Excess energy and equation of state of fluids with hard-core potential models from a second-order Monte Carlo perturbation theory

Monte Carlo simulations in the NVT ensemble of the reference hard-sphere fluid have been performed to obtain the “exact” first- and second-order terms in the inverse temperature expansion of the free energy of fluids with hard-core potentials. The results have been used to obtain parametrizations of the free energy of fluids with Sutherland potentials with variable range as well as for a fluid with a hard-core Lennard–Jones potential. The results for the excess energy and the equation of state are compared with simulation data available in the literature for these fluids.     

Transient cavities and the excess chemical potentials of hard-spheroid solutes in dipolar hard-sphere solvents

Monte Carlo computer simulations are used to study transient cavities and the solvation of hard-spheroid solutes in dipolar hard-sphere solvents. The probability distribution of spheroidal cavities in the solvent is shown to be well described by a Gaussian function, and the variations of fit parameters with cavity elongation and solvent properties are analyzed. The excess chemical potentials of hard-spheroid solutes with aspect ratios x in the range of 15< or =x< or =5, and with volumes between 1 and 20 times that of a solvent molecule, are presented. It is shown that for a given molecular volume and solvent dipole moment (or temperature) a spherical solute has the lowest excess chemical potential and hence the highest solubility, while a prolate solute with aspect ratio x should be more soluble than an oblate solute with aspect ratio 1x. For a given solute molecule, the excess chemical potential increases with increasing temperature; this same trend can be observed in hydrophobic solvation. A scaled-particle theory based on the solvent equation of state and a fitted solute-solvent interfacial tension shows excellent agreement with the simulation results over the whole range of solute elongations and volumes considered. An information-theoretic model based on the solvent density and radial distribution function is less successful, being accurate only for small solute volumes and low solvent densities.     

A gas chromatographic study of the charge-transfer complexes formed between 1,3,5-trinitrobenzene and aromatic hydrocarbons

Summary Gas-liquid chromatography was used for studying the complexing equilibrium at 60°C between aromatic hydrocarbons and 1,3,5-trinitrobenzene (TNB) dissolved in dinonyl phthalate (DNP). On increasing the molar fraction of TNB in the stationary phase, a significant increase in the activity coefficients at infinite dilution was observed for several non-complexing solutes; said increase cannot be exclusively attributed to variations in the molar volume of the stationary phase. It appears to be evident that the activity coefficient of TNB varies appreciably with its concentration in DNP. A semiempirical method, combining theories for regular and athermal solutions, is applied for calculating the activity coefficient of uncomplexed solute in different stationary phases. The thermodynamic stability constants for the complexes can then be calculated by means of a series of relations that are fulfilled when the molar fraction of the additive tends to zero. Values thus obtained are compared with spectrophotometric data.     

Thermodynamic studies of binary methanol and ethanol solutions of 1-dodecanol and 1-tetradecanol at 25°C

The osmotic coefficients of binary methanol and ethanol solutions of 1-dodecanol and 1-tetradecanol wer measured at 25°C up to 8 mol-kg^–1 in methanol and 5.5 mol-kg^–1 in ethanol. The activity coefficients of the solute were calculated from Bjerrum's relation. From the osmotic and activity coeficients the excess Gibbs energies of solution as well as the respective partial molar functions of solute and solvent and the virial pair interaction coefficients for the excess Gibbs energies were calculated. In addition, the difference in the Gibbs energy of solvation for the solvent in solution relative to the pure solvent was calculated, as well as the partial molar volumes and excess partial molar volumes of solutes at infinite dilution, and the coefficients of pairwise contributions to the excess volume were determined. The thermodynamic parameters obtained are discussed on the basis of solute-solvent and solute-solute interactions.     

Thermodynamics and partitioning of homopolymers into a slit-A grand canonical Monte Carlo simulation study

