  The contribution to the free energy for a film of liquid of thickness $h$ on
a solid surface, due to the interactions between the solid-liquid and
liquid-gas interfaces is given by the binding potential, $g(h)$. The precise
form of $g(h)$ determines whether or not the liquid wets the surface. Note that
differentiating $g(h)$ gives the Derjaguin or disjoining pressure. We develop a
microscopic density functional theory (DFT) based method for calculating
$g(h)$, allowing us to relate the form of $g(h)$ to the nature of the molecular
interactions in the system. We present results based on using a simple lattice
gas model, to demonstrate the procedure. In order to describe the static and
dynamic behaviour of non-uniform liquid films and drops on surfaces, a
mesoscopic free energy based on $g(h)$ is often used. We calculate such
equilibrium film height profiles and also directly calculate using DFT the
corresponding density profiles for liquid drops on surfaces. Comparing
quantities such as the contact angle and also the shape of the drops, we find
good agreement between the two methods. We also study in detail the effect on
$g(h)$ of truncating the range of the dispersion forces, both those between the
fluid molecules and those between the fluid and wall. We find that truncating
can have a significant effect on $g(h)$ and the associated wetting behaviour of
the fluid.
