Model calculations for Setchenow coefficients

The calculations of Setchenow coefficients reported earlier [H. L. Friedman, C. V. Krishnan, and C. Jolicoeur,Ann. N.Y. Acad. Sci. 204, 79 (1973)] have been extended to aqueous solutions of various nonelectrolytes mixed with alkali or alkylammonium halides. A few data for Setchenow coefficients in methanol have also been treated. The GurneyA _ij parameters for nonelectrolyte-ion interactions in models which fit the data are mostly negative, and more so the larger the solute molecules. A value ofA _ij near-100 cal-mole^–1 seems to characterize hydrophobic bonding. In several systems these is evidence that some nonsolvation contribution to theu _ij pair potential which is not explicitly accounted for in the models is important in the real systems. Quite possibly this contribution is due to dispersion forces or to the chargepolarizability interaction. On the whole, theA _ij parameters do not seem to depend upon the charges on solute particlesi andj; this is evidence that the model is fairly realistic.     

Phase behavior of carbon dioxide-aromatic hydrocarbon mixtures

Occhiogrosso, R.N., Igel, J.T. and McHugh, M.A., 1986. Phase behavior of carbon dioxide-aromatic hydrocarbon mixtures. Fluid Phase Equilibria, 26: 165–179.Vapor-liquid-equilibria experiments are conducted at 299.25, 305.65, 316.25, 338.35, 363.15, and 383.15 K and for pressures up to 175 bar for the CO₂-isopropyl benzene (cumene) system. Pressure-composition information is obtained. The resulting experimental data are modeled using the Peng-Robinson equation-of-state. Two temperature-independent model parameters, δ_ij, which accounts for molecular interactions between CO₂ and cumene, and η_ij, which accounts for the size difference between CO₂ and cumene, are used to obtain good agreement between calculated and experimental data.The results for the CO₂-cumene system are compared to the CO₂-toluene and CO₂-m-xylene systems which are available in the literature. The CO₂-toluene and CO₂-m-xylene systems can be modeled using the same δ_ij and η_ij values used for the CO₂-cumene system.     

Peng-Robinson equation of state for vapor-liquid equilibrium calculations for carbon dioxide + hydrocarbon mixtures

Lin, H.-M., 1984. Peng-Robinson equation of state for vapor-liquid equilibrium calculations for carbon dioxide + hydrocarbon mixtures. Fluid Phase Equilibria, 16: 151–169.Binary interaction parameters δ_ij in the Peng-Robinson equation of state have been determined from vapor-liquid equilibrium data for binary mixtures of carbon dioxide with a variety of hydrocarbons. A constant value of δ_ij ? 0.125 appears to represent the experimental data well in most cases. Comments are made on the recent work of Kato, Nagahama and Hirata, who correlated δ_ij as a function of temperature for CO₂ + n-paraffin binary mixtures.     

Intermolecular potential parameters and combining rules determined from viscosity data

The law of corresponding states has been demonstrated for a number of pure substances and binary mixtures and provides evidence that the transport properties viscosity and diffusion can be determined from a molecular shape function, often taken to be a Lennard–Jones 12‐6 potential, that requires two scaling parameters: a well depth ε_ij and a collision diameter σ_ij, both of which depend on the interacting species i and j. We obtain estimates for ε_ij and σ_ij of interacting species by finding the values that provide the best fit to viscosity data for binary mixtures and compare these to calculated parameters using several “combining rules” that have been suggested for determining parameter values for binary collisions from parameter values that describe collisions of like molecules. Different combining rules give different values for σ_ij and ε_ij, and for some mixtures the differences between these values and the best‐fit parameter values are rather large. There is a curve in (ε_ij, σ_ij) space such that parameter values on the curve generate a calculated viscosity in good agreement with measurements for a pure gas or a binary mixture. The various combining rules produce couples of parameters ε_ij, σ_ij that lie close to the curve and, therefore, generate predicted mixture viscosities in satisfactory agreement with experiment. Although the combining rules were found to underpredict the viscosity in most of the cases, Kong's rule was found to work better than the others, but none of the combining rules consistently yields parameter values near the best‐fit values, suggesting that improved rules could be developed. © 2010 Wiley Periodicals, Inc. *

