Lorentz-Berthelot Research Articles

Molecular Dynamics Simulation of the Three-Phase Equilibrium Line of CO2 Hydrate with OPC Water Model.

The three-phase coexistence line of the CO2 hydrate was determined using molecular dynamics (MD) simulations. By using the classical and modified Lorentz-Berthelot (LB) parameters, the simulations were carried out at 10 different pressures from 3 to 500 MPa. For the OPC water model, simulations with the classic and the modified LB parameters both showed negative deviations from the experimental values. For the TIP4P/Ice water model, good agreement with experimental equilibrium data can be achieved when the LB parameter is adjusted based on the solubility of CO2 in water. Our results also show that the influence of the water model on the equilibrium prediction is much larger than the CO2 model. Current simulations indicated that the H2O-H2O and H2O-CO2 cross-interactions' parameters might contribute equally to the accurate prediction of T3. According to our simulations, the prediction of T3 values showed relatively higher accuracy while using the combination of TIP4P/Ice water and EPM2 CO2 with modified LB parameter. Furthermore, varied χ values are recommended for accurate T3 estimation over a wide pressure range. The knowledge obtained in this study will be helpful for further accurate MD simulation of the process of CO2/CH4 replacement.

Influence of the Lennard-Jones Combination Rules on the Simulated Properties of Organic Liquids at Optimal Force-Field Parametrization.

We recently introduced the CombiFF scheme [Oliveira et al., J. Chem. Theory Comput. 2020, 16, 7525], an approach for the automated refinement of force-field parameters against experimental condensed-phase data for large compound families. Using this scheme, once the time-consuming task of target-data selection and curation has been performed, the force-field optimization itself is both straightforward and fast. As a result, CombiFF provides an ideal framework for evaluating the influence of functional-form decisions on the accuracy of a force field at an optimal level of parametrization. We already used this approach to assess the effect of using an all-atom representation compared to united-atom representations in the force field [Oliveira et al., J. Chem. Theory Comput. 2022, 18, 6757]. Here, CombiFF is applied to assess the effect of three Lennard-Jones combination rules, geometric-mean (GM), Lorentz-Berthelot (LB), or Waldman-Hagler (WH), on the simulated properties of organic liquids. The comparison is performed in terms of the experimental liquid density ρliq, vaporization enthalpy ΔHvap, surface-tension coefficient γ, static relative dielectric permittivity ϵ, and self-diffusion coefficient D. The calibrations of the three force-field variants are carried out independently against 2044 experimental values for ρliq, and ΔHvap concerning 1516 compounds. The resulting root-mean-square deviations from experiment are 30.0, 26.9, and 36.7 kg m-3 for ρliq and 2.8, 2.8, and 2.9 kJ mol-1 for ΔHvap, when applying the GM, LB, and WH combination rules, respectively. In terms of these (and the other) properties, the three combination rules perform comparatively well, with the GM and LB results being more similar to each other and slightly more accurate compared to experiment. In contrast, the use of distinct combination rules for the parameter calibration and property calculation leads to much larger errors.

The performance of OPC water model in prediction of the phase equilibria of methane hydrate.

Molecular dynamics (MD) simulations were performed to determine the three-phase coexistence line of sI methane hydrates. The MD simulations were carried out at four different pressures (4, 10, 40, and 100 MPa) by using the direct phase coexistence method. In current simulations, water was described by either TIP4P/Ice or "optimal" point charge (OPC) models and methane was described as a simple Lennard-Jones interaction site. Lorentz-Berthelot (LB) combining rules were used to calculate the parameters of the cross interactions. For the OPC model, positive deviations from the energetic LB rule were also considered based on the solubility of methane in water. For the TIP4P/Ice water model, the obtained three phase coexistence temperatures showed good agreement with experiment data at higher pressures, which is consistent with previous predictions. For the OPC water model, simulations using the classic and the modified LB parameters both showed negative deviations to the experimental values. Our results also indicated that the deviation of the T3 prediction by the OPC model was not closely correlated with the predicted melting point of ice. At 4 MPa, the modified OPC model showed a better prediction of hydrate equilibrium temperature, even better than the prediction by TIP4P/Ice. Considering the relatively higher accuracy in biomolecular MD of the OPC model, it is suggested that this model may have a better performance in hydrate MD simulations of biomolecule-based additives.