Grand canonical ensemble Monte Carlo simulation (GCMC) combined with the histogram reweighting technique was used to study the thermodynamic equilibrium of a homopolymer solution between a bulk and a slit pore. GCMC gives the partition coefficients that agree with those from canonical ensemble Monte Carlo simulations in a twin box, and it also gives results that are not accessible through the regular canonical ensemble simulation such as the osmotic pressure of the solution. In a bulk polymer solution, the calculated osmotic pressure agrees very well with the scaling theory predictions both for the athermal polymer solution and the theta solution. However, one cannot obtain the osmotic pressure of the confined solution in the same way since the osmotic pressure of the confined solution is anisotropic. The chemical potentials in GCMC simulations were found to differ by a translational term from the chemical potentials obtained from canonical ensemble Monte Carlo simulations with the chain insertion method. This confirms the equilibrium condition of a polymer solution partition between the bulk and a slit pore: the chemical potentials of the polymer chain including the translational term are equal at equilibrium. The histogram reweighting method enables us to obtain the partition coefficients in the whole range of concentrations based on a limited set of simulations. Those predicted bulk-pore partition coefficient data enable us to perform further theoretical analysis. Scaling predictions of the partition coefficient at different regimes were given and were confirmed by the simulation data.     

Solvent phase behavior and the interaction of uniform and patterned solutes

Isotropic and anisotropic hypernetted-chain (HNC) integral equation theories are used to obtain the interaction of solutes both near and far from the solvent liquid-vapor coexistence. Spherically symmetrical and chemically patterned (patched) solutes are considered, and the influences of particle and patch sizes are investigated. Solvophilic and solvophobic solutes (or patches) are examined. Near coexistence, in the solvophobic case drying-like behavior occurs for solutes (patches) of sufficient size. This gives rise to relatively long ranged attractive forces that are strongly orientation dependent for the patched solute particles. We also report grand canonical Monte Carlo results for a pair of spherically symmetric solutes. This demonstrates that the anisotropic HNC theory gives qualitatively correct solvent structure in the vicinity of the solutes. Comparison with previous simulations also shows that the solute-solute potentials of mean force given by the anisotropic theory are more accurate (particularly at small separations) than those obtained using the isotropic method.     

Estimation of the Activity Coefficients in Liquid Mixtures by Using Volumetric Data

We present an equation that relates the partial molar volume of binary liquid mixtures with the natural logarithms of the activity coefficients of solute and solvent. This equation, in combination with one of the activity coefficient models such as those of Margules, Wilson, Van Laar or NRTL, can be used to estimate the activity coefficients of binary liquid mixtures, knowing only the densities of the mixtures over the full range of concentration. In addition, we show a comparison of the estimated activities and activity coefficients at infinite dilution with experimental values for aqueous solutions of 1,2-butanediol, 2,3-butanediol, 1,3-butanediol, and 1,4-butanediol at 298.15?K. This method for the estimation of activity coefficients can be applied to aqueous binary mixtures, because the equation presented is deduced from physicochemical principles.     

Volumetric Study of Aqueous Solutions of Polyethylene Glycol as a Function of the Polymer Molar Mass in the Temperature Range 283.15 to 313.15 K and 0.1 MPa

Density measurements were made for binary aqueous solutions of polyethylene glycol at seven temperatures: 283.15, 288.15, 293.15, 298.15, 303.15, 308.15, and 313.15 K. Polyethylene glycol samples with nominal average molar masses of 3000 g⋅mol⁻¹ (PEG 3000), 6000 g⋅mol⁻¹ (PEG 6000), 10000 g⋅mol⁻¹ (PEG 10000) and 20000 g⋅mol⁻¹ (PEG 20000) were used. These results were used to determine the specific volumes of solutions with solute-to-solvent mass ratios (mass of the solute/mass of the solvent) in the range 0.0546 to 1.4932 for PEG 3000, from 0.0553 to 1.4986 for PEG 6000, from 0.0552 to 1.2241 for PEG 10000, and from 0.0530 to 1.2264 for PEG 20000. The differences between the specific volume of a solution and the specific volume of the pure solvent, at a given temperature, were represented by a virial-type equation in terms of solute concentration. The first-order coefficient of the expansion is the partial specific volume of the solute at infinite dilution. The higher-order coefficients are related to the contribution of pairs, triplets, and higher-order solute aggregates, according to the Constant-Pressure Solution Theory. The functional dependence of the virial coefficients upon temperature is discussed in terms of solute-solute and solute-solvent interactions. The effect of the PEG molar mass on the partial specific volume of solute at infinite dilution, as well as the contributions of pairs of solute molecules to the solution volume, are also investigated. The apparent specific volume, apparent specific expansibility, apparent specific expansibility at infinite dilution and virial coefficients of the apparent specific expansibility are also presented.     

