Dale A. Huckaby
Our research group introduces and studies the properties of statistical mechanical models for unusual or complicated phase behavior in molecular systems.
We introduced both two- and three-dimensional models for enantiomeric phase separation which include orientationally-dependent intermolecular inter-actions. For one domain of inter-actions, enantiomeric phase sepa-ration was proved to occur in the solid. A tricritical point was located in the two-dimensional model. Such a point, at which three phases simultaneously become a single phase, can occur in this two-component system because of the special symmetry present between enantiomers. For another domain of interactions, the solid in the three-dimensional model was proved to be racemic. Although there are an infinite number of ground-state configurations, all of them racemic, only a finite number of dominant ground states allow a maximum number of lowest energy excitations. The low temperature phases have the structure, except for excitations, of the dominant ground state configurations. We hope to study the interesting possibility of enantiomeric phase separation in the liquid within the framework of this type of model.
There are several different phases of ice. Cubic ice and hexagonal ice are the two phases which are less dense than liquid water. To calculate the relative stability of these forms at low temperatures, we developed a method to calculate the dipole-dipole energy of these structures, both of which have disordered hydrogen bonding. The calculated energy difference favors hexagonal ice in stability and agrees well with experiment. Two high density forms, ice VII and ice VIII, differ in that the hydrogen bonds in ice VII are disordered while those in ice VIII are ordered. We introduced a model for this system and proved that an ordered ice VIII phase exists at low temperature, a transition to a disordered ice VII phase occurring as the temperature is raised.
Voltammograms of the underpotential deposition of metals on perfect crystal electrodes often contain sharp spikes as a result of phase transitions occurring at the fluid-crystal interface. We developed a statistical mechanical model and used it to study the underpotential deposition of copper on a gold (111) surface in the presence of bisulfate ions. The model repro-duced the two sharp spikes seen in the experimental voltammogram of the deposition. Within this model we conjectured the molecular structures of the voltage-dependent phases which occur at the fluid-crystal interface, years before these structures were confirmed by experiment. Later, using both the rigorous Pirogov-Sinai theory and a cluster variation approximation, we showed that these phases exist in the model for reasonable choices of the interaction parameters.