Determining explicit ion-lipid cross-terms for MD simulation using high-dimensional parameter search

Molecular dynamics simulations depend on carefully developed force-fields to give results that reproduce experimental data. Force-fields for lipids and ions are typically constructed separately to work in water. Mutual interactions between lipids and ions are estimated using approximate mixing rules for their Lennard-Jones (LJ) components. Herein, we assess the use of the Lorentz-Berthelot (LB) mixing rules, which are typically used for computing the LJ components of ion-ligand interactions, including ion-lipid interactions.

Use of a New Size-Weighted Combining Rule to Predict Adsorption in Siliceous Zeolites

The results of extensive grand canonical Monte Carlo simulations of adsorption in siliceous zeolites are reported and used to assess the accuracy of a size-weighted (SW) combining rule for Lennard-Jones cross-parameters. Adsorption isotherms, Henry’s Law constants, and isosteric heats were computed for 45 different systems consisting of unary, binary, ternary, and quaternary mixtures of light hydrocarbons in silicalite, pure methanol, and carbon dioxide in silicalite and light hydrocarbons in siliceous forms of the zeolites TON, LTA, and CHA. A comparison is made with the conventional Lorentz–Berthelot (LB) combining rule as well as other force fields and experimental data. In addition, the influence of intramolecular scaling methods and long-range tail corrections on computed properties was evaluated. Overall, the SW combining rule gives similar, and sometimes superior, results when compared to the LB combining rule as well as force fields tuned to experimental data.

A Systematic Study of Cubic Equations of State with van der Waals Mixing Rules and Different Combining Rules in Predicting the Densities of LNG and Natural Gas Model Systems

Cubic equations (EoSs) of state are successfully used in petroleum and natural gas industry. In order to extend these equations to mixtures, van der Waals mixing rules with Lorentz-Berthelot (LB) combining rules are often employed; however, the accuracies of these EoSs in predicting the densities of hydrocarbon mixtures are not adequate. The main objective of this study was comparing 13 EoSs coupled with 10 combining rules in predicting the densities of hydrocarbon mixtures. Binary and ternary liquid mixtures, LNG mixtures and synthetic natural gas mixtures comprising 752 data points were collected and used in this study. Results revealed that for predicting the liquid densities of binary and ternary mixtures, the Schmidt and Wenzel (SW) EoS coupled with Hudson-McCoubrey (HMC) or LB combining rules are the best among the others. The SW EoS coupled with the LB combining rules were also the best in predicting the densities of the LNG mixtures. Additionally, the LB combining rules are the best in predicting natural gas mixtures densities using the Patel and Teja (PT), SW and Patel-Teja-Valderrama (PTV) EoSs. In general, it was found that the Redlich-Kwong (RK) family EoSs, SW and Trebble-Bishnoi-Salim (TBS) EoSs are best coupled with the LB combining rules. However, the Peng and Robinson (PR) family EoSs with Halgren (HHG) combining rules were in better agreement with experimental data. The Waldman-Hagler (WH) combining rules lacked predictability when coupled with the most EoSs.

Free Energy-Based Coarse-Grained Force Field for Binary Mixtures of Hydrocarbons, Nitrogen, Oxygen, and Carbon Dioxide.

The free energy based Lennard-Jones 12-6 (FE-12-6) coarse-grained (CG) force field developed for alkanes1 has been extended to model small molecules of light hydrocarbons (methane, ethane, propane, butane, and isobutane), nitrogen, oxygen, and carbon dioxide. The adjustable parameters of the FE-12-6 potential are determined by fitting against experimental vapor-liquid equilibrium (VLE) curves and heat of vaporization (HOV) data for pure substance liquids. Simulations using the optimized FE-12-6 parameters correctly reproduced experimental measures of the VLE, HOV, density, vapor pressure, compressibility, critical point, and surface tension for pure substances over a wide range of thermodynamic states. The force field parameters optimized for pure substances were tested on methane/butane, nitrogen/decane, and carbon dioxide/decane binary mixtures to predict their vapor-liquid equilibrium phase diagrams. It is found that for nonpolar molecules represented by different sized beads, a common scaling factor (0.08) that reduces the strength of the interaction potential between unlike beads, generated using Lorentz-Berthelot (LB) combination rules, is required to predict vapor-liquid phase equilibria accurately.

