Then→0vector model and equilibrium polymerization

Abstract

Equilibrium polymerization of a monomer to long-chain polymers can be usefully described by the $n\to 0$ limit of the $n$-vector model of magnetism in a small magnetic field. In the molecular-field approximation, the $n\to 0$ vector model becomes identical to the earlier Tobolsky-Eisenberg theory of equilibrium polymerization. An error in an earlier analysis of the $n\to 0$ vector model is corrected and the consequences for polymerization and polymer solutions are discussed. A curiosity of the $n\to 0$ vector model—that its free energy does not everywhere satisfy the usual convexity requirements of thermodynamic stability—is also discussed. In an appendix the $n\to 0$ limit of the cubic discrete $n$-vector model (Hillhorst model) is also shown to be equivalent in mean field to the Tobolsky-Eisenberg theory of equilibrium polymerization.