Mixing rules for hardsphere chain mixtures and their extension to heteronuclear hardsphere polyatomic fluids and mixtures

Mixing rules are very important for the calculation of fluid properties using different equations of state. In order to find the theoretical lead of the mixing rule for the size parameter, a mixing rule [1] for hardsphere mixtures has been proposed on the basis of Carnahan-Starling equation and Boublik-Mansoori equation. As its extension, mixing rules for hardsphere chain mixtures are proposed in this work. A mixing rule for the segment number (or chain length) is derived on the limitation of the equality of segment diameters, from the first order thermodynamic perturbation theories (TPT1) for pure chain fluids and for chain mixtures. Meanwhile, the mixing rule for the segment diameter is the same as the mixing rule for hardsphere mixtures on the limitation of monomer mixtures. The two mixing rules are checked together over wide ranges of conditions for hardsphere chain mixtures and compared with the first order thermodynamic perturbation theory (TPT1) and also with simulation data available in literature. An another interesting usage of new mixing rules is to describe the heteronuclear hardsphere polyatomic pure fluids, which consist of hardspheres with different segment diameters as in methane and ethane in which carbon and hydrogen atoms are looked as bonded spheres, and heteronuclear hardsphere polyatomic mixtures. The comparison with simulation data shows the validity of the mixing rules.     

Mixtures of lattice polymers with structured monomers

The influence of monomer structure on the thermodynamic properties of lattice model polymer blends is investigated through Monte Carlo computations. The model of lattice polymers with monomer structure has been used extensively in the context of the lattice cluster theory (LCT), a thermodynamic theory for polymer mixtures in the liquid state. The Monte Carlo computations provide the first unequivocal test of the accuracy of the LCT predictions for binary mixtures of polymers with structured monomers. Four types of monomer structures are analyzed, corresponding to to the monomers of polyethylene, polypropylene, polyethylethylene, and polyisobutylene (PIB). Most computations use chains with M=12 and 24 beads and the total volume fraction of the beads is phi=0.6. Both structurally symmetric and asymmetric blends are investigated. For the symmetric case, the predictions of the LCT for the energies of mixing and the liquid-liquid coexistence curves are in qualitative agreement with the Monte Carlo computations, except for the PIB/PIB symmetric blend. For structurally asymmetric blends, the LCT does not capture contributions to the energy of mixing arising solely from structural differences between the components. Computational estimates of the nonideal entropy of mixing indicate that the LCT also underestimates the entropic cost of mixing chains with different structures, thus explaining some discrepancies between the theoretical and the Monte Carlo liquid--liquid coexistence curves.     

Thermodynamic consistency of high pressure ternary mixtures containing a compressed gas and solid solutes of different complexity

A thermodynamic consistency test applicable to high pressure binary gas–solid mixtures is extended to ternary mixtures containing a compressed gas and two solid solutes. A high pressure mixture containing carbon dioxide as solvent and two chemically similar solutes (2,3 dimethylnaphthalene and 2,6 dimethylnaphthalene) and a high pressure mixture containing carbon dioxide as solvent and two chemically different solutes (capsaicin and β-carotene), are considered in the study. Several sets of isothermal solubility data for binary and ternary mixtures are considered in the study. The Peng–Robinson equation of state with the mixing rules of Wong and Sandler have been employed for modeling the solubility of the solid in the case of binary mixtures, while the classical van der Waals mixing rules were used for modeling the ternary mixtures containing two solid solutes. Then the proposed thermodynamic consistency test has been applied. The results show that the thermodynamic test for ternary mixtures can be applied with confidence determining consistency or inconsistency of the experimental data used.     

Structural and thermodynamic properties and intermolecular interactions in aqueous and acetonitrile solutions of aprotic amides

The structural and thermodynamic properties are calculated for mixtures of aprotic amides with water and acetonitrile. The simulation approach is used to identify the specific and nonspecific components of the total energy of intermolecular interactions, which are used to calculate the corresponding contributions to the enthalpy of mixing. The negative enthalpies of mixing in the aqueous mixtures are found to be caused not by heterocomponent specific interactions, but by nonspecific ones. The difference in the structural and thermodynamic properties of the aqueous and nonaqueous mixtures of aprotic amides is shown to be largely due to the behavior of the hydrogen bond network of water and the packing of the resulting solutions.     

