The conventional Gibbs energy minimization methods apply elemental amounts of system components as conservation constraints in the form of a stoichiometric conservation matrix. The linear constraints designate the limitations set on the components described by the system constituents. The equilibrium chemical potentials of the constituents are obtained as a linear combination of the component-specific contributions, which are solved with the Lagrange method of undetermined multipliers. When the Gibbs energy of a multiphase system is also affected by conditions due to immaterial properties, the constraints must be adjusted by the respective entities. The constrained free energy (CFE) minimization method includes such conditions and incorporates every immaterial constraint accompanied with its conjugate potential. The respective work or affinity-related condition is introduced to the Gibbs energy calculation as an additional Lagrange multiplier. Thus, the minimization procedure can include systemic or external potential variables with their conjugate coefficients as well as non-equilibrium affinities. Their implementation extends the scope of Gibbs energy calculations to a number of new fields, including surface and interface systems, multi-phase fiber suspensions with Donnan partitioning, kinetically controlled partial equilibria, and pathway analysis of reaction networks.
References
1 W. R. Smith, R. W. Missen. Chemical Reaction Equilibrium Analysis: Theory and Algorithms, Krieger, Malabar, FL (1991).Search in Google Scholar
2 S. Gordon, B. J. McBride. Computer Program for Calculation of Complex Equilibrium Compositions and Applications, NASA Reference Publication 1311 (1994).Search in Google Scholar
3 10.3891/acta.chem.scand.25-2651, G. Eriksson. Acta Chem. Scand.25, 2651 (1971).Search in Google Scholar
4 10.1007/BF02868269, M. Hillert. Bull. Alloy Phase Diagrams2, 265 (1981).Search in Google Scholar
5 L. Kaufman, H. Bernstein. Computer Calculation of Phase Diagrams, Academic Press, New York (1970).Search in Google Scholar
6 K. Hack (Ed.). The SGTE Casebook: Thermodynamics at Work, 2nd ed., p. 14, Woodhead, Cambridge (2008).Search in Google Scholar
7 S. M. Walas. Phase Equilibria in Chemical Engineering, Butterworth, Stoneham, MA (1985).Search in Google Scholar
8 10.1016/j.fluid.2003.08.005, A. L. Ballard, E. D. Sloan. Fluid Phase Equilib.218, 15 (2004).Search in Google Scholar
9 10.1016/S0098-1354(02)00144-8, D. V. Nichita, S. Gomez, E. Luna. Comput. Chem. Eng.26, 1703 (2002).Search in Google Scholar
10 10.1023/A:1021768011887, E. Königsberger, G. Eriksson. J. Solution Chem.28, 721 (1998).Search in Google Scholar
11 10.1351/pac200274101831, E. Königsberger. Pure Appl. Chem.74, 1831 (2002).Search in Google Scholar
12 10.3183/NPPRJ-2001-16-01-p024-032, J. Lindgren, L. Wiklund, L.-O. Öhman. Nordic Pulp Paper Res. J.16, 24 (2001).Search in Google Scholar
13 10.1023/A:1020201909118, P. Koukkari, R. Pajarre, H. Pakarinen. J. Solution Chem.31, 627 (2002).Search in Google Scholar
14 10.1016/j.jcis.2008.09.027, P. Sundman, P. Persson, L.-O. Öhman. J. Colloid Interface Sci.328, 248 (2008).Search in Google Scholar PubMed
15 10.1149/1.2069243, M. Lampinen, J. Vuorisalo. J. Electrochem. Soc.139, 484 (1992).Search in Google Scholar
16 10.1021/j100345a081, R. A. Alberty. J. Phys. Chem.93, 3299 (1989).Search in Google Scholar
17 10.1016/S0010-2180(71)80166-9, J. C. Keck, D. Gillespie. Combust. Flame17, 237 (1971).Search in Google Scholar
18 10.1016/0360-1285(90)90046-6, J. C. Keck. Prog. Energy Combust. Sci.16, 125 (1990).Search in Google Scholar
19 10.1016/0098-1354(93)80096-6, P. Koukkari. Comput. Chem. Eng.17, 1157 (1993).Search in Google Scholar
20 10.1016/j.calphad.2005.11.007, P. Koukkari, R. Pajarre. CALPHAD30, 18 (2006).Search in Google Scholar
