We have measured the contact angle of microsized and nanosized alkane droplets partially wetting a model substrate using true noncontact atomic force microscopy. The large range of droplet sizes accessible using this technique allowed us to determine the contact line curvature dependence of the contact angle with unprecedented accuracy. Whereas previous studies aimed at explaining such a dependence by a line tension effect, our results and calculations on a model system exclude such an effect and point to an extreme sensitivity to weak substrate heterogeneities confirmed by numerical simulations.

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Liquid-vapour interfaces, particularly those involving water, are common in both natural and artificial environments. They were first described as regions of continuous variation of density, caused by density fluctuations within the bulk phases. In contrast, the more recent capillary-wave models assumes a step-like local density profile across the liquid-vapour interface, whose width is the result of the propagation of thermally excited capillary waves. The model has been validated for length scales of tenths of micrometres and larger, but the structure of liquid surfaces on submicrometre length scales--where the capillary theory is expected to break down--remains poorly understood. Here we report grazing-incidence X-ray scattering experiments that allow for a complete determination of the free surface structure and surface energy for water and a range of organic liquids. We observe a large decrease of up to 75% in the surface energy of submicrometre waves that cannot be explained by capillary theory, but is in accord with the effects arising from the non-locality of attractive intermolecule interactions as predicted by a recent density functional theory. Our data, and the results of comparable measurements on liquid solutions, metallic alloys, surfactants, lipids and wetting films should thus provide a stringent test for any new theories that attempt to describe the structure of liquid interfaces with nanometre-scale resolution.

A single lipid molecular bilayer of 17 or 18 carbon chain phosphocholines, floating in water near a flat wall, is prepared in the bilayer gel phase and then heated to the fluid phase. Its structure (electron density profile) and height fluctuations are determined by using x-ray reflectivity and nonspecular scattering. By fitting the offspecular signal to that calculated for a two-dimensional membrane using a Helfrich Hamiltonian, we determine the three main physical quantities that govern the bilayer height fluctuations: The wall attraction potential is unexpectedly low; the surface tension, roughly independent on chain length and temperature, is moderate (Ϸ5 ؋ 10 ؊4 J⅐m ؊2 ) but large enough to dominate the intermediate range of the fluctuation spectrum; and the bending modulus abruptly decreases by an order-of-magnitude from 10 ؊18 J to 10 ؊19 J at the bilayer gel-to-fluid transition. L ipid bilayers (1, 2) have been often studied as models of two-dimensional soft systems (3). They are increasingly used as controlled idealized models of cell membranes for biophysical studies of membrane-membrane and membrane-protein interactions (1, 4). Lipid bilayers can be characterized by their static structure and dynamic, equilibrium thermal fluctuations. Structural measurements yield information on the variation of chemical composition (using neutrons) or electron density (using x-rays) along the z axis normal to the bilayer plane (for a review, see ref. 5). Thermal fluctuations of the bilayer plane are classically described (6) within the harmonic approximation originally proposed by Helfrich (3) with three physical quantities: (i) The intrinsic bilayer bending modulus stabilizes fluctuations with short in-plane (x, y) wavelengths; (ii) the surface tension ␥, if strong enough, dominates the intermediate scales; and (iii) an external potential per unit surface, U, due, for instance, to the attraction by a nearby surface or neighboring bilayers, stabilizes (through its second derivative UЉ ϭ d 2 U͞dz 2 ) large in-plane wavelength fluctuation modes. The cross-over between these regimes is usually [with few exceptions (7)] at submicronic scales and more accessible to x-ray off-specular surface scattering than to optical microscopy measurements.A considerable effort has been devoted to the measurement of the bending rigidity , which controls both the physical properties (bilayer fluctuations and vesicle shape) and biophysical properties (adhesion, invagination, and membrane-protein interactions) of the bilayers (2,4,8). Experiments have been based on indirect effects (9, 10) or on the direct determination (7) of the fluctuation spectrum, usually on vesicles (7, 11) or on multilayer stacks (5, 12). They have yielded results mostly in the fluid phase (7, 9, 11, 13-16) but also in the gel phase (17) and, more recently, as a function of temperature across the melting transition (10,18,19).We report an experimental determination of the structure and fluctuations of a lipid bilayer, in a planar configuration (in the vicinity of an...

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We have investigated the small-scale structure of the liquid-vapor interface using synchrotron x-ray scattering for liquids with different molecular structures and interactions. The effective momentum-dependent surface energy first decreases from its macroscopic value due to the effect of long-range forces, and then increases with increasing wave vector. The results are analyzed using a recent density functional theory. The large wave-vector increase is attributed to a bending energy for which local and nonlocal contributions are equally important.

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