Grand Equilibrium: vapour-liquid equilibria by a new molecular simulation method

Molecular modeling and simulation of organic electrolyte solutions for lithium ion batteries

Multi-criteria optimization is used for developing molecular models for ethylene carbonate (EC) and propylene carbonate (PC), organic solvents commonly used in Li-ion batteries. The molecular geometry and partial charges of the solvents are obtained from quantum mechanical calculations. Using a novel optimization strategy that combines systematic variations of the Lennard-Jones parameters with a reduced units approach, the models are fitted to experimental data on the liquid density, vapor pressure, relative permittivity, and self-diffusion coefficient. Since no experimental data for the self-diffusion coefficient of pure EC were available in the literature, they are measured in this work using a gradient-based nuclear magnetic resonance technique. For all pure component properties, excellent agreement between experiment and simulation is obtained. Moreover, the predictive capabilities of the new solvent models are assessed by comparison to experimental data for the liquid density and relative permittivity of mixtures of EC and PC. In addition, molecular models for the anions PF6-, BF4-, and ClO4- in solutions of their lithium electrolytes in PC are developed using experimental data on the solution densities. Finally, the self-diffusion coefficients of LiPF6 in PC and in aqueous solution are predicted and compared, showing that diffusion is much slower in the organic solution due to the formation of larger solvent shells around the ions. Furthermore, an analysis of the radial distribution functions in these solutions suggests that the ions have much less impact on the structure of the solvent PC than on water.

Hierarchical Multicriteria Optimization of Molecular Models of Water

Many widely used molecular models of water are built from a single Lennard-Jones site on which three point charges are positioned, one negative and two positive ones. Models from that class, denoted LJ3PC here, are computationally efficient, but it is well known that they cannot represent all relevant properties of water simultaneously with good accuracy. Despite the importance of the LJ3PC water model class, its inherent limitations in simultaneously describing different properties of water have never been studied systematically. This task can only be solved by multicriteria optimization (MCO). However, due to its computational cost, applying MCO to molecular models is a formidable task. We have recently introduced the reduced units method (RUM) to cope with this problem. In the present work, we apply the RUM in a hierarchical scheme to optimize LJ3PC water models taking into account five objectives: the representation of vapor pressure, saturated liquid density, self-diffusion coefficient, shear viscosity, and relative permittivity. Of the six parameters of the LJ3PC models, five were varied; only the H-O-H bond angle, which is usually chosen based on physical arguments, was kept constant. Our hierarchical RUM-based approach yields a Pareto set that contains attractive new water models. Furthermore, the results give an idea of what can be achieved by molecular modeling of water with models from the LJ3PC class.

Influence of repulsion on entropy scaling and density scaling of monatomic fluids

Entropy scaling is applied to the shear viscosity, self-diffusion coefficient, and thermal conductivity of simple monatomic fluids. An extensive molecular dynamics simulation series is performed to obtain these transport properties and the residual entropy of three potential model classes with variable repulsive exponents: n, 6 Mie (n = 9, 12, 15, and 18), Buckingham's exponential-six (α = 12, 14, 18, and 30), and Tang-Toennies (αT = 4.051, 4.275, and 4.600). A wide range of liquid and supercritical gas- and liquid-like states is covered with a total of 1120 state points. Comparisons to equations of state, literature data, and transport property correlations are made. Although the absolute transport property values within a given potential model class may strongly depend on the repulsive exponent, it is found that the repulsive steepness plays a negligible role when entropy scaling is applied. Hence, the plus-scaled transport properties of n, 6 Mie, exponential-six, and Tang-Toennies fluids lie basically on one master curve, which closely corresponds with entropy scaling correlations for the Lennard-Jones fluid. This trend is confirmed by literature data of n, 6 Mie, and exponential-six fluids. Furthermore, entropy scaling holds for state points where the Pearson correlation coefficient R is well below 0.9. The condition R > 0.9 for strongly correlating liquids is thus not necessary for the successful application of entropy scaling, pointing out that isomorph theory may be a part of a more general framework that is behind the success of entropy scaling. Density scaling reveals a strong influence of the repulsive exponent on this particular approach.

