^{1}and Jeffrey R. Errington

^{1,a)}

### Abstract

We examine several issues related to the calculation of interfacial properties via analysis of an interface potential obtained from grand canonical Monte Carlo simulation. Two model systems are examined. One includes a monatomic Lennard-Jones fluid that interacts with a structureless substrate via a long-ranged substrate potential. The second model contains a monatomic Lennard-Jones fluid that interacts with an atomistically detailed substrate via a short-ranged potential. Our results are presented within the context of locating the wetting point. Two methods are used to compute the wetting temperature. In both cases we examine the system size dependence of the key property used to deduce the wetting temperature as well as the robustness of the scaling relationship employed to describe the evolution of this property with temperature near the wetting point. In the first approach we identify the wettingtransition as the point at which the prewetting and bulk saturation curves meet. In this case, the prewetting saturation chemical potential is the key quantity of interest. In the second approach we find the point at which the spreading coefficient evaluates to zero. We find that the effect of system size is adequately described by simple scaling functions. Moreover, estimates of the wetting temperature for finite-sized systems characterized by a linear dimension greater than 12 fluid diameters differ by less than 1% from an otherwise equivalent macroscopic system. Modification of the details regarding the use of simulation data to compute the wetting temperature can also produce a shift in this quantity of up to 1%. As part of this study, we also examine techniques for describing the shape of the interface potential at a relatively high surface density. This analysis is particularly relevant for systems with long-ranged substrate potentials for which the interface potential approaches a limiting value asymptotically.

We gratefully acknowledge the financial support of the donors of the American Chemical Society Petroleum Research Fund (Grant No. 43452-AC5) and the National Science Foundation (Grant No. CBET-0828979). Computational resources were provided in part by the University at Buffalo Center for Computational Research and the Rensselaer Polytechnic Institute Computational Center for Nanotechnology Innovations.

I. INTRODUCTION

II. MODEL SYSTEMS

III. COMPUTATIONAL METHODS

A. Density probability distribution

B. Simulation details

IV. INTERFACIAL PROPERTIES

A. Prewetting route to

B. Spreading coefficient approach to

V. RESULTS AND DISCUSSION

A. Probability distributions

B. Prewetting approach

C. Spreading coefficient approach

VI. CONCLUSIONS

### Key Topics

- Wetting
- 49.0
- Probability theory
- 30.0
- Chemical potential
- 19.0
- Interfacial properties
- 19.0
- Free energy
- 15.0

## Figures

Illustration of the approach used to analyze particle number probability distributions obtained from interfacial gc simulations. Solid and dashed lines represent quantities evaluated at and near, respectively, bulk saturation conditions. The lower curves provide the natural logarithm of the particle number probability distribution and the upper curves show the difference between the probability distribution and the dimensionless surface energy. The bulk saturation version of the latter curve reaches a constant value, corresponding to the limiting value of the probability distribution, at large particle number. The inset is focused on at large . The abscissa and ordinate contain the same quantities as the main panel. The ordinate range is marked and the abscissa spans the range denoted for the main panel. The range of values highlighted within the inset corresponds to that used to extract via Eq. (9).

Illustration of the approach used to analyze particle number probability distributions obtained from interfacial gc simulations. Solid and dashed lines represent quantities evaluated at and near, respectively, bulk saturation conditions. The lower curves provide the natural logarithm of the particle number probability distribution and the upper curves show the difference between the probability distribution and the dimensionless surface energy. The bulk saturation version of the latter curve reaches a constant value, corresponding to the limiting value of the probability distribution, at large particle number. The inset is focused on at large . The abscissa and ordinate contain the same quantities as the main panel. The ordinate range is marked and the abscissa spans the range denoted for the main panel. The range of values highlighted within the inset corresponds to that used to extract via Eq. (9).

Natural logarithm of the particle number probability distribution for the homogeneous system with , , and . The curves from top to bottom are evaluated at bulk saturation conditions, cn-based prewetting saturation, and gc-based prewetting saturation.

Natural logarithm of the particle number probability distribution for the homogeneous system with , , and . The curves from top to bottom are evaluated at bulk saturation conditions, cn-based prewetting saturation, and gc-based prewetting saturation.

