Lattice models for hydrogen-bonded solvents

A class of lattice models for a binary mixture is defined by assuming that one of the components may form bonds to neighboring molecules of the same species. It is assumed that the fugacity of a molecule depends on the number of bonds which connect the molecule to other molecules. If no molecule is allowed to be connected by more than two bonds to other molecules, then no phase transition occurs, while phase transition can occur if more than two bonds are allowed. If only two or no bonds are allowed, then the model can be solved rigorously for certain planar lattices by transforming it to a dimer covering problem; this model shows behavior similar to the Ising model in zero magnetic field.Work supported by National Science Foundation grant GP-26526.On leave of absence from Corpus Christi College, Cambridge, England.On leave from the University of Copenhagen.