Rescaled density expansions and demixing in hard-sphere binary mixtures

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Physical Chemistry

Background:

• Understanding fluid mixture phase behavior is crucial in physical chemistry.
• Hard sphere models provide fundamental insights into macroscopic properties from microscopic interactions.
• Demixing transitions in binary mixtures are complex phenomena influenced by particle size and interactions.

Purpose of the Study:

• To analyze the demixing transition in binary fluid mixtures of additive hard spheres.
• To investigate the impact of varying size asymmetries on the phase behavior.
• To evaluate the influence of virial coefficients and theoretical approximations on the critical consolute point.

Main Methods:

• Utilizing the exact low-density expansion of pressure for binary hard sphere mixtures.
• Incorporating successive virial coefficients (second through fifth) into the analysis.
• Rescaling the low-density expansion to higher densities using Percus-Yevick theory approximations.

Main Results:

• The second virial approximation predicts fluid demixing with a lower consolute critical point.
• Increasing virial coefficients shift the critical consolute point to higher pressures and lower fractions of large spheres.
• Rescaling with Percus-Yevick theory yields different qualitative movements of the critical point in the phase diagram.

Conclusions:

• The demixing transition and critical point location are sensitive to the inclusion of higher-order virial coefficients.
• Percus-Yevick approximations significantly influence the predicted phase diagram, necessitating caution in interpreting results.
• Accurate phase diagram prediction requires careful consideration of theoretical approximations and their impact on thermodynamic properties.