Cluster-Based Thermodynamics of Interacting Dice in a Lattice

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

Discrete Modeling of Lattice Systems: The Concept of Shannon Entropy Applied to Strongly Interacting Systems

Discrete modeling is a novel approach that uses the concept of Shannon entropy to develop thermodynamic models that can describe fluid-phase behavior. While previous papers have focused on reviewing its theoretical background and application to the ideal-gas model as one limiting case for fluid phases, this paper addresses its application to lattice models for strongly interacting condensed phase systems, which constitute the other limiting case for fluids. The discrete modeling approach is based on the discrete energy classes of a lattice system of finite size, represented by a distribution of discrete local compositions. In this way, the model uses the same level of discretization as classical statistical thermodynamics in terms of its partition functions, yet avoids (1) a priori averaging of local compositions by utilizing a distribution, and (2) confinement to systems of infinite size. The subsequent formulation of the probabilities of discrete energy classes serves as the basis for introducing the concept of Shannon information, equivalent to thermodynamic entropy, and for deriving the equilibrium distribution of probabilities by constrained maximation of entropy. The results of the discrete model are compared to those derived from Monte Carlo simulations and by applying the Guggenheim model of chemical theory. We point out that this applicability of discrete modeling to systems of finite size suggests new possibilities for model development

Discrete Modeling: Thermidynamics Based on Shannon Entropy and Discrete States of Molecules

peer reviewedaudience: researcher, professional, student, otherThermodynamic modeling using the concept of Shannon entropy is a promising approach, especially in the field of describing fluid-phase behavior. This paper introduces the method of discrete modeling, using the ideal-gas model as an illustrative example, and derives a general equation of state. Discrete modeling is based on discrete states of individual molecules. It utilizes the special characteristics of Shannon entropy to model the statistical behavior of systems by applying the maximum entropy principle to its constituents in a straightforward manner. The presented method and the general form of the equation of state thus obtained allow the derivation of equations of states for real fluids. As a novelty, it also allows for the description of the microscopic distribution of the mechanical states of individual molecules. Considering the kinetic states of the particles this includes the Maxwell−Boltzmann distribution, the caloric equation of state, and the heat capacity of the ideal gas

Surrogate Generation and Evaluation for Diesel Fuel

peer reviewedThe correct representation of a fuel in terms of its physical and chemical properties and its combustion kinetics poses a challenge to modern engine development when state-of-the-art simulation technology is used. In this context, a promising approach is the use of surrogates that emulate the properties of real fuels, where the surrogates are made up of a significantly lower number of components than the original fuels. The goal of this paper is to present an algorithm that can be used to generate surrogates composed of real chemical components, as opposed to pseudo-components. The algorithm was developed by simultaneously fitting the true boiling point (TBP) curve, the liquid density at 15 °C, and the cetane number. To illustrate the algorithm, surrogates for four different fuels were generated: a commercially available European diesel and three research diesel proposed by the Fuels for Advanced Combustion Engines (FACE) CRC Research Group. Two of the resulting surrogates were produced on a lab scale and subjected to laboratory examination. For validation, the experimental data for these two surrogates were compared to those for the target fuels and to data generated by thermodynamic models on the basis of the compositions of the surrogates. Both the fitted properties and additional properties, which were not used for fitting, were compared to experimental properties, such as the ASTM D86 boiling curve, content of aromatics, flash point, heating value, cloud point, viscosity, and temperature dependency of the liquid-phase viscosity and density. We demonstrate that the proposed algorithm generates surrogates of approximately 10 real components, which show excellent agreement with the original target fuels