Abstract
A systematic and fundamental approach to associating mixtures is presented. It is shown how the thermodynamic functions may be computed starting from a partition function based on the cluster concept such as occurs in chemical theory. The theory provides a basis for and an extension of the existing chemical theory of (continuous) association. It is applicable to arbitrary association schemes. Analysis of separate cases is not necessary. The assumptions that were made to allow the development were chosen such as to make the principle of reactivity valid. It is this same principle that links various theories: the chemical theory of continuous association, the lattice fluid hydrogen bonding model, and first-order perturbation theory. The equivalence between these theories in appropriate limits is shown in a general and rigorous way. The theory is believed to provide a practical framework for engineering modeling work. Binary interaction parameters can be incorporated. The association scheme is accounted for by a set of generic equations, which should facilitate robust implementation in computer programs.
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References
W. G. Chapman, K. E. Gubbins, G. Jackson, and M. Radosz, New reference equation of state for associating liquids,Ind. Eng. Chem. Res. 29:1709–1721 (1990).
P. C. J. van Dongen and M. H. Ernst,J. Stat. Phys. 37:301 (1984)
I. G. Economou and M. D. Donohue, Chemical, quasi-chemical and perturbation theories for associating fluids.AIChE J. 37:1875 (1991).
I. G. Economou and M. D. Donohue,Ind. Eng. Chem. Res. 31:2388 (1992).
P. J. Flory,Principles of Polymer Chemistry (Cornell University Press, Ithaca, New York, 1953).
A. J. Guggenheim,Mixtures (Clarendon Press, Oxford, 1952).
R. B. Gupta and K. P. Johnston, Lattice fluid hydrogen bonding model with a local segment density,Fluid Phase Equilibria 99:135–151 (1994).
R. A. Heidemann and J. M. Prausnitz, A van-der-Waals-type equation of state for fluids with associating molecules,Proc. Natl. Acad. Sci. USA 73:1773 (1976).
E. M. Hendriks, Analytic expression for the distribution of gel species in spatially homogeneous systems,J. Phys. A: Math. Gen. 18:L579-L583 (1985).
E. M. Hendriks and A. R. D. van Bergen, Application of reduction method to phase equilibria equations,Fluid Phase Equilibria 74:17–34 (1992).
S. H. Huang and M. Radosz, Equation of state for small, large, polydisperse, and associating molecules,Ind. Eng. Chem. Res. 29:2284–2294, (1990).
G. D. Ikonomou and M. D. Donohue, Thermodynamics of hydrogen-bonded molecules: The associated perturbed anisotropic chain theory.AIchE J. 32:1716 (1986).
G. Jackson, W. G. Chapman, and K. E. Gubbins, Phase equilibrium of associating fluids: Spherical molecules with multiple bonding sites,Mol. Phys. 65:1 (1988).
G. M. Kontogeorgis, E. C. Voutsas, I. V. Yakoumis, and D. P. Tassios, An equation of state for associating fluids,Ind. Eng. Chem. Res. 35:4310 (1996).
A. M. Lockett III,J. Chem. Phys. 72:4822, (1980).
D. Missopolinou and Panayiotou, Thermodynamic systems of (oxy)alcohols and (poly)ethers,Fluid Phase Equilibria 110:73–88 (1995).
C. Panayiotou and I. C. Sanchez, Hydrogen bonding in fluids: An quation-of-state approach,J. Phys. Chem. 95:10090–10097 (1991).
J. M. Prausnitz, R. N. Lichtenthaler, and E. Gomez de Azevedo,Molecular Thermodynamics of fluid phase equilibria (Prentice-Hall, Englewood Cliffs, New Jersey, 1986).
R. C. Reid, J. M. Prausnitz, and B. E. Poling,The Properties of Gases and Liquids (McGraw-Hill, New York, 1987).
J. Suresh and E. J. Beckman, Prediction of liquid-liquid equilibria in ternary mixtures from binary data,Fluid Phase Equilibria 99:219–240 (1994).
E. C. Voutsas, G. M. Kontogeorgis, I. V. Yakoumis, and D. P. Tassios, Correlation of liquid-liquid equilibria for alcohol/hydrocarbon mixtures using the CPA equation of state,Fluid Phase equilibria, submitted.
S. M. Walas,Phase Equilibria in Chemical Engineering (Butterworth, Stoneham, Massachusetts, 1985).
M. S. Wertheim,J. Stat. Phys. 35:19 (1984).
M. S. Wertheim,J. Stat. Phys. 42:459 (1986).
I. V. Yakoumis, G. M. Kontogeorgis, E. C. Voutsas, and D. P. Tassios, An equation of state for associating fluids: Part ii. Vapour-liquid equilibria for alcohol/hydrocarbon mixtures,Fluid Phase Equilibria, submitted.
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Hendriks, E.M., Walsh, J. & van Bergen, A.R.D. A general approach to association using cluster partition functions. J Stat Phys 87, 1287–1306 (1997). https://doi.org/10.1007/BF02181285
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DOI: https://doi.org/10.1007/BF02181285