A SAFT model for associating Lennard-Jones chain mixtures

The recently proposed equation of state of statistical associated fluid theory (SAFT) is extended to associating Lennard-Jones (LJ) chain mixtures. In this extension, a new radial distribution function (RDF) for LJ mixtures is derived around the LJ potential size (σ _ij ). The RDF expression is completely analytical and real. Comparisons with computer simulation data under various conditions indicate that the RDF is very accurate up to its first peak. The new RDF, together with a previously established equation of state for LJ mixtures, is employed to study LJ chain mixtures by combining with Wertheim's first-order perturbation theory. The resulting equation of state is tested satisfactorily against computer simulation data for both non-associating and associating LJ chain mixtures, with a performance similar to its predecessors for pure LJ chains and LJ mixtures. The SAFT model is uniquely featured by being totally mixing-rule free and by being adjustable at both chain bonding and association sites. Moreover, the SAFT model is formulated very generally, so that it is applicable to both homonuclear and heteronuclear chain mixtures.     

Equation of state SAFT-CP for vapour–liquid equilibria and mutual solubility of carbon dioxide and water

ABSTRACT

The statistical associating fluid theory (SAFT) was proposed first in 1990, and has been extended to various forms for the calculation of thermodynamic properties of complex systems, such as oil reservoir fluids, polar systems, polymers, electrolytes, near-critical systems, interfacial phenomena, solids and even biomaterials. SAFT-CP (critical point) has been established for nonpolar fluids in 2001 with excellent expression of thermodynamic properties across critical points. It was extended later for polar and associating fluids with the addition of just a dipole–dipole interaction, which leads simple calculation procedure without an association term. In this article SAFT-CP is applied to carbon dioxide, water and their mixture. Vapour–liquid equilibria for pure components CO₂ and H₂O, CO₂ solubility in water and H₂O solubility in dense CO₂ are analysed. Expression of pure CO₂ properties is improved with the dipole–dipole interaction term used, while expression of pure water is a little bit improved with the non-spherical degree parameter less than 1.0. For the high asymmetry in polarity and association between CO₂ and H₂O molecules, the Stryjek–Vera combining rule is used with different temperature-dependent parameters. With the quadratic temperature-dependent parameters, the mutual solubilities in the system are calculated with good agreement with experimental ones over the wide range of temperature as 298–474 K and of pressure as 0.1–70 MPa.     

极性分子摆动态的三体量子关联

极性分子具有较长的相干时间和较强的偶极-偶极相互作用,因此它被视为量子信息处理的有效量子载体.基于分子摆动态作为量子比特,研究了处于热平衡状态下三极性分子线性链系统的三体量子关联特性,分析了三体负性熵纠缠度、测量诱导扰动和三体量子失协随与电场强度、分子电偶极矩、分子转动常数、偶极-偶极相互作用和温度等参数有关的三个无量纲变量之间的变化关系.研究表明:在其他参数给定的情况下,随电场强度的增加,三体量子关联均变小;随偶极-偶极相互作用强度的增大,三体量子关联先增加到峰值再逐渐变小;温度越高,负性熵纠缠度和三体量子失协越小,但测量诱导扰动随温度的改变在电场强度和偶极-偶极相互作用影响下呈现不同的变化趋势.此外,通过调节电场强度、偶极-偶极相互作用和温度,可改变与操控极性分子摆动态的三体量子关联.     

Modeling the phase equilibria of a H2O–CO2 mixture with PC-SAFT and tPC-PSAFT equations of state

Water–carbon dioxide binary mixtures are important for a number of industrial and environmental applications. Accurate modeling of the thermodynamic properties is a challenging task due to the highly non-ideal intermolecular interactions. In this work, two models based on the Statistical Associating Fluid Theory (SAFT) are used to correlate reliable experimental vapor–liquid equilibria (VLE) and liquid–liquid equilibria (LLE) data in the temperature range 298–533?K. CO₂ is modeled as a non-associating or associating component within the Perturbed Chain-SAFT (PC-SAFT) and as a quadrupolar component within the truncated PC-Polar SAFT (tPC-PSAFT). It is shown that PC-SAFT with explicit account of H₂O–CO₂ cross-association and tPC-PSAFT with explicit account of CO₂ quadrupolar interactions are the most accurate of the models examined. Saturated liquid mixture density data are accurately predicted by the two models.     

