A modified square well model in obtaining the surface tension of pure and binary mixtures of hydrocarbons

A model based on the perturbation theory of fluids was proposed to correlate the experimental data for surface tension of pure hydrocarbons in a wide range of temperature. The results obtained for the pure hydrocarbons were directly used to predict the surface tension for binary hydrocarbon mixtures at various temperatures. In the proposed model, a modified form of the square well potential energy between the molecules of the reference fluid was taken into account while the Lennard–Jones dispersion energy was considered to be dominant amongst the molecules as the perturbed term to the reference part of the model. In general, the proposed model has three adjustable parameters which are chain length, m, size, σ, and energy, ε/κ, parameters, but in some cases the number of parameters was reduced to two, thereby setting the chain length to be unity for pure hydrocarbons. The regressed values of these parameters were obtained using the experimental data for pure hydrocarbons at different temperatures. The results showed that these parameters can be related to the molar mass of hydrocarbons. The model was also extended to predict the surface tension of binary hydrocarbon mixtures using the parameters obtained for the pure compounds. It is worth noting that no additional parameter has been introduced into the model in the extension of the model to the mixtures studied in this work. The results showed that the proposed model can accurately correlate the surface tension of pure hydrocarbons. Also the results showed that the surface tension for binary mixture of hydrocarbons can be accurately predicted using the proposed model over a wide temperature range.     

What makes ionic fluids characteristically ionic? A corresponding-states analysis of the surface tension of an ionic model fluid with variable dispersion interactions

Inorganic molten salts, such as NaCl, are known to show characteristically lower values of Guggenheim's corresponding-states surface tension γ(red) at a given reduced temperature T∕T(c) than simple or aprotic polar fluids. Recently, the corresponding values of γ(red) for (some) room temperature ionic liquids (RTILs) were found in the same region as those for weakly polar fluids, that is, markedly above the values typical of inorganic molten salts despite the ionic character of RTILs. Here, we present the results of simulations of an ionic model fluid in which the strength of attractive dispersion interactions among the ions is varied relative to the Coulomb interactions. For weak dispersive interactions, the behavior known for real inorganic molten salts is found. If the attractive dispersion energy of two unlike ions at contact exceeds 20% of the Coulombic attraction in such an isolated ion pair, γ(red) increases markedly and approaches the region of values for simple and polar fluids. Rough theoretical estimates of the relative strengths of dispersive and Coulombic attractions in molten inorganic salts and in RTILs support our conclusion that the dispersion interactions in RTILs are strong enough for their corresponding-states surface tension to behave regularly and, thus, to deviate from the values one would expect for strongly ionic systems.     

Anomalous corresponding-states surface tension of hydrogen fluoride and of the Onsager model

In a corresponding-states analysis of the liquid-vapor surface tension originally suggested by Guggenheim, we study the behavior of different simple (i.e., nonpolar), polar and ionic fluids. The results are compared to the corresponding ones for model fluids of each of the three types. For simple and weakly polar fluids (both real and model), the data map onto a master curve, as demonstrated by Guggenheim. For strongly dipolar, associating fluids, which also exhibit hydrogen bonding, one finds deviations from the master curve at low temperatures and, thus, observes the characteristic sigmoid behavior of the reduced surface tension as a function of temperature. The same is obtained for the model ionic fluid, the restricted primitive model. Truly exceptionally low values of the reduced surface tension are found for hydrogen fluoride and for the Onsager model of dipolar fluids, the surface tension of which we evaluate using an approximate hypernetted chain relation to obtain the square-gradient term in a modified van der Waals theory. Remarkably, in the corresponding-states plot, the surface tensions of HF and of the Onsager model agree very closely, while being well separated from the values for the other fluids. We also study the gradual transition of a model fluid from a simple fluid to a strongly dipolar one by varying the relative strength of dipolar and dispersion forces.     

Radial distribution function of a hard-sphere fluid for the nearest neighbor surroundings

An expression for RDF as a function of two variables, the distance r and the packing factor η, was obtained by approximating the results of Monte Carlo simulation of a hard-sphere fluid. The mean square accuracy of the expressions presented is about ±0.0002 (1 ≤ r ≤ 1.5, 0 ≤ η ≤ 0.5). A continuous extension of RDF to the region of r < 1 is proposed, which provides the continuity of the first and second derivatives of RDF at the point r = 1. Analysis of the problem of determining the hard sphere diameter in WCA theory of simple liquids shows that the proposed expression makes it possible to directly calculate the hard sphere diameter without any simplifying approximations.     

