267501 Lattice Model Based Upon Information Theory

Monday, October 29, 2012
Hall B (Convention Center )
Thomas Wallek, Martin Pfleger and Andreas Pfennig, Institute of Chemical Engineering and Environmental Technology, Graz University of Technology, Graz, Austria

Lattice Models

Lattice theories are widely-used approaches for modeling condensed-phase behaviour, allowing for relatively straightforward realizing conceptions on intermolecular energies. Such models can conveniently be verified by molecular simulation. While the predominant number of lattice models, like those in the broadest sense following Guggenheim's work, is based upon classical statistical thermodynamics, the present contribution describes application of an information-theory based approach, subsumed under the ‘method of discrete modeling'.

The Method of Discrete Modeling

Discrete Modeling is based upon straightforward formulation of internal energy U and entropy S of the system as functions of distribution variables, i.e. frequencies of discrete states of the lattice sites. These distribution variables are directly related to the molecule numbers Ni of the system components i by summation over all states. S is derived from Shannon's approach for information, interpreting ‘probability' as the relative frequency of a discrete state of a lattice site among all possible states. Since both U and S are formulated as homogeneous functions of the distribution variables, Euler's homogeneous function theorem can be utilised for establishing a set of equations that permits the formulation of system properties like U, S and free enthalpy G, as explicit functions of molecule numbers Ni. From these functions, activity coefficients and other excess properties can easily be derived for model evaluation. The method has successfully been applied to the ideal gas model by derivation of the equation of state, heat capacity as well as the Maxwell-Boltzmann distribution of energies [1]-[2], while the present contribution focuses on application of discrete modeling to condensed phases [3].

Application and Analysis

Application of the method is illustrated by a simple example lattice model with focus on demonstrating both analogies and differences between conventionally used statistical thermodynamics and discrete modeling as well as identifying the potential of discrete modeling for effective implementation of conceptions on intermolecular energies.

References

[1] Pfleger M., ‘A Statistical Approach for Deducing Equations of State', oral presentation, 8th European Congress of Chemical Engineering together with ProcessNet-Annual Meeting, Berlin, 2011

[2] Pfleger M., ‘Applying Discrete Modeling to Ideal Gas and Real Gases', oral presentation, 20th International Congress of Chemical and Process Engineering,  Prague, 2012

[3] Wallek T., ‘Thermodynamic Modeling Based Upon Information Theory', oral presentation, 20th International Congress of Chemical and Process Engineering,  Prague, 2012


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