remained untested. In this Letter we report the microscopic evolution of the wetting film of methyl-cyclohexane (MCH) on silicon surfaces patterned with nanoscale arrays of parabolically shaped cavities. We demonstrate that the nanoscale wetting behavior of thin liquid films, 1– 20 nm thick, can be studied by probing nanopatterned surfaces using x-ray reflectivity (XR) and grazing incidence diffraction (GID), both well developed quantitative techniques [25]. At small , where a liquid film completely covers the surface patterns, we observed the 1=3 dependence for the adsorption, similar to the vdW interacting film on flat surface. At larger , the adsorption behavior on patterned surface crosses over to a geometry dominated dependence with steeper FIG. 1. (a) Scanning electron microscopy (top view) of the hexagonally packed array of nanocavities. (b) GID pattern of the hexagonal surface array. (c) TEM cross section of the individual cavity. The cavity depth is 17:2 0:8 nm and the diameter at opening is 24:6 2 nm (averaged over 5 pits). (d) The cavity shape (solid line) reconstructed from the electron-density profile dry z as rz 1 h dry zi= Silicon A= q (dot-dashed line), where A 3 p =2c 2 is the hexagonal unit cell area and c 39:4 nm is the nearest neighbor distance. This curve is also shown in (c) as the dashed line. Since XR is not sensitive to the structures near the bottom of the cavity, the power-law shape discussed in the text was only fitted to rz in the range 2:3 nm < r< 12 nm. The region for r< 2:3 nm (dotted line) was inter- polated. PRL 95, 217801 (2005) PHYSICAL REVIEW LETTERS week ending 18 NOVEMBER 2005 0031-9007= 05=95(21)=217801(4)$23.00 217801-1 2005 The American Physical Society