(535b) Modeling Three-Dimensional Ising System Using Local Composition Models with Global Renormalization Group Theory

This study focuses on the modeling of phase transition and separation in ferromagnetic materials as a special case of liquid-liquid phase transitions, using four prevalent local composition models (Margules [1], NRTL [2], Wilson [3], and COSMO-SAC [4]) in the mean-field framework. Although local composition models have been shown to be powerful in correlating liquid-liquid phase transitions in non-ideal liquid mixtures, their ability to predict the phase behavior of liquid mixtures based on given molecular interactions is not yet fully understood.

To investigate the predictive power of local composition models, the exact magnetization (or, equivalently the equilibrium composition) and the Curie temperature (or the upper critical solution temperature) of square-lattice systems are utilized [5]. The results reveal that all four local composition models are capable of correctly predicting the liquid-liquid phase boundary at low temperatures, but their accuracy decreases significantly at high temperatures and overestimates the upper critical solution temperature.

To overcome the limitation caused by mean field approximation in local composition models, the global renormalization group theory (GRGT) [6] is introduced to account for composition fluctuations, which are most significant near the critical point. By optimizing the two GRGT parameters, it is found that the COSMO-SAC model is the most accurate in describing the phase boundary of ferromagnetic materials, while other local composition models show significant deviations near the critical point.

References

[1] M. Margules, Über die Zusammensetzung der gesättigten Dämpfe von Mischungen, Sitzungsber. Akad. Wiss. Wien, math.-naturwiss. Klasse, 104 (1895) 1243-1278.

[2] H. Renon, J.M. Prausnitz, Local compositions in thermodynamic excess functions for liquid mixtures, AIChE journal, 14 (1968) 135-144.

[3] G. Scatchard, G.M. Wilson, Vapor-liquid equilibrium. XIII. The system water-butyl glycol from 5 to 85, Journal of the American Chemical Society, 86 (1964) 133-137.

[4] S.-T. Lin, S.I. Sandler, A priori phase equilibrium prediction from a segment contribution solvation model, Industrial & engineering chemistry research, 41 (2002) 899-913.

[5] A. Talapov, H. Blöte, The magnetization of the 3D Ising model, Journal of Physics A: Mathematical and General, 29 (1996) 5727.

[6] F. Yu, J. Cai, Renormalization Group Approach to Binary Liquid–Liquid Equilibria, Industrial & Engineering Chemistry Research, 59 (2020) 9611-9618.