Polymers in random media: An introduction

Abstract

The chapter introduces the (lattice) self-avoiding walk (SAW) model of polymer chains, their configurational statistics and the criteria indicating effects of lattice disorder on the critical behavior. The study of conformational properties of polymer in good solvent uses a lattice model of linear polymers where the polymer is viewed as a walk on a lattice: the monomer size is represented by the lattice constant and the size of the polymer chain by the walk length. Model of a polymer chain in a good solvent is a random SAW on a lattice. These SAWs are random walks without self-intersection or crossing; as such they are the self-avoiding subset of random walks. Prominent indications for the effect of disorder on the SAW statistics are also discussed. The chapter tries to estimate the SAW size exponent using some approximate theories like Floor theory and scaling theory. Approximate mean field-like and scaling arguments have been presented to indicate that the SAW critical behavior on disordered lattices, percolating lattice in particular, could be significantly different from those of SAWs on pure lattices.