1 This article is a U.S. Government work and, as such, is in the public domain of the United States of America.

Int J Chem Kinet 42: 713–723, 2010     

Correlations for binary phase equilibria in high-pressure carbon dioxide

The high-pressure phase equilibrium in binary mixtures of carbon dioxide and various liquids such as benzene, toluene, m-xylene, chlorobenzene, 1,2-dichlorobenzene, low molecular weight alcohols, amides and a solid, hexachlorobenzene, was modeled using the Peng–Robinson equation of state with quadratic mixing rules. Though the technique of modeling is not new, the key conclusion of the study is that the two adjustable parameters, k_ij and l_ij, vary linearly with the addition of functional groups. In addition, the adjustable parameters are found to be nearly independent of temperature and the same values of k_ij and l_ij can be used for a range of temperatures for the systems considered in the present study.     

Modeling of phase equilibria with CPA using the homomorph approach

For association models, like CPA and SAFT, a classical approach is often used for estimating pure-compound and mixture parameters. According to this approach, the pure-compound parameters are estimated from vapor pressure and liquid density data. Then, the binary interaction parameters, k_ij, are estimated from binary systems; one binary interaction parameter per system. No additional mixing rules are needed for cross-associating systems, but combining rules are required, e.g. the Elliott rule or the so-called CR-1 rule. There is a very large class of mixtures, e.g. water or glycols with aromatic hydrocarbons, chloroform-acetone, esters-water, CO₂-water, etc., which are classified as “solvating” or “induced associating”. The classical approach cannot be used and the cross-association interactions are difficult to be estimated a priori since usually no appropriate experimental data exist, while the aforementioned combining rules cannot capture the physical meaning of such interactions (as at least one of the compounds is non-self-associating). Consequently, very often one or more of the interaction parameters are optimized to experimental mixture data. For example, in the case of the CPA EoS, two interaction parameters are often used for solvating systems; one for the physical part (k_ij) and one for the association part (β^cross). This limits the predictive capabilities and possibilities of generalization of the model. In this work we present an approach to reduce the number of adjustable parameters in CPA for solvating systems. The so-called homomorph approach will be used, according to which the k_ij parameter can be obtained from a corresponding system (homomorph) which has similar physical interactions as the solvating system studied. This leaves only one adjustable parameter for solvating mixtures, the cross-association volume (β^cross). It is shown that the homomorph approach can be used with success for mixtures of water and glycols with aromatic hydrocarbons as well as for mixtures of acid gases (CO₂, H₂S) with alcohols and water. The homomorph approach is less satisfactory for mixtures with fluorocarbons as well as for aqueous mixtures with ethers and esters. In these cases, CPA can correlate liquid-liquid equilibria for solvating systems using two adjustable parameters. The capabilities and limitations of the homomorph approach are discussed.     

Calculating poly(ethylene-co-acrylic acid)-solvent phase behavior with the SAFT equation of state

Statistical Associating Fluid Theory (SAFT) is used to model the cloud-point behavior of poly(ethylene-co-acrylic acid), with up to 7 mol % acid content, in propane, butane, propylene, butene, and dimethyl ether at temperatures to 250°C and pressure to 2600 bar. The values for the pure component temperature-independent segment volumes, nonspecific interaction energies, and the numbers of segments per molecule are equal to those used for polyethylene, because these copolymers contain modest amounts of acrylic acid repeat units. Two different approaches are used to determine values of the pure component energy of hydrogen bonding, ?/k, and the binary interaction parameter, k_ij. In one approach, ?/k for acid dimerization is obtained from literature spectroscopic data and a constant value of k_ij is fit to each copolymer-solvent cloud-point curve. Increasing the value of k_ij shifts the predicted cloud-point curves to higher temperatures and pressures. For the five solvents used in this study, k_ij decreased steadily in the range of 0.040 to ?0.025 as the acid content in the copolymer increased. The predicted cloud-point curves are in good agreement with experimental data, and the impact of hydrogen bonding on the phase behavior is well represented, even if k_ij is set equal to zero. For the second approach, ?/k is set to ～ 90% of the value obtained from spectroscopic data as determined from a fit of a single poly(ethylene-co-acrylic acid)-butane cloud-point curve, while k_ij is fit to the corresponding polyethylene-solvent system. This approach requires less mixture data than the previous approach, and the calculated cloud-point curves are also in good agreement with experimental data, except for the EAA-DME systems. © 1995 John Wiley & Sons, Inc.     

