Discrete Modeling Approach as a Basis of Excess Gibbs-Energy Models for Chemical Engineering Applications

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.