  We consider the van der Waals' free energy functional, with a scaling small
parameter epsilon, in the plane domain given by the first quadrant, and
inhomogeneous Dirichlet boundary conditions. The boundary data are chosen in
such a way that the interface between the pure phases tends to be horizontal
and is pinned at some point on the y-axis which approaches zero as epsilon
converges to zero. We show that there exists a critical scaling for the pinning
point, such that, as the small parameter epsilon tends to zero, the competing
effects of repulsion from the boundary and penalization of gradients play a
role in determining the optimal shape of the (properly rescaled) interface.
This result is achieved by means of an asymptotic development of the free
energy functional. As a consequence, such analysis is not restricted to
minimizers but also encodes the asymptotic probability of fluctuations.