Equation of state of long chain molecules and rings

An equation of state for long chain molecules has been proposed using statistical associating fluid theory (SAFT). The formalism derived here is based on the assumption that the chain is formed by the pairs of trimers. The equations of state for 48-mers and 192-mers are formulated and compared with Monte Carlo results. The theory has been developed to treat hard sphere molecules with two attraction sites to form a ring molecule. The equations of state for trimer, hexamer and 12-mer ring molecules have been formulated. There is excellent agreement with available Monte Carlo results. Second virial coefficients of tangent chain molecules and ring molecules have been determined numerically and compared with simulation results.     

Intramolecular bonding in a statistical associating fluid theory of ring aggregates

The first-order thermodynamic perturbation theory of Wertheim (TPT1) is extended to treat ring aggregates, formed by inter- and intramolecular association. The expression for the residual association contribution to the Helmholtz free energy for ring aggregates, incorporating the appropriate terms in Wertheim's fundamental graph sum of the TPT1 density expansion, is derived to calculate the distribution of the molecular bonding states. This requires the introduction of two new parameters to characterise each possible ring type: the ring size τ, which is equal to one in the case of intramolecular association, and a parameter W that captures the likelihood of two ring-forming sites bonding. The resulting framework can be incorporated in equations of state that account for the residual association contribution to the free energy, such as the statistical associating fluid theory (SAFT) family, or the cubic plus association (CPA) equation of state. This extends the applicability of these equations of state to mixtures with an arbitrary number of association sites capable of hydrogen bonding to form intramolecular and intermolecular rings. The formalism is implemented within SAFT-VR Mie to calculate the fluid-phase equilibria of model chain-like molecules containing two associating sites A and B, allowing for the formation of open-chain aggregates and intramolecular bonds. The effect of adding a second component that competes for the association sites that mediate intramolecular association in the chain is also examined. Accounting for intramolecular bonding is shown to have a significant impact on the phase equilibria of such systems.     

Y型Langmuir-Blodgett膜中分子聚集行为的偶极作用模型

利用经典静电场理论，描述了Y型Langmuir-Blodgett (LB) 膜中棒状分子聚集行为的偶极作用模型，给出了Y型LB膜结构与光谱性质的关系.讨论了Y型膜中分子间距、层间距、分子取向、膜层数等结构参数对分子聚集行为的影响，并在此基础上比较了Y型膜和Z型膜分子聚集行为的异同.理论结果与实验规律符合较好.     

A molecular-based theory for the thermodynamic properties of water

Following the rules set by the molecular theories of fluids, a perturbed form of the Helmholtz free energy for water has been developed. The reference term corresponds to short range water, and is approximated by the properties of a primitive model; the perturbation term is given by contributions of the dispersion forces and the dipole-dipole interaction. The method is first verified by applying it to TIP4P water and then used for real water without reference to any specific potential. The parameters of the model are determined in order to obtain the best representation of the vapour pressure and coexistence liquid densities from the triple point to 643.15K; no attempt is made to fit the critical region. Despite a number of approximations employed, the accuracy of the equation of state is comparable with that of the modified Redlich-Kwong-Soave equation and SAFT Yukawa-dipole-dipole equation, and considerably better than the accuracy of SAFT-HS and SAFT-VR equations. Because of its true molecular footing, the equation remains reliable also for various thermodynamic properties outside the coexistence region. It reproduces the anomaly in the isothermal compressibility, locating its minimum at T = 38 °C (versus the experimental value T = 46 °C) for P = 1 bar. It also predicts a density maximum, but outside the experimental temperature range (at temperatures below the triple-point temperature).     

