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.