Correlation and comparison of the infinite dilution activity coefficients in aqueous and organic mixtures from a modified excess Gibbs energy model

Activity coefficients at infinite dilution (ln γ^∞) of aqueous systems were calculated using a modified excess Gibbs energy model. More than 95 binary systems with 15 solute families from nonpolar alkanes to polar alcohols and acids were employed in this study. Based on the local composition lattice model developed by Aranovich and Donohue, a modified excess Gibbs energy equation (m-AD model) was derived in this study. With two generalized parameters for each homologous series of solutes, this modified model yields satisfactory results for the limiting activity coefficients. The overall absolute average deviation (AAD) of ln γ^∞ for all aqueous systems investigated in this study is 2% for the m-AD model, and the corresponding AAD in γ^∞ unit is 7%. The calculated infinite dilution activity coefficients from the m-AD model are comparable to those from the MOSCED, SPACE, PDD, LSER or the modified UNIFAC model. The m-AD model shows lower peak deviation than those from other methods. Satisfactory generalized correlation results are also observed for organic solvents other than water. With the generalized parameters, the m-AD model satisfactorily predicts the limiting activity coefficients for other solutes not included in the correlation.     

非水溶液盐效应的气液色谱研究——非电解质(烃、芳烃、氯代烃、酮)+盐(Nal、NaSCN、KSCN)+碳酸丙烯酯体系

The gas-liquid chromatographic method was used to measure the activity coefficients at infinite dilution (γ_1~∞) of some nonelectrolyte solutes in salt containing solutions of propylene carbonate at 333.2 K. For examining the relationship between lgγ_1~∞ and salt concentrations, the salt effect coefficients of solutes were calculated, and the interactions of solute with salt were disscused. Furthermore, the equilibrium constant of complex interaction between chloroform with anions has been obtained.     

Structure and anomalous solubility for hard spheres in an associating lattice gas model

In this paper we investigate the solubility of a hard-sphere gas in a solvent modeled as an associating lattice gas. The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties are investigated both through Monte Carlo simulations and a cluster approximation. The model solubility is computed via simulations and is shown to exhibit a minimum as a function of temperature. The line of minimum solubility (TmS) coincides with the line of maximum density (TMD) for different solvent chemical potentials, in accordance with the literature on continuous realistic models and on the "cavity" picture.     

An analytical approximation for the orientation-dependent excluded volume of tangent hard sphere chains of arbitrary chain length and flexibility

Onsager-like theories are commonly used to describe the phase behavior of nematic (only orientationally ordered) liquid crystals. A key ingredient in such theories is the orientation-dependent excluded volume of two molecules. Although for hard convex molecular models this is generally known in analytical form, for more realistic molecular models that incorporate intramolecular flexibility, one has to rely on approximations or on computationally expensive Monte Carlo techniques. In this work, we provide a general correlation for the excluded volume of tangent hard-sphere chains of arbitrary chain length and flexibility. The flexibility is introduced by means of the rod-coil model. The resulting correlation is of simple analytical form and accurately covers a wide range of pure component excluded volume data obtained from Monte Carlo simulations of two-chain molecules. The extension to mixtures follows naturally by applying simple combining rules for the parameters involved. The results for mixtures are also in good agreement with data from Monte Carlo simulations. We have expressed the excluded volume as a second order power series in sin?(γ), where γ is the angle between the molecular axes. Such a representation is appealing since the solution of the Onsager Helmholtz energy functional usually involves an expansion of the excluded volume in Legendre coefficients. Both for pure components and mixtures, the correlation reduces to an exact expression in the limit of completely linear chains. The expression for mixtures, as derived in this work, is thereby an exact extension of the pure component result of Williamson and Jackson [Mol. Phys. 86, 819-836 (1995)].     

Analysis and applications of a group contribution sPC-SAFT equation of state

A group contribution (GC) method for estimating pure compound parameters for the molecular-based perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) is proposed in a previous work [A. Tihic, G.M. Kontogeorgis, N. von Solms, M.L. Michelsen, L. Constantinou, Ind. Eng. Chem. Res. 47 (2008) 5092–5101]. In this paper, an investigation of the predictive capability of the GC sPC-SAFT EoS through comparison of the method’s predictions for compounds with high molecular weights and several selected binary mixtures of industrial significance with experimental data such as thiols, sulphides and polynuclear aromatics is presented. Additionally, predictions of activity coefficient at infinite dilution for athermal systems are compared with the results using existing activity coefficient models. The results show that calculated pure compound parameters using the proposed GC method allow satisfactory representation of experimental data of investigated systems with the sPC-SAFT EoS. Moreover, the variety of functional groups in the available GC scheme ensures broad applications of the GC sPC-SAFT EoS.     