21 10.1016/S1570-7946(08)80153-8, R. Pajarre, P. Blomberg, P. Koukkari. Comput.-Aided Chem. Eng.25, 883 (2008).Search in Google Scholar
22 10.1016/j.mbs.2009.04.004, P. B. A. Blomberg, P. Koukkari. Math. Biosci.220, 81 (2009).Search in Google Scholar PubMed
23 10.1351/pac200173081349, R. Alberty. Pure Appl. Chem.73, 1349 (2001).Search in Google Scholar
24 E. A. Guggenheim. Thermodynamics, p. 335, North-Holland, Amsterdam (1977).Search in Google Scholar
25 P. Koukkari, R. Pajarre, K. Hack. Int. J. Mater. Res.98, 926 (2007).Search in Google Scholar
26 10.1016/j.calphad.2005.08.003, R. Pajarre, P. Koukkari, T. Tanaka, Y. Lee. CALPHAD30, 196 (2006).Search in Google Scholar
27 E. T. Turkdogan. Physical Chemistry of High-Temperature Technology, p. 96, Academic Press, London (1980).Search in Google Scholar
28 J. A. V. Butler. Proc. R. Soc., London, A135, 348 (1932).10.1098/rspa.1932.0040Search in Google Scholar
29 J. C. Joud, N. Eustathopoulos, P. Desse. J. Chim. Phys.70, 1290 (1973).Search in Google Scholar
30 G. Metzger. Z. Phys. Chem.211, 1 (1959).Search in Google Scholar
31 T. Tanaka, K. Hack, T. Ida, S. Hara. Z. Metallkunde87, 380 (1996).10.1515/ijmr-1996-870509Search in Google Scholar
32 10.1016/j.jcis.2009.05.023, R. Pajarre, P. Koukkari. J. Colloid Interface Sci.337, 39 (2009).Search in Google Scholar
33 R. Pajarre, P. Koukkari, T. Tanaka. To be published.Search in Google Scholar
34 P. Koukkari, R. Pajarre, E. Räsänen. In Chemical Thermodynamics for Industry, T. M. Letcher (Ed.), pp. 23–32, Royal Society of Chemistry, Cambridge, UK (2004).Search in Google Scholar
35 10.1016/j.molliq.2005.11.016, R. Pajarre, P. Koukkari, E. Räsänen. J. Mol. Liq.125, 58 (2006).Search in Google Scholar
36 M. Towers, A. M. Scallan. J. Pulp Paper Sci.22, J332 (1996).Search in Google Scholar
37 10.1351/PAC-CON-10-09-09, P. Koukkari, R. Pajarre, P. Blomberg. Pure Appl. Chem.83, 1063 (2011).Search in Google Scholar
38 10.1016/S0378-3812(97)00123-4, P. Koukkari, I. Laukkanen, S. Liukkonen. Fluid Phase Equilib.136, 345 (1997).Search in Google Scholar
39 10.1016/j.combustflame.2009.05.013, M. Janbozorgi, S. Ugarte, H. Metghalchi, J. C. Keck. Combust. Flame156, 1871 (2009).Search in Google Scholar
40 R. Gani, T. S. Jepsen, E. S. Pérez-Cisneros Comput. Chem. Eng.22, Suppl., S363 (1998).10.1016/S0098-1354(98)00076-3Search in Google Scholar
41 10.1016/0378-3812(95)02870-6, G. Maurer. Fluid Phase Equilib.116, 39 (1996).Search in Google Scholar
42 10.1134/S004057950902002X, A. Toikka, M. Toikka, Yu. Pisarenko, L. Serafimov. Theor. Found. Chem. Eng.43, 129 (2009).Search in Google Scholar
43 A. Roine, Outokumpu. HSC Chemistry® for Windows, Version 4.1 (1999).Search in Google Scholar
44 10.1016/j.fluid.2004.06.043, A. C. Vawdrey, J. L. Oscarson, R. L. Rowley, W. V. Wilding. Fluid Phase Equilib.222–223, 239 (2004).Search in Google Scholar
45 10.1016/0021-9614(77)90017-9, D. Ambrose, J. H. Ellender, C. H. S. Sprake, R. Townsend. J. Chem. Thermodyn.9, 735 (1977).Search in Google Scholar
46 10.1016/0378-3812(95)02798-J, P. Sauermann, K. Holzapfel, J. Oprzynski, F. Kohler, W. Poot, T. W. de Loos. Fluid Phase Equilib.112, 249 (1995).Search in Google Scholar
47 10.1021/je00052a030, H. S. Wu, S. I. Sandler. J. Chem. Eng. Data33, 157 (1988).Search in Google Scholar
48 B. E. Poling, J. M. Prausnitz, J. M. O’Connell. Properties of Gases and Liquids, 5th ed., McGraw-Hill (2001).Search in Google Scholar
49 10.1016/j.compchemeng.2006.03.001, P. Koukkari, R. Pajarre. Comput. Chem. Eng.30, 1189 (2006).Search in Google Scholar
Conference
International Conference on Chemical Thermodynamics (ICCT-2010), Conference on Chemical Thermodynamics, ICCT, Chemical Thermodynamics, 21st, Tsukuba, Japan, 2010-08-01–2010-08-06
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