A phase transition in a one-dimensional lattice of axisymmetric bodies: A model for monomolecular films

Abstract

This work was motivated by recent experiments that show the “liquid-expanded” to “liquid-condensed” phase transition to be first order for monolayers of pentadecanoic acid spread on water. The partition function was studied for an array of axisymmetric, hard bodies (capped cylinders, etc.) with each fixed at the head on a regular one-dimensional lattice. Other possibilities, such as the heads of molecules being randomly distributed on a one-dimensional line, are also being discussed. We report results specifically for a system of thin, hard rods. We show necessary and sufficient conditions for a first order transition to occur in the thermodynamic limit: there is only one transition in the lattice model and that happens when the spacing parameter is the length of the rod. As expected there is no phase transition when the rod is contracted to a point.