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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� Molecular dynamics simulations of vapor-

liquid equilibria with [2].ls1

� 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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