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267501 Lattice Model Based Upon Information Theory

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 *N _{i}*
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

*N*. 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].

_{i}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, 8^{th}
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, 20^{th} International Congress of Chemical and Process
Engineering, Prague, 2012

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

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