Estimation of Pitzer's ion interaction parameters for electrolytes involved in complex formation using a chemical equilibrium model

Pitzer's ion interaction model has been widely accepted for calculating the thermodynamic properties for electrolytes at high ionic strength. For weak electrolytes, a better estimation can be obtained by combining the model with chemical equilibria. The method of calculation is to treat each individual species as a single, separated ion. The concentration of each ion will be constrained by the mass balance equation and its activity will be guarded by the stability constants. Including chemical equilibria in Pitzer's model provides not only a better estimation of the thermodynamic properties of weak electrolytes but also a better understanding of the equilibrium among the complexes. The results may be used for correcting the effect from high ionic strength solution when determining the stability constants. When considering chemical equilibria, some of the parameters reported by Pitzer may have to be reestimated. The method of estimation and comparison between final results are presented. The binary system of HF, and the ternary systems of CuCl₂ in NaCl and in HCl are used for demonstration.     

Molecular modeling of polymers: I. Correct and efficient enumeration of intrachain conformational energetics

Polymer conformational analyses can require being able to model the intramolecular energetics of a very long (infinite) chain employing calculations carried out on a relatively short chain sequence. A method to meet this need, based upon symmetry considerations and molecular mechanics energetics, has been developed. Given N equivalent degrees of freedom in a linear polymer chain, N unique molecular groups are determined within the chain. A molecular unit is defined as a group of atoms containing backbone rotational degrees of conformational freedom on each of its ends. The interaction of these N molecular groups, each with a finite number of nearest neighbors, properly describe the intramolecular energetics of a long (infinite) polymer chain. Thus, conformational energetics arising from arbitrarily distant neighbor interactions can be included in the estimation of statistical and thermodynamic properties of a linear polymeric system. This approach is called the polymer reduced interaction matrix method (PRIMM) and the results of applying it to isotactic polystyrene (I-PS) are presented by way of example.     

Integral equation theory for atactic polystyrene melt with a coarse-grained model

In this work, an integral equation approach to investigate the atactic polystyrene (aPS) melt based on polymer reference interaction site model (PRISM) theory is proposed. The intramolecular structure factors, required as input to PRISM theory, are obtained from the semiflexible chain model. With a novel coarse-graining procedure and the explicit-atom molecular-dynamics (MD) simulations for aPS, the parameters needed for the coarse-grained model are obtained by using an automatic simplex optimization. These parameters can be used to describe the structure and thermodynamic properties of the complex aPS melt and good agreement is obtained between the theory and MD simulations. The proposed integral equation approach provides a basis for describing the structure and properties of PS nanocomposites where the application of molecular simulation is difficult.     

Molecular origin of the hydrophobic effect: analysis using the angle-dependent integral equation theory

The molecular origin of the hydrophobic effect is investigated using the angle-dependent integral equation theory combined with the multipolar water model. The thermodynamic quantities of solvation (excess quantities) of a nonpolar solute are decomposed into the translational and orientational contributions. The translational contributions are substantially larger with the result that the temperature dependence of the solute solubility, for example, can well be reproduced by a model simple fluid where the particles interact through strongly attractive potential such as water and the particle size is as small as that of water. The thermodynamic quantities of solvation for carbon tetrachloride, whose molecular size is approximately 1.9 times larger than that of water, are roughly an order of magnitude smaller than those for water and extremely insensitive to the strength of solvent-solvent attractive interaction and the temperature. The orientational contributions to the solvation energy and entropy are further decomposed into the solute-water pair correlation terms and the solute-water-water triplet and higher-order correlation terms. It is argued that the formation of highly ordered structure arising from the enhanced hydrogen bonding does not occur in the vicinity of the solute. Our proposition is that the hydrophobic effect is ascribed to the interplay of the exceptionally small molecular size and the strongly attractive interaction of water, and not necessarily to its hydrogen-bonding properties.     

Prediction of thermodynamic properties of sodium dodecyl sulfate aqueous solutions through the hetero-SAFT equation of state

A special version of statistical associating fluid theory (SAFT), the so-called hetero-segmented SAFT equation of state, has been extended to calculate the thermodynamic properties of sodium dodecyl sulfate aqueous solutions. The predicted properties were included the vapor pressure as well as second thermodynamic properties, such as speed of sound. Evaluation of the model has been done through comparison of the calculated vapor pressure with experimental data in the range of 298.15–313.15 K. The hetero-SAFT model is found to be able to correctly describe the thermodynamic derivative properties as well as pVT and VLE properties of ionic surfactant solutions.     

