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

Abstract

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 g E -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 g E -model development in view of activity coefficients for liquid mixtures.

Cluster-Based Thermodynamics of Interacting Dice in a Lattice

“…Therefore, only the component type at each cluster position influences the equilibrium distribution of the probabilities. This case, where the molecules are modeled like uniform spheres rather than six-sided dice, connects this work to previous work [ 41 ]. The effects of such a gross simplification on the model are discussed for both pure components and two-component mixtures in the following section.…”

“…Now, if the insertions at B , C , and D are assumed to be only dependent upon A and not upon one another, Equation ( 21 ) can be split up into which is analogous to a constraint originally that was proposed by Vinograd et al [ 36 ] and that was extended in a previous work to three-dimensional lattices for pure components [ 41 ]. The interpretation of Equation ( 22 ) is that, first, the central molecule at position A is selected based on the global composition of the lattice; then, each of the neighbors is added to the cluster, with a probability of its respective component that is dependent on a .…”

“…As a continuation of our previous work [ 38 , 39 , 40 , 41 ], in this paper, the basic cluster approach proposed by Vinograd [ 36 , 37 ] is extended to two-component systems of six-sided dice in a simple cubic lattice.…”

Orientalism in Joseph Conrad’s novel Almayer’s Folly (1895): a post-colonial approach

“…Quality refers to the what, how, when, and where of a thing its essence and ambience. Qualitative research thus refers to the meanings, concepts, definitions, characteristics, metaphors, symbols, and descriptions of things (Wallek, Mayer, & Pfennig, 2018). In contrast, quantitative research refers to counts and measures of things (Berg, 2015).…”

“…In analyzing data, the writer uses descriptive technique. Descriptive technique is an explanation and interpretation the data related to the topic (Wallek et al, 2018).…”