Collapsed and adsorbed states of a directed polymer chain in   two-dimensions
  A phase diagram for a surface interacting long flexible partially directed polymer chain in a two-dimensional poor solvent where the possibility of collapse in the bulk exists is determined using exact enumeration method. We used a model of self attracting self-avoiding walk and evaluated 30 steps in series. An intermediate phase in between the desorbed collapsed and adsorbed expanded phases having the conformation of a surface attached globule is found. The four phases, viz. (i) desorbed expanded, (ii) desorbed collapsed, (iii) adsorbed expanded, (iv) surface attached globule are found to meet at a multicritical point. These features are in agreement with those of an isotropic (or non directed) polymer chain. 
Pramod K Mishra and Yashwant Singh (Dept. of Physics, Banaras Hindu   University, Varanasi)