Modification of PSRK mixing rules and results for vapor–liquid equilibria, enthalpy of mixing and activity coefficients at infinite dilution

The predictive Soave–Redlich–Kwong (PSRK) equation of state (EOS) is a well-established method for the prediction of thermodynamic properties required in process simulation. But there are still some problems to be solved, e.g. the reliability for strong asymmetric mixtures of components which are very different in size. The following modifications are introduced in the PSRK mixing rules: the Flory–Huggins term in the mixing rule for the EOS parameter a, and the combinatorial part in the UNIFAC model are skipped simultaneously; a nonlinear mixing rule for the EOS parameterb, instead of the linear mixing rule, is proposed. With these two modifications better results are obtained for vapor–liquid equilibria and activity coefficients at infinite dilution for alkane–alkane systems, specially for asymmetric systems. In order to obtain better results for enthalpy of mixing, temperature-dependent parameters are used. Group interaction parameters have been fitted for several groups, and the results are compared with the Modified UNIFAC (Dortmund), and the PSRK methods.     

含醇溶液的热力学研究I.超额焓模型

提出了一个醇与烃混合的热力学模型,据此,得到了一个简单的超额焓方程, 它由物理和化学贡献两部分组成。这个方程具有一定的通用性,能够推广到其它含 醇溶液。方程不仅能满意地用来描述超额焓与组成间的关系,而且还能显示组分间 的相互作用。     

缔合溶液热力学性质与谱学性质的关联

缔合溶液具有与理想溶液显著不同的热力学和谱学性质,对于热力学和谱学的研究,有助于我们理解缔合溶液的特殊行为.谱学技术中核磁共振(NMR)、红外(IR)和拉曼(Raman)光谱是研究分子间相互作用和溶液结构等微观性质的有效方法,谱学已成为分子热力学研究体系"四面体结构"中的第四个顶点.本文对缔合溶液中热力学(汽液平衡和焓)和谱学(NMR,IR和Raman)联系的最新研究进展进行了综述,着重介绍相关的模型,如化学缔合模型、局部组成(LC)、格子流体氢键(LFHB)理论以及统计缔合流体理论(SAFT).     

Solvation model for estimating the properties of (vapour + liquid) equilibrium

A solvation energy relation (SERAS) has been developed for correlating the properties and (vapour + liquid) equilibrium (VLE) of associated systems capable of hydrogen bonding or dipole–dipole interaction. The model clarifies the simultaneous impact of hydrogen bonding, solubility and thermodynamic factors of activity coefficients derived from the UNIFAC-original model. The consistency test has been processed against binary VLE data for six isobaric systems of hydrogen bonding (I to III) and dipole–dipole interaction (IV to VI) types, and two isothermal systems of both types (VII and VIII). Systems II, III, and VIII show negative non-ideal deviations. The reliability analysis has been conducted on the performance of the SERAS model with 5- and 10-parameters. The model matches relatively well with the observed performance, yielding mean error of 9.7% for all the systems and properties considered.     

Thermodynamic properties of dendrimers compared with linear polymers: General observations

The pressure‐volume‐temperature and thermal properties of dendrimers based on benzyl ether were measured and compared with literature values for monodisperse, linear polystyrenes. In addition, property measurements are presented for an exact linear analogue to the fifth‐generation dendrimer. The thermodynamic properties' molecular weight behavior for the dendrimers is unique when compared with that of linear polystyrene. All of the evidence presented in this work suggests that some form of structural transition occurs in the bulk at a molecular mass near that for the fourth‐generation dendrimer. No such transition is seen for polystyrene. Dendrimers exhibit an increased packing efficiency as evidenced by a decreased specific volume (increased density) as compared with an exact linear analogue of the fifth‐generation dendrimer analogue, and the dendrimer highlights the entropic differences between the two molecules. In addition, differences in the change in heat capacity with temperature for the two systems further allude to their entropic differences. A crystalline state can be formed for the lower generation dendrimer and linear analogue. This crystalline state is not seen in dendrimers above the third generation. These behaviors compiled with the difference in the glass‐transition temperature for the linear analogue suggest that the dendrimers' microstructure has a significant influence on the bulk thermodynamic state of the material. The Tait equation was fitted to the volume data for comparative purposes; the Tait equation has known limitations but was selected because of its widespread application. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1766–1777, 2001     

Description of the Structure and Properties of Atactic Polystyrene Melt Using Integral Equation Theory

The polymer reference interaction site model （PRISM） integral equation theory was used to describe the structure and thermodynamic properties of atactic polystyrene （aPS） melt, in which the monomer of aPS is represented with an eight-site model to characterize its microstructure. The intramolecular structure factors needed in the PRISM calculations were obtained from single chain MD simulations. The calculated results indicate that the results by the integral equation method agrees well with experiments, and can reflect the fine microscopic structure of real aPS melt. This work shows that the PRISM theory is a powerful tool for investigating the structure and properties of complex polymers.     