A Corresponding-state Model for Predicting Surface Tension

A generalized corresponding-state model based on two reference fluids was developed for the prediction of surface tensions for non-polar and weakly polar pure fluids and their binary mixtures. Four parameters,po, Tc, Vc and ω, were used in this model, and the acentric factor ω was used as a scaling parameter. This model has been tested for 69 pure substances and 20 binary mixtures; the average absolute deviations are 0. 28 and 0. 20 mN/m, respectively. The results indicate that the predictions by means of this model were in good agreement with experimental data. In addition, the calculated deviation would increase with the excess surface tension rising, and if the excess surface tension is less than 3 mN/m, the prediction will be good and credible.     

On predicting self-diffusion coefficients in fluids

A modification of an existing correlative equation for self-diffusion coefficients is presented. A free-volume theory for liquids has been corrected to reproduce diffusivities of hard-sphere and Lennard–Jones fluids from low-density limit to melting points, and has been applied to correlate a wide database of non-polar, polar, quantic and hydrogen-bonding substances, although it is unable to fit helium, water and hydrogen fluoride. The adjustable parameters are generalized with available fluid properties, and the three resulting predictive formulas present lower deviations than other correlative equations used in a predictive way for non-quantic and non-associated fluids.     

共聚高分子混合物的分子热力学模型

以硬球链流体的分子热力学模型为基础 ,引入方阱位能相互作用的贡献 ,建立了共聚高分子混合物的分子热力学模型 .模型中具有物理意义的链节参数 (链节数、链节直径和链节间的相互作用能 )由纯物质的pVT关系拟合得到 ,而用来校正交叉作用能和交叉碰撞直径的可调参数需由液液平衡的实验数据回归得到 .采用了相对简单的处理方法来确定这些可调参数 .对所选共聚高分子混合物的共存曲线、互溶窗和互溶图等相行为的关联结果令人满意 .     

Wetting study of imidazolium ionic liquids

In this work, we present a systematic contact angles study of a series of 1-alkyl, 3-methyl-imidazolium ionic liquids (ILs) on well-defined polar and nonpolar monolayer surfaces supported on Si wafers. The advancing and receding contact angles of ILs were used to determine the surface energy of the monolayer surfaces using Neumann's equation-of-state and Zisman's critical surface tension approaches. In parallel, the contact angles of conventional probe fluids (molecular liquids) including water, formamide, methylene iodide, ethylene glycol, and hexadecane were determined on the same surfaces. The results obtained showed a great deal of similarity in wetting behavior of ionic vs molecular probe fluids: the contact angles of both sets of liquids followed the same patterns in accord with the surface tension of the fluid. A good agreement was found between the surface energy determined by different sets of liquids.     

Surface tensions of imidazolium based ionic liquids: anion, cation, temperature and water effect

This work addresses the experimental measurements of the surface tension of eight imidazolium based ionic liquids (ILs) and their dependence with the temperature (288-353 K) and water content. The set of selected ionic liquids was chosen to provide a comprehensive study of the influence of the cation alkyl chain length, the number of cation substitutions and the anion on the properties under study. The influence of water content in the surface tension was studied for several ILs as a function of the temperature as well as a function of water mole fraction, for the most hydrophobic IL investigated, [omim][PF(6)], and one of the more hygroscopic IL, [bmim][PF(6)]. The surface thermodynamic functions such as surface entropy and enthalpy were derived from the temperature dependence of the surface tension values.     

Shape factors in equations of state. Part II. Repulsion phenomena in multicomponent chain fluids

An equation of state for the multicomponent fluid phase of nonattracting rigid particles of arbitrary shape is presented. The equation is a generalization of a previously presented equation of state for pure fluids of rigid particles; the approach describes the volumetric properties of a pure fluid in terms of a shape factor, zeta, which can be back calculated by scaling the volumetric properties of pure fluids to that of a hard sphere. The performance of the proposed equation is tested against mixtures of chain fluids immersed in a "monomeric" solvent of hard spheres of equal and different sizes. Extensive new Monte Carlo simulation data are presented for 19 binary mixtures of hard homonuclear tangent freely-jointed hard sphere chains (pearl-necklace) of various lengths (three to five segments), with spheres of several size ratios and at various compositions. The performance of the proposed equation is compared to the hard-sphere SAFT approach and found to be of comparable accuracy. The equation proposed is further tested for mixtures of spheres with spherocylinders. In all cases, the equation proved to be accurate and simple to use.     

Surface tension of associating fluids by Monte Carlo simulations

Canonical Monte Carlo (NVT-MC) simulations were performed to obtain surface tension and coexistence densities at the liquid-vapor interface of one-site associating Lennard-Jones and hard-core Yukawa fluids, as functions of association strength and temperature. The method to obtain the components of the pressure tensor from NVT-MC simulations was validated by comparing the equation of state of the associative hard sphere system with that coming from isothermal-isobaric Monte Carlo simulations. Surface tension of the associative Lennard-Jones fluid determined from NVT-MC is compared with previously reported results obtained by molecular dynamics simulations of a pseudomixture model of monomers and dimers. A good agreement was found between both methods. Values of surface tension of associative hard-core Yukawa fluids are presented here for the first time.     

