Thermodynamic behavior of electrolytes at low temperature

The primitive models of electrolytes considered in this project, Restricted Primitive Model and Size Asymmetrical Primitive Model, are all concerned with understanding and describing the thermodynamics and structural properties of strong electrolytes and molten salts. Such models undergo a first order phase transition at low temperature. In order to understand the properties of this phase transition, appropriate theoretical tools are needed to describe the low temperature behavior of such systems. The importance of ion pairing for such systems at low temperature has long been recognized since the first quarter of the 20th century, but we still lack a systematic approach to this nonlinear behavior. The conventional approaches to ion pairing, following the spirit of the treatment by Bjerrum (1926), become rather inadequate when the temperature is close or below the critical temperature of the phase transition.; This thesis project attempts to make an advance in the theoretical study of the models at low temperature. The energy profile of the pairs formed by a special pairing procedure, due to Stillinger and Lovette (1968), is examined numerically to establish the adequacy of the base system to be chosen. A differential procedure is proposed to calculate the Partition Function of the Grand Canonical Ensemble of the base system. Whose result naturally separates the system into pairs (/clusters) and ions. An energy standard is then proposed in the formation of neutral clusters, whose effect is accounted for through a Van der Waals term. In the end, we calculate the critical points of the Size Asymmetrical Primitive Model through one parameter fitting to eliminate the messy calculation of a multi-body effect.; A recent focus on the study of Size Asymmetrical Model is the effect of size asymmetry on the location of the critical point. While all the conventional methods predict wrong trends on the change of both the critical temperature and the critical density, when compared with the result of Monte Carlo simulation, the result of this work gives not only the correct trends, but also very good numerical agreement.