(181m) 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_i. 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, 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