Molecular Modelling of Thermodynamic and Related Properties of Mixtures

The results of recent developments on modelling of supramolecular ordering and physicochemical properties of molecular mixtures have been reviewed. The main attention is paid to the unified approach based on a generalized quasichemical model for a set of thermodynamic, dielectric and optical properties of mixtures, self-organized by specific bonding. Interrelations between thermodynamic, as well as dielectric, and optical properties of liquid mixtures, reflecting different molecular parameters, and the characteristics of quasichemical processes are presented. Applications for thermodynamic functions of mixing, permittivity, coefficients Rayleigh light scattering in molecular mixtures are considered. Data on thermodynamics of aggregation in mixtures have been obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Refractive Index of Liquid Mixtures: Theory and Experiment

An innovative approach is presented to interpret the refractive index of binary liquid mixtures. The concept of refractive index “before mixing” is introduced and shown to be given by the volume‐fraction mixing rule of the pure‐component refractive indices (Arago–Biot formula). The refractive index of thermodynamically ideal liquid mixtures is demonstrated to be given by the volume‐fraction mixing rule of the pure‐component squared refractive indices (Newton formula). This theoretical formulation entails a positive change of refractive index upon ideal mixing, which is interpreted in terms of dissimilar London dispersion forces centred in the dissimilar molecules making up the mixture. For real liquid mixtures, the refractive index of mixing and the excess refractive index are introduced in a thermodynamic manner. Examples of mixtures are cited for which excess refractive indices and excess molar volumes show all of the four possible sign combinations, a fact that jeopardises the finding of a general equation linking these two excess properties. Refractive indices of 69 mixtures of water with the amphiphile (R,S)‐1‐propoxypropan‐2‐ol are reported at five temperatures in the range 283–303 K. The ideal and real refractive properties of this binary system are discussed. Pear‐shaped plots of excess refractive indices against excess molar volumes show that extreme positive values of excess refractive index occur at a substantially lower mole fraction of the amphiphile than extreme negative values of excess molar volume. Analysis of these plots provides insights into the mixing schemes that occur in different composition segments. A nearly linear variation is found when Balankina’s ratios between excess and ideal values of refractive indices are plotted against ratios between excess and ideal values of molar volumes. It is concluded that, when coupled with volumetric properties, the new thermodynamic functions defined for the analysis of refractive indices of liquid mixtures give important complementary information on the mixing process over the whole composition range.     

Liquid Structure and Thermodynamics of Alkane Mixtures

Spectroscopic investigations and light scattering experiments with saturated, liquid hydrocarbons and their mixtures indicate a specific and distinct influence of the constitution, conformation, and flexibility of the molecule on the structure and macroscopic behavior of such liquids. Orientational order present in pure liquid n-alkanes, for example, characteristically affects the thermodynamic mixing properties, such as the enthalpy of mixing ΔH_M and the entropy of mixing ΔS_M , when these liquids are mixed with each other, or with other liquids. Nowadays it is possible to determine thermodynamic mixing properties experimentally with such precision that systematic investigations of these properties allow the behavior of liquids to be studied qualitatively and–with molecular theories of liquids–to some extent also quantitatively. The latest results in this respect, exemplified by mixtures of alkanes, are discussed. These results not only demonstrate the progress made in understanding the relations between molecular (microscopic) and macroscopic properties, but are also of importance for industrial applications (e.g. separation processes) in which mixtures of hydrocarbons are involved.     

Prediction of thermodynamic properties of polymer solutions by a group-contribution method

The Flory–Huggins lattice-theory expression for solvent activity in a polymer-solution is commonly used to calculate the thermodynamic interaction parameter χ with the aid of experimental data from vapor pressure osmometry. This expression assumes that χ is independent of composition. However, experimental data for a variety of polymer-solvent mixtures indicate that χ exhibits an appreciable concentration dependence. A group contribution method, UNIFAC (UNIQUAC Functional-Group Activity Coefficients) incorporating the free-volume correction of Oishi and Prausnitz is used to predict the dependence of χ on solvent concentration. Agreement with previously reported experimental data is within 15%. Calculated values of χ obtained from the Flory–Huggins expression for solvent activity and from the corresponding Gibbs free energy of mixing (which does not assume that χ is independent of composition) are compared. Calculations based on the Gibbs free energy of mixing predict a somewhat larger value of χ relative to those based on solvent activity. The specific Gibbs free energy of mixing for polystyrene-solvent mixtures is calculated using the UNIFAC model, and is found to represent qualitatively the phase equilibrium behavior. Quantitative discrepancies are observed, however, for the polystyrene-acetone system in light of the actual experimental solubility reported by Suh and Clark (20). Most of the thermodynamic predictions for polymer-solvent systems investigated herein are correlated qualitatively with the relative mismatch between solubility parameters of both components.     

