Finite size scaling in polymer systems

We discuss finite size scaling for common models of polymer systems, both in the dilute and in the concentrated cases. In the dilute case, we find that some extension of ideas of Redner and Reynolds shows that the transition to a collapsed phase should be regarded as thermodynamically first order. In the concentrated case, paying careful attention to the relationship of the number of polymers to the number of monomers per chain length shows that the effects of an analogous chain collapse should be observable in polymer melts confined to pores of submicron size. We discuss some possible experimental consequences.