Computer Simulation Study of the Structure of LiCl Aqueous Solutions: Test of Non-Standard Mixing Rules in the Ion Interaction

Aqueous solutions of LiCl have recently received much attention in connection with the study of the anomalies of supercooled water and its polyamorphism. From the point of view of computer simulation, there is need for a force field that can reproduce the structural and dynamical properties of this solution, and more importantly it is also simple enough to use in large scale simulations of supercooled states. We study by molecular dynamics the structure of the LiCl-water solutions with the force field proposed by Joung and Cheatham (J. Phys. Chem. B 2008, 112, 9020) appropriate for the water TIP4P-Ew model potential. We found that this force field does not reproduce the experimental ion pairing when the Lorentz-Berthelot (LB) rules are used. By incorporating deviations to the LB rules to obtain the crossed interactions between the ions, it is possible to get agreement with experiment. We have studied how the modification of the LB rule affects the structural and thermodynamic properties of the solution at increasing concentration of the solution from the low (around 2%) to medium (around 14%) concentration regimes. We also tested the transferability of the Joung and Cheatham force field to the water TIP4P/2005 model that works very well for supercooled water.

Influence of combining rules on the cavity occupancy of clathrate hydrates by Monte Carlo simulations

Assessing the exact amount of gas stored in clathrate-hydrate structures can be addressed by either molecular-level simulations (e.g. Monte Carlo) or continuum-level modelling (e.g. van der Waals–Platteeuw-theory-based models). In either case, the Lorentz–Berthelot (LB) combining rules are by far the most common approach for the evaluation of the parameters between the different types of atoms that form the hydrate structure. The effect of combining rules on the calculations has not been addressed adequately in the hydrate-related literature. Only recently the use of the LB combining rules in hydrate studies has been questioned.In the current study, we report an extensive series of Grand Canonical Monte Carlo simulations along the three-phase (H–Lw–V) equilibrium curve. The exact geometry of hydrate crystals is known from diffraction experiments and, therefore, the formation of hydrates can be simulated as a process of gas adsorption in a solid porous material. We examine the effect of deviations from the LB combining rules on the cavity occupancy of argon hydrates and work towards quantifying it. The specific system is selected as a result of the characteristic behaviour of argon to form hydrates of different structures depending on the prevailing pressure. In particular, an sII hydrate is formed at lower pressures, while an sI hydrate is formed at intermediate pressures, and finally an sH hydrate is formed at higher pressures.

Development of kinetic Monte Carlo and Bin-Monte Carlo schemes for simulation of mixtures – vapor–liquid equilibria & adsorption

We describe algorithms for the recently developed Bin-Monte Carlo (Bin-MC) method (Fan et al., 2012) and kinetic Monte Carlo (kMC) (Ustinov and Do, 2012) to simulate binary liquid mixtures, and compare them with simulations of vapour–liquid equilibria from the canonical and Gibbs MC methods. We have found that in kMC, the rule to choose a molecule to move rests purely on the mobility, irrespective of molecular weight. In the Bin-MC, the choice of a molecule to move from one bin to another bin depends on the selection of a component with equal probability. Our simulations show that the Bin-MC and kMC schemes are very effective for the purpose of describing thermodynamic properties and density profiles across the vapour–liquid interface, and show that the Lorentz–Berthelot (LB) mixing rule works well for subcritical systems, and to improve the description of systems having one component under supercritical condition the cross collision diameter and the cross well depth have to be modified from the LB mixing rules, which is in agreement with previous studies (for example, (Wu and Sadus, 2000)). The benefits of the kMC scheme for the direct determination of chemical potential were also demonstrated with a study of adsorption of an argon–krypton mixture on graphite.

