Abstract
We perform an analytic study of the main features of the phase diagram of symmetric binary Gaussian mixtures such that the range and strength of the interactions between particles of one species are the same as those of the other species. We focus on the relative locations of the spinodal and \(\lambda \)-lines, i.e., the boundaries beyond which the uniform mixture becomes unstable respectively towards bulk demixing and microphase formation. We find that, when the \(\lambda \)-line is present, three situations may occur: (i) The spinodal line does not exist, and the \(\lambda \)-line spans the whole concentration axis. (ii) Both the \(\lambda \)- and spinodal lines are present and span the whole concentration axis, but the spinodal instability is always preempted by the \(\lambda \)-line. (iii) The spinodal instability is the only one present at intermediate concentrations, but is preempted by the \(\lambda \)-line at high and low concentrations.
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P.J. Flory, J. Krigbaum, Statistical mechanics of dilute polymer solutions II. J. Chem. Phys. 18, 1086 (1950). https://doi.org/10.1063/1.1747866
J. Dautenhahn, C.K. Hall, Monte Carlo simulation of off-lattice polymer chains: effective pair potentials in dilute solution. Macromolecules 27, 5399 (1994). https://doi.org/10.1021/ma00097a021
A.A. Louis, P.G. Bolhuis, J.P. Hansen, E.J. Meijer, Can polymer coils be modeled as “soft colloids”? Phys. Rev. Lett. 85, 2522 (2000). https://doi.org/10.1103/PhysRevLett.85.2522
A.A. Louis, P.G. Bolhuis, J.-P. Hansen, Mean-field fluid behavior of the Gaussian core model. Phys. Rev. E. 62, 7961 (2000). https://doi.org/10.1103/PhysRevE.62.7961
R. Finken, J.-P. Hansen, A.A. Louis, Phase separation of penetrable core mixtures. J. Stat. Phys. 110, 1015 (2003). https://doi.org/10.1023/A:1022136624854
A.J. Archer, R. Evans, Binary Gaussian core model: fluid-fluid phase separation and interfacial properties. Phys. Rev. E 64, 041501 (2001). https://doi.org/10.1103/PhysRevE.64.041501
A.J. Archer, R. Evans, Wetting in the binary Gaussian core model. J. Phys.: Condens. Matter 14, 1131 (2002). https://doi.org/10.1088/0953-8984/14/6/302
A.J. Archer, R. Evans, Solvent-mediated interactions and solvation close to fluid-fluid phase separation: a density functional treatment. J. Chem. Phys. 118, 9726 (2003). https://doi.org/10.1063/1.1570406
I.O. Götze, A.J. Archer, C.N. Likos, Structure, phase behavior, and inhomogeneous fluid properties of binary dendrimer mixtures. J. Chem. Phys. 124, 084901 (2006). https://doi.org/10.1063/1.2172596
A.J. Archer, C.N. Likos, R. Evans, Soft-core binary fluid exhibiting a \(\lambda \)-line and freezing to a highly delocalized crystal. J. Phys.: Condens. Matter 16, L297 (2004). https://doi.org/10.1088/0953-8984/16/23/L03
D. Pini, A. Parola, L. Reatto, An unconstrained DFT approach to microphase formation and application to binary Gaussian mixtures. J. Chem. Phys. 143, 034902 (2015). https://doi.org/10.1063/1.4926469
J.-P. Hansen, I.R. McDonald, Theory of Simple Liquids (Academic Press, London, 2006)
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Pini, D. (2018). A Study of the Phase Diagram of Symmetric Binary Gaussian Mixtures. In: Bortignon, P., Lodato, G., Meroni, E., Paris, M., Perini, L., Vicini, A. (eds) Toward a Science Campus in Milan. CDIP 2017. Springer, Cham. https://doi.org/10.1007/978-3-030-01629-6_17
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DOI: https://doi.org/10.1007/978-3-030-01629-6_17
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