Thermodynamic calculation of supercritical-fluid equilibria: New mixing rules for equations of state

Simple cubic equations of state with conventional mixing rules have played an important role in the calculation of phase equilibria and other thermodynamic properties of non-polar fluid mixtures. In the application of supercritical fluids to separation processes, volumetric as well as phase equilibrium properties are very important for rational process design.

Heyen (1980) proposed a cubic equation of state which shows better accuracy in the calculation of volumetric properties, compared to the Peng-Robinson equation of state. In order to apply his equation to polar mixtures, Heyen recently proposed a density-independent mixing rule, but this does not obey the universally-observed quadratic mixing rule of the second virial coefficient in the low-density limit.

This paper proposes a new density-dependent mixing rule for the Heyen equation of state. The Heyen equation of state with our new mixing rule appears to calculate the phase equilibria and the volumetric properties of CO₂-containing non-polar as well as polar mixtures with good accuracy.     

X-ray structural studies on microscopic mixing in binary mixtures of dimethyl sulphoxide with acetonitrile and N,N-dimethylformamide

The liquid structures of binary acetonitrile (AN)–dimethyl sulphoxide (DMSO) and N,N-dimethylformamide (DMF)–DMSO mixtures were investigated by the X-ray scattering method. Comparison of the X-ray scattering data of AN–DMSO liquid mixtures with those of neat AN and DMSO revealed that the intermolecular AN–DMSO interactions are practically not detected; that is, the X-ray scattering data of the liquid mixtures are well reproduced by summing up those of neat AN and DMSO weighted by their mole fractions. The same applies for DMF–DMSO mixtures. Thus, each component solvent molecule independently forms self-assembled clusters in the liquid mixtures, the structures of which are the same as those in the neat liquids. The clusters are mixed to form macroscopically homogeneous liquid mixtures. The thermodynamic quantities on mixing process for the AN–DMSO, DMF–DMSO and AN–DMF systems in the literature are well elucidated on the basis of the microscopic structure of the liquid mixtures.     

Theory of the thermodynamic properties of binary mixtures of organic molecules with size mismatch

The Flory expression for the Gibbs free energy of mixing of a binary mixture is improved by introducing a hard-sphere form for the entropy of mixing. The resulting expression is used to describe the characteristic features of organic mixtures of globular molecules with size mismatch. In particular, we show that the above model, with an interchange energy depending on temperature, accounts for the thermodynamic properties and concentration fluctuations of a number of octamethylcyclotetrasiloxane-based mixtures.     

Thermodynamics of dipolar hard sphere mixtures

The thermodynamic properties of mixtures of hard spheres with imbedded point dipoles are investigated by an extension of the perturbation theory used by Rushbrooke et al. for pure fluids. Equations are presented for the general multicomponent mixture in which all the hard spheres have the same diameter. Numerical calculations are presented of the phase behaviour and excess thermodynamic mixing functions for the special case of the binary mixture in which only one species is polar. A brief discussion is given of the relationship of this model to experimental results for real fluid mixtures and of possible extensions of this work.     

Evaluation of co-volume mixing rules for bitumen liquid density and bubble pressure estimation

The Peng–Robinson cubic equation of state (CEOS) is widely used to predict thermodynamic properties of pure fluids and mixtures. The usual implementation of this CEOS requires critical properties of each pure component and combining rules for mixtures. Determining critical properties for components of heavy asymmetric mixtures such as bitumen is a challenge due to thermolysis at elevated temperatures. Group contribution (GC) methods were applied for the determination of critical properties of molecular representations developed by Sheremata for Athabasca vacuum tower bottoms (VTB). In contrast to other GC methods evaluated, the Marrero–Gani GC method yielded estimated critical properties with realistic, non-negative values, followed more consistent trends with molar mass and yielded normal boiling points consistent with high temperature simulated distillation data. Application of classical mixing rules to a heavy asymmetric mixture such as bitumen yields saturated liquid density and bubble pressure estimates in qualitative agreement with experimental data. However the errors are too large for engineering calculations. In this work, new composite mixing rules for computing co-volumes of asymmetric mixtures are developed and evaluated. For example, composite mixing rules give improved bubble point predictions for the binary mixture ethane + n-tetratetracontane. For VTB and VTB + decane mixtures the new composite mixing rules showed encouraging results in predicting bubble point pressures and liquid phase densities.     

Comparison of different mixing rules for prediction of density and residual internal energy of binary and ternary Lennard–Jones mixtures

Mixing rules are necessary when equations of state for pure fluids are used to calculate various thermodynamic properties of fluid mixtures. The well-known van der Waals one-fluid (vdW1) mixing rules are proved to be good ones and widely used in different equations of state. But vdW1 mixing rules are valid only when molecular size differences of components in a mixture are not very large. The vdW1 type density-dependent mixing rule proposed by Chen et al. [1] is superior for the prediction of pressure and vapor–liquid equilibria when components in the mixture have very different sizes. The extension of the mixing rule to chain-like molecules and heterosegment molecules was also made with good results. In this paper, the comparison of different mixing rules are carried out further for the prediction of the density and the residual internal energy for binary and ternary Lennard–Jones (LJ) mixtures with different molecular sizes and different molecular interaction energy parameters. The results show that the significant improvement for the prediction of densities is achieved with the new mixing rule [1], and that the modification of the mixing rule for the interaction energy parameter is also necessary for better prediction of the residual internal energy.     

Study of weak molecular interactions through thermodynamic mixing properties

The electron donor-acceptor abilities of some cyclic ethers (tetrahydropyran or tetrahydrofuran), benzene, and halobenzenes (fluorobenzene or chlorobenzene) and the molecular interactions between these compounds have been investigated through a wide set of thermodynamic mixing properties of their mixtures. The mixing properties have been derived from experimental measurements of density, speed of sound, refractive index, surface tension, heat of mixing, and vapor-liquid equilibrium at the temperature of 298.15 K.     

聚己内酯和酚氧树脂共混物的结晶行为和熔融转变

通过采用不同变温程序对溶液铸膜PCL与酚氧共混物进行了热分析。实验结果显示,在准平衡状态下,对PCL含量大于30％的共混对,PCL均可从混合物熔体中降温结晶出来。进一步研究发现熔融温度随PCL含量减少而下降,此现象可籍结晶、非晶聚合物之间的热力学混容解释,并应用由Scott方程推导出的关系式计算,发现对该聚合物对,相互作用参数在320K时为-0.155。从熔融态等速降温,对PCL含量大于50％的共混对均观察到结晶转变,转变温度强烈依赖于组成和降温速率,主要原因在于对这种“动力学”实验,熔体中PCL链段向晶体表面的扩散过程控制结晶,任何使PCL链段扩散能力减弱的因素,都将降低结晶温度。在等速降低温度过程中还发现,共混物产生双结晶峰。     

Application of a new equation of state to liquid refrigerant mixtures

A new general equation of state recently reported for pure liquids has been developed to predict the volumetric and thermodynamic properties of six binary and two ternary liquid refrigerant mixtures (including HCs and HFCs mixtures) at different temperatures, pressures, and compositions. The results show this equation of state can be used to reproduce and predict different thermodynamic properties of liquid refrigerant mixtures within experimental errors. The composition dependence of the parameters of this equation of state has been assumed as quadratic functions of mole fraction. Using these mixing rules, the agreement between calculated and experimental densities is better than 0.6% for binary mixtures and 2.3% for ternary mixtures. To compare the performance of this new equation of state against other well-known methods such as the COSTALD method, the density of some refrigerant mixtures, for which the parameters of COSTALD were available, has been computed and compared with those of this new equation of state.     

Thermodynamic consistency of experimental VLE data for asymmetric binary mixtures at high pressures

A thermodynamic consistency of isothermal vapor–liquid equilibrium data for 9 non-polar and 8 polar binary asymmetric mixtures at high pressures has been evaluated. A method based on the isothermal Gibbs–Duhem equation was used for the test of thermodynamic consistency using a Φ–Φ approach. The Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules were used for modeling the vapor–liquid equilibrium (VLE) within the thermodynamic consistency test. The VLE parameters calculations for asymmetric mixtures at high pressures were highly dependent on bubble pressure calculation, making more convenient to eliminate the data points yielding the highest deviations in pressure. However the results of the thermodynamic consistencies test of experimental data for many cases were found not fully consistent. As a result, the strategies for solving these problems were discussed in detailed.