System size dependence of the prewetting saturated activity for the homogeneous system at . Circles and squares represent cn- and gc-based estimates.

System size dependence of the prewetting saturated activity for the homogeneous system at . Circles and squares represent cn- and gc-based estimates.

System size dependence of (top panel), (middle panel), and (bottom panel) for the homogeneous system at . Circles and squares represent cn- and gc-based estimates.

System size dependence of (top panel), (middle panel), and (bottom panel) for the homogeneous system at . Circles and squares represent cn- and gc-based estimates.

Particle number probability distributions evaluated at bulk saturation conditions for the homogeneous (top panel) and atomistic (bottom panel) systems. Curves correspond to progressively higher temperatures when moving from bottom to top, with a minimum temperature of and increments of 0.05.

Particle number probability distributions evaluated at bulk saturation conditions for the homogeneous (top panel) and atomistic (bottom panel) systems. Curves correspond to progressively higher temperatures when moving from bottom to top, with a minimum temperature of and increments of 0.05.

System size dependence of the prewetting saturated activity for the homogeneous (top panel) and atomistic (bottom panel) systems. cn (gc) estimates approach the limiting value from above (below). Circles, squares, diamonds, up triangles, left triangles, down triangles, right triangles, symbols, × symbols, and symbols correspond to temperatures of , 0.7625, 0.7750, 0.7875, 0.8000, 0.8125, 0.8250, 0.8500, 0.8750, and 0.9000, respectively. The single error bar in each plot denotes a typical uncertainty. Note that not all of the aforementioned temperatures are included in both plots.

System size dependence of the prewetting saturated activity for the homogeneous (top panel) and atomistic (bottom panel) systems. cn (gc) estimates approach the limiting value from above (below). Circles, squares, diamonds, up triangles, left triangles, down triangles, right triangles, symbols, × symbols, and symbols correspond to temperatures of , 0.7625, 0.7750, 0.7875, 0.8000, 0.8125, 0.8250, 0.8500, 0.8750, and 0.9000, respectively. The single error bar in each plot denotes a typical uncertainty. Note that not all of the aforementioned temperatures are included in both plots.

Temperature dependence of the chemical potential difference for the homogeneous (top panel) and atomistic (bottom panel) systems. Solid curves stem from linear curve fits to the data points they pass through (the three points closest to ). Broken curves represent continuations of these lines outside the range in which they were fit.

Temperature dependence of the chemical potential difference for the homogeneous (top panel) and atomistic (bottom panel) systems. Solid curves stem from linear curve fits to the data points they pass through (the three points closest to ). Broken curves represent continuations of these lines outside the range in which they were fit.

System size dependence of the spreading coefficient for the homogeneous (top panel) and atomistic (bottom panel) systems. cn (gc) estimates display relatively weak (strong) system size dependence. Circles, squares, diamonds, up triangles, left triangles, symbols, × symbols, and symbols correspond to temperatures of , 0.625, 0.650, 0.675, 0.700, 0.725, 0.750, and 0.775, respectively. The single error bar in each plot denotes a typical uncertainty.

System size dependence of the spreading coefficient for the homogeneous (top panel) and atomistic (bottom panel) systems. cn (gc) estimates display relatively weak (strong) system size dependence. Circles, squares, diamonds, up triangles, left triangles, symbols, × symbols, and symbols correspond to temperatures of , 0.625, 0.650, 0.675, 0.700, 0.725, 0.750, and 0.775, respectively. The single error bar in each plot denotes a typical uncertainty.

Temperature dependence of the spreading coefficient. Circles and squares represent the homogeneous and atomistic systems, respectively. Solid curves stem from linear curve fits to the data points they pass through. Broken curves represent continuations of these lines outside the range in which they were fit.

Temperature dependence of the spreading coefficient. Circles and squares represent the homogeneous and atomistic systems, respectively. Solid curves stem from linear curve fits to the data points they pass through. Broken curves represent continuations of these lines outside the range in which they were fit.

## Tables

Wetting temperatures.

Wetting temperatures.

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