Simple expression for the dependence of the nanodrop contact angle on liquid-solid interactions and temperature

The density distributions and contact angles of nanodrops on smooth solid surfaces are calculated on the basis of a nonlocal density functional theory in wide ranges of temperature and parameters of the Lennard-Jones potentials representing the fluid-fluid and fluid-solid interactions. A simple linear dependence of the contact angle on the fluid-solid energy parameter epsilon(fs) was found for various temperatures, hard core fluid-solid parameters sigma(fs), and average fluid density of the system. A simple expression is suggested which represents all the above results in a unified form that relates the contact angle theta to the parameters of the interaction potentials and temperature. The most intriguing feature was that for each considered sigma(fs) there is a value epsilon(fs) (0) of epsilon(fs) for which the contact angle theta=theta(0) can be considered independent of temperature and of sigma(fs). It is shown that epsilon(fs)=epsilon(fs) (0) divides the materials for which theta increases from those for which theta decreases with increasing temperature. The results obtained for the dependence of the contact angle on the parameters of the model are in qualitative agreement with known molecular dynamics results.