^{1,2,a)}and Bruno Mendiboure

^{3,b)}

### Abstract

We extend the well-known Test-Area methodology of Gloor et al. [J. Chem. Phys.123, 134703 (Year: 2005)]10.1063/1.2038827, originally proposed to evaluate the surface tension of planar fluid-fluid interfaces along a computer simulation in the canonical ensemble, to deal with the solid-fluid interfacial tension of systems adsorbed on cylindrical pores. The common method used to evaluate the solid-fluid interfacial tension invokes the mechanical relation in terms of the tangential and normal components of the pressure tensor relative to the interface. Unfortunately, this procedure is difficult to implement in the case of cylindrical geometry, and particularly complex in case of nonspherical molecules. Following the original work of Gloor *et al.*, we perform free-energy perturbations due to virtual changes in the solid-fluid surface. In this particular case, the radius and length of the cylindrical pore are varied to ensure constant-volume virtual changes of the solid-fluid surface area along the simulation. We apply the modified methodology for determining the interfacial tension of a system of spherical Lennard-Jones molecules adsorbed inside cylindrical pores that interact with fluid molecules through the generalized 10-4-3 Steele potential recently proposed by Siderius and Gelb [J. Chem. Phys.135, 084703 (Year: 2011)]10.1063/1.3626804. We analyze the effect of pore diameter, density of adsorbed molecules, and fluid-fluid cutoff distance of the Lennard-Jones intermolecular potential on the solid-fluid interfacial tension. This extension, as the original Test-Area formulation, offers clear advantages over the classical mechanical route of computational efficiency, easy of implementation, and generality.

The authors would like to acknowledge helpful discussions with A. I. Moreno-Ventas Bravo, M. M. Piñeiro, and J. M. Míguez. This work was supported by Acción Integrada España-Francia from Ministerio de Ciencia e Innovación and Picasso Project (Project Nos. FR2009-0056 and PHC PICASSO2010). Further financial support from Proyecto de Excelencia from Junta de Andalucía (Project No. P07-FQM02884), Ministerio de Ciencia e Innovación (Project No. FIS2010-14866), and Universidad de Huelva are also acknowledged.

I. INTRODUCTION

II. TEST-AREA METHODOLOGY FOR CYLINDRICAL GEOMETRY

III. MODELS AND SIMULATION DETAILS

IV. RESULTS

V. CONCLUSIONS

### Key Topics

- Surface tension
- 21.0
- Liquid liquid interfaces
- 19.0
- Computer simulation
- 14.0
- Tensor methods
- 13.0
- Intermolecular potentials
- 12.0

## Figures

Density profiles of LJ molecules adsorbed on cylindrical pores with pore radius (a) *R** = 7.5 and (b) *R** = 5.0 at *T** = 2.0 obtained from MC *NVT* simulations. The curves correspond to total densities inside the cylindrical pore of ρ* = 0.1886 (continuous line), 0.2829 (dotted line), 0.3215 (dashed line), 0.3773 (dotted-dashed line), and 0.6431 (dotted-dotted-dashed line).

Density profiles of LJ molecules adsorbed on cylindrical pores with pore radius (a) *R** = 7.5 and (b) *R** = 5.0 at *T** = 2.0 obtained from MC *NVT* simulations. The curves correspond to total densities inside the cylindrical pore of ρ* = 0.1886 (continuous line), 0.2829 (dotted line), 0.3215 (dashed line), 0.3773 (dotted-dashed line), and 0.6431 (dotted-dotted-dashed line).

Interfacial tension for the SF interface in a system of *N* = 500 LJ molecules adsorbed on a cylindrical pore of radius *R** = 7.5 as obtained from surface area perturbations in MC *NVT* simulations with fluid-fluid interaction cutoff distance at . The reduced temperature is *T** = 2.0 and density inside the cylindrical pore is (a) ρ* = 0.1886, (b) ρ* = 0.2829, (c) ρ* = 0.3215, and (d) ρ* = 0.3773. Data are shown for different values of the relative surface area of the perturbation. The circles correspond to the results obtained from perturbations with ξ > 0 (increasing-area, γ^{+}*), the squares to the data for perturbations with ξ < 0 (decreasing-area, γ^{−}*), and the diamonds to the data from combined increasing/decreasing surface area (central difference scheme given by Eq. (11) , γ*). The error bars are larger than the vertical scale of figure and are not shown for clarity.