Equation of state molecular parameters for a theory of pure r-mer fluids in the liquid phase

Costas, M. and Sanctuary, B.C., 1984. Equation of state molecular parameters for a theory of pure r-mer fluids in the liquid phase. Fluid Phase Equilibria, 18: 47–60.Equation of state parameters for a theory of pure r-mers (Costas and Sanctuary, 1981) are presented for sixty common substances. The equation of state is tested for its ability to reproduce and predict thermodynamic data in the liquid phase. The theory has only two adjustable parameters: ν^*, the close-packed volume of the r-mer, and ?^* = z?/2, where ? is the nonbonded mer-mer attractive interaction energy and z is the lattice coordination number, set to be a constant equal to 12. The number of r-mers per molecule, r, is also fixed for a given liquid to be equal to the number of atoms in the molecule other than hydrogen. The fitting proceduce is fast and simple. The adjustment only involves the use of widely available density data. Comparisons between experimental and calculated first- and second-order thermodynamic properties are shown for several substances. A comparison with the equation of state due to Jain and Simha (1981) for PVT data for n-dodecane is presented. The theory qualifies as a useful tool, especially in engineering applications, for estimating thermodynamic properties in the liquid phase.     

Thermodynamics of the GaCl3-HCl-H2O System at 25°C

A comprehensive equation for the thermodynamic properties of the systemGaCl₃-HCl-H₂O at 25°C in the ion-interaction (Pitzer) equation form has been generatedon the basis of a recent and comprehensive array of electrochemical cellmeasurements of the HCl activity at total stoichiometric ionic strengths from 0.01 to 3.0mol-kg^–1. Alternate equations with and without explicit consideration of thehydrolyzed product GaOH²⁺ as a separate species have been tested. Excellentagreement is obtained between the calculated and measured cell potentials forthe formulation, which includes GaOH²⁺ as an additional species. The effect offurther hydrolysis as well as that of complex formation has been found to benegligible. While a satisfactory set of Pitzer parameters has been found, it wasnot possible to obtain a unique thermodynamic representation for this systembecause of large uncertainties in the first hydrolysis constant of Ga(III) and becauseof redundancies and intrinsic correlations between some of the Pitzer parameters.Deceased December 26, 1997     

On extension of UNIQUAC-NRF model to study the phase behavior of aqueous two phase polymer–salt systems

The UNIQUAC-NRF model for aqueous two-phase polymer–polymer systems is extended to correlate liquid–liquid equilibria of aqueous polymer–salt two-phase systems. The systems investigated are polyethylene glycol+ammonium sulfate+water and polyethylene glycol+potassium monohydrogen phosphate (K₂HPO₄)+water for five molecular weights of PEG. In this model, the nonrandom state is selected as a reference state. The model has six binary adjustable parameters that were determined by an optimization program. The Debye–Huckel equation based on Fowller–Guggenheim equation is used to calculate the long-range electrostatic interaction of the ions. The results obtained by this model are in good agreement with experimental data.     

The significant structure theory applied to halobenzenes

Abstract

Just as molecular structure, as revealed by X-ray diffraction, can be interpreted in terms of intuitive models, so liquid structure can be interpreted in terms of a model which leads to a partition function giving the Helmholtz free energy in terms of volume, temperature, and composition. From this explicit expression for the Helmholtz free energy all thermodynamic properties are calculable and can be compared with experiment. Absolute Rate Theory permits the prediction of transport properties from this same model, providing still further insight into liquid structure. Here, Significant Liquid Structure Theory has been applied to twelve substituted benzenes and the results compared with experiment. A single equation is derived for the twelve substances differing in ten of the cases only in three parameters having to do with the solid-like part of the liquid. For simple liquids these properties are those of the solid at the melting point. These properties are the energy of sublimation, molar volume of the solid, and the Einstein characteristic temperature, θ. Hindered rotation is explained in terms of a barrier to rotation of one tenth the energy of sublimation     

An explicit molecular thermodynamic model for polyelectrolyte solutions

Polyelectrolyte solutions are modeled as linear tangent jointed and charged hard-sphere chains and counterions. Besides coulombic interaction, stickiness between polyions and counterions is taken into account as a short-range non-coulombic perturbation. The solvent is considered as a continuum medium with a certain permittivity. Expressions of thermodynamic properties derived in this work consist of two contributions. The first contribution responsible for the formation of polyion chains from monomers is derived by the statistical association theory that is the same as our previous work. The second contribution accounting for the additional stickiness is obtained by the same method. A molecular thermodynamic model with explicit expressions is then obtained. Thermodynamic properties for polyelectrolyte solutions can be described satisfactorily.     

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.