EQUILIBRIUM POLYMERIZATION WITH A FREE-SURFACE

Equilibrium polymerization of a monomer to long chain polymers has been shown to be described by the formal n --> 0 limit of the n-vector model of magnetism. We address the problem of equilibrium polymerization with a substrate represented by a free surface. Thus we obtain the mean-field solution of the cubic symmetric n-vector model on a semi-infinite lattice and study its thermodynamic properties. We consider the situation in which the surface attracts polymer ends. We also examine the possibility of an attractive interaction between the surface and polymer bonds. We obtain the profiles for the densities of polymers and of monomers incorporated into polymers. The behaviour of the mean molecular weight is also studied.