Reduction in the surface energy of liquid interfaces at short length scales

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 model 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.

[1]  Surface structure of liquid metals and the effect of capillary waves: X-ray studies on liquid indium , 2004, cond-mat/0406582.

[2]  Huang,et al.  X-ray-scattering study of capillary-wave fluctuations at a liquid surface. , 1991, Physical review letters.

[3]  J. Benattar,et al.  Structural properties and elasticity of amphiphilics on water , 1991 .

[4]  Kayser Effect of capillary waves on surface tension. , 1986, Physical review. A, General physics.

[5]  J. Weeks Structure and thermodynamics of the liquid–vapor interface , 1977 .

[6]  Seungju M. Yu,et al.  X-Ray Measurements of Noncapillary Spatial Fluctuations from a Liquid Surface , 1998 .

[7]  K. Mecke,et al.  Effective Hamiltonian for liquid-vapor interfaces. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  Michael E. Fisher,et al.  Finite-size effects in fluid interfaces , 1990 .

[9]  B. Widom,et al.  Structure and Free Energy of the Interface between Fluid Phases in Equilibrium near the Critical Point , 1969 .

[10]  R. Tolman The Effect of Droplet Size on Surface Tension , 1949 .

[11]  J. Waals The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density , 1979 .

[12]  F. Stillinger,et al.  Interfacial Density Profile for Fluids in the Critical Region , 1965 .

[13]  J. Daillant,et al.  Surface scattering of x rays in thin films. Part I. Theoretical treatment , 1992 .

[14]  John S. Rowlinson,et al.  Molecular Theory of Capillarity , 1983 .

[15]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[16]  Sengers,et al.  Capillary waves of a vapor-liquid interface near the critical temperature. , 1989, Physical review. A, General physics.

[17]  Sirota,et al.  X-ray and neutron scattering from rough surfaces. , 1988, Physical review. B, Condensed matter.

[18]  J. Stecki Extended capillary wave theory and the ellipsometric coefficient , 1998 .

[19]  A. A. Maradudin,et al.  Modern Problems in Condensed Matter Sciences , 1991 .

[20]  Deutsch,et al.  Surface roughness of water measured by x-ray refelctivity. , 1985, Physical review letters.

[21]  S. Rice Surface structure: X-ray reflection from liquids , 1985, Nature.

[22]  M. Napiórkowski,et al.  Structure of the effective Hamiltonian for liquid-vapor interfaces , 1993 .

[23]  E. M. Blokhuis,et al.  Mean field curvature corrections to the surface tension , 1998 .

[24]  J. Meunier Liquid interfaces : role of the fluctuations and analysis of ellipsometry and reflectivity measurements , 1987 .

[25]  G. Grübel,et al.  BENDING ENERGY OF AMPHIPHILIC FILMS AT THE NANOMETER SCALE , 1997 .

[26]  S. Dietrich,et al.  Scattering of X-rays and neutrons at interfaces , 1995 .