[en] Discrete modeling is a concept to establish thermodynamics on Shannon entropy expressed by variables that characterize discrete states of individual molecules in terms of their interacting neighbors in a mixture. To apply this method to condensed-phase lattice fluids, this paper further develops an approach proposed by Vinograd which features discrete Markov-chains for the sequential lattice construction and rigorous use of Shannon information as thermodynamic entropy, providing an in-depth discussion of the modeling concept evolved. The development comprises (1) improved accuracy compared to Monte Carlo data and (2) an extension from a two-dimensional to a three-dimensional simple lattice. The resulting model outperforms the quasichemical approximation proposed by Guggenheim, a frequently used reference model for the simple case of spherical molecules with uniform energetic surface properties. To illustrate its potential as a starting point for developing gE-models in chemical engineering applications, the proposed modeling methodology is extended, using the example of a simple approach for dicelike lattice molecules with multiple interaction sites on their surfaces, to address more realistic substances. A comparison with Monte Carlo simulations shows the model’s capability to distinguish between isomeric configurations, which is a promising basis for future gE-model development in view of activity coefficients for liquid mixtures.
Disciplines :
Chemical engineering
Author, co-author :
Wallek, Thomas; TU Graz
Mayer, Christoph; TU Graz
Pfennig, Andreas ; Université de Liège - ULiège > Department of Chemical Engineering > PEPs - Products, Environment, and Processes
Language :
English
Title :
Discrete Modeling Approach as a Basis of Excess Gibbs-Energy Models for Chemical Engineering Applications
Publication date :
2018
Journal title :
Industrial and Engineering Chemistry Research
ISSN :
0888-5885
eISSN :
1520-5045
Publisher :
American Chemical Society, United States - District of Columbia
Shannon, C. E. A Mathematical Theory of Communication Bell Syst. Tech. J. 1948, 27, 379-423 10.1002/j.1538-7305.1948.tb01338.x
Pfleger, M.; Wallek, T.; Pfennig, A. Constraints of compound systems: Prerequisites for thermodynamic modeling based on Shannon entropy Entropy 2014, 16, 2990-3008 10.3390/e16062990
Pfleger, M.; Wallek, T.; Pfennig, A. Discrete modeling: Thermodynamics based on shannon entropy and discrete states of molecules Ind. Eng. Chem. Res. 2015, 54, 4643-4654 10.1021/ie504919b
Wallek, T.; Pfleger, M.; Pfennig, A. Discrete modeling of lattice systems: The concept of Shannon entropy applied to strongly interacting systems Ind. Eng. Chem. Res. 2016, 55, 2483-2492 10.1021/acs.iecr.5b04430
Guggenheim, E. A. Statistical thermodynamics of mixtures with zero energies of mixing Proc. R. Soc. London, Ser. A 1944, 183, 203-212 10.1098/rspa.1944.0032
Guggenheim, E. A.; McGlashan, M. L. Statistical Mechanics of Regular Mixtures Proc. R. Soc. London, Ser. A 1951, 206, 335-353 10.1098/rspa.1951.0074
Guggenheim, E. A. Mixtures; Clarendon Press: Oxford, 1952.
Egner, K.; Gaube, J.; Pfennig, A. GEQUAC, an excess Gibbs energy model for simultaneous description of associating and non-associating liquid mixtures Ber. Bunsenges. Phys. Chem. 1997, 101, 209-218 10.1002/bbpc.19971010208
Bronneberg, R.; Pfennig, A. MOQUAC, a new expression for the excess Gibbs energy based on molecular orientations Fluid Phase Equilib. 2013, 338, 63-77 10.1016/j.fluid.2012.10.020
Klamt, A. Conductor-like screening model for real solvents: a new approach to the quantitative calculation of solvation phenomena J. Phys. Chem. 1995, 99, 2224-2235 10.1021/j100007a062
Klamt, A.; Jonas, V.; Bürger, T.; Lohrenz, J. C. Refinement and parametrization of COSMO-RS J. Phys. Chem. A 1998, 102, 5074-5085 10.1021/jp980017s
Klamt, A.; Eckert, F. COSMO-RS: a novel and efficient method for the a priori prediction of thermophysical data of liquids Fluid Phase Equilib. 2000, 172, 43-72 10.1016/S0378-3812(00)00357-5
Klamt, A. Encyclopedia of Computational Chemistry; John Wiley & Sons, Ltd, 2002.