Addition of the sulfhydryl group (–SH) to the PPR78 model (predictive 1978, Peng–Robinson EOS with temperature dependent kij calculated through a group contribution method)

In 2004, we started to develop a group contribution method aimed at estimating the temperature dependent binary interaction parameters (k_ij(T)) for the widely used Peng–Robinson equation of state (EOS). This model was called PPR78 (predictive 1978, Peng–Robinson EOS) because it relies on the Peng–Robinson EOS as published by Peng and Robinson in 1978 and because the addition of a group contribution method to estimate the k_ij makes it predictive. In our previous papers, 14 groups were defined: CH₃, CH₂, CH, C, CH₄ (methane), C₂H₆ (ethane), CH_aro, C_aro, C_{fused aromatic rings}, CH_2,cyclic, CH_cyclicC_cyclic, CO₂, N₂, and H₂S. It was thus possible to estimate the k_ij for any mixture containing alkanes, aromatics, naphthenes, CO₂, N₂, and H₂S whatever the temperature. In this study, the PPR78 model is extended to systems containing thiols (also called mercaptans). To do so, the sulfhydryl group: –SH was added.     

Kirkwood—Buff integrals in non-electrolyte solutions. An evaluation of the local composition from experimental data

Rubio, R.G., Prolongo, M.G., Cabrerizo, U., Díaz Peña, M. and Renuncio, J.A.R., 1986. Kirkwood—Buff integrals in non-electrolyte solutions. An evaluation of the local composition from experimental data. Fluid Phase Equilibria, 26: 1–13.A relation between the Kirkwood—Buff integrals G_ij, and the local mole fractions in mixtures of non-electrolytes has been derived. The G_ij have been calculated for mixtures of simple fluids using experimental data for excess Gibbs energy, excess volumes and compressibilities at a given temperature. The proposed method allows one to test the predictions of theoretical models for systems for which no computer simulation results are available.     

Product Relation of Copolymerization Reactivity Ratios

The copolymerization reactivity ratios designated as r_i = k_ii/k_ij are characteristic of thermodynamic conditions, such as temperature, pressure, and concentration, in which the temperature dependence has been demonstrated by kinetic procedures [14]. It is noted that in radical copolymerization the simple product of the reactivity ratios, e.g., r₁, r₂ generally tends to move toward unity with increasing temperature [2] and that for ionic copolymerization it is usually close to unity [5]. Such an inclination, however, involves some ambiguity in evaluating all the reported data [6] concerning the polymerization conditions.     

Prediction of the second cross virial coefficients of nonpolar binary mixtures

The binary interaction parameter, k_ij, of 268 nonpolar mixtures were determined from the database of second cross virial coefficients containing 1728 experimental data points by fitting the second cross virial coefficients with a new correlation for pure compounds [L. Meng, Y.Y. Duan, L. Li, Fluid Phase Equilib. 226 (2004) 109–120] and classical mixing rules. Regularity distributions were found for both n-alkane/n-alkane binaries and fluorocarbon/fluorocarbon binaries. Correlations were developed following Tsonopoulos’ ideas [C. Tsonopoulos, Adv. Chem. Ser. 182 (1979) 143–162] with the quantity of binary compounds enlarged using Dymond's latest complication [J.H. Dymond, K.N. Marsh, R.C. Wilhoit, Virial Coefficients of Pure Gases and Mixtures, Subvolume B, Virial Coefficients of Mixtures, Series IV/21B, Landolt-Börnstein, 2002]. Correlations were also developed for inorganic/n-alkane binaries using new k_ij values. The predictions do not need any thermodynamic property parameters besides the carbon number. Comparisons with the existing correlations show that the present work is more accurate for nonpolar binary mixtures.     