Quantum Cluster Equilibrium Theory for Multicomponent Liquids

In this work, we present a new theory to treat multicomponent liquids based on quantum-chemically calculated clusters. The starting point is the binary quantum cluster equilibrium theory, which is able to treat binary systems. The theory provides one equation with two unknowns. In order to obtain another linearly independent equation, the conservation of mass is used. However, increasing the number of components leads to more unknowns, and this requires linearly independent equations. We address this challenge by introducing a generalization of the conservation of arbitrary quantities accompanied by a comprehensive mathematical proof. Furthermore, a case study for the application of the new theory to ternary mixtures of chloroform, methanol, and water is presented. Calculated enthalpies of vaporization for the whole composition range are given, and the populations or weights of the different clusters are visualized.

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.

Modelling Sorption and Transport of Gases in Polymeric Membranes across Different Scales: A Review

Professor Giulio C. Sarti has provided outstanding contributions to the modelling of fluid sorption and transport in polymeric materials, with a special eye on industrial applications such as membrane separation, due to his Chemical Engineering background. He was the co-creator of innovative theories such as the Non-Equilibrium Theory for Glassy Polymers (NET-GP), a flexible tool to estimate the solubility of pure and mixed fluids in a wide range of polymers, and of the Standard Transport Model (STM) for estimating membrane permeability and selectivity. In this review, inspired by his rigorous and original approach to representing membrane fundamentals, we provide an overview of the most significant and up-to-date modeling tools available to estimate the main properties governing polymeric membranes in fluid separation, namely solubility and diffusivity. The paper is not meant to be comprehensive, but it focuses on those contributions that are most relevant or that show the potential to be relevant in the future. We do not restrict our view to the field of macroscopic modelling, which was the main playground of professor Sarti, but also devote our attention to Molecular and Multiscale Hierarchical Modeling. This work proposes a critical evaluation of the different approaches considered, along with their limitations and potentiality.

Multicriteria Optimization of Molecular Models of Water Using a Reduced Units Approach

Multicriteria optimization (MCO) is used to parametrize molecular models of water. The set of the best possible compromises between different objectives, the Pareto set, is determined. Calculating Pareto sets for optimization problems involving molecular simulations is computationally expensive. Therefore, we use a novel, highly efficient method, which is based on the fact that numerical results from molecular simulations can be interpreted as dimensionless numbers. Hence, they carry information on an entire class of models in physical units. This approach was applied here for the MCO of water models of the "one-center Lennard-Jones + point charge" type, in which the objectives were the quality of the description of the vapor pressure, liquid density, and enthalpy of vaporization. The results were compared to models from the literature. Significant improvements were observed. The new optimization method for the development of molecular models is efficient, robust, and broadly applicable.

Molecular Simulations and Mechanistic Analysis of the Effect of CO2 Sorption on Thermodynamics, Structure, and Local Dynamics of Molten Atactic Polystyrene

A simulation strategy encompassing different scales was applied to the systematic study of the effects of CO₂ uptake on the properties of atactic polystyrene (aPS) melts. The analysis accounted for the influence of temperature between 450 and 550 K, polymer molecular weights (M _w) between 2100 and 31000 g/mol, and CO₂ pressures up to 20 MPa on the volumetric, swelling, structural, and dynamic properties of the polymer as well as on the CO₂ solubility and diffusivity by performing molecular dynamics (MD) simulations of the system in a fully atomistic representation. A hierarchical scheme was used for the generation of the higher M _w polymer systems, which consisted of equilibration at a coarse-grained level of representation through efficient connectivity-altering Monte Carlo simulations, and reverse-mapping back to the atomistic representation, obtaining the configurations used for subsequent MD simulations. Sorption isotherms and associated swelling effects were determined by using an iterative procedure that incorporated a series of MD simulations in the NPT ensemble and the Widom test particle insertion method, while CO₂ diffusion coefficients were extracted from long MD runs in the NVE ensemble. Solubility and diffusivity compared favorably with experimental results and with predictions of the Sanchez-Lacombe equation of state, which was reparametrized to capture the M _w dependence of polymer properties with greater accuracy. Structural features of the polymer matrix were correctly reproduced by the simulations, and the effects of gas concentration and M _w on structure and local dynamics were thoroughly investigated. In the presence of CO₂, a significant acceleration of the segmental dynamics of the polymer occurred, more pronouncedly at low M _w. The speed-up effect caused by the swelling agent was not limited to the chain ends but affected the whole chain in a similar fashion.

