Phase Transitions in One-Dimensional Order—Disorder Systems: Application to Helix—Random-Coil Transition in Polymers

Abstract

In this work a discussion is given of the present theory of the helix—random‐coil transition in polypeptides. The seeming conflict between the description of this transition in terms of a one‐dimensional model and the proofs that a phase transition cannot occur in a one‐dimensional system is resolved. It is shown that the kind of interaction introduced in such models is singular and therefore falls outside the class for which the aforementioned proofs hold. A discussion is given of the mechanism of helix formation in the actual polymers, and it is shown how the description of the transition requires the use of such interactions. The properties which the singular interaction must have in order to cause a phase transition to occur in a one‐dimensional discrete system are precisely stated and illustrated by simple examples. A general treatment of one‐dimensional discrete systems with an arbitrary (but finite) range of interaction is given.