Cluster-based thermodynamics of interacting dice in a lattice

Christoph Mayer, Thomas Wallek*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number1111
Pages (from-to)1-19
Number of pages19
Issue number10
Publication statusPublished - Oct 2020


  • Activity coefficients
  • Cluster
  • Cooperative effects
  • Dice model
  • Discrete modeling
  • Lattice model
  • Shannon entropy

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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