Limitations of the Derjaguin Approximation and the Lorentz−Berthelot Mixing Rule

We investigate the Derjaguin approximation by explicitly determining the interactions between two spherical colloids using density functional theory solved in cylindrical coordinates. The colloids are composed of close-packed Lennard-Jones particles. The solvent particles are also modeled via Lennard-Jones interactions. Cross interactions are assumed to follow the commonly used Lorentz-Berthelot (LB) mixing rule. We demonstrate that this system may display a net repulsive interaction across a substantial separation range. This contradicts the Hamaker-Lifshitz theory, which predicts attractions between identical polarizable particles immersed in a polarizable medium. The source of this repulsion is traced to the LB mixing rule. Surprisingly, we also observe nonmonotonic convergences to the Derjaguin limit. This behavior is best understood by decomposing the total interaction between the colloids into separate contributions. With increasing colloid size, each of these contributions approach the Derjaguin limit in a monotonic manner, but their different rates of convergence mean that their sum may display nonmonotonic behavior.

Coarse-grained models for fluids and their mixtures: Comparison of Monte Carlo studies of their phase behavior with perturbation theory and experiment

The prediction of the equation of state and the phase behavior of simple fluids (noble gases, carbon dioxide, benzene, methane, and short alkane chains) and their mixtures by Monte Carlo computer simulation and analytic approximations based on thermodynamic perturbation theory is discussed. Molecules are described by coarse grained models, where either the whole molecule (carbon dioxide, benzene, and methane) or a group of a few successive CH(2) groups (in the case of alkanes) are lumped into an effective point particle. Interactions among these point particles are fitted by Lennard-Jones (LJ) potentials such that the vapor-liquid critical point of the fluid is reproduced in agreement with experiment; in the case of quadrupolar molecules a quadrupole-quadrupole interaction is included. These models are shown to provide a satisfactory description of the liquid-vapor phase diagram of these pure fluids. Investigations of mixtures, using the Lorentz-Berthelot (LB) combining rule, also produce satisfactory results if compared with experiment, while in some previous attempts (in which polar solvents were modeled without explicitly taking into account quadrupolar interaction), strong violations of the LB rules were required. For this reason, the present investigation is a step towards predictive modeling of polar mixtures at low computational cost. In many cases Monte Carlo simulations of such models (employing the grand-canonical ensemble together with reweighting techniques, successive umbrella sampling, and finite size scaling) yield accurate results in very good agreement with experimental data. Simulation results are quantitatively compared to an analytical approximation for the equation of state of the same model, which is computationally much more efficient, and some systematic discrepancies are discussed. These very simple coarse-grained models of small molecules developed here should be useful, e.g., for simulations of polymer solutions with such molecules as solvent.

Thermophysical Properties of Low-Density Pure Alkanes and Their Binary Mixtures Calculated by Means of an (n-6) Lennard-Jones Temperature-Dependent Potential

Self-consistent calculations of interaction pVT-virial coefficients B 12(T), viscosities η mix (T), and diffusion coefficients D 12(T) of binary mixtures of the alkanes C n H2n + 2 (n < 6) are presented. This study is based on the recently developed model of the (n-6) Lennard-Jones temperature-dependent potential (LJTDP) and uses already obtained potential parameters of the pure alkanes as input data. The well-known and simple Lorentz-Berthelot (LB) and the more laborate Tang-Toennies (TT) mixing rules are applied to the potential parameters of the pure alkanes in order to determine those of the mixtures. The new Hohm–Zarkova–Damyanova (HZD) mixing rule, which is an extension of the TT-mixing rule, is also considered. The HZD takes into account that for the LJTDP model, in general, the repulsive parameter is an independent variable whose value n ≠ 12. As in a recent examination of binary mixtures of globular molecules, the LB-mixing rule is superior to TT- and HZD-mixing rules when calculating equilibrium properties such as B 12(T). For the transport properties η mix (T) and D 12(T), the new mixing rule performs slightly better.

Effects of surface heterogeneity on the adsorption of nitrogen on graphitized thermal carbon black

