The influence of the liquid slab thickness on the ......The influence of the liquid slab thickness...
Transcript of The influence of the liquid slab thickness on the ......The influence of the liquid slab thickness...
The influence of the liquid slab thickness on the interfacial tension
Stephan Wertha b b a a, Gabor Rutkai , Jadran Vrabec , Martin Horsch , Hans Hasse
aLaboratory of Engineering Thermodynamics (LTD), University of Kaiserslautern, Germany
Thermodynamics and Energy Technology (ThET), University of Paderborn, Germanyb
One of the long standing challenges in molecular simulation is the description of interfaces. The long range interactions play an important role at interfaces. Anew long range correction for planar
interfaces is presented. On the molecular length scale, finite size effects significantly influence the properties of the interface such as ist surface tension, which can reliably be investigated by
molecular dynamics simulation of planar vapor-liquid interfaces. For the Lennard-Jones fluid, finite size effects are examined here by varying the thickness of the liquid slab. It is found that the
surface tension and density in the center of the liquid region decreases significantly for thin slabs. The influence of the slab thickness on both the liquid density and the surface tension is found to
scale with 1/S3in terms of the slab thickness S, and a linear correlation between both effects is obtained [1].
http://thermo.mv.uni-kl.de
Summary
Introduction
Acknowledgement
The authors gratefully acknowledge financial support for the project by the DFG „SFB 926 - Bauteiloberflächen: Morphologie auf der
Mikroskala“ and computational support by the Steinbuch Centre for Computing under the grant MOCOS and Regional University Computing
Center Kaiserslautern (RHRK) under the grant TUKL-MSWS. The present work was conducted under the auspices of the Boltzmann-Zuse
Society of Computational Molecular Engineering (BZS)
References
[1] S. Werth, S. Lishchuk, M. Horsch, H. Hasse, „The influence of the liquid slab thickness on the planar vapor-liquid interfacial tension“,
Physica A, 2013, 392, 2359-2367
[2] M. Buchholz, H.-J. Bungartz, J. Vrabec, „Software design for a highly parallel molecular dynamics simulation framework in chemical
engineering“, , 2, 124 - 129Journal of Computational Science, 2011
[3] J. Jane ek, „Long Range Corrections in Inhomogeneous Simulations“, , ,110, 6264 - 6269Journal of Physical Chemistry B 2006č
[4] R. Lustig, „Angle-average of the powers of the distance between two separated vectors“, Molecular Physics, 65, 174-1791988,
[5] J. Stoll, J. Vrabec, H. Hasse, „Comprehensive study of the vapour-liquid equilibria of the two-centre Lennard-Jones plue point dipole fluid“,
Fluid Phase Equilibria, 209, 29-532003,
[6] A. Malijevský, G. Jackson, „A perspective on the interfacial properties of liquid drops“ , , , 24,Journal of Physics: Condensed Matter 2012
464121
Fig. 6: Density (top) and differential pressure
(bottom) for different slab thicknesses with
. The black dashed lines denote the
equimolar slab thickness.
Fig. 7: Reduced surface tension (top) and
reduced liquid density in the center of the slab
(bottom) over the slab thickness for different
temperatures.
The long range correction plays an important role for the simulation of vapor-liquid equlibria. A
new slab based long range correction for planar interfaces and a center-of-mass cutoff radius
is presented. The simulation results of the saturated liquid density and surface tension for
anisotropic Lennard-Jones models are almost independent of the cutoff radius. The thickness
of the liquid slab has an influence on the interfacial properties for planar vapor-liquid
interfaces. The surface tension decreases with decreasing slab thickness, and so does the
density in the center of the liquid slab. The confinement effects for the surface tension and the
density are found to scale with 1/S in terms of the slab thickness, so that a linear relation3
between both effects could be obtained.
Acknowledgement and References
Laboratory of EngineeringThermodynamicsProf. Dr.-Ing. H. Hasse
Long range correction Influence of the liquid slab thickness
� Thickness of the liquid slab is reduced until
the minimum stable thickness for the given
temperature is found.
� Minimum stable thickness is increasing with
increasing temperature.
� For smaller slab thicknesses the density in
the center of the liquid slab does not reach
the bulk liquid density.
� Differential pressure does not reach the zero
line in these cases.
� Differential pressure is an indicator for a fluid
phase to be isotropic (bulk region) or
anisotropic (interface region).
Fig. 5: Snapshot of a simulation with
and a slab thickness of .
� Surface tension and density in the center of
the liquid region decrease with decreasing
slab thickness.
� Reduction of surface tension and density are
related effects.
� Reduction scales with 1/S3
� Results are in best agreement with the work
of Malijevský and Jackson [6], who found a
similar effect for droplets.
� A linear correlation between the surface
tension and liquid density reduction is found.
� A slab thickness of at least 12 is needed to
obtain reasonable values for the surface
tension; for the density even higher values
are needed.
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� Center-of-mass cutoff radius is used, which
is beneficial for the neighborhood search.
� Calculation of the surface tension via virial
route.
� A new slab based long range correction
(LRC) for planar interfaces was developed.
� LRC combines the slab based LRC by
Jane ek [3] for inhomogeneous systems withč
the angle averaging technique by Lustig [4].
� Jane ek´s approach is equivalent to theč
center-center case (CC) in Fig. 3.
� Jane ek´s approach, our new approach andč
simulations without any corrections are
compared for anisotropic two-center
Lennard-Jones fluids.
Fig. 4: Saturated liquid density (top) and surface
tension (bottom) over the cutoff radius for different
approaches, temperatures and an elongation
. The dotted lines correspond to the
reference data by Stoll et al. [5].
Fig. 3: Illustration of the three different interaction
types. Sites in the center of mass interact as a
center-center (CC) interaction, as opposed to the
center-site (CS) and site-site interaction. The dots
indicate the center of mass, while the crosses
denote the site positions.
Fig. 2: Deviation of the saturated liquid density
from the reference values by Stoll et al. [5] over
the elongation . Simulations are performed withL
a cutoff radius of and a temperature
close to the triple point.2.5cr ��
� Simulations are performed from triple point
up to 96 % of the critical temperature.
� Deviation of the saturated liquid density from
reference data simulated with Jane ek´sč
approach rises with increasing temperature
and elongation.
� Simulations without LRC exhibit a much
larger deviation than Jane ek´s approach.č
� Our new approach yields very good results
for the saturated liquid density and surface
tension and shows hardly any dependence
on the cutoff radius.
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Fig. 1: Illustration of the two-center Lennard-
Jones fluid.
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