Berthelot Mixing Rules Research Articles

Molecular dynamics simulation of argon isochoric transition to supercritical state

AbstractThe effect of the initial atoms distribution on the molecular dynamics (MD) simulation of a model atomic fluid (argon) is investigated for the case of the isochoric phase transition to the supercritical state. In particular, the case of uniformly distributed atoms in the simulation domain is compared with the case of separated liquid and vapor atoms. The sensitivity of simulations to asymmetric nanoscale perturbations in the boundary is also studied. Despite its high computational cost, the MD approach has the potential to successfully address long‐standing problems in computational fluid dynamics (CFD), especially those associated with mathematical singularities, such as contact angles, vortices, phase transitions and so forth. Unlike conventional CFD simulations, where the initial condition is the pressure or velocity distribution in the simulation domain, MD simulations also require the initial position of each molecule. Thus, it is important to understand whether a judicious choice of the initial distribution of molecules can reduce the overall computation time of the simulation. The evolution of the model fluid system during the phase transition was simulated using a Lennard‐Jones interatomic potential, corrected with the Lorentz–Berthelot mixing rule for the interactions with the solid walls. The system was allowed to relax until equilibrium, and then a Heaviside temperature step was applied to the wall to bring the system to supercritical conditions. Results show the initial choice of the atoms distribution can significantly affect the computational time, while the effect of asymmetric perturbations on the boundary is negligible.

Modeling the Solubility of Hydrogen Sulfide in Ionic Liquids Using van der Waals Equation of State

This study mathematically models the solubility of hydrogen sulfide in ten ionic liquids including 1-(2-hydroxyethyl)-3-imidazolium [Hoemim]+ with three different anions, 1-ethyl-3-methylimidazolium [emim]+ with two different anions, 1-hexyl-3-methylimidazolium [hmim]+ with two different anions, and 1-butyl-3-methylimidazolium [bmim]+ with three different anions. The modeling was performed by van der Waals (vdW) equation of state as a φ-φ approach in which the modified van der Waals–Berthelot mixing rule is used. The critical properties of ionic liquids have been estimated by a group of supplementary methods suggested by Valderrama and Robles, known as the modified Lyderson–Joback–Reid method. It is concluded that since the absolute average relative deviation is less than 1%, the developed model has a high accuracy.

Investigation of Thermodynamic Consistency Test of Carbon Dioxide (CO2) in Room-Temperature Ionic liquids using Generic van der Waals Equation of State

Thermodynamic consistency test of isothermal vapor-liquid equilibrium (VLE) data of various binary systems containing Carbon dioxide (CO2)/Room temperature ionic liquids (RTILs) have been investigated in wide ranges of pressures in each isotherm precisely. In this paper Generic van der Waals (GvdW) equation of state (EoS) coupled with modified van der Waals Berthelot mixing rule has successfully been applied for correlating P-T-x binary data. The optimum parameters were obtained by minimizing the average relative deviation between modeled and experimental data based on the bubble pressure algorithm. Modeling is highly shown satisfactory in all cases which means that deviations in correlated data are low subsequently can prove that the flexibility and capability of the proposed model for thermodynamic consistency. Results of the consistency test represented ten isothermal experimental data set to be thermodynamically consistent, fourteen were declared to be not fully consistent and just four isothermal experimental data sets were represented to be thermodynamically inconsistent.

Energy accommodation under non-equilibrium conditions for aluminum-inert gas systems

ABSTRACT Molecular dynamics (MD) simulations are conducted to determine non-equilibrium energy accommodation coefficients for aluminum-inert gas systems for a surface temperature of 300 K and gas temperatures in the range of 1000–3000 K. Three different gases are considered: helium, argon, and xenon. Density functional theory (DFT) simulations are conducted to obtain gas-surface interaction potentials and these are then fed as inputs to MD simulations. Effects of temperature and atomic weight of the gas on the accommodation coefficient are explored. Calculated accommodation coefficients are of the order of 0.1 and it is weakly dependent on gas temperature, in contrast to the predictions of Altman's model. Results suggest that energy accommodation coefficients are greatest for argon and lowest for helium for all temperatures considered in this study. This is explained by independently probing the effects of well depth and mass ratio and determining the relative importance of these two effects for the systems under consideration. Lorentz–Berthelot mixing rules substantially over predict the potential well depth, resulting in higher accommodation coefficients. The underlying physics and mechanisms are unraveled using a simple 1-D collision model.