Klamt, A.; Krooshof, G. J. P.; Taylor, R. COSMOSPACE: Alternative to conventional activity-coefficient models AIChE J. 2002, 48, 2332-2349 10.1002/aic.690481023
Sweere, A. J. M.; Fraaije, J. G. E. M. Force-field based quasi-chemical method for rapid evaluation of binary phase diagrams J. Phys. Chem. B 2015, 119, 14200-14209 10.1021/acs.jpcb.5b06100
Sweere, A. J. M.; Serral Gracia, R.; Fraaije, J. G. E. M. Extensive accuracy test of the force-field-based quasichemical method PAC-MAC J. Chem. Eng. Data 2016, 61, 3989-3997 10.1021/acs.jced.6b00474
Sweere, A. J.; Fraaije, J. G. Prediction of polymer-solvent miscibility properties using the force field based quasi-chemical method PAC-MAC Polymer 2016, 107, 147-153 10.1016/j.polymer.2016.11.024
Sweere, A. J. M.; Fraaije, J. G. E. M. Accuracy test of the OPLS-AA force field for calculating free energies of mixing and comparison with PAC-MAC J. Chem. Theory Comput. 2017, 13, 1911-1923 10.1021/acs.jctc.6b01106
Kikuchi, R. A theory of cooperative phenomena Phys. Rev. 1951, 81, 988-1003 10.1103/PhysRev.81.988
Kikuchi, R.; Brush, S. G. Improvement of the cluster-variation method J. Chem. Phys. 1967, 47, 195-203 10.1063/1.1711845
Sanchez, J. M.; Ducastelle, F.; Gratias, D. Generalized cluster description of multicomponent systems Phys. A 1984, 128, 334-350 10.1016/0378-4371(84)90096-7
Pelizzola, A. Cluster variation method in statistical physics and probabilistic graphical models J. Phys. A: Math. Gen. 2005, 38, R309-R339 10.1088/0305-4470/38/33/R01
Kikuchi, R. Natural iteration method and boundary free energy J. Chem. Phys. 1976, 65, 4545-4553 10.1063/1.432909
Gratias, D.; Sanchez, J. M.; De Fontaine, D. Application of group theory to the calculation of the configurational entropy in the cluster variation method Phys. A 1982, 113, 315-337 10.1016/0378-4371(82)90023-1
Pelizzola, A. Generalized belief propagation for the magnetization of the simple cubic Ising model Nucl. Phys. B 2014, 880, 76-86 10.1016/j.nuclphysb.2014.01.008
Vinograd, V. L.; Perchuk, L. L. Informational models for the configurational entropy of regular solid solutions: Flat lattices J. Phys. Chem. 1996, 100, 15972-15985 10.1021/jp960416s
Vinograd, V. L.; Perchuk, L. L. Markov's chains and the configurational thermodynamics of a solid solution Vestnik Moskovskogo Universiteta (ser. Geol) 1992, 3, 44-58
Kemeny, J. G.; Snell, J. L. Finite Markov Chains; Springer-Verlag, 1976.
Ferschl, F. Markovketten; Lecture notes in operations research and mathematical systems; Springer-Verlag, 1970; Vol. 35.
Pielen, G. Detaillierte molekulare Simulationen und Parameterstudie fr ein ternäres Gemisch zur Weiterentwicklung des GEQUAC-Modells. Ph.D. Thesis, RWTH Aachen, 2005.
Mehrotra, S. On the implementation of a primal-dual interior point method SIAM Journal on optimization 1992, 2, 575-601 10.1137/0802028
Zapf, F. Monte-Carlo Verfahren zur Diskretisierung von Gittersystemen. MSc Thesis, Graz University of Technology, 2015, in German.
Maltezos, G. Simulation lokaler Zusammensetzungen. MSc Thesis, RWTH Aachen, 1987, in German.
König, L. Auswertung von Monte Carlo-Simulationen zur Validierung thermodynamischer Modelle. MSc Thesis, Graz University of Technology, 2013, in German.
Ehlker, G. H. Entwicklung der Gruppenbeitragsmethode GEQUAC zur thermodynamischen Beschreibung ausgeprägt nichtidealer Gemische. Ph.D. thesis, RWTH Aachen, 2001, in German.