#### Date of Award

2022

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Materials Science

#### Committee Chair

James K. Baird

#### Committee Member

Guangsheng Zhang

#### Committee Member

Lingze Duan

#### Committee Member

Gregory Thompson

#### Committee Member

Robert A. Frederick

#### Subject(s)

Critical phenomena (Physics), Liquid-liquid interfaces, Phase rule and equilibrium

#### Abstract

This dissertation investigates critical phenomena in the liquid mixture near its liquid-liquid critical solution temperature, especially for critical effects on solubilities and turbidities. According to the Griffiths-Wheeler rule, the critical effect is expected for the derivatives of a density variable with respect to a field variable in the system with less than two fixed density variables. The power of the phase rule for solving the number of fixed densities and predicting critical effects is examined in multicomponent systems with the numbers of fixed density variables between zero to two. When the excess solid solute is added into a binary liquid mixture, and the concentration of solute in the liquid phase is plotted in van’t Hoff form, the data lie in a straight line away from the critical temperature. According to the phase rule, in the vicinity of critical point, the divergence of the van’t Hoff slope depends on the number of fixed mole fractions. In the case of none of the mole fractions being fixed, the strong divergence of the van’t Hoff slope is expected at the critical point. If one mole fraction is fixed, the van’t Hoff slope diverges weakly to infinity. In addition, van’t Hoff slope remains finite when two mole fractions are fixed at the critical point. The results of solubility measurements are in exact agreement with the principle of critical point isomorphism. The turbidities of seven systems were measured in the homogeneous liquid phase equilibria along the critical isopleth. The critical opalescence is observed in each of the binary mixtures. The phase rule indicates that one mole fraction is fixed in the binary mixture. Given this restriction, the result of solubility measurements is in exact agreement with the principle of critical point isomorphism. We have found the critical opalescence disappears upon the addition of a completely soluble solute. According to the phase rule, two mole fractions can be fixed. With this restriction, the data is consistent with the principle of critical point isomorphism.

#### Recommended Citation

Wang, Xingjian, "Phase rule and isomorphism principle analysis of critical phenomena in multicomponent systems" (2022). *Dissertations*. 248.

https://louis.uah.edu/uah-dissertations/248

## Comments

Submitted ... in the joint tri-campus Materials Science program.