Does a surface attached globule phase exist ?

A long flexible neutral polymer chain immersed in a poor solvent and interacting with an impenetrable attractive surface exhibits a phase known as surface attached globule ({\bf SAG}) in addition to other adsorbed and desorbed phases. In the thermodynamic limit, the {\bf SAG} phase has the same free energy per monomer as the globular phase, and the transition between them is a surface transition. We have investigated the phase diagrams of such a chain in both two- and three- dimensions and calculated the distribution of monomers in different domains of the phase diagram.