The effects of wall roughness on the methane flow in nano-channels using non-equilibrium multiscale molecular dynamics simulation

This paper presents a non-equilibrium multiscale molecular dynamics simulation method to investigate the effects of periodic wall surface roughness on the structure and mass transfer of methane fluid through the silicon nano-channels. In order to accurately capture the trajectories and microstructure of methane nano-fluidics, the present modification of OPLS fully atomic model is employed. Meanwhile, we introduce the corresponding coarse-grained model to solve the problem of wall–fluid interaction for methane Poiseuille flow within silicon atomic walls using the classical Lorentz–Berthelot mixing rules. The geometries of the upper wall roughness are modeled by rectangular waves with different amplitudes and wavelengths. The three-dimensional number densities of C (H) atom and kinetic energy distribution plots give a clear observation of the impacts of surface roughness on the localization micro-information of methane fluid. Moreover, the slip length of fluid over rough surface decreases with the increase in amplitude. The diffusion coefficients appear anisotropic, and the radial distribution functions decrease with the increase in the amplitude. These properties should be taken into account in the design of energy-saving emission reduction nano-fluidic devices. All numerical results also indicate that the presented method not only can well solve the issue of wall–fluid interactions, but also could accurately predict the micro-information and dynamic properties of methane Poiseuille flow.

Transferable force-field for modelling of CO2, N2, O2 and Ar in all silica and Na+ exchanged zeolites

In this work we propose a new force field for modelling of adsorption of CO2, N2, O2 and Ar in all silica and Na+ exchanged Si–Al zeolites. The force field has a standard molecular-mechanical functional form with electrostatic and Lennard-Jones interactions satisfying Lorentz–Berthelot mixing rules and thus has a potential for further extension in terms of new molecular types. The parameters for the zeolite framework atom types are optimized by an iterative procedure minimizing the difference with experimental adsorption data for a number of different zeolite structures and Si:Al ratios. The new force field shows a good agreement with available experimental data including those not used in the optimization procedure, and which also shows a reasonable transferability within different zeolite topologies. We suggest a potential usage in screening of different zeolite structures for carbon capture and storage process, and more generally, for separation of other gases.

Conformational Properties of a Polymer in an Ionic Liquid: Computer Simulations and Integral Equation Theory of a Coarse-Grained Model.

We study the conformational properties of polymers in room temperature ionic liquids using theory and simulations of a coarse-grained model. Atomistic simulations have shown that single poly(ethylene oxide) (PEO) molecules in the ionic liquid 1-butyl 3-methyl imidazolium tetrafluoroborate ([BMIM][BF4]) are expanded at room temperature (i.e., the radius of gyration, Rg), scales with molecular weight, Mw, as Rg ∼ Mw(0.9), instead of the expected self-avoiding walk behavior. The simulations were restricted to fairly short chains, however, which might not be in the true scaling regime. In this work, we investigate a coarse-grained model for the behavior of PEO in [BMIM][BF4]. We use existing force fields for PEO and [BMIM][BF4] and Lorentz–Berthelot mixing rules for the cross interactions. The coarse-grained model predicts that PEO collapses in the ionic liquid. We also present an integral equation theory for the structure of the ionic liquid and the conformation properties of the polymer. The theory is in excellent agreement with the simulation results. We conclude that the properties of polymers in ionic liquids are unusually sensitive to the details of the intermolecular interactions. The integral equation theory is sufficiently accurate to be a useful guide to computational work.

