Behavior of a Binary Asymmetric Mixture of Interacting Particles in the Supercritical Region
Keywords:asymmetric binary mixture, cell fluid model, collective variables, equation of state, Widom line
We propose a method for describing the phase behavior of a system consisting of particles of two sorts. The interaction of each species is described by interaction potentials containing the repulsive and attractive components. Asymmetry is ensured by different values of the interaction potentials of each sort. The grand partition function of a binary mixture is calculated in the zero-mode approximation. A line of critical points, which correspond to different proportions of the components, is calculated for specific values of parameters of the interaction potential. We have obtained an equation that relates the introduced mixing parameter x to the concentration of the system. An explicit expression of the pressure of the binary mixture is derived as a function of the relative temperature and the mixing parameter x to plot the Widom line. It is established that, for boundary values of this parameter (x = 0 and x = 1), the equation of state of a mixture turns into equations of state of its separate species.
A. Oleinikova, L. Bulavin, V. Pipich. Critical anomaly of shear viscosity in a mixture with an ionic impurity. Chem. Phys. Let. 278, 121 (1997). https://doi.org/10.1016/S0009-2614(97)00945-7
V.I. Petrenko, M.V. Avdeev, L.A. Bulavin, P. Kopcansky. Impact of polyethylene glycol on aqueous micellar solutions of sodium oleate studied by small-angle neutron scattering, Colloids and Surfaces A: Physicochemical and Engineering Aspects 480, 191 (2015). https://doi.org/10.1016/j.colsurfa.2014.11.064
M. Isaiev, S. Burian, L. Bulavin, M. Gradeck, F. Lemoine, K. Termentzidis. Efficient tuning of potential parameters for liquid-solid interactions. Molecular Simulation 42, 910 (2016). https://doi.org/10.1080/08927022.2015.1105372
P.H. Van Konynenberg, R.L. Scott. Critical lines and phase equilibria in binary van der Waals mixtures. Phil. Trans. Royal Soc. of London. Series A 298, 495 (1980). https://doi.org/10.1098/rsta.1980.0266
Y. Levin, M.E. Fisher. Criticality in the hard-sphere ionic fluid. Physica A 225, 164 (1996). https://doi.org/10.1016/0378-4371(95)00336-3
A. Parola, L. Reatto. Liquid state theories and critical phenomena. Advances in Phys. 44, 221 (1995). https://doi.org/10.1080/00018739500101536
O.V. Patsagan, I.R. Yukhnovskii. Functional of the grand partition function in the method of collective variables with distinguished reference system. Multicomponent system. Theor. Math. Phys. 83, 387 (1990). https://doi.org/10.1007/BF01019137
O.V. Patsahan. On the microscopic theory of phase transitions in binary fluid mixtures. Physica A 272, 358 (1999). https://doi.org/10.1016/S0378-4371(99)00213-7
I.R. Yukhnovskii, M.F. Holovko. Statistical theory of classical equilibrium systems(Naukova dumka, 1980) (in Russian).
O. Patsahan, I. Mryglod. Functional representation of the grand partition function of a multicomponent system of charged particles. Condens. Matter Phys. 9, 659 (2006). https://doi.org/10.5488/CMP.9.4.659
M.P. Kozlovskii, O.V. Patsahan, R.S. Melnyk. A study of the gas-liquid critical point of a binary symmetric mixture. Ukr. J. Phys. 45, 381 (2000).
M.P. Kozlovskii, O.V. Patsahan, R.S. Melnyk. Thermodynamic characteristics of binary symmetric mixture in the vicinity of the vapor-liquid critical point. Ukr. J. Phys. 49, 55 (2004).
J.D. Bernal. A geometrical approach to the structure of liquids. Nature 183, 141 (1959). https://doi.org/10.1038/183141a0
J.M. Stubbs. Molecular simulations of supercritical fluid systems. J. Supercrit. Fluid 108, 104 (2016). https://doi.org/10.1016/j.supflu.2015.10.027
T.J. Yoon, Y.-W. Lee. Current theoretical opinions and perspectives on the fundamental description of supercritical fluids. J. Supercrit. Fluid 134, 21 (2018). https://doi.org/10.1016/j.supflu.2017.11.022
P.F. McMillan, H.E. Stanley. Going supercritical. Nature Physics 6, 479 (2010). https://doi.org/10.1038/nphys1711
ˇ Z. Knez, E. Markoˇciˇc, M. Leitgeb, M. Primoˇziˇc, M.K. Hrnˇciˇc, M. ˇ Skerget. Industrial applications of supercritical fluids: A review. Energy 77, 235 (2014). https://doi.org/10.1016/j.energy.2014.07.044
G. Brunner. Applications of Supercritical Fluids. Annu. Rev. Chem. Biomol. Eng. 1, 321 (2010). https://doi.org/10.1146/annurev-chembioeng-073009-101311
B. Widom. Equation of state in the neighborhood of the critical point J. Chem. Phys. 43, 3898 (1965). https://doi.org/10.1063/1.1696618
D.T. Banuti. Crossing the Widom-line-supercritical pseudo-boiling. J. Supercrit. Fluid 98, 12 (2015). https://doi.org/10.1016/j.supflu.2014.12.019
G.G.Simeoni, T. Bryk, F.A. Gorelli, M. Krisch, G. Ruocco, M. Santoro, T. Scopigno. The Widom line as the crossover between liquid-like and gas-like behaviour in supercritical fluids. Nature Physics 6, 503 (2010). https://doi.org/10.1038/nphys1683
M. Raju, D.T. Banuti, P.C Ma, M. Ihme. Widom lines in binary mixtures of supercritical fluids. Sci. Rep. 7, 3027 (2017). https://doi.org/10.1038/s41598-017-03334-3
M.P. Kozlovskii, O.A. Dobush. Phase transition in a cell fluid model. Condens. Matter Phys. 20, 23501 (2017). https://doi.org/10.5488/CMP.20.23501
M. Kozlovskii, O. Dobush. Representation of the grand partition function of the cell model: The state equation in the mean-field approximation. J. Mol. Liq. 215, 58 (2016). https://doi.org/10.1016/j.molliq.2015.12.018
M.P. Kozlovskii, O.A. Dobush. arXiv:1912.00769, (2019).
Y. Kozitsky, M. Kozlovskii, O. Dobush. Phase transitions in a continuum Curie-Weiss system: A quantitative analysis. In: Modern Problems of Molecular Physics (Springer, 2018), p. 229. https://doi.org/10.1007/978-3-319-61109-9_11
I.R. Yukhnovskii, M.P. Kozlovskii, I.V. Pylyuk. Thermodynamics of three-dimensional Ising-like systems in the higher non-Gaussian approximation: Calculational method and dependence on microscopic parameters. Phys. Rev. B 66, 134410 (2002). https://doi.org/10.1103/PhysRevB.66.134410
M.V. Fedoryuk. Asymptotic methods in analysis. In: Analysis I: Integral Representations and Asymptotic Methods. Edited by M.A. Evgrafov, R.V. Gamkrelidze (Springer, 1989). https://doi.org/10.1007/978-3-642-61310-4_2
R.C. Lincoln, K.M. Koliwad, P.B. Ghate. Morse-potential evaluation of second-and third-order elastic constants of some cubic metals. Phys. Rev. 157, 463 (1967). https://doi.org/10.1103/PhysRev.157.463
J.K. Singh, J. Adhikari, S.K. Kwak. Vapor-liquid phase coexistence curves for Morse fluids. Fluid Phase Equilibria 248, 1 (2006). https://doi.org/10.1016/j.fluid.2006.07.010
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