On the critical behaviour of a surface interacting linear polymer chain

A method based on a real space renormalization group transformation is developed to describe the critical behaviour of a surface interacting linear flexible polymer chain, represented by a self-avoiding walk. It is shown that a lattice model based on a central rule in which the starting point of the walk and the surface are taken to be in the middle of one cell, provides a suitable framework to study both the penetrable and impenetrable surfaces. In contrast to this, a method based on a corner rule in which the starting point of the walk and the surface are fixed to be one corner of a cell cannot describe the behaviour of a chain interacting with an impenetrable surface. The value of crossover exponent found by us for a square lattice are in agreement with those expected to be exact for both the cases.