Supplementary graphical analysis for the multi-density expansion of associating fluids

Jaeeon Chang

Korean Journal of Chemical Engineering, Vol.31, No.3, 374-380, March, 2014

DOI10.1007/s11814-013-0283-5 Export Citation

Supplementary graphical analysis for the multi-density expansion of associating fluids

Jaeeon Chang^†

Department of Chemical Engineering, University of Seoul, Siripdae-gil 13, Dongdaemun-gu, Seoul 130-743, Korea

E-mail:

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 singledensity 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.

Keywords:Associating Fluid;Graph Theory;Cluster Integral;Multi-density;TPT;SAFT

[References]

Wertheim MS, J. Stat. Phys., 35, 19 (1984)
Wertheim MS, J. Stat. Phys., 35, 35 (1984)
Wertheim MS, J. Stat. Phys., 42, 459 (1986)
Wertheim MS, J. Stat. Phys., 42, 477 (1986)
Wertheim MS, J. Chem. Phys., 87, 7323 (1987)
Chapman WG, Jackson G, Gubbins KE, Mol. Phys., 65, 1057 (1988)
Jackson G, Chapman WG, Gubbins KE, Mol. Phys., 65, 1 (1988)
Chapman WG, Gubbins KE, Jackson G, Radosz M, Fluid Phase Equilib., 52, 31 (1989)
Chapman WG, Gubbins KE, Jackson G, Radosz M, Ind. Eng. Chem. Res., 29, 1709 (1990)
Huang SH, Radosz M, Ind. Eng. Chem. Res., 29, 2284 (1990)
Huang SH, Radosz M, Ind. Eng. Chem. Res., 30, 1994 (1991)
Gilvillegas A, Galindo A, Whitehead PJ, Mills SJ, Jackson G, Burgess AN, J. Chem. Phys., 106(10), 4168 (1997)
Blas FJ, Vega LF, Ind. Eng. Chem. Res., 37(2), 660 (1998)
Tavares FW, Chang J, Sandler SI, Fluid Phase Equilib., 140(1-2), 129 (1997)
Paredes MLL, Nobrega R, Tavares FW, Fluid Phase Equilib., 179(1-2), 231 (2001)
Yeom MS, Chang J, Kim H, Korean J. Chem. Eng., 17(1), 52 (2000)
Gross J, Sadowski G, Ind. Eng. Chem. Res., 40(4), 1244 (2001)
Gross J, Sadowski G, Ind. Eng. Chem. Res., 41(22), 5510 (2002)
Muller EA, Gubbins KE, Ind. Eng. Chem. Res., 40(10), 2193 (2001)
Economou IG, Ind. Eng. Chem. Res., 41(5), 953 (2002)
Tan SP, Adidharma H, Radosz M, Ind. Eng. Chem. Res., 47(21), 8063 (2008)
Wertheim MS, J. Chem. Phys., 85, 2929 (1986)
Holovko MF, Kalyuzhnyi YV, Mol. Phys., 73, 1145 (1991)
Kalyuzhnyi YV, Holovko MF, Haymet ADJ, J. Chem. Phys., 95, 9151 (1991)
Kalyuzhnyi YV, Stell G, Llanorestrepo ML, Chapman WG, Holovko MF, J. Chem. Phys., 101(9), 7939 (1994)
Kim S, Chang J, Kim H, Mol. Phys., 99, 1033 (2001)
Chang JE, Sandler SI, J. Chem. Phys., 102(1), 437 (1995)
Chang J, Sandler SI, J. Chem. Phys., 103(8), 3196 (1995)
Kalyuzhnyi YV, Cummings PT, J. Chem. Phys., 103(8), 3265 (1995)
Kalyuzhnyi YV, Lin CT, Stell G, J. Chem. Phys., 106(5), 1940 (1997)
Lin CT, Kalyuzhnyi YV, Stell G, J. Chem. Phys., 108(15), 6513 (1998)
Kalyuzhnyi YV, Lin CT, Stell G, J. Chem. Phys., 108(15), 6525 (1998)
Stell G, Lin CT, Kalyuzhnyi YV, J. Chem. Phys., 110(11), 5444 (1999)
Chang J, Kim H, J. Chem. Phys., 109(6), 2579 (1998)
Chang J, Kim H, Mol. Phys., 96, 1789 (1999)
Protsykevytch IA, Kalyuzhnyi YV, Holovko MF, Blum L, J. Mol. Liq., 73-4, 1 (1997)
Kalyuzhnyi YV, Mol. Phys., 94, 735 (1998)
Kalyuzhnyi YV, Lin CT, Stell G, Yethiraj A, J. Mol. Liq., 92, 85 (2001)
Kalyuzhnyi YV, McCabe C, Whitebay E, Cummings PT, J. Chem. Phys., 121(16), 8128 (2004)
Kalyuzhnyi YV, Docherty H, Cummings PT, J. Chem. Phys., 133, 044502 (2010)
Kalyuzhnyi YV, Hlushak SP, Cummings PT, J. Chem. Phys., 137, 244910 (2012)
Kim HM, Schultz AJ, Kofke DA, J. Phys. Chem. B, 114(35), 11515 (2010)
Kim HM, Schultz AJ, Kofke DA, J. Phys. Chem. B, 116(48), 14078 (2012)
Chang J, Sandler SI, Chem. Eng. Sci., 49(17), 2777 (1994)
Tavares FW, Chang J, Sandler SI, Mol. Phys., 86, 1451 (1995)
Stell G, Lin CT, Kalyuzhnyi YV, J. Chem. Phys., 110(11), 5458 (1999)
Ghonasgi D, Chapman WG, J. Chem. Phys., 100(9), 6633 (1994)
Yeom MS, Chang J, Kim H, Fluid Phase Equilib., 173(2), 177 (2000)
Hansen JP, McDonald I, Theory of Simple Liquids 3rd Ed., Elsevier, USA (2006)
Stell G, Cluster expansions for classical systems in equilibrium, pp.171-266, in The Equilibrium Theory of Classical Fluids, Frisch HL, Lebowitz JL Eds., Benjamin, New York (1964)