Modified 2CLJDQP model and the second virial coefficients for linear molecules

A modified form of 2CLJDQP potential model is proposed to calculate the second virial coefficients of two-center Lennard-Jones molecules. In the presented potential model, the potential parameters σ and ε are considered as the temperature-dependent parameters in the form of hyperbolical temperature function based on the theory of temperature-dependent potential parameters. With this modified model, the second virial coefficients of some homonuclear molecules (such as O2, Cl2, CH3CH3, and CF3CF3) and heteronuclear molecules (such as CO, NO, CH3F, CH3Cl, CH3CF3, CH3CHF2, and CF3CH2F) are calculated. Then the Lorentz—Berthelot mixing rule is modified with a temperature-dependent expression, and the second virial coefficients of the heteronuclear molecules (such as CH3F, CH3Cl, and CH3CF3) are calculated. Moreover, CO2 and N2O are also studied with the modified 3CLJDQP model. The calculated results from the modified 2CLJDQP model accord better with the experimental data than those from the original model. It is shown that the presented model improves the positive deviation in low temperature range and negative deviation in high temperature range. So the modified 2CLJDQP potential model with the temperature-dependent parameters can be employed satisfactorily in large temperature range.

Wetting characterisation of silicon (1,0,0) surface

Water droplets on bare silicon surfaces are studied to examine the wetting behaviour as a function of the surface energy and to parameterise water–silicon interactions in order to recover the hydrophobic behaviour measured by experiments. Two different wetting regimes characterised by a critical interaction strength value are observed. At a threshold value of the water–silicon interaction parameter, water molecules start penetrating into the first layer of silicon surface under thermally vibrating walls, resulting in two distinct wetting behaviours. Fixed (cold) silicon walls do not exhibit the two different wetting characteristics. Size effects are studied for nano-scale droplets, and line tension influence is observed depending on the surface wettability. Decrease in the droplet size increases the contact angle values for the low wetting cases, while contact angles decrease for smaller droplets on the high wetting surfaces. Considering the line tension effects and droplet size, ϵSi–O for water–silicon interactions to recover the hydrophobic behaviour of silicon surfaces is estimated to be 12.5% of the value predicted using the Lorentz–Berthelot mixing rule.

The role of ion–water interactions in the solubility of ionic solutions

Molecular dynamics simulations are performed to analyze the solubility of NaCl and NaI salts from dilute to saturated aqueous solutions. The TIP4Q water model, which reproduces the experimental dielectric constant, is used with ions where the interaction parameters were obtained to reproduce some experimental properties of the crystal and in solution. It is shown the models fail to describe the correct behavior of ions at high concentrations when the Lorentz–Berthelot mixing rules for the cross interactions are used. The hydration of ions at low concentrations and the precipitation of ions at saturated solutions are observed after adding a screening short range function on electrostatic interactions on pairs where the short range repulsion was not taken into account.

Potential parameters for helium adsorption in silicalite

The pore volume of a micro or a nanoporous material is one of the crucial parameters in molecular simulation of gas adsorption. It is necessary to compare the results of the simulations with that of the experiments. In simulations, the pore volume is usually obtained from the configuration integral using the potential parameters of helium–solid interactions. The state of the art in obtaining these helium–solid parameters is through Lorentz–Berthelot mixing rules, used in conjunction with potential parameters of another “adsorbing” gas. In such an approach, the parameters (and hence helium pore volume) depend on choice of the adsorbing gas. However, “true” helium pore volume in simulations can only be obtained by mimicking the experimental adsorption behavior of helium itself, without involving any other gas. In this work, we report a consistent method to obtain the potential parameters for helium adsorption on a porous solid from low pressure helium adsorption data. The method is applied to helium–silicalite system and the parameters for He–O interactions in silicalite were obtained to be 3.06 Å and 22.9 K. Using these parameters, a helium pore volume of 0.151 cm 3/g (at 300 K) is obtained for silicalite. The results are further validated by comparing the adsorption isotherms of helium in the high pressure region.

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.

The effects of deviations from Lorentz–Berthelot rules on the properties of a simple mixture

Generally, the parameters in the interaction potential between like molecules in a mixture can be determined in a relatively straightforward manner from the properties of the pure components. However, the determination of the parameters in the interaction potential between the unlike pairs in the mixtures is more difficult. As a result, these parameters are usually estimated from averages of the like parameters. The most common recipes are the Lorentz–Berthelot mixing rules, where the energy and molecular size parameters are presumed to be geometric and arithmetic averages, respectively. There have been some studies of the consequences of deviations from the energy rule but almost no studies of the consequences of deviations from the size rule. Here, we study the effects of deviations from both rules on the radial distribution functions of a simple mixture. We find from simulations that, for this mixture, the effect of deviations from the energy rule on the radial distribution function are rather small but that the effect of deviations from the size rule can be significant and are interesting.

