  The study of wetting phenomena is of great interest due to the multifaceted
technological applications of hydrophobic and hydrophilic surfaces. The
theoretical approaches proposed by Wenzel and later by Cassie and Baxter to
describe the behaviour of a droplet of water on a rough solid were extensively
used and improved to characterize the apparent contact angle of a droplet.
However, the equilibrium hypothesis implied in these models means that they are
not always predictive of experimental contact angles due to strong
metastabilities typically occurring on heterogeneous surfaces. A predictive
scheme for contact angle is thus urgently needed both to characterise a surface
by contact angle measurements and to design superhydrophobic and oleophobic
surfaces with the desired properties, e.g., contact angle hysteresis. In this
work a combination of Monte Carlo simulation and the string method is employed
to calculate the free energy profile of a liquid droplet deposited on a
pillared surface. For the analyzed surfaces, we show that there is only one
minimum of the free energy that corresponds to the superhydrophobic wetting
state while the wet state can present multiple minima. Furthermore, when the
surface roughness decreases the amount of local minima observed in the free
energy profile increases.
