  The interfacial profile between coexisting phases of a binary mixture (A,B)
in a thin film of thickness D and lateral linear dimensions L depends
sensitively on both linear dimensions and on the nature of boundary conditions
and statistical ensembles applied. These phenomena generic for systems in
confined geometry are demonstrated by Monte-Carlo simulations of the bond
fluctuation model of symmetric polymer mixtures. Both the canonical and
semi-grand-canonical ensemble are studied. In the canonical ensemble, the
interfacial width w increases (from small values which are of the same order as
the intrinsic profile) like sqrt{D}, before a crossover to a saturation value
w_max (w_max^2 proportional to ln L) sets in. In the semi-grand-canonical
ensemble, however, one finds the same widths (w proportional to sqrt{D}) as in
the canonical ensemble for not too large L, while for large L the interfacial
profile is smeared out over a finite fraction of the film thickness (w
proportional to D for D -> infinity). We discuss the implications of these
findings for the interpretation of both simulations and experiments.