Molecular Modeling Investigations of Sorption and Diffusion of Small Molecules in Glassy Polymers

With a wide range of applications, from energy and environmental engineering, such as in gas separations and water purification, to biomedical engineering and packaging, glassy polymeric materials remain in the core of novel membrane and state-of the art barrier technologies. This review focuses on molecular simulation methodologies implemented for the study of sorption and diffusion of small molecules in dense glassy polymeric systems. Basic concepts are introduced and systematic methods for the generation of realistic polymer configurations are briefly presented. Challenges related to the long length and time scale phenomena that govern the permeation process in the glassy polymer matrix are described and molecular simulation approaches developed to address the multiscale problem at hand are discussed.

Adsorption Thicknesses of Confined Pure and Mixing Fluids in Nanopores

In this paper, adsorption thicknesses of confined pure and mixing fluids in nanopores are quantitatively determined and their influential factors are specifically evaluated. First, a new analytical formulation is developed thermodynamically to calculate the adsorption thicknesses. Second, a new generalized equation of state (EOS), which considers the confinement effect-induced phenomena, is developed analytically for calculating the thermodynamic confined fluid phase behavior. Third, the modified model based on the generalized EOS and coupled with the parachor model is applied to calculate the vapor-liquid equilibrium (VLE) and fluid adsorptions for the pure CO₂, alkanes of C₁-C₁₀, and two mixtures of CO₂-C₁₀H₂₂ and CH₄-C₁₀H₂₂ in nanopores. Finally, the following five important factors are studied to evaluate their effects on the adsorption thickness: temperature, pressure, pore radius, wall-effect distance, and feed gas-to-liquid ratio (FGLR). The proposed modified EOS is found to be accurate for the VLE and adsorption isotherm calculations. The adsorption thicknesses of confined pure or mixing alkanes are increased with the increasing carbon number but decreased with the temperature increase. For the alkanes of C₁-C₁₀, the degree of temperature effect is strengthened with the carbon number increase. Moreover, the adsorption thicknesses are significantly decreased with the pore radius increase until r_p = 50 nm, after which they have slight changes or are even constant at any pore radii. On the other hand, the wall-effect distance (δ_p) increase causes the adsorption thickness to be linearly increased at δ_p/ r_p ≥ 0.02. In addition, the effects of the FGLR and pressure on the adsorption thicknesses at the nanoscale are found to be negligible.

Molecular simulation of the thermophysical properties and phase behaviour of impure CO2 relevant to CCS

Impurities from the CCS chain can greatly influence the physical properties of CO₂. This has important design, safety and cost implications for the compression, transport and storage of CO₂. There is an urgent need to understand and predict the properties of impure CO₂ to assist with CCS implementation. However, CCS presents demanding modelling requirements. A suitable model must both accurately and robustly predict CO₂ phase behaviour over a wide range of temperatures and pressures, and maintain that predictive power for CO₂ mixtures with numerous, mutually interacting chemical species. A promising technique to address this task is molecular simulation. It offers a molecular approach, with foundations in firmly established physical principles, along with the potential to predict the wide range of physical properties required for CCS. The quality of predictions from molecular simulation depends on accurate force-fields to describe the interactions between CO₂ and other molecules. Unfortunately, there is currently no universally applicable method to obtain force-fields suitable for molecular simulation. In this paper we present two methods of obtaining force-fields: the first being semi-empirical and the second using ab initio quantum-chemical calculations. In the first approach we optimise the impurity force-field against measurements of the phase and pressure-volume behaviour of CO₂ binary mixtures with N₂, O₂, Ar and H₂. A gradient-free optimiser allows us to use the simulation itself as the underlying model. This leads to accurate and robust predictions under conditions relevant to CCS. In the second approach we use quantum-chemical calculations to produce ab initio evaluations of the interactions between CO₂ and relevant impurities, taking N₂ as an exemplar. We use a modest number of these calculations to train a machine-learning algorithm, known as a Gaussian process, to describe these data. The resulting model is then able to accurately predict a much broader set of ab initio force-field calculations at comparatively low numerical cost. Although our method is not yet ready to be implemented in a molecular simulation, we outline the necessary steps here. Such simulations have the potential to deliver first-principles simulation of the thermodynamic properties of impure CO₂, without fitting to experimental data.

