Abstract
We present a new methodology to estimate the contact angles of sessile drops from molecular simulations by using the Gaussian convolution method of Willard and Chandler [J. Phys. Chem. B 114, 1954-1958 (2010)] to calculate the coarse-grained density from atomic coordinates. The iso-density contour with average coarse-grained density value equal to half of the bulk liquid density is identified as the average liquid-vapor (LV) interface. Angles between the unit normal vectors to the average LV interface and unit normal vector to the solid surface, as a function of the distance normal to the solid surface, are calculated. The cosines of these angles are extrapolated to the three-phase contact line to estimate the sessile drop contact angle. The proposed methodology, which is relatively easy to implement, is systematically applied to three systems: (i) a Lennard-Jones (LJ) drop on a featureless LJ 9-3 surface; (ii) an SPC/E water drop on a featureless LJ 9-3 surface; and (iii) an SPC/E water drop on a graphite surface. The sessile drop contact angles estimated with our methodology for the first two systems are shown to be in good agreement with the angles predicted from Young's equation. The interfacial tensions required for this equation are computed by employing the test-area perturbation method for the corresponding planar interfaces. Our findings suggest that the widely adopted spherical-cap approximation should be used with caution, as it could take a long time for a sessile drop to relax to a spherical shape, of the order of 100 ns, especially for water molecules initiated in a lattice configuration on a solid surface. But even though a water drop can take a long time to reach the spherical shape, we find that the contact angle is well established much faster and the drop evolves toward the spherical shape following a constant-contact-angle relaxation dynamics. Making use of this observation, our methodology allows a good estimation of the sessile drop contact angle values even for moderate system sizes (with, e.g., 4000 molecules), without the need for long simulation times to reach the spherical shape.
Highlights
The contact angle, the angle between a two-fluid interface and a solid substrate, is crucial in the characterization and quantification of the wetting properties and wettability characteristics of fluid-solid systems.1–4 It is the result of the balance between the interfacial tensions of the different phases involved and is expressed by Young’s equation.5 When one of the two fluids is liquid and the other is its own vapor, Young’s equation is written as cos θY =γsv − γlv γsl (1)Two popular approaches to obtain the contact angles from molecular dynamics (MD) simulations have been followed over the years
Our study reveals that water sessile nanodrops can take a long simulation time to equilibrate to a spherical shape, of the order of 100 ns starting from a lattice configuration
We find that the contact angle relaxes much faster than the typical time scale required for a sessile drop to adopt the spherical shape
Summary
The contact angle, the angle between a two-fluid interface and a solid substrate, is crucial in the characterization and quantification of the wetting properties and wettability characteristics of fluid-solid systems. It is the result of the balance between the interfacial tensions of the different phases involved and is expressed by Young’s equation. When one of the two fluids is liquid and the other is its own vapor, Young’s equation is written as cos θY =γsv − γlv γsl (1)Two popular approaches to obtain the contact angles from molecular dynamics (MD) simulations have been followed over the years. The contact angle, the angle between a two-fluid interface and a solid substrate, is crucial in the characterization and quantification of the wetting properties and wettability characteristics of fluid-solid systems.. The contact angle, the angle between a two-fluid interface and a solid substrate, is crucial in the characterization and quantification of the wetting properties and wettability characteristics of fluid-solid systems.1–4 It is the result of the balance between the interfacial tensions of the different phases involved and is expressed by Young’s equation.. The contact angle is calculated by applying Young’s relation [Eq (1)] with the interfacial tension values obtained by simulating the corresponding planar interfaces. Studies followed the mechanical route involving the calculation of the components of the pressure tensor to compute the required interfacial tension values (which in turn are used in the calculation of the contact angle from Young’s relation). In addition to the mechanical route, there have been a number of new techniques proposed to calculate interfacial tensions, such as the test-area perturbation
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