^{1}and Jeffrey R. Errington

^{1,a)}

### Abstract

We introduce Monte Carlo simulation methods for determining interfacial properties of binary fluid mixtures. The interface potential approach, in which the interfacial properties of a system are related to the surface excess free energy of a thin fluid film in contact with a surface, is utilized to deduce the wetting characteristics of a fluid mixture. The strategy described here provides an effective means to obtain the evolution of interfacial properties with the chemical composition of the fluid. This task is accomplished by implementing an activity fraction expanded ensemble technique, which allows one to obtain elements of the interface potential as a function of composition. We also show how this technique can be utilized to calculate bulk coexistence properties of fluid mixtures in an efficient manner. The computational strategies introduced here are applied to three model systems. One includes an argon-methane fluid mixture that is known to display simple behavior in the bulk. The second fluid model contains a size asymmetric mixture that exhibits azeotropy. The third model fluid is the well-studied size symmetric mixture that displays liquid-liquid-vapor phase coexistence. The techniques outlined here are used to compile the composition dependence of spreading and drying coefficients, liquid-vapor surface tension, and contact angle for these systems. We also compare our surface tension results with values estimated from predictive-style models that provide the surface tension of a fluid mixture in terms of pure component properties. Overall, we find that the general approach pursued here provides an efficient and precise means to calculate the bulk and wetting properties of fluid mixtures.

We gratefully acknowledge the financial support of the National Science Foundation (NSF) (Grant No. CHE-1012356). Computational resources were provided in part by the University at Buffalo Center for Computational Research and the Rensselaer Polytechnic Institute Computational Center for Nanotechnology Innovation.

I. INTRODUCTION

II. SIMULATION METHODS

A. The interface potential

1. Spreading potential

2. Drying potential

B. Long-ranged potentials

C. Activity fraction expanded ensemble

D. Bulk coexistence properties

E. Predictive models for liquid-vapor surface tension of mixtures

III. MODEL SYSTEM AND SIMULATION DETAILS

IV. RESULTS AND DISCUSSION

A. Mixture I

B. Mixture II

C. Mixture III

V. CONCLUSION

### Key Topics

- Interfacial properties
- 45.0
- Wetting
- 42.0
- Surface tension
- 33.0
- Free energy
- 28.0
- Free surface
- 24.0

## Figures

Illustrative example of a spreading interface potential for a system within the partial wetting regime. The curve was generated with Mixture I at T = 1.0, η = 0.5, and εww = 1.8882. The configuration images provide representative snapshots from a GC simulation. The placement of the snapshot along the abscissa is coupled to the surface density of the system.

Illustrative example of a spreading interface potential for a system within the partial wetting regime. The curve was generated with Mixture I at T = 1.0, η = 0.5, and εww = 1.8882. The configuration images provide representative snapshots from a GC simulation. The placement of the snapshot along the abscissa is coupled to the surface density of the system.

Illustrative example of a drying interface potential for a system within the partial wetting regime. The curve was generated with Mixture I at T = 1.0, η = 0.5, and εww = 1.8882. The configuration images provide representative snapshots from a GC simulation. The placement of the snapshot along the abscissa is coupled to the surface density of the system.

Illustrative example of a drying interface potential for a system within the partial wetting regime. The curve was generated with Mixture I at T = 1.0, η = 0.5, and εww = 1.8882. The configuration images provide representative snapshots from a GC simulation. The placement of the snapshot along the abscissa is coupled to the surface density of the system.

Spreading (blue) and drying (red) interface potentials. Solid curves provide the particle number dependence of the interface potential at fixed η deduced from direct GC simulation. Dashed curves provide the activity fraction dependence of the interface potential deduced from activity fraction EE simulation. Illustrative examples for calculating the spreading coefficient s and drying coefficient d are provided. The curves were generated with Mixture I at T = 1.0 and εww = 1.8882.

Spreading (blue) and drying (red) interface potentials. Solid curves provide the particle number dependence of the interface potential at fixed η deduced from direct GC simulation. Dashed curves provide the activity fraction dependence of the interface potential deduced from activity fraction EE simulation. Illustrative examples for calculating the spreading coefficient s and drying coefficient d are provided. The curves were generated with Mixture I at T = 1.0 and εww = 1.8882.

(Top panel) Relationship between activity and activity fraction along the bulk liquid-vapor saturation line for Mixture I. Green filled circles represent data obtained from direct GC simulations. These points are used to form an initial guess for the coexistence relationship, which is represented by a dashed green line. The red and blue solid curves provide the final solution obtained for the saturation curve. (Bottom panel) The p-xy relationship of Mixture I. The curves are drawn by connecting 200 points associated with the subensembles sampled within an activity fraction expanded ensemble simulation.

(Top panel) Relationship between activity and activity fraction along the bulk liquid-vapor saturation line for Mixture I. Green filled circles represent data obtained from direct GC simulations. These points are used to form an initial guess for the coexistence relationship, which is represented by a dashed green line. The red and blue solid curves provide the final solution obtained for the saturation curve. (Bottom panel) The p-xy relationship of Mixture I. The curves are drawn by connecting 200 points associated with the subensembles sampled within an activity fraction expanded ensemble simulation.

