  We consider a lattice model of a mixture of repulsive, attractive, or neutral
monodisperse star (species A) and linear (species B) polymers with a third
monomeric species C, which may represent free volume. The mixture is next to a
hard, infinite plate whose interactions with A and C can be attractive,
repulsive, or neutral. These two interactions are the only parameters necessary
to specify the effect of the surface on all three components. We numerically
study monomer density profiles using the method of Gujrati and Chhajer that has
already been previously applied to study polydisperse and monodisperse
linear-linear blends next to surfaces. The resulting density profiles always
show an enrichment of linear polymers in the immediate vicinity of the surface,
due to entropic repulsion of the star core. However, the integrated surface
excess of star monomers is sometimes positive, indicating an overall enrichment
of stars. This excess increases with the number of star arms only up to a
certain critical number and decreases thereafter. The critical arm number
increases with compressibility (bulk concentration of C). The method of Gujrati
and Chhajer is computationally ultrafast and can be carried out on a PC, even
in the incompressible case, when simulations are unfeasible. Calculations of
density profiles usually take less than 20 minutes on PCs.
