On the equilibrium contact angle of sessile liquid drops from molecular dynamics

We present a new methodology to estimate the contact angles of sessile drops from molec- ular simulations, by using the Gaussian convolution method of Willard and Chandler (J. Phys. Chem. B, Vol. 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) inter- face. 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 sur- face; 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 agree- ment 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 cor- responding 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 towards the spherical shape following a constant-contact-angle relaxation dynamics. Making use of this observation, our methodology allows a good es- timation of the sessile drop contact angle values even for moderate system sizes (with e.g. 4 , 000 molecules), without the need for long simulation times to reach the spherical shape