Molecular mirror images, dense ice phases, organic salts at interfaces, and electrochemical deposition: exotic applications of the Pirogov–Sinai theory

The Pirogov–Sinai theory of phase transitions is used to prove the existence of ordered molecular phases at low temperatures in statistical mechanical models for several types of molecular systems. A three-dimensional lattice gas containing two molecular mirror images (enantiomers) was proved to undergo enantiomeric phase separation for one domain of interactions and to contain ordered racemic phases for another domain of interactions. A model for ice VII, which contains disordered hydrogen bonds, was introduced and proved to undergo a transition to a low-temperature phase which has the ordered hydrogen-bonded structure of ice VIII. A lattice gas model for guanidinium nitrate at the mercury–water interface was introduced and proved to form a condensed monolayer with an open, hexagonal hydrogen-bonded structure that agrees with the structure proposed on the basis of experiments. A model for the underpotential deposition of copper on the (111) surface of a gold electrode in the presence of bisulfate was proved to undergo a sequence of voltage-dependent ordered interfacial phases that agree with experiment.