Estimation of the parameters in the Kirkwood-Buff theory of solution using Percus-Yevick fluid mixtures

Parameters G _ij in the Kirkwood-Buff theory of solution were calculated for binary fluid mixtures of Lennard-Jones (LJ) 6–12 molecules by using the Percus-Yevick theory. Calculations were carried out for various parameters in the LJ potential. Under the Lorentz-Berthelot rules, G ₁₁ and/or G ₂₂ -composition curves do not show a maximum for any parameters in the LJ potential. When the intermolecular interaction between different species becomes much weaker than that expected from the Berthelot rule, G ₁₁ and G ₂₂ show a maximum and G ₁₂ a minimum. The pressure effect on G _ij was examined and calculations at constant pressure were also carried out. G _ij is almost independent of the pressure when the ratio of the molecular volume of two components is in the range 1.0 to 2.5. Comparison was made between experimental and calculated G _ij for cyclohexane-2,3-dimethylbutane and acetonitrile-toluene systems. For the latter system, the quantitative agreement between the calculated and experimental could not be obtained but showed that the characteristics of G _ij -composition curves can be explained qualitatively by using the PY theory.Adjunct Associate Professor of Institute for Molecular Science (April 1982–March 1984)     

High pressure phase behavior in systems containing CO2 and heavier compounds with similar vapor pressures

The separation of the para and ortho isomers of xylene as well as the azeotropic mixture of butyl ether/o-xylene using carbon dioxide at high pressure was investigated. The phase behavior of carbon dioxide and each of these compounds along with the ternary systems; CO₂/p-xylene/o-xylene and CO₂/butyl ether/o-xylene were experimentally determined. The relative volatilities of p-xylene to o-xylene in the CO₂/p-xylene/o-xylene system compared favorably with those obtained in distillation. The results also indicated a substantial shift in the butyl ether/o-xylene azeotrope to higher butyl ether concentrations in the presence of carbon dioxide thus indicating a potential for the separation of these mixtures using carbon dioxide at low temperatures. Thermodynamic models using the Peng—Robinson equation of state were developed and better predictions of the bubble point pressures were obtained when the interaction parameter, δ_ij, was allowed to vary with phase density. This approach results in an analytically solvable quartic equation in volume and gives different δ_ij's for the vapor and liquid phases. In this model, the temperature dependence of the binary interaction parameter is contained within its density dependence and, δ_ij's obtained from fitting VLE data at a single temperature could be used for accurate prediction of equilibrium data at other temperatures. The results of such predictions were better than predictions obtained by fitting the actual data using the conventional VDW-1 mixing rules.     

A test of the onsager reciprocal relations and a discussion of the ionic isothermal vector transport coefficientsI Ij for aqueous AgNO3 at 25°C

Values ofI _ij calculated from experimental data are given for AgNO₃ at 25°C. Experimental values of the ratioI ₁₂/I₂₁ are calculated to provide a sensitive direct test of the Onsager reciprocal relations,I ₁₂=I₂₁. This ratio is found to be unity within experimental error (ca. 2%). The general physical interpretation ofI _ij/N as mobilities is discussed. An approximate way of estimatingI _ij for dissociated salts is considered. A comparison is made between AgNO₃ I _ij data and corresponding data for NaCl and KCl. It is concluded that ion-pair formation (1) sharply increases the magnitude of the interaction mobility,I ₁₂/N; and (2) increases the intrinsic mobility of Ag⁺,I ₁₁/N, and decreases the intrinsic mobility of NO ₃ ^– ,I ₂₂/N.     

Auswahl von Phasensystemen in der Lösungs-, Adsorptions- und Ionenaustausch-Chromatographie

In contrast to GC selectivity in LC is determined by the composition of