How to extend hard sphere density functional approximation to nonuniform nonhard sphere fluids: applicable to both subcritical and supercritical temperature regions

A methodology for the formulation of density functional approximation (DFA) for nonuniform nonhard sphere fluids is proposed by following the spirit of a partitioned density functional approximation [Zhou, Phys. Rev. E 68, 061201 (2003)] and mapping the hard core part onto an effective hard sphere whose high order part of the functional perturbation expansion is treated by existing hard sphere DFAs. The resultant density functional theory (DFT) formalism only needs a second order direct correlation function and pressure of the corresponding coexistence bulk fluid as inputs and therefore can be applicable to both supercritical and subcritical temperature cases. As an example, an adjustable parameter-free version of a recently proposed Lagrangian theorem-based DFA is imported into the present methodology; the resultant DFA is applied to Lennard-Jones fluid under the influence of external fields due to a single hard wall, two hard walls separated by a small distance, a large hard sphere, and a spherical cavity with a hard wall. By comparing theoretical predictions with previous simulation data and those recently supplied for coexistence bulk fluid situated at "dangerous" regions, it was found that the present DFA can predict subtle structure change of the density profile and therefore is the most accurate among all existing DFT approaches. A detailed discussion is given as to why so excellent DFA for nonhard sphere fluids can be drawn forth from the present methodology and how the present methodology differs from previous ones. The methodology can be universal, i.e., it can be combined with any other hard sphere DFAs to construct DFA for other nonhard sphere fluids with a repulsive core.     

Surface tension and refractive index of pure and water-saturated tetradecyltrihexylphosphonium-based ionic liquids

Experimental data on the surface tension and refractive index of tetradecyltrihexylphosphonium-based ionic liquids with bromide, chloride, decanoate, methanesulfonate, dicyanimide, bis(2,4,4-trimethylpentyl)phosphinate and bis(trifluoromethylsulfonyl)imide anions are reported. The data were obtained for pure and water saturated samples at temperatures from 283 K to 353 K and at atmospheric pressure. The refractive index of the investigated ionic liquids decreases with increasing the water content in the sample. On the other hand, no clearly dependence of the surface tension with the water content up to a weight fraction of 16% was found. The prediction of the refractive index for the studied ionic liquids was also accomplished by a group contribution method and new values for the cation and diverse anions were estimated and proposed. The studied ionic liquids show lower surface tension in comparison with imidazolium-, pyridinium- or pyrrolidinium-based ionic liquids with a similar anion; also they show higher surface entropy than cyclic nitrogen-based fluids which indicates a lower surface organization. The anion dependence of the surface tension and surface entropy for the investigated ionic liquids is weaker than that for short-chain imidazolium-based ionic liquids. Their critical temperatures evaluated from Eötvos and Guggenheim equations are also lower than those of N-heterocyclic ionic fluids.     

A noncontinuum model of van der Waals interactions for describing the physicochemical properties of pure molecular liquids

A noncontinuum model based on the use of such molecular characteristics as molecular refraction, dipole moment, and molar volume is suggested for quantitatively describing the physicochemical properties (surface tension, enthalpy of vaporization, boiling temperature, viscosity, etc.) of pure molecular liquids. The ratio between the coefficients of correlation equations relating electrostatic and dispersion contributions to all the properties analyzed was found to be invariant.     

Free energy density functional for adsorption of fluids in nanopores

A classical free energy density functional, which is isomorphic to a usual effective hard sphere model + mean field approximation for tail contribution, is proposed for treatment of real fluids in inhomogeneous states. In the framework of the classical density functional theory (DFT), the present functional is applied to two representative model fluids, namely, a Lennard-Jones fluid and a hard core attractive Yukawa fluid, subject to influence of various external fields. A comprehensive comparison with simulation results and a detailed analysis show that the present functional holds simultaneously all of the desirable properties inherent in an excellent functional, such as high accuracy, computational simplicity, consistency with a hard wall sum rule, nonrecourse to use of adjustable parameter(s) and weighted densities, reproduction of bulk second-order direct correlation function (DCF) in bulk limit, and applicability to subcritical fluid phenomena.     

