Many-Body Effects on the Thermodynamics of Fluids, Mixtures, and Nanoconfined Fluids

Bulk viscosity of gaseous argon from molecular dynamics simulations

The bulk viscosity of dilute argon gas is calculated using molecular dynamics simulations in the temperature range 150-500 K and is found to be proportional to density squared in the investigated range of densities 0.001-1 kg m^{-3}. A comparison of the results obtained using Lennard-Jones and Tang-Toennies models of pair interaction potential reveals that the value of the bulk viscosity coefficient is sensitive to the choice of the pair interaction model. The inclusion of the Axilrod-Teller-Muto three-body interaction in the model does not noticeably affect the values of the bulk viscosity in dilute states, contrary to the previously investigated case of dense fluids.

Entropy scaling close to criticality: From simple to metallic systems

Entropy has recently drawn considerable interest both as a marker to detect the onset of phase transitions and as a reaction coordinate, or collective variable, to span phase transition pathways. We focus here on the behavior of entropy along the vapor-liquid phase coexistence and identify how the difference in entropy between the two coexisting phases vary in ideal and metallic systems along the coexistence curve. Using flat-histogram simulations, we determine the thermodynamic conditions of coexistence, critical parameters, including the critical entropy, and entropies along the binodal. We then apply our analysis to a series of systems that increasingly depart from ideality and adopt a metal-like character, through the gradual onset of the Friedel oscillation in an effective pair potential, and for a series of transition metals modeled with a many-body embedded-atoms force field. Projections of the phase boundary on the entropy-pressure and entropy-temperature planes exhibit two qualitatively different behaviors. While all systems modeled with an effective pair potential lead to an ideal-like behavior, the onset of many-body effects results in a departure from ideality and a markedly greater exponent for the variation of the entropy of vaporization with temperature away from the critical temperature.

Entropy in Molecular Fluids: Interplay between Interaction Complexity and Criticality

Using flat-histogram simulations, we calculate the entropy of molecular fluids along the vapor-liquid phase boundary. Our simulation approach is based on the evaluation of the canonical and grand-canonical partition functions, which, in turn, provide access to entropy through the statistical mechanics formalism. The results allow us to determine the critical entropy of molecular fluids and to uncover that the transition occurs symmetrically from an entropic standpoint. This can best be seen through the patterns exhibited by the thermodynamic variables temperature and pressure when plotted against the entropy of the coexisting phases. This behavior is found to hold for apolar, quadrupolar, and dipolar fluids. Finally, we identify functional forms that characterize the relation between thermodynamic variables and entropy along the coexistence curve up to the critical point.

A collection of forcefield precursors for metal-organic frameworks

A host of important performance properties for metal-organic frameworks (MOFs) and other complex materials can be calculated by modeling statistical ensembles. The principle challenge is to develop accurate and computationally efficient interaction models for these simulations. Two major approaches are (i) ab initio molecular dynamics in which the interaction model is provided by an exchange-correlation theory (e.g., DFT + dispersion functional) and (ii) molecular mechanics in which the interaction model is a parameterized classical force field. The first approach requires further development to improve computational speed. The second approach requires further development to automate accurate forcefield parameterization. Because of the extreme chemical diversity across thousands of MOF structures, this problem is still mostly unsolved today. For example, here we show structures in the 2014 CoRE MOF database contain more than 8 thousand different atom types based on first and second neighbors. Our results showed that atom types based on both first and second neighbors adequately capture the chemical environment, but atom types based on only first neighbors do not. For 3056 MOFs, we used density functional theory (DFT) followed by DDEC6 atomic population analysis to extract a host of important forcefield precursors: partial atomic charges; atom-in-material (AIM) C6, C8, and C10 dispersion coefficients; AIM dipole and quadrupole moments; various AIM polarizabilities; quantum Drude oscillator parameters; AIM electron cloud parameters; etc. Electrostatic parameters were validated through comparisons to the DFT-computed electrostatic potential. These forcefield precursors should find widespread applications to developing MOF force fields.

Predicting vapor liquid equilibria using density functional theory: A case study of argon

Predicting vapor liquid equilibria (VLE) of molecules governed by weak van der Waals (vdW) interactions using the first principles approach is a significant challenge. Due to the poor scaling of the post Hartree-Fock wave function theory with system size/basis functions, the Kohn-Sham density functional theory (DFT) is preferred for systems with a large number of molecules. However, traditional DFT cannot adequately account for medium to long range correlations which are necessary for modeling vdW interactions. Recent developments in DFT such as dispersion corrected models and nonlocal van der Waals functionals have attempted to address this weakness with a varying degree of success. In this work, we predict the VLE of argon and assess the performance of several density functionals and the second order Møller-Plesset perturbation theory (MP2) by determining critical and structural properties via first principles Monte Carlo simulations. PBE-D3, BLYP-D3, and rVV10 functionals were used to compute vapor liquid coexistence curves, while PBE0-D3, M06-2X-D3, and MP2 were used for computing liquid density at a single state point. The performance of the PBE-D3 functional for VLE is superior to other functionals (BLYP-D3 and rVV10). At T = 85 K and P = 1 bar, MP2 performs well for the density and structural features of the first solvation shell in the liquid phase.

