Höfling, F. and Dietrich, S. (2020) Finitesize corrections for the static structure factor of a liquid slab with open boundaries. Journal of Chemical Physics, 153 (5). pp. 113.

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Official URL: https://doi.org/10.1063/5.0017923
Abstract
The presence of a confining boundary can modify the local structure of a liquid markedly. In addition, small samples of finite size are known to exhibit systematic deviations of thermodynamic quantities relative to their bulk values. Here, we consider the static structure factor of a liquid sample in slab geometry with open boundaries at the surfaces, which can be thought of as virtually cutting out the sample from a macroscopically large, homogeneous fluid. This situation is a relevant limit for the interpretation of grazingincidence diffraction experiments at liquid interfaces and films. We derive an exact, closed expression for the slab structure factor, with the bulk structure factor as the only input. This shows that such free boundary conditions cause significant differences between the two structure factors, in particular at small wavenumbers. An asymptotic analysis of this result yields the scaling exponent and an accurate, useful approximation of these finitesize corrections. Furthermore, the open boundaries permit the interpretation of the slab as an open system, supporting particle exchange with a reservoir. We relate the slab structure factor to the particle number fluctuations and discuss conditions under which the subvolume of the slab represents a grand canonical ensemble with chemical potential � and temperature T. Thus, the open slab serves as a testbed for the smallsystem thermodynamics in a �T reservoir. We provide a microscopically justified and exact result for the size dependence of the isothermal compressibility. Our findings are corroborated by simulation data for LennardJones liquids at two representative temperatures.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  2445 
Deposited By:  Monika Drueck 
Deposited On:  07 Aug 2020 09:51 
Last Modified:  07 Aug 2020 09:51 
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