Interfacial tension for the SF interface in a system of *N* = 500 LJ molecules adsorbed on a cylindrical pore of radius *R** = 7.5 as obtained from surface area perturbations in MC *NVT* simulations with fluid-fluid interaction cutoff distance at . The reduced temperature is *T** = 2.0 and density inside the cylindrical pore is (a) ρ* = 0.1886, (b) ρ* = 0.2829, (c) ρ* = 0.3215, and (d) ρ* = 0.3773. Data are shown for different values of the relative surface area of the perturbation. The circles correspond to the results obtained from perturbations with ξ > 0 (increasing-area, γ^{+}*), the squares to the data for perturbations with ξ < 0 (decreasing-area, γ^{−}*), and the diamonds to the data from combined increasing/decreasing surface area (central difference scheme given by Eq. (11) , γ*). The error bars are larger than the vertical scale of figure and are not shown for clarity.

Interfacial tension for the SF interface in a system of *N* = 500 LJ molecules adsorbed on a cylindrical pore of radius *R** = 7.5 as obtained from surface area perturbations in MC *NVT* simulations with fluid-fluid interaction cutoff distance at . The reduced temperature is *T** = 2.0 and density inside the cylindrical pore is (a) ρ* = 0.1886, (b) ρ* = 0.2829, (c) ρ* = 0.3215, and (d) ρ* = 0.3773. The meaning of data is the same as in Fig. 2 .

Interfacial tension for the SF interface in a system of *N* = 500 LJ molecules adsorbed on a cylindrical pore of radius *R** = 7.5 as obtained from surface area perturbations in MC *NVT* simulations with fluid-fluid interaction cutoff distance at . The reduced temperature is *T** = 2.0 and density inside the cylindrical pore is (a) ρ* = 0.1886, (b) ρ* = 0.2829, (c) ρ* = 0.3215, and (d) ρ* = 0.3773. The meaning of data is the same as in Fig. 2 .

Interfacial tension for the SF interface in a system of *N* = 500 LJ molecules adsorbed on a cylindrical pore of radius *R** = 5.0 as obtained from surface area perturbations in MC *NVT* simulations at reduced temperature *T** = 2.0 and different densities and fluid-fluid interaction cutoff distances: (a) ρ* = 0.3778 and , (b) ρ* = 0.3778 and , (c) ρ* = 0.6366 and , and (d) ρ* = 0.6366 and . The meaning of data is the same as in Fig. 2 .

Interfacial tension for the SF interface in a system of *N* = 500 LJ molecules adsorbed on a cylindrical pore of radius *R** = 5.0 as obtained from surface area perturbations in MC *NVT* simulations at reduced temperature *T** = 2.0 and different densities and fluid-fluid interaction cutoff distances: (a) ρ* = 0.3778 and , (b) ρ* = 0.3778 and , (c) ρ* = 0.6366 and , and (d) ρ* = 0.6366 and . The meaning of data is the same as in Fig. 2 .

## Tables

Interfacial tension for the SF interface in systems of LJ molecules with fluid-fluid cutoff distance of (a) and (b) adsorbed on cylindrical pores with two different radii as obtained by a linear extrapolation to |ξ| → 0 of the values obtained from increasing-area (γ^{+}*) and decreasing-area (γ^{−}*) perturbations, and a combined increasing-decreasing (γ*) perturbation given by Eq. (11) in MC *NVT* simulations at reduced temperature *T** = 2.0, and different reduced densities and system sizes.

Interfacial tension for the SF interface in systems of LJ molecules with fluid-fluid cutoff distance of (a) and (b) adsorbed on cylindrical pores with two different radii as obtained by a linear extrapolation to |ξ| → 0 of the values obtained from increasing-area (γ^{+}*) and decreasing-area (γ^{−}*) perturbations, and a combined increasing-decreasing (γ*) perturbation given by Eq. (11) in MC *NVT* simulations at reduced temperature *T** = 2.0, and different reduced densities and system sizes.

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