[Referenced By]

[1] Wertheim MS, J. Stat. Phys., 35, 19 (1984)

[2] Wertheim MS, J. Stat. Phys., 35, 35 (1984)

[3] Wertheim MS, J. Stat. Phys., 42, 459 (1986)

[4] Wertheim MS, J. Stat. Phys., 42, 477 (1986)

[5] Wertheim MS, J. Chem. Phys., 87, 7323 (1987)

[6] Chapman WG, Jackson G, Gubbins KE, Mol. Phys., 65, 1057 (1988)

[7] Jackson G, Chapman WG, Gubbins KE, Mol. Phys., 65, 1 (1988)

[8] Chapman WG, Gubbins KE, Jackson G, Radosz M, Fluid Phase Equilib., 52, 31 (1989)

[9] Chapman WG, Gubbins KE, Jackson G, Radosz M, Ind. Eng. Chem. Res., 29, 1709 (1990)

[10] Huang SH, Radosz M, Ind. Eng. Chem. Res., 29, 2284 (1990)

[11] Huang SH, Radosz M, Ind. Eng. Chem. Res., 30, 1994 (1991)

[12] Gilvillegas A, Galindo A, Whitehead PJ, Mills SJ, Jackson G, Burgess AN, J. Chem. Phys., 106(10), 4168 (1997)

[13] Blas FJ, Vega LF, Ind. Eng. Chem. Res., 37(2), 660 (1998)

[14] Tavares FW, Chang J, Sandler SI, Fluid Phase Equilib., 140(1-2), 129 (1997)

[15] Paredes MLL, Nobrega R, Tavares FW, Fluid Phase Equilib., 179(1-2), 231 (2001)

[16] Yeom MS, Chang J, Kim H, Korean J. Chem. Eng., 17(1), 52 (2000)

[17] Gross J, Sadowski G, Ind. Eng. Chem. Res., 40(4), 1244 (2001)

