  Using a coarse-grained bead-spring model of flexible polymer chains, the
structure of a polymeric nanodroplet adsorbed on a chemically decorated flat
wall is investigated by means of Molecular Dynamics simulation. We consider
sessile drops on a lyophilic (attractive for the monomers) region of circular
shape with radius R_D while the remaining part of the substrate is lyophobic.
The variation of the droplet shape, including its contact angle, with R_D is
studied, and the density profiles across these droplets also are obtained.
  In addition, the interaction of droplets adsorbed on two walls forming a slit
pore with two lyophilic circular regions just opposite of one another is
investigated, paying attention to the formation of a liquid bridge between both
walls. A central result of our study is the measurement of the force between
the two substrate walls at varying wall separation as well as the kinetics of
droplet merging. Our results are compared to various phenomenological theories
developed for liquid droplets of mesoscopic rather than nanoscopic size.
