We examine two free-energy-based methods for studying the wetting properties of a fluid in contact with a solid substrate. Application of the first approach involves examination of the adsorption behavior of a fluid at a single substrate, while the second technique requires investigation of the properties of a system confined between two parallel substrates. Both of the techniques rely upon computation and analysis of the density dependence of a system's surface free energy and provide the contact angle and solid-vapor and solid-liquid interfacial tensions for substrate-fluid combinations within the partial wetting regime. Grand canonical transition matrix Monte Carlo simulation is used to obtain the required free-energy curves. The methods examined within this work are general and are applicable to a wide range of molecular systems. We probe the performance of the methods by computing the interfacial properties for two systems in which an atomistic fluid interacts with a fcc crystal. For both of the systems studied we find good agreement between our results and those obtained via the mechanical definition of the interfacial tension.

We examine the extent to which nanoscale geometric substrate roughness influences the contact angle droplets establish on solid surfaces. Free-energy-based Monte Carlo simulation methods are used to compute contact angles and interfacial tensions of a model Lennard-Jones fluid on substrates with regular one-dimensional heterogeneities characterized by amplitudes and periodicities in the 2-25 nm range. We focus on a relatively strong surface that facilitates the formation of Wenzel droplets. Our results enable us to probe the validity of Wenzel's model at these length scales. We find that the aforementioned model predicts the evolution of the contact angle with near-quantitative accuracy over a wide range of amplitudes for substrates with periodicities larger than approximately 20 fluid diameters, or 10 nm for an argon-like system. However, below this length scale the Wenzel model provides progressively poorer estimates of the contact angle as the periodicity of the substrate features decreases. At these relatively small length scales, the Wenzel model overestimates the influence of roughness. To complete our analysis, we introduce a means to overcome sampling difficulties that arise at intermediate densities during grand canonical simulation. Specifically, we describe a two-step process that enables us to access the free energy of a system containing a thick liquid film in contact with the substrate. The process involves high-temperature grand canonical simulation followed by temperature-expanded ensemble simulation at relatively high surface density.

We study anisotropic wetting in systems governed by Lennard-Jones interactions. Molecular simulation is used to obtain the macroscopic contact angle a fluid adopts on face-centered-, body-centered-, and simple-cubic lattices with the (100), (110), or (111) face in contact with the fluid. Several amorphous substrates are also examined. Substrates are modeled as a static collection of particles. For a given set of calculations, the atomistic density of the substrate and the particle-particle interactions (surface-fluid and fluid-fluid) remain fixed. These constraints enable us to focus on the extent to which substrate structure influences the contact angle. Three substrate-fluid interaction strengths are considered, which provide wetting conditions that span from near-dry to near-wet. Our results indicate that the manner in which particles are organized within the substrate significantly influences the contact angle. For strong substrates (near-wet case), a change in the substrate structure can change the cosine of the contact angle by as much as 0.5. We also examine how well certain structural and energetic features of the substrate-fluid system serve as suitable metrics for predicting the variation of the contact angle with substrate topography. Three parameters are considered: the density of atoms within the crystalline plane closest to the fluid, a measure of the effective strength of the substrate-fluid interaction, and the roughness of the solid-liquid interface. The effective strength of the substrate potential shows the strongest correlation with the contact angle. This energy-based parameter is defined in a general manner and therefore could serve as a useful tool for describing the anisotropic wetting of solids. In contrast, the metrics based on planar density and interface roughness are found to correlate with contact angle data relatively weakly.

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 wetting transition 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.

Molecular simulation of clathrate hydrate has provided significant advancements in our understanding of hydrate properties and formation. In this work, we report the application of Voronoi tessellation to characterize the structuring of water and guest molecules forming hydrates. Tessellation of perfect sI and sII hydrate reveals positions of Voronoi vertices similar to the oxygen atoms of enclathrating water molecules. Applying tessellation to a simulation trajectory of hydrate formation, and using a further selection criteria based on polyhedra volume and coordination number, we identify numbers and types of cagelike polyhedra. Voronoi analysis of this type results in similar numbers of identified cages but with differing topologies. However, once nearest neighbor methanes are also enclathrated, the topologies of the Voronoi polyhedra approach that of the actual water cages. Since only methane coordinates are required, Voronoi tessellation is a fast and simple tool that can be used as an order parameter to identify the structuring of molecules when studying hydrates in simulations.