Statistical mechanics of the melting transition in lattice models of polymers

Abstract

Five two-dimensional lattice models, four with rotational isomeric and excluded volume interactions and one with cross links, are used to discuss the theory of the melting transition in polymers. The models have been chosen because they are isomorphic to exactly solvable six vertex and dimer models. The orders of the thermodynamic transitions are extremely varied from model to model, including first-order, $\frac{3}{2}$ order and infinite order transitions. These models are used to test and reveal the shortcomings of the Flory-Huggins approximate theory, which is most aptly described as an infinite dimensional theory.