Composition dependence of the spreading and drying coefficient for Mixture I at T = 1.0. Filled and empty symbols correspond to spreading and drying coefficient data, respectively. Red squares, blue up triangles, and green down triangles correspond to substrate strengths of εww = 2.2846, 1.8882, and 1.5294, respectively. Uncertainty estimates are provided at select compositions.

Composition dependence of the spreading and drying coefficient for Mixture I at T = 1.0. Filled and empty symbols correspond to spreading and drying coefficient data, respectively. Red squares, blue up triangles, and green down triangles correspond to substrate strengths of εww = 2.2846, 1.8882, and 1.5294, respectively. Uncertainty estimates are provided at select compositions.

Liquid-vapor surface tension as a function of liquid composition for Mixture I at T = 1.0. Filled orange circles correspond to data obtained via area expanded simulations. Red squares, blue up triangles, and green down triangles represent data obtained from the interface potential method with εww = 2.2846, 1.8882, and 1.5294, respectively (uncertainties are smaller than the symbol size). Magenta dotted-dashed and maroon dashed lines correspond to predictions from the HS and linear models, respectively.

Liquid-vapor surface tension as a function of liquid composition for Mixture I at T = 1.0. Filled orange circles correspond to data obtained via area expanded simulations. Red squares, blue up triangles, and green down triangles represent data obtained from the interface potential method with εww = 2.2846, 1.8882, and 1.5294, respectively (uncertainties are smaller than the symbol size). Magenta dotted-dashed and maroon dashed lines correspond to predictions from the HS and linear models, respectively.

Evolution of the contact angle as a function of liquid composition for Mixture I at T = 1.0. Red squares, blue up triangles, and green down triangles correspond to substrate strengths of εww = 2.2846, 1.8882, and 1.5294, respectively. Measures of the uncertainty are provided at select compositions.

Evolution of the contact angle as a function of liquid composition for Mixture I at T = 1.0. Red squares, blue up triangles, and green down triangles correspond to substrate strengths of εww = 2.2846, 1.8882, and 1.5294, respectively. Measures of the uncertainty are provided at select compositions.

(Top panel) Relationship between activity and activity fraction along the bulk liquid-vapor saturation line and (bottom panel) the p-xy diagram for Mixture II at T = 0.9. Data are labeled in the same manner as in Fig. 4 .

(Top panel) Relationship between activity and activity fraction along the bulk liquid-vapor saturation line and (bottom panel) the p-xy diagram for Mixture II at T = 0.9. Data are labeled in the same manner as in Fig. 4 .

Evolution of interfacial properties as a function of liquid composition for Mixture II with εww = 1.8882 at T = 0.9. Measures of the uncertainty are provided at select compositions.

Evolution of interfacial properties as a function of liquid composition for Mixture II with εww = 1.8882 at T = 0.9. Measures of the uncertainty are provided at select compositions.

Evolution of the contact angle as a function of liquid composition for Mixture II at T = 0.9. Red, blue, and green curves correspond to simulation results obtained with εww = 4.0, 1.8882, and 0.25, respectively. The black dashed line indicates the location of the wetting point. Measures of uncertainty are provided at select compositions.

Evolution of the contact angle as a function of liquid composition for Mixture II at T = 0.9. Red, blue, and green curves correspond to simulation results obtained with εww = 4.0, 1.8882, and 0.25, respectively. The black dashed line indicates the location of the wetting point. Measures of uncertainty are provided at select compositions.

Liquid-vapor surface tension as a function of liquid composition for Mixture II at T = 0.9. Red squares represent data obtained from the interface potential approach (measures of uncertainty are provided at select compositions). Magenta dotted-dashed and maroon dashed lines correspond to predictions from the HS and linear models, respectively.

Liquid-vapor surface tension as a function of liquid composition for Mixture II at T = 0.9. Red squares represent data obtained from the interface potential approach (measures of uncertainty are provided at select compositions). Magenta dotted-dashed and maroon dashed lines correspond to predictions from the HS and linear models, respectively.

(Top panel) Relationship between activity and activity fraction along the two bulk liquid-vapor saturation lines for Mixture III at T = 0.7. Green filled circles represent data obtained from direct GC simulation. These points are used to form an initial guess for the coexistence relationship, which is represented by a dashed green line. The red and blue solid curves provide the final solution obtained for the saturation curve. (Bottom panel) The p-xy diagram for Mixture III at T = 0.7. Dashed curves represent metastable states.

(Top panel) Relationship between activity and activity fraction along the two bulk liquid-vapor saturation lines for Mixture III at T = 0.7. Green filled circles represent data obtained from direct GC simulation. These points are used to form an initial guess for the coexistence relationship, which is represented by a dashed green line. The red and blue solid curves provide the final solution obtained for the saturation curve. (Bottom panel) The p-xy diagram for Mixture III at T = 0.7. Dashed curves represent metastable states.

Evolution of interfacial properties as a function of vapor composition for Mixture III with εww = 1.8882 at T = 0.7. Measures of uncertainty are provided at select compositions.

Evolution of interfacial properties as a function of vapor composition for Mixture III with εww = 1.8882 at T = 0.7. Measures of uncertainty are provided at select compositions.

## Tables

Binary Lennard-Jones parameters.

Binary Lennard-Jones parameters.

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