In this paper, we study the surface heterogeneity and the surface mediation on the intermolecular potential energy for nitrogen adsorption on graphitized thermal carbon black (GTCB). The surface heterogeneity is modeled as the random distribution of “effective” carbonyl functional groups on the graphite surface. The molecular parameters and the discrete charges of this carbonyl group are taken from Jorgensen, et al. (J. Am. Chem. Soc., (1984) 106, 6638) while those for nitrogen (dispersive parameters and discrete charges) are taken from Murthy et al. (Mol. Phys., (1983) 50, 531) in our Grand Canonical Monte Carlo (GCMC) simulation. The solid surface mediation in the reduction of intermolecular potential energy between two fluid molecules was taken from a recent work by Do et al. (Langmuir, (2004) 20, 7623). Our simulation results accounting for the surface heterogeneity and surface mediation on intermolecular potential energy were compared with the experimental data of nitrogen at 77 and 90 K. The solid-fluid dispersive parameters are determined from the Lorentz-Berthelot (LB) rule. The fraction of the graphite surface covered with carbonyl functional groups was then derived from the consideration of the Henry constant, and for the data of Kruk et al. (Langmuir, (1999) 15, 1435) we have found that 1% of their GTCB surface is covered with “effective” carbonyl functional groups. The damping constant, due to surface mediation, was determined from the consideration of the portion of the adsorption isotherm where the first layer is being completed, and it was found to take a value of 0.0075. With these parameters, we have found that the GCMC simulation results describe the data over the complete range of pressure substantially better than any other MC models in the literature. The implication of this work is demonstrated with local adsorption isotherms of 10 and 20 A slit pores. One was obtained without allowance for surface mediation, while the other correctly accounts for these factors. The two local isotherms differ substantially, and the implication is that if we used incorrect local isotherms (i.e. without the surface mediation) the pore size distribution would be incorrectly derived.

Determination of collision cross-sectional parameters from experimentally measured gas diffusion coefficients

Collision cross-sectional parameters such as collision diameters, σ AB, and maximum attractive energies, ε AB, between two molecules A and B, were obtained from experimentally measured gas diffusion coefficients. The diffusion coefficients at infinite dilution were measured at different temperatures (315.2–449.8 K), by a gas chromatographic method called reverse-flow gas chromatography (RF-GC), for the following systems: CO–H 2, CO–He, CO 2–H 2, CO 2–He, C 2H 4–N 2 and C 2H 6–N 2. The obtained diffusion coefficients and cross-sectional parameters, are compared with literature values, which have been determined by other experimental and theoretical methods. The most interesting finding is the large deviation of the directly determined cross interactions of the present work, from those obtained by using simple combining Lorentz–Berthelot (LB) rules and/or other than diffusion transport properties of molecules.

Some effects of deviations from the Lorentz-Berthelot combining rules for mixtures of Lennard-Jones fluids

Some effects of deviations from the Lorentz-Berthelot (LB) combining rules for LennardJones binary mixtures are studied with a model in which both constituents have the same size and energy interaction parameters but the cross interaction deviates substantially from the LB rules. A single temperature and density and two compositions are studied by molecular dynamics simulations and the recently proposed Duh-Haymet-Henderson (DHH) intergral equation theory. The agreement is satisfactory in both cases. The excess volume and enthalpy of mixing are also studied systematically with the DHH theory. Some interesting phenomena are observed for these no-LB mixtures.

Integral equation theory for Lennard-Jones fluids: The bridge function and applications to pure fluids and mixtures

The pure Lennard-Jones fluid and various binary mixtures of Lennard-Jones fluids are studied by both molecular dynamics simulation and with a new integral equation which is based on that proposed by Duh and Haymet recently [J. Chem. Phys. 103, 2625 (1995)]. The structural and thermodynamic properties calculated from this integral equation show excellent agreement with simulations for both pure fluids and mixtures under the conditions which we have studied. For mixtures, the effect of deviations from the Lorentz-Berthelot (LB) mixing rules for the interaction parameters between unlike species is studied. Positive deviations from the nonadditivity of the molecular cores leads to an entropy driven tendency for the species to separate. This tendency persists even in the presence of a deviation from the LB rule for the energy parameter which enhances the attraction of the unlike species. On the other hand, in the case of negative deviations from nonadditivity, the tendency for association may be either energy or entropy driven, depending on the size ratio.

Excess properties of liquid mixtures from computer simulation: a coupling-parameter approach to the determination of their dependence on molecular asymmetry

A computer simulation technique is developed for the accurate determination of the change in the excess properties of binary model mixtures due to deviations of the unlike interaction parameters from the Lorentz-Berthelot (LB) combining rules. The technique avoids the explicit calculation of excess (mixing) properties, and the subsequent subtraction. The method requires a single isobaric-isothermal simulation of the reference Lorentz-Berthelot mixture, regardless of the extent of the deviations. The extension of the present approach to the general case of non-Lorentz-Berthelot reference systems is also discussed.