[18] Gross J, Sadowski G, Ind. Eng. Chem. Res., 41(22), 5510 (2002)

[19] Muller EA, Gubbins KE, Ind. Eng. Chem. Res., 40(10), 2193 (2001)

[20] Economou IG, Ind. Eng. Chem. Res., 41(5), 953 (2002)

[21] Tan SP, Adidharma H, Radosz M, Ind. Eng. Chem. Res., 47(21), 8063 (2008)

[22] Wertheim MS, J. Chem. Phys., 85, 2929 (1986)

[23] Holovko MF, Kalyuzhnyi YV, Mol. Phys., 73, 1145 (1991)

[24] Kalyuzhnyi YV, Holovko MF, Haymet ADJ, J. Chem. Phys., 95, 9151 (1991)

[25] Kalyuzhnyi YV, Stell G, Llanorestrepo ML, Chapman WG, Holovko MF, J. Chem. Phys., 101(9), 7939 (1994)

[26] Kim S, Chang J, Kim H, Mol. Phys., 99, 1033 (2001)

[27] Chang JE, Sandler SI, J. Chem. Phys., 102(1), 437 (1995)

[28] Chang J, Sandler SI, J. Chem. Phys., 103(8), 3196 (1995)

[29] Kalyuzhnyi YV, Cummings PT, J. Chem. Phys., 103(8), 3265 (1995)

[30] Kalyuzhnyi YV, Lin CT, Stell G, J. Chem. Phys., 106(5), 1940 (1997)

[31] Lin CT, Kalyuzhnyi YV, Stell G, J. Chem. Phys., 108(15), 6513 (1998)

[32] Kalyuzhnyi YV, Lin CT, Stell G, J. Chem. Phys., 108(15), 6525 (1998)

[33] Stell G, Lin CT, Kalyuzhnyi YV, J. Chem. Phys., 110(11), 5444 (1999)

[34] Chang J, Kim H, J. Chem. Phys., 109(6), 2579 (1998)

[35] Chang J, Kim H, Mol. Phys., 96, 1789 (1999)

[36] Protsykevytch IA, Kalyuzhnyi YV, Holovko MF, Blum L, J. Mol. Liq., 73-4, 1 (1997)

[37] Kalyuzhnyi YV, Mol. Phys., 94, 735 (1998)

[38] Kalyuzhnyi YV, Lin CT, Stell G, Yethiraj A, J. Mol. Liq., 92, 85 (2001)

[39] Kalyuzhnyi YV, McCabe C, Whitebay E, Cummings PT, J. Chem. Phys., 121(16), 8128 (2004)

[40] Kalyuzhnyi YV, Docherty H, Cummings PT, J. Chem. Phys., 133, 044502 (2010)

[41] Kalyuzhnyi YV, Hlushak SP, Cummings PT, J. Chem. Phys., 137, 244910 (2012)

[42] Kim HM, Schultz AJ, Kofke DA, J. Phys. Chem. B, 114(35), 11515 (2010)

[43] Kim HM, Schultz AJ, Kofke DA, J. Phys. Chem. B, 116(48), 14078 (2012)

[44] Chang J, Sandler SI, Chem. Eng. Sci., 49(17), 2777 (1994)

[45] Tavares FW, Chang J, Sandler SI, Mol. Phys., 86, 1451 (1995)

[46] Stell G, Lin CT, Kalyuzhnyi YV, J. Chem. Phys., 110(11), 5458 (1999)

[47] Ghonasgi D, Chapman WG, J. Chem. Phys., 100(9), 6633 (1994)

[48] Yeom MS, Chang J, Kim H, Fluid Phase Equilib., 173(2), 177 (2000)

[49] Hansen JP, McDonald I, Theory of Simple Liquids 3rd Ed., Elsevier, USA (2006)

[50] Stell G, Cluster expansions for classical systems in equilibrium, pp.171-266, in The Equilibrium Theory of Classical Fluids, Frisch HL, Lebowitz JL Eds., Benjamin, New York (1964)