Abstract
We present a detailed analysis of Wertheim’s multi-density formulation for the thermodynamic properties of associating fluids with a single attraction site. Graphical expressions are explicitly illustrated for the partition function, multi-densities and direct correlation functions, and they are compared with those from the classical single-density formulation of simple fluids. The steric incompatibility among three monomers greatly simplifies cluster integrals of associating fluids, which allows dimerizing association only. Graphical expressions for the pressure and the Helmholtz energy are derived by using functional derivatives, which provide a theoretical base for TPT and SAFT equations of state.
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References
M. S. Wertheim, J. Stat. Phys., 35, 19 (1984).
M. S. Wertheim, J. Stat. Phys., 35, 35 (1984).
M. S. Wertheim, J. Stat. Phys., 42, 459 (1986).
M. S. Wertheim, J. Stat. Phys., 42, 477 (1986).
M. S. Wertheim, J. Chem. Phys., 87, 7323 (1987).
W.G. Chapman, G. Jackson and K.E. Gubbins, Mol. Phys., 65, 1057 (1988).
G. Jackson, W.G. Chapman and K. E. Gubbins, Mol. Phys., 65, 1 (1988).
W.G. Chapman, K. E. Gubbins, G. Jackson and M. Radosz, Fluid Phase Equilib., 52, 31 (1989).
W.G. Chapman, K. E. Gubbins, G. Jackson and M. Radosz, Ind. Eng. Chem. Res., 29, 1709 (1990).
S.H. Huang and M. Radosz, Ind. Eng. Chem. Res., 29, 2284 (1990).
S.H. Huang and M. Radosz, Ind. Eng. Chem. Res., 30, 1994 (1991).
A. GilVillegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson and A. N. Burgess, J. Chem. Phys., 106, 4168 (1997).
F. J. Blas and L. F. Vega, Ind. Eng. Chem. Res., 37, 660 (1998).
F.W. Tavares, J. Chang and S. I. Sandler, Fluid Phase Equilib., 140, 129 (1997).
M. L. L. Paredes, R. Nobrega and F.W. Tavares, Fluid Phase Equilib., 179, 231 (2001).
M. S. Yeom, J. Chang and H. Kim, Korean J. Chem. Eng., 17, 52 (2000).
J. Gross and G. Sadowski, Ind. Eng. Chem. Res., 40, 1244 (2001).
J. Gross and G. Sadowski, Ind. Eng. Chem. Res., 41, 5510 (2002).
E. A. Muller and K. E. Gubbins, Ind. Eng. Chem. Res., 40, 2193 (2001).
I. G. Economou, Ind. Eng. Chem. Res., 41, 953 (2002).
S. P. Tan, H. Adidharma and M. Radosz, Ind. Eng. Chem. Res., 47, 8063 (2008).
M. S. Wertheim, J. Chem. Phys., 85, 2929 (1986).
M. F. Holovko and Y.V. Kalyuzhnyi, Mol. Phys., 73, 1145 (1991).
Y. V. Kalyuzhnyi, M. F. Holovko and A. D. J. Haymet, J. Chem. Phys., 95, 9151 (1991).
Y.V. Kalyuzhnyi, G. Stell, M. L. Llanorestrepo, W.G. Chapman and M. F. Holovko, J. Chem. Phys., 101, 7939 (1994).
S. Kim, J. Chang and H. Kim, Mol. Phys., 99, 1033 (2001).
J. Chang and S. I. Sandler, J. Chem. Phys., 102, 437 (1995).
J. Chang and S. I. Sandler, J. Chem. Phys., 103, 3196 (1995).
Y.V. Kalyuzhnyi and P. T. Cummings, J. Chem. Phys., 103, 3265 (1995).
Y.V. Kalyuzhnyi, C. T. Lin and G. Stell, J. Chem. Phys., 106, 1940 (1997).
C. T. Lin, Y.V. Kalyuzhnyi and G. Stell, J. Chem. Phys., 108, 6513 (1998).
Y.V. Kalyuzhnyi, C. T. Lin and G. Stell, J. Chem. Phys., 108, 6525 (1998).
G. Stell, C. T. Lin and Y.V. Kalyuzhnyi, J. Chem. Phys., 110, 5444 (1999).
J. Chang and H. Kim, J. Chem. Phys., 109, 2579 (1998).
J. Chang and H. Kim, Mol. Phys., 96, 1789 (1999).
I. A. Protsykevytch, Y.V. Kalyuzhnyi, M. F. Holovko and L. Blum, J. Mol. Liq., 73–4, 1 (1997).
Y. V. Kalyuzhnyi, Mol. Phys., 94, 735 (1998).
Y.V. Kalyuzhnyi, C. T. Lin, G. Stell and A. Yethiraj, J. Mol. Liq., 92, 85 (2001).
Y.V. Kalyuzhnyi, C. McCabe, E. Whitebay and P. T. Cummings, J. Chem. Phys., 121, 8128 (2004).
Y.V. Kalyuzhnyi, H. Docherty and P. T. Cummings, J. Chem. Phys., 133, 044502 (2010).
Y.V. Kalyuzhnyi, S. P. Hlushak and P.T. Cummings, J. Chem. Phys., 137, 244910 (2012).
H. M. Kim, A. J. Schultz and D. A. Kofke, J. Phys. Chem. B, 114, 11515 (2010).
H. M. Kim, A. J. Schultz and D. A. Kofke, J. Phys. Chem. B, 116, 14078 (2012).
J. Chang and S. I. Sandler, Chem. Eng. Sci., 49, 2777 (1994).
F.W. Tavares, J. Chang and S. I. Sandler, Mol. Phys., 86, 1451 (1995).
G. Stell, C. T. Lin and Y.V. Kalyuzhnyi, J. Chem. Phys., 110, 5458 (1999).
D. Ghonasgi and W.G. Chapman, J. Chem. Phys., 100, 6633 (1994).
M. S. Yeom, J. Chang and H. Kim, Fluid Phase Equilib., 173, 177 (2000).
J.-P. Hansen and I. McDonald, Theory of Simple Liquids 3rd Ed., Elsevier, USA (2006).
G. Stell, Cluster expansions for classical systems in equilibrium, pp. 171–266, in The Equilibrium Theory of Classical Fluids, H. L. Frisch and J. L. Lebowitz Eds., Benjamin, New York (1964).
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Chang, J. Supplementary graphical analysis for the multi-density expansion of associating fluids. Korean J. Chem. Eng. 31, 374–380 (2014). https://doi.org/10.1007/s11814-013-0283-5
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DOI: https://doi.org/10.1007/s11814-013-0283-5