Crossover of a polymer chain from bulk to surface states

Using exact enumeration, conformational properties of a surface-interacting long flexible polymer chain are determined in a two-dimensional poor solvent where the possibility of collapse in bulk exists. A model of a self-attracting self-avoiding walk (SASAW) on a square lattice is considered and up to 28 steps in series were evaluated. A new state having the conformation of a surface attached globule in between the adsorbed and desorbed collapsed phases is found. The fact that this state may not represent a new thermodynamic phase is emphasised. The phase diagram is drawn showing the region of existence of the four phases: (i) desorbed expanded, (ii) desorbed collapsed, (iii) adsorbed expanded, and (iv) surface attached globule. The uncertainities in locating the phase boundaries particularly in the vicinity of multicritical point is mentioned.