Abstract
We consider a model of star copolymers, based on self-avoiding walks, where the arms of the star can be chemically distinct. The copolymeric star is attached to an impenetrable surface at the end of an arm and the different monomers constituting the star have different interaction strengths with the surface. When the star is adsorbed at the surface it can be desorbed by applying a force, either at a vertex of degree 1 or at the central vertex of the star. We give some rigorous results about the free energy of the system and use these to establish the general form of the phase diagrams, and the orders of certain phase transitions in the system. We also consider the special case of spiders, i.e. stars constrained to have all the endpoints of their arms in the surface.
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