Tension of polymers in a strip

We consider polymers, modelled as self-avoiding chains, confined on a strip defined on the square lattice with spacing a in the (x,y) plane, limited by two walls which are impenetrable to the chains and located at x=0 and x=am. The activity of a monomer incorporated into the chain is defined as z=exp (βμ) and each monomer adsorbed on the wall, that is, located at sites with x=0 or x=m, contributes with a Boltzmann factor ω= exp (−β∈) to the partition function. Therefore, ∈ > 0 corresponds to walls which are attractive to the monomers, while for ∈ > 0 the walls are repulsive. In particular, we calculate the tension between the walls, as a function of m and ω, for the critical activity z c , at which the mean number of monomers diverges (the so called polymerization transition). For ω > 1 → 1.549375..., the tension on the walls is repulsive for small values of m, becoming attractive as m is increased and finally becoming repulsive again. As ω is increased, the region of values of m for which the tension is attractive grows. Copyright EDP Sciences, Springer-Verlag 1998