Application of a new simplified SAFT to VLE study of associating and non-associating fluids

A new equation of state based on the Statistical Associating Fluid Theory (SAFT) is presented to study the phase behavior of associating and non-associating fluids. In the new equation of state, the hard sphere contribution to compressibility factor of the simplified version of the SAFT (SSAFT) is replaced with that proposed by Ghotbi and Vera. The Ghotbi–Vera SSAFT (GV-SSAFT) was also extended to study the phase behavior of associating and non-associating mixtures. The GV-SSAFT like the SSAFT equation of state has three adjustable segment parameters for non-associating fluids and five parameters for associating fluids. The experimental data of liquid densities and vapor pressures for pure fluids studied in this work were used to obtain the best values for the parameters of the GV-SSAFT. The results obtained from the GV-SSAFT for liquid densities and vapor pressures of pure associating and non-associating fluids were compared with those obtained from the SSAFT equation of state. The results showed that the GV-SSAFT similar to the SSAFT can accurately correlate the experimental data of liquid density and vapor pressure for systems studied. On the other hand the results obtained from two SAFT-based equations of state are almost identical. In order to show capability of the GV-SSAFT and SSAFT equations of state, they were used to directly calculate heat of vaporization for a number of pure associating and non-associating fluids. Slightly better results for heat of vaporization comparing to the experimental data were obtained from the GV-SSAFT EOS than those obtained from the SSAFT. The GV-SSAFT was also used to study the VLE phase behavior for a number of binary associating and non-associating mixtures. The results also showed that the GV-SSAFT can be successfully used to study the phase behavior of mixtures studied in this work.     

The effect of trimethylsilyl substituents in the monomer unit on the energy characteristics of surfaces of polynorbornenes obtained via metathesis polymerization

The surface properties of polynorbornenes obtained via metathesis polymerization are investigated via the wetting method. The incorporation of trimethylsilyl groups into the monomer unit causes decreases in the specific free surface energies of the investigated polymers. It is found that the dispersion terms of the specific free surface energies correlate with the free-volume and gas-permeability values of the polymers. As shown through the methods of differential scanning calorimetry and FTIR spectroscopy, during heating in air, the considered polynorbornenes undergo oxidative crosslinking, which increases their specific free surface energies. The interphase energies of crosslinked polynorbornenes are determined at their interfaces with liquids modeling polar and nonpolar phases, and the values of the work of adhesion of the crosslinked polynorbornenes to the model liquids are calculated. It is shown that the work of adhesion of the polymer to the polar phase decreases after introduction of trimethylsilyl groups, while the combination of polar and nonpolar phases give rise to an increase in the work of adhesion.     

丁醛等离子体处理云母粉对其表面特性及与聚合物界面特性的影响

用电容耦合式等离子体聚合方法对云母粉进行丁醛等离子体处理,通过测定各种液体对密堆积云母粉的渗透速度,确定了液体在云母粉表面的接触角,估算了云母粉的表面张力及与典型线形聚合物的界面张力。结果表明,极性液体在云母粉表面的浸润性因处理而削弱,非极性液体的浸润性基本来变;云母粉表面张力由处理前的41.34(N·m~(-1)·10~(-3))下降到处理5min时的31.51和处理30min时的25.59(N·m~(-1)·10~(-3));处理对云母粉与线形聚合物界面张力的影响因聚合物而不同,但该界面张力的极性分量均因处理而减小。     

Description of the pVT behavior of ionic liquids and the solubility of gases in ionic liquids using an equation of state

A molecular thermodynamic model developed previously for fluids of chain-like molecules has been extended to correlate the pVT behavior of ionic liquids and the solubilities of gases such as CO₂, C₃H₆, C₃H₈, C₄H₁₀ in various ionic liquids. The relative deviation between the calculated molar volume and experimental data is less than 0.2%. It is shown that this equation of state can be used to correlate the solubility of CO₂ in ionic liquids with only one temperature-independent adjustable interaction parameter, and the accuracy of the correlation can be further improved using two temperature-independent adjustable parameters. The water content of ionic liquids has a large influence on the calculated results. For systems with water content lower than 0.1%, the average relative deviations of bubble point pressure are 3.14 and 4.90% using two parameters and one parameter, respectively. For systems containing C₃H₆, C₃H₈ and C₄H₁₀ two temperature dependent adjustable parameters are needed to obtain a good fit, and the corresponding deviation of the gas solubility is less than 2%, except for C₃H₈.     

Correlation and Prediction of Osmotic Pressures for Aqueous Bovine Serum Albumin-NaCl Solutions Based on Two Yukawa Potentials

A new equation of state is proposed to correlate and predict the osmotic pressure data for aqueous bovine serum albumin (BSA) solutions with different NaCl concentrations and pH values with only one adjustable parameter. The Carnahan-Starling equation represents the contribution of the hard sphere repulsion to the osmotic pressure. The attractive dispersion and double-layer repulsion interactions are represented by two Yukawa potentials, respectively. The equation of state of Duh and Mier-Y-Teran for one Yukawa potential is expanded to two Yukawa potentials to describe the nonidealities of the charged BSA-aqueous NaCl solution, instead of the classical DLVO theory. The average relative deviation of correlation of the osmotic pressure in 0.15 M NaCl solution is 18%. The average relative deviation of prediction in 1-5 M NaCl solutions is 20.33%. A comparison with other models and the limitations of our model are discussed. Copyright 2001 Academic Press.