Solute absorption into molten polystyrene

The equilibrium volatilities at near infinite dilution of various solutes absorbed in molten polystyrene have been determined by a gas chromatographic technique. This method is much more rapid, although, with the present apparatus, probably less accurate than conventional static techniques. The primary parameters obtained from measurements of retention volumes are the Henry's law constants, from which are derived the weight and volume fraction activity coefficients, the Flory-Huggins interaction parameters, and the heats of dilution and solution. Of the solutes investigated, 2-butanone (MEK) was the least, and benzene the most compatible (highest and lowest volume fraction activity coefficients, respectively) with molten polystyrene. A small, but definite, variation of the activity coefficients with polystyrene molecular weight was observed.     

Development of Abraham model correlations for describing the transfer of molecular solutes into propanenitrile and butanenitrile from water and from the gas phase

Experimental solubilities were measured for 20 crystalline organic solutes dissolved in propanenitrile and for 13 crystalline organic solutes dissolved in butanenitrile at 298.15 K. Infinite dilution activity coefficient data for solutes dissolved in propanenitrile and butanenitrile have been compiled from the published chemical and engineering literature and converted into gas-to-liquid partition coefficients and water-to-organic solvent partition coefficients through standard thermodynamic relationships. Abraham model correlations were developed for describing solute transfer into both propanenitrile and butanenitrile by combining our measured solubility data with the partition coefficients that we calculated from the published activity coefficient data. The derived Abraham model correlations were found to back-calculate the observed partition coefficients and molar solubility data to within 0.14 log units.     

On using the NMR chemical shift to assess polar–nonpolar cross-intermolecular interactions

The possibility of using the NMR chemical shift to evaluate and develop intermolecular potentials for cross-interactions between polar and nonpolar molecules has been examined using the method of molecular dynamics. Such interaction potential models are known to be notoriously difficult to develop. Our work has shown that chemical shift can be obtained quite efficiently in simulations and converges much faster than other properties traditionally used for such evaluations (for example, the infinite dilution activity coefficients, Henry’s constants or the solubility of solutes in solvents). We have also found chemical shift to be quite sensitive to the intermolecular potentials which makes it a rather promising property to investigate polar–nonpolar interactions in fluids.     

The nature of the calculation of the pressure in molecular simulations of continuous models from volume perturbations

We consider some fundamental aspects of the calculation of the pressure from simulations by performing volume perturbations. The method, initially proposed for hard-core potentials by Eppenga and Frenkel [Mol. Phys.52, 1303 (1984)] and then extended to continuous potentials by Harismiadis et al. [J. Chem. Phys. 105, 8469 (1996)], is based on the numerical estimate of the change in Helmholtz free energy associated with the perturbation which, in turn, can be expressed as an ensemble average of the corresponding Boltzmann factor. The approach can be easily generalized to the calculation of components of the pressure tensor and also to ensembles other than the canonical ensemble. The accuracy of the method is assessed by comparing simulation results obtained from the volume-perturbation route with those obtained from the usual virial expression for several prototype fluid models. Monte Carlo simulation data are reported for bulk fluids and for inhomogeneous systems containing a vapor-liquid interface.     

Henry’s law constants of methane,nitrogen, oxygen and carbon dioxide in ethanol from 273 to 498 K: Prediction from molecular simulation

Henry’s law constants of the solutes methane, nitrogen, oxygen and carbon dioxide in the solvent ethanol are predicted by molecular simulation. The molecular models for the solutes are taken from previous work. For the solvent ethanol, a new rigid anisotropic united atom molecular model based on Lennard–Jones and coulombic interactions is developed. It is adjusted to experimental pure component saturated liquid density and vapor pressure data. Henry’s law constants are calculated by evaluating the infinite dilution residual chemical potentials of the solutes from 273 to 498 K with Widom’s test particle insertion. The prediction of Henry’s law constants without the use of binary experimental data on the basis of the Lorentz–Berthelot combining rule agree well with experimental data, deviations are 20%, except for carbon dioxide for which deviations of 70% are reached. Quantitative agreement is achieved by using the modified Lorentz–Berthelot combining rule which is adjusted to one experimental mixture data point.