Solubility of Carbon Dioxide in Pentaerythritol Hexanoate: Molecular Dynamics Simulation of a Refrigerant-Lubricant Oil System

We have investigated the solubility and the solvation structure between a refrigerant (carbon dioxide, CO2) and a lubricant oil (pentaerythritol hexanoate, PEC6) by molecular dynamics simulations. First, to investigate the solubility, we calculated the vapor-liquid equilibrium pressure. The chemical potential of the liquid phase and the gas phase were calculated, and the equilibrium state was obtained from the crossing point of these chemical potentials. The equilibrium pressures agreed well with experimental data over a wide range of temperatures and mole fractions of CO2. Second, the solvation structure was also investigated on a molecular scale. We found the following characteristics. First, the tails of the lubricant oil are relatively rigid inside the ester groups but flexible beyond. Second, CO2 molecules barely enter the lubricant core as delimited by the ester groups. Third, the double-bonded oxygen atoms of the ester groups are good sorption sites for CO2. Fourth, only a few CO2 molecules are attached to more than one carbonyl oxygen simultaneously. Finally, there is also significant unspecific sorption of CO2 in the alkane tail region. These results indicate that increasing the size of the rigid lubricant core would probably decrease the solubility, whereas increasing the number of polar groups would increase it.

ls1 mardyn: The Massively Parallel Molecular Dynamics Code for Large Systems

The molecular dynamics simulation code ls1 mardyn is presented. It is a highly scalable code, optimized for massively parallel execution on supercomputing architectures and currently holds the world record for the largest molecular simulation with over four trillion particles. It enables the application of pair potentials to length and time scales that were previously out of scope for molecular dynamics simulation. With an efficient dynamic load balancing scheme, it delivers high scalability even for challenging heterogeneous configurations. Presently, multicenter rigid potential models based on Lennard-Jones sites, point charges, and higher-order polarities are supported. Due to its modular design, ls1 mardyn can be extended to new physical models, methods, and algorithms, allowing future users to tailor it to suit their respective needs. Possible applications include scenarios with complex geometries, such as fluids at interfaces, as well as nonequilibrium molecular dynamics simulation of heat and mass transfer.

Sorption and diffusion of carbon dioxide and nitrogen in poly(methyl methacrylate)

Molecular dynamics simulations are performed to determine the solubility and diffusion coefficient of carbon dioxide and nitrogen in poly(methyl methacrylate) (PMMA). The solubilities of CO2 in the polymer are calculated employing our grand canonical ensemble simulation method, fixing the target excess chemical potential of CO2 in the polymer and varying the number of CO2 molecules in the polymer matrix till establishing equilibrium. It is shown that the calculated sorption isotherms of CO2 in PMMA, employing this method well agrees with experiment. Our results on the diffusion coefficients of CO2 and N2 in PMMA are shown to obey a common hopping mechanism. It is shown that the higher solubility of CO2 than that of N2 is a consequence of more attractive interactions between the carbonyl group of polymer and the sorbent. While the residence time of CO2 beside the carbonyl group of polymer is about three times higher than that of N2, the diffusion coefficient of CO2 in PMMA is higher than that of N2. The higher diffusion coefficient of CO2, compared to N2, in PMMA is shown to be due to the higher (≈3 times) swelling of polymer upon CO2 uptake.

Grand canonical ensemble molecular dynamics simulation of water solubility in polyamide-6,6

Grand canonical ensemble molecular dynamics simulation is employed to calculate the solubility of water in polyamide-6,6. It is shown that performing two separate simulations, one in the polymeric phase and one in the gaseous phase, is sufficient to find the phase coexistence point. In this method, the chemical potential of water in the polymer phase is expanded as a first-order Taylor series in terms of pressure. Knowing the chemical potential of water in the polymer phase in terms of pressure, another simulation for water in the gaseous phase, in the grand canonical ensemble, is done in which the target chemical potential is set in terms of pressure in the gas phase. The phase coexistence point can easily be calculated from the results of these two independent simulations. Our calculated sorption isotherms and solubility coefficients of water in polyamide-6,6, over a wide range of temperatures and pressures, agree with experimental data.