By employing monomer-resolved computer simulations and analytical considerations based on polymer scaling theory, we analyze the conformations and interactions of multiarm star polymers strongly adsorbed on a smooth, two-dimensional plane. We find a stronger stretching of the arms as well as a stronger repulsive, effective interaction than in the three dimensional case. In particular, the star size scales with the number of arms $f$ as $sim f^{1/4}$ and the effective interaction as $sim f^{2}$, as opposed to $sim f^{1/5}$ and $sim f^{3/2}$, respectively, in three dimensions. Our results demonstrate the dramatic effect that geometric confinement can have on the effective interactions and the subsequent correlations of soft colloids in general, for which the conformation can be altered as a result of geometrical constraints imposed on them.
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