Adsorption equilibria of single gas and gas mixture on homogeneous surfaces: a unified approach based on statistical thermodynamics developments. Part II: extension to gas mixture adsorption

Theoretical description of single gas and gas mixture adsorption equilibria can be achieved in many different ways depending on the kind of approach (microscopic or macroscopic). In this paper, we present a statistical thermodynamics approach for the calculation of mixed gas adsorption equilibrium data on uniform surfaces. The non-ideality of both the mixed gas phase and the adsorbed phase is considered by using the Redlich–Kwong EOS associated to the classic Lorentz–Berthelot mixing rules. This is an interesting way to extend the model presented in Part I and to predict multicomponent gas adsorption equilibria for highly non-ideal systems from parameters deduced from pure gas data. We present mixture adsorption isotherms and selectivity curves calculated using our model.

Description of intra-diffusion in liquid mixtures

Employing a previously derived model to describe intra-diffusion coefficients in liquid mixtures based on molecular simulations of spherical Lennard–Jones particles [T. Merzliak, A. Pfennig, Mol. Simul. 30 (7) (2004) 459–468], an improved set of coefficients was obtained from optimized molecular dynamics simulations. In these simulations, the thermodynamic states were planned with the help of optimal experimental design, which allows to reduce the number of simulations necessary for significant determination of the coefficients by roughly a decade. The model was then applied to the real liquid mixtures toluene + cyclohexane, toluene + 1,4-dioxane, n-hexane + toluene, 1,4-dioxane + cyclohexane and cyclohexane + n-hexane, which have molecular properties that correspond to the model assumptions. Experimental intra-diffusion coefficients for the mixtures toluene + cyclohexane, toluene + 1,4-dioxane, n-hexane + toluene and 1,4-dioxane + cyclohexane were determined with nuclear magnetic resonance (NMR) techniques in this work. Even without additional parameters for the mixture the proposed model can describe the diffusion coefficients with an average accuracy of 5%. Allowing a deviation from Lorentz–Berthelot mixing rules leads generally only to slight improvement.

Pair-correlation functions and phase separation in a two-component point Yukawa fluid

We investigate the structure of a binary mixture of particles interacting via purely repulsive point Yukawa pair potentials with a common inverse screening length lambda. Using the hypernetted chain closure to the Ornstein-Zernike equations, we find that for a system with "ideal" (Berthelot mixing rule) pair-potential parameters for the interaction between unlike species, the asymptotic decay of the total correlation functions crosses over from monotonic to damped oscillatory on increasing the fluid total density at fixed composition. This gives rise to a Kirkwood line in the phase diagram. We also consider a "nonideal" system, in which the Berthelot mixing rule is multiplied by a factor (1+delta). For any delta>0 the system exhibits fluid-fluid phase separation and remarkably the ultimate decay of the correlation functions is now monotonic for all (mixture) state points. Only in the limit of vanishing concentration of either species does one find oscillatory decay extending to r=infinity. In the nonideal case the simple random-phase approximation provides a good description of the phase separation and the accompanying Lifshitz line.