TPT2 and SAFTD equations of state for mixtures of hard chain copolymers

We present the second-order thermodynamic perturbation theory (TPT2) and the dimer statistical associating fluid theory (SAFTD) equations of state for mixtures consisting of hetero-nuclear hard chain molecules based on extensions of Wertheim's theory for associating fluids. The second-order perturbation theory, TPT2, is based on the hard sphere mixture reference fluid. SAFTD is an extension of TPT1 (= SAFT) and is based on the non-spherical (hard disphere mixture) reference fluid. The TPT2 equation of state requires only the contact values of the hard sphere mixture site-site correlation functions, while the SAFTD equation of state requires the contact values of site-site correlation functions of both hard sphere and hard disphere mixtures. We test several approximations for site-site correlation functions of hard disphere mixtures and use these in the SAFTD equation of state to predict the compressibility factor of copolymers. Since simulation data are available only for a few pure copolymer systems, theoretical predictions are compared with molecular simulation results for the compressibility factor of pure hard chain copolymer systems. Our comparisons show a very good performance of TPT2, which is found to be more accurate than TPT1 (= SAFT). Using a modified Percus-Yevick site-site correlation function SAFTD is found to represent a significant improvement over SAFT and is slightly more accurate than TPT2. Comparison of SAFTD with generalized Flory dimer (GFD) theory shows that both are equivalent at intermediate to high densities for the compressibility factor of copolymer systems investigated here.     

Influence of dipole-dipole correlations on the stability of the biaxial nematic phase in the model bent-core liquid crystal

A molecular theory of biaxial nematic ordering in the system of bent-core molecules has been developed in the two-particle cluster approximation which enables one to take into account short-range polar correlations determined by both electrostatic dipole-dipole interaction and polar molecular shape. All orientational order parameters and short-range correlation functions are calculated numerically as functions of temperature in the uniaxial and in the biaxial nematic phases, and the results are compared with the ones obtained in the mean-field approximation and in the cluster approximation but without taking into consideration the dipole-dipole interaction. It is shown that short-range polar correlations and, in particular, the dipole-dipole correlations dramatically increase the temperature of the transition into the biaxial nematic phase and enhancing its stability range. The results are also very sensitive to the value of the opening angle of a model bent-core molecule.     

亲水性两性离子聚合物刷的构象与结构

本文应用分子场理论,研究暴露于水蒸气中的亲水性两性离子聚合物(HP)刷的构象与结构.理论模型考虑HP-水(P-W)氢键和水-水(W-W)氢键效应,以及HP单体之间的偶极-偶极相互作用.研究发现,P-W与W-W氢键决定着HP的水合性,P-W氢键形成,会诱导HP刷溶胀.我们通过考察HP单体间的偶极-偶极相互作用发现,随着偶极-偶极相互作用增强,HP链在垂直培基表面沿着链方向,形成了结节状结构.这是由于HP单体之间的偶极-偶极静电吸引作用导致单体间汇聚结节,这种结节在刷内产生了较强的排斥体积作用,因此,这种HP刷具有抗污性能.在较高的接枝密度环境下,由于HP链间单体之间的偶极-偶极静电吸引作用,会形成链间单体-单体的结节,在刷内形成结节网络状凝胶结构,这种结构的出现,会使得HP刷呈现极强的抗污性.另外,当体系中水蒸气浓度增加、水合相互作用增强时,增加的P-W氢键将平衡HP单体之间的偶极-偶极相互作用,使得结节解开,聚合物链伸展.我们的理论结果符合实验观测,由此表明,P-W氢键效应,以及HP单体之间的偶极-偶极相互作用决定着HP刷的构象转变和结构特性,刷内出现的两性离子聚合物链内单体间的结节和链间单体结节状凝胶结构,是两性离子聚合物刷呈现较强抗污性的本质特性.     