Modeling of adsorption of CO2 in the deformed pores of MIL-53(Al)

Molecular simulations were performed to predict CO₂ adsorption in flexible metal-organic frameworks (MOFs). A generic force field was fitted to our experimental data to describe the non-bonded (electrostatic and van der Waals) interactions between CO₂ molecules and the large pore (lp) and narrow pore (np) forms of the MIL-53(Al) framework. With the new validated force field, it is possible to predict CO₂ uptake and enthalpy of adsorption at various applied external pressures that will modify the structure's pore configuration and allow us to have more control over the adsorption/desorption process. A sensitivity analysis of MOF adsorption properties to the variation of the force field parameters was also intensively studied. It was shown that relatively small variations of the adsorbate gas model can improve the quality of the numerical predictions of the experimental data. However, the variations must be kept small enough to not modify the properties of the gas itself.

Classical and quantum many-body effects on the critical properties and thermodynamic regularities of silicon

Using molecular simulation, we determine the critical properties of Si as well as the loci for several remarkable thermodynamic contours spanning the supercritical region of the phase diagram. We consider a classical three-body potential as well as a quantum (tight-binding) many-body model, and determine the loci for the ideality contours, including the Zeno line and the H line of ideal enthalpy. The two strategies (classical or quantum) lead to strongly asymmetric binodals and to critical properties in good agreement with each other. The Zeno and H lines are found to remain linear over a wide temperature interval, despite the changes in electronic structure undergone by the fluid along these contours. We also show that the classical and quantum model yield markedly different results for the parameters defining the H line, the exponents for the power-laws underlying the line of minima for the isothermal enthalpy and for the density required to achieve ideal behavior, most notably for the enthalpy.

Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. IV. Performance of many-body force fields and tight-binding schemes for the fluid phases of silicon

We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body (CMB) force fields, which allow to recover the tetrahedral organization in condensed phases of Si through, e.g., a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10%-15% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram with, e.g. at 6000 K, a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si.

Impact of Friedel oscillations on vapor-liquid equilibria and supercritical properties in two and three dimensions

We determine the impact of the Friedel oscillations on the phase behavior, critical properties, and thermodynamic contours in films [two dimensions (2D)] and bulk phases [three dimensions (3D)]. Using expanded Wang-Landau simulations, we calculate the grand-canonical partition function and, in turn, the thermodynamic properties of systems modeled with a linear combination of the Lennard-Jones and Dzugutov potentials, weighted by a parameter X (0<X<1). Varying X allows us to control the height of the first Friedel oscillation and to provide a complete characterization of the effect of the metal-like character in the potential on the thermodynamic properties over a wide range of conditions. For 3D systems, we are able to show that the critical parameters exhibit a linear dependence on X and that the loci for the thermodynamic state points, for which the system shows the same compressibility factor or enthalpy as an ideal gas, are two straight lines spanning the subcritical and supercritical regions of the phase diagram for all X values. Reducing the dimensionality to 2D results in a loss of impact of the Friedel oscillation on the critical properties, as evidenced by the virtually constant critical density across the range of X values. Furthermore, our results establish that the straightness of the two ideality lines is retained in 2D and is independent from the height of the first Friedel oscillation in the potential.

Scaling Laws and Critical Properties for fcc and hcp Metals

The determination of the critical parameters of metals has remained particularly challenging both experimentally, because of the very large temperatures involved, and theoretically, because of the many-body interactions that take place in metals. Moreover, experiments have shown that these systems exhibit an unusually strong asymmetry of their binodal. Recent theoretical work has led to new similarity laws, based on the calculation of the Zeno line and of the underlying Boyle parameters, which provided results for the critical properties of atomic and molecular systems in excellent agreement with experiments. Using the recently developed expanded Wang-Landau (EWL) simulation method, we evaluate the grand-canonical partition function, over a wide range of conditions, for 11 fcc and hcp metals (Ag, Al, Au, Be, Cu, Ir, Ni, Pb, Pd, Pt, and Rh), modeled with a many-body interaction potential. This allows us to calculate the binodal, Zeno line, and Boyle parameters and, in turn, obtain the critical properties for these systems. We also propose two scaling laws for the enthalpy and entropy of vaporization, and identify critical exponents of 0.4 and 1.22 for these two laws, respectively.