Abstract
Spatial confinement induces microscopic ordering of fluids, which in turn alters many of their dynamic and thermodynamic properties. However, the isothermal compressibility has hitherto been largely overlooked in the literature, despite its obvious connection to the underlying microscopic structure and density fluctuations in confined geometries. Here, we address this issue by probing density profiles and structure factors of hard-sphere fluids in various narrow slits, using x-ray scattering from colloid-filled nanofluidic containers and integral-equation-based statistical mechanics at the level of pair distributions for inhomogeneous fluids. Most importantly, we demonstrate that density fluctuations and isothermal compressibilities in confined fluids can be obtained experimentally from the long-wavelength limit of the structure factor, providing a formally exact and experimentally accessible connection between microscopic structure and macroscopic, thermodynamic properties. Our approach will thus, for example, allow direct experimental verification of theoretically predicted enhanced density fluctuations in liquids near solvophobic interfaces.
2 More- Received 11 June 2015
DOI:https://doi.org/10.1103/PhysRevX.6.011014
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Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Nanoscopic confinement of fluids—in which fluids are confined between solid surfaces at separations of a few particle diameters—induces microscopic ordering, which in turn alters many of the thermodynamic properties of fluids. However, experimental difficulties have thus far hindered studies of one of the most obvious relationships between structure and thermodynamics: the one between pair correlations (i.e., the distribution of separations between pairs of molecules or colloids) and density fluctuations or isothermal compressibility. Here, we apply a recently developed x-ray scattering technique and state-of-the-art theoretical calculations to address this relationship for confined hard-sphere fluids. We report a direct, experimentally accessible, and formally exact connection between the confined fluid’s microscopic structure and its thermodynamics, at the fundamental level of pair correlations.
Our approach consists of confining colloidal suspensions of spherical silica particles in specifically designed nanofluidic containers and using x-ray scattering for structural characterization. This methodology allows us to probe the fluid’s pair correlations in terms of an anisotropic structure factor, the long-wavelength limit of which yields the fluid’s density fluctuations and isothermal compressibility. Moreover, this approach makes it possible to formulate a quantitative comparison with statistical mechanics calculations of pair correlations in inhomogeneous fluids. Most importantly, we show that isothermal compressibilities of confined fluids can now be experimentally accessed in a quantitative manner and that the experimental data are consistent with theoretical predictions.
We expect that our findings will facilitate direct observations of theoretically predicted density fluctuations in water near extended hydrophobic interfaces, thereby addressing the long-standing question of how water meets extended hydrophobic surfaces.