Liquid crystalline behavior of a semifluorinated oligomer

Monte Carlo simulations with a coarse-grained model were performed to study the microstructure of a semifluoroalkane C20 diblock oligomer [F(CF(2))(10)(CH(2))(10)H]. The coarse-grained model adopted is based on previously reported united-atom force fields for alkanes and perfluoroalkanes and was first validated by simulating the phase behavior of a mixture of hexane and perfluorohexane. These preliminary simulations established the need of a significant correction factor in the Berthelot mixing rule between alkane and perfluoroalkane groups. Using such a force field, the semifluorinated C20 oligomer liquid was simulated using efficient Monte Carlo moves to sample different molecular arrangements and box dimensions so as to allow different layering structures to form. In qualitative agreement with experimental observations, a smectic-to-isotropic phase transition occurs as temperature is increased but the transition point and the structure of the smectic phase depend on the stiffness of the torsional potential and the model of van der Waals interactions adopted. We identify two smectic phases LC1' and LC2', whose structures do not agree with those that have been postulated before to explain x-ray diffraction data, namely, LC1 and LC2. LC1' has a layer spacing similar to LC1 but the antiparallel packing is not observed with individual chains but with groups of chains producing a checkerboard pattern. LC2' has fully microsegregated blocks such as LC2 but the alkyl tails are not fully stretched or interdigitated. Despite these inconsistencies, and considering that reported experimental data also reveal the presence of mixed phases, the simulated structures suggest other plausible ways how the semifluorinated chains could pack and microsegregate to best negotiate energetic and entropic constraints.

The one-dimensional fully non-additive binary hard rod mixture: exact thermophysical properties

The non-additive binary hard particle mixture is characterized by a collision parameter between unlike hard particles that is not the arithmetic mean of the two pure component collision diameters. Instead, σ12=(σ11+σ22)(1+Δ)/2, where σ12 is the collision diameter between species 1 and 2 and Δ is a non-additivity parameter in which Δ≥−1 (Δ=0 corresponds to the additive mixture). For mixtures in which repulsive forces are mostly responsible for the observed behavior, the binary non-additive hard particle mixture provides a useful model for examining the thermophysical properties of a wide class of real fluid mixtures. To extend further the range of applicability of these mixtures, another layer of complexity can be considered by including potential interactions that exist past contact which themselves may also be defined as non-additive. For example, the well depth of the interaction of unlike species can be defined as ε12=δ∣ε11ε22∣1/2, where δ is another non-additivity parameter which may take on any real value (note that Δ=0 and δ=1 correspond to the Lorentz–Berthelot mixing rules).To gain insight into these complicated mixtures in higher dimensions, we consider the one-dimensional non-additive binary hard rod mixture with various attractive interactions. We generate the exact thermophysical properties of these mixtures, including a general form of the equation of state. Similarly, we also determine the radial distribution functions, g ij(r), using the exactly known nearest-neighbor probability density distributions. Such relations enable one to determine the effects of the various non-additive parameters on the properties of the mixtures.

Phase separation kinetics in compressible polymer solutions: computer simulation of theearly stages

A coarse-grained model for solutions of polymers in supercritical fluids is introduced andapplied to the system of hexadecane and carbon dioxide as a representative example.Fitting parameters of the model to the gas–liquid critical point properties of the puresystems, and allowing for a suitably chosen parameter that describes the deviation from theLorentz–Berthelot mixing rule, we model the liquid–gas and fluid–fluid unmixingtransitions of this system over a wide range of temperatures and pressures inreasonable agreement with experiment. Interfaces between the polymer-rich phaseand the gas can be studied at temperatures both above and below the end pointof the triple line where liquid and vapour carbon dioxide and a polymer-richphase coexist. In the first case interfacial adsorption of fluid carbon dioxide canbe demonstrated. Our model can also be used to simulate quenches from theone-phase to the two-phase region. A short animation and a series of snapshots helpto visualize the early stages of bubble nucleation and spinodal decomposition.Furthermore we discuss deviations from classical nucleation theory for small nuclei.

Fluid variational theory for pressure dissociation in dense hydrogen: Multicomponent reference system and nonadditivity effects

In a recent paper, standard hard-sphere variational theory has been applied to pressure dissociation in dense fluid hydrogen (Juranek and Redmer, J. Chem. Phys. 112, 3780 (2000)). The correlation contributions to the dissociation equilibrium were determined from the free energy functional using effective pair potentials and minimization with respect to the hard-sphere reference system. For simplicity, the Berthelot mixing rule was used to determine the H–H2 pair potential (which entails additive effective hard spheres), and single-component reference pair correlation functions were employed for evaluating the correlation integrals. In this paper, we employ multicomponent reference pair correlations, and we study the sensitivity of the results with respect to nonadditivity of the effective hard spheres. We compare our results with available ab initio simulation data.