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Cluster-Based Thermodynamics of Interacting Dice in a Lattice

by and *,†
Institute of Chemical Engineering and Environmental Technology, Graz University of Technology, 8010 Graz, Austria
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2020, 22(10), 1111; https://doi.org/10.3390/e22101111
Received: 24 August 2020 / Revised: 23 September 2020 / Accepted: 28 September 2020 / Published: 1 October 2020
(This article belongs to the Section Thermodynamics)
In this paper, a model for two-component systems of six-sided dice in a simple cubic lattice is developed, based on a basic cluster approach previously proposed. The model represents a simplified picture of liquid mixtures of molecules with different interaction sites on their surfaces, where each interaction site can be assigned an individual energetic property to account for cooperative effects. Based on probabilities that characterize the sequential construction of the lattice using clusters, explicit expressions for the Shannon entropy, synonymously used as thermodynamic entropy, and the internal energy of the system are derived. The latter are used to formulate the Helmholtz free energy that is minimized to determine thermodynamic bulk properties of the system in equilibrium. The model is exemplarily applied to mixtures that contain distinct isomeric configurations of molecules, and the results are compared with the Monte-Carlo simulation results as a benchmark. The comparison shows that the model can be applied to distinguish between isomeric configurations, which suggests that it can be further developed towards an excess Gibbs-energy, respectively, activity coefficient model for chemical engineering applications. View Full-Text
Keywords: Shannon entropy; discrete modeling; lattice model; dice model; cluster; cooperative effects; activity coefficients Shannon entropy; discrete modeling; lattice model; dice model; cluster; cooperative effects; activity coefficients
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MDPI and ACS Style

Mayer, C.; Wallek, T. Cluster-Based Thermodynamics of Interacting Dice in a Lattice. Entropy 2020, 22, 1111.

AMA Style

Mayer C, Wallek T. Cluster-Based Thermodynamics of Interacting Dice in a Lattice. Entropy. 2020; 22(10):1111.

Chicago/Turabian Style

Mayer, Christoph; Wallek, Thomas. 2020. "Cluster-Based Thermodynamics of Interacting Dice in a Lattice" Entropy 22, no. 10: 1111.

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