Development of intermolecular potential models for electrolyte solutions using an electrolyte SAFT-VR Mie equation of state

ABSTRACT

We present a theoretical framework and parameterisation of intermolecular potentials for aqueous electrolyte solutions using the statistical associating fluid theory based on the Mie interaction potential (SAFT-VR Mie), coupled with the primitive, non-restricted mean-spherical approximation (MSA) for electrolytes. In common with other SAFT approaches, water is modelled as a spherical molecule with four off-centre association sites to represent the hydrogen-bonding interactions; the repulsive and dispersive interactions between the molecular cores are represented with a potential of the Mie (generalised Lennard-Jones) form. The ionic species are modelled as fully dissociated, and each ion is treated as spherical: Coulombic ion–ion interactions are included at the centre of a Mie core; the ion–water interactions are also modelled with a Mie potential without an explicit treatment of ion–dipole interaction. A Born contribution to the Helmholtz free energy of the system is included to account for the process of charging the ions in the aqueous dielectric medium. The parameterisation of the ion potential models is simplified by representing the ion–ion dispersive interaction energies with a modified version of the London theory for the unlike attractions. By combining the Shannon estimates of the size of the ionic species with the Born cavity size reported by Rashin and Honig, the parameterisation of the model is reduced to the determination of a single ion–solvent attractive interaction parameter. The resulting SAFT-VRE Mie parameter sets allow one to accurately reproduce the densities, vapour pressures, and osmotic coefficients for a broad variety of aqueous electrolyte solutions; the activity coefficients of the ions, which are not used in the parameterisation of the models, are also found to be in good agreement with the experimental data. The models are shown to be reliable beyond the molality range considered during parameter estimation. The inclusion of the Born free-energy contribution, together with appropriate estimates for the size of the ionic cavity, allows for accurate predictions of the Gibbs free energy of solvation of the ionic species considered. The solubility limits are also predicted for a number of salts; in cases where reliable reference data are available the predictions are in good agreement with experiment.     

Improved models for the phase behaviour of hydrogen fluoride: chain and ring aggregates in the SAFT approach and the AEOS model

Hydrogen fluoride presents one of the strongest hydrogen bonds known. Ring aggregates exist both in the vapour and liquid phases at low temperatures resulting in an anomalously high low-temperature vapour pressure. The effect of ring-like aggregates on the vapour—liquid phase equilibria of associating fluids is studied within the framework of the statistical associating fluid theory (SAFT) and in the chemical model of Lencka and Anderko (AEOS). The SAFT approach incorporates separate contributions to describe chain formation, association (hydrogen bonding), and long range dispersion forces. The treatment of the association interactions stems from the thermodynamic perturbation theory of Wertheim. At the first level of approximation the contribution of ring-like aggregates is neglected and only chain- and treelike structures are treated. In this work an earlier extension of the approach to incorporate ring aggregates is used to model the phase behaviour of hydrogen fluoride. The chemical model of Lencka and Anderko for associating fluids is also considered together with a modification that takes into account the formation of ring aggregates. Vapour pressures and coexistence densities are examined together with heats of vapourization, and the calculations are compared with experimental data.     

Modelling the phase equilibria of multicomponent mixtures containing CO2, alkanes,water, and/or alcohols using the quadrupolar CPA equation of state

ABSTRACT

In this work, a quadrupolar cubic plus association (qCPA) equation of state is evaluated for its ability to predict the phase equilibria of multicomponent mixtures containing CO₂ and alkanes, alcohols, and/or water. A single binary interaction parameter is employed in qCPA for all binary combinations. All parameters are based solely on pure fluid or binary mixture data and multicomponent data are used only to evaluate the predictions. The performance of qCPA is, for all mixtures, compared to CPA where CO₂ is considered to be either non-associating (inert), solvating or self-associating. In the latter two approaches, an additional adjustable parameter is employed for binary pairs of CO₂ and an associating compound. The results show that the predictions with qCPA are very similar to the best performing CPA approaches, even though the model uses fewer adjustable binary parameters. The predictions with qCPA and the best CPA approaches are typically satisfactory and predict the general behaviour of the systems. As expected, qCPA and CPA with solvation or association typically performs better than inert CPA for two- and three phase vapour–liquid and vapour–liquid–liquid equilibria. However, inert CPA yields the best results of all the models for the prediction of dew point pressures.     

The chemical potential of Lennard-Jones associating fluids from osmotic Monte Carlo simulations

The chemical potential for a two-component Lennard-Jones fluid with associative interaction between opposite species promoting the formation of dimers is calculated using osmotic Monte Carlo (OMC) canonical ensemble simulations. Grand canonical Monte Carlo simulations also are performed to verify the accuracy of the OMC approach. The data from both methods agree very well for thermodynamic states with different degrees of dimerization. It follows that the OMC is a promising approach for the determination of the thermodynamics of and equilibria between associating and non-associating fluids and associating fluid mixtures.     

Study of the complexation and solvation of polar molecules in binary solvents by differential spectroscopy

A method of application of differential absorption spectroscopy for determining the absorption spectra of primary 1: 1 solvated complexes between polar molecules of an organic dye and the active component of a binary solvent whose neutral component is a nonpolar liquid is proposed. The method was tested on diluted solutions of 4-dimethylaminochalcone (4-DMC) (which is one of the most efficient spectral-luminescent probes used in present-day medical and biological investigations) in mixtures of n-hexane with acetone at extremely small concentrations of the polar component. It is shown that the experimentally found absolute shift of the long-wavelength absorption band of 4-DMC is in satisfactory quantitative agreement with the analogous value obtained independently on the basis of the theory describing the joint effect of nonlinear (complexation) and linear (solvation) dipole-dipole interactions on the spectral band positions.     

Optimisation of the dipole-Coulomb approximation for high-l Rydberg states of polar molecules

ABSTRACT

The present work deals with the question of the origin choice to get the maximal accuracy of the dipole-Coulomb approximation in the theory of molecular Rydberg states with high orbital momentum l. Concerning birefringence in polar molecules, the question of adequate origin choice has first been raised in the classical work by Buckingham & Longuet-Higgins in 1968, where it has been taken into account that the dipole moment of a polar molecular core (cation) depends on the origin choice. This dependence also leads to inseparability of dipole and quadrupole corrections to the Rydberg electron spectra in polar molecules. In the present work a new option for the problem is proposed as applied to the dipole-Coulomb approximation. Considering a simplified model of a molecular core as a system of N effective fixed point charges, we show both analytically and numerically that the optimal choice of origin, at least for a linear core, is the geometric centre of the core. On the other hand, results of the present work as well as previous publications show that the problem raised by Buckingham and Longuet-Higgins does not have a universal solution.

Abbreviations: RS: Rydberg state; RSs: Rydberg states; ZEKE: zero electron kinetic energy; MATI: mass-analysed threshold ionisation; QDT: quantum defect theory; DCA: dipole-Couloumb approximation; CD: centre of dipole; CC: centre of charge; GC: geometric centre; DCAGC: dipole-Couloumb approximation with origin in the geometric centre; DCACD: dipole-Couloumb approximation with origin in the centre of dipole     

From realistic to simple models of fluids. III. Primitive models of carbon dioxide,hydrogen sulphide and acetone,and their properties

Recently developed methodology to construct primitive models of associating fluids as direct descendants of complex realistic intermolecular potential functions [L. Vl?ek, I. Nezbeda. Molec. Phys., 102, 485 (2004).] is extended to polar fluids and applied to three substances of practical importance: quadrupolar carbon dioxide, and dipolar hydrogen sulphide and acetone. It is shown that the structural properties (in terms of the site–site correlation functions) of the primitive models of polar fluids reproduce very well those of their parent realistic models but, nonetheless, they perform worse than in the case of associating fluids. A number of thermodynamic properties of the developed models obtained by computer simulations is also reported (for their later use in theoretical investigation) and discussed.