Characteristic Curves of the Lennard-Jones Fluid

Topology of thermodynamic potentials using physical models: Helmholtz, Gibbs, Grand, and Null

Thermodynamic potentials play a substantial role in numerous scientific disciplines and serve as basic constructs for describing the behavior of matter. Despite their significance, comprehensive investigations of their topological characteristics and their connections to molecular interactions have eluded exploration due to experimental inaccessibility issues. This study addresses this gap by analyzing the topology of the Helmholtz energy, Gibbs energy, Grand potential, and Null potential that are associated with different isothermal boundary conditions. By employing Monte Carlo simulations in the NVT, NpT, and μVT ensembles and a molecular-based equation of state, methane, ethane, nitrogen, and methanol are investigated over a broad range of thermodynamic conditions. The predictions from the two independent methods are overall in very good agreement. Although distinct quantitative differences among the fluids are observed, the overall topology of the individual thermodynamic potentials remains unaffected by the molecular architecture, which is in line with the corresponding states principle-as expected. Furthermore, a comparative analysis reveals significant differences between the total potentials and their residual contributions.

100 Years of the Lennard-Jones Potential

It is now 100 years since Lennard-Jones published his first paper introducing the now famous potential that bears his name. It is therefore timely to reflect on the many achievements, as well as the limitations, of this potential in the theory of atomic and molecular interactions, where applications range from descriptions of intermolecular forces to molecules, clusters, and condensed matter.

Using the Zeno line to assess and refine molecular models

The Zeno line is the locus of points on the temperature-density plane where the compressibility factor of the fluid is equal to one. It has been observed to be straight for a broad variety of real fluids, although the underlying reasons for this are still unclear. In this work, a detailed study of the Zeno line and its relation to the vapor-liquid coexistence curve is performed for two simple model pair-potential fluids: attractive square-well fluids with varying well-widths λ and Mie n-6 fluids with different repulsive exponents n. Interestingly, the Zeno lines of these fluids are curved, regardless of the value of λ or n. We find that for square-well fluids, λ ≈ 1.8 presents a Zeno line, which is the most linear over the largest temperature range. For Mie n-6 fluids, we find that the straightest Zeno line occurs for n between 8 and 10. Additionally, the square-well and Mie fluids with the straightest Zeno line showed the closest quantitative agreement with the vapor-liquid coexistence curve for experimental fluids that follow the principle of corresponding states (e.g., argon, xenon, krypton, methane, nitrogen, and oxygen). These results suggest that the Zeno line can provide a useful additional feature, in complement to other properties, such as the phase envelope, to evaluate molecular models.

Solid-liquid phase transition inside van der Waals nanobubbles: an atomistic perspective

The liquid-solid phase transition during the confinement of a van der Waals bubble is studied using molecular dynamics simulations. In particular, argon is considered inside a graphene bubble, where the outer membrane is a sheet of graphene, and the substrate is atomically flat graphite. A methodology to avoid metastable states of argon is developed and implemented to derive a melting curve of trapped argon. It is found that in the confinement, the melting curve of argon shifts toward higher temperatures, and the temperature shift is about 10-30 K. The ratio of the height to the radius of the GNB (H/R) decreases with increasing temperature. It also most likely undergoes an abrupt change through the liquid-crystal phase transition. The semi-liquid state of argon was detected in the transition region. At this state, the argon structure stays layered, but the atoms travel distances of several lattice constants.

Phase equilibria of symmetric Lennard-Jones mixtures and a look at the transport properties near the upper critical solution temperature

This study investigates phase equilibria and transport properties of five symmetric binary Lennard-Jones mixtures using molecular simulation and equation of state models. The mixtures are selected for their representation of different types of phase behavior and the research contributes to the development of simulation techniques, mixture theories and understanding of thermophysical mixture properties. A novel method is introduced for determining the critical end point (CEP) and critical azeotropic end point (CAEP) by molecular simulation. The van der Waals one-fluid theory is assessed for its performance in conjunction with Lennard-Jones equation of state models, while addressing different phase equilibrium types simultaneously. An empirical correlation is introduced to account for deviations between the equation of state and simulation that arise when using the same binary interaction parameter. This study also investigates the influence of the liquid-liquid critical point on thermophysical properties, which are found to exhibit no significant anomalies or singularities. System-size effects of diffusion coefficients are addressed by extrapolating simulation data to the thermodynamic limit and applying analytical finite-size corrections.

Development of thermodynamically consistent machine-learning equations of state: Application to the Mie fluid

A procedure for deriving thermodynamically consistent data-driven equations of state (EoS) for fluids is presented. The method is based on fitting the Helmholtz free energy using artificial neural networks to obtain a closed-form relationship between the thermophysical properties of fluids (FE-ANN EoS). As a proof-of-concept, an FE-ANN EoS is developed for the Mie fluids, starting from a database obtained by classical molecular dynamics simulations. The FE-ANN EoS is trained using first- (pressure and internal energy) and second-order (e.g., heat capacities, Joule-Thomson coefficients) derivative data. Additional constraints ensure that the data-driven model fulfills thermodynamically consistent limits and behavior. The results for the FE-ANN EoS are shown to be as accurate as the best available analytical model while being developed in a fraction of the time. The robustness of the "digital" equation of state is exemplified by computing physical behavior it has not been trained on, for example, fluid phase equilibria. Furthermore, the model's internal consistency is successfully assessed using Brown's characteristic curves.

Determining Brown's Characteristic Curves Using Molecular Simulation

Brown's characteristic curves define lines on the thermodynamic surface where special thermodynamic conditions hold. These curves are an important tool for the development of thermodynamic models of fluids. Yet, practically no experimental data for Brown's characteristic curves is available. In this work, a rigorous and generalized method for determining Brown's characteristic curves based on molecular simulation was developed. As multiple thermodynamic equivalent definitions apply for the characteristic curves, different simulation routes were compared. Based on this systematic approach, the most favorable route for determining each characteristic curve was identified. The computational procedure developed in this work combines molecular simulation, molecular-based equation of state, and the evaluation of the second virial coefficient. The new method was tested on a simple model system (the classical Lennard-Jones fluid) and different types of real substances (toluene, methane, ethane, propane, and ethanol). It is thereby shown that the method is robust and yields accurate results. Moreover, a computer code implementation of the method is presented.

Equation of state for the Mie (λr,6) fluid with a repulsive exponent from 11 to 13

An empirical multi-parameter equation of state in terms of the reduced Helmholtz energy is presented for the Mie (λ_r-6) fluid with a repulsive exponent λ_r from 11 to 13. The equation is fitted to an extensive dataset from molecular dynamics simulation as well as the second and third thermal virial coefficients. It is comprehensively compared with the SAFT-VR model and is a more accurate description of the considered fluid class. The equation is valid for reduced temperatures T/T_c from 0.55 to 4.5 and for reduced pressures of up to p/p_c = 265. A good extrapolation behavior and the occurrence of a single Maxwell loop down to the vicinity of the triple point temperature are realized.

The Line of Ideal Isothermal Compressibility

We have considered the line along which the values of the isothermal compressibility of a system are the same as they would be for an ideal gas. It was called the κ_T line. Various substances and models have been studied with the use of the multi-parameter equations of states, implemented in REFPROP (Lemmon, E. W.; Bell, I. H.; Huber, M. L.; McLinden, M. O. NIST standard reference database 23: Reference fluid thermodynamic and transport properties-REFPROP, version 10.0 (National Institute of Standards and Technology, 2018)), and numerical simulations, respectively. It is shown that in the reduced variables, all κ_T lines can be described by the same relation following from the van der Waals equation. This similarity appears to be valid even for the systems with non-straight Zeno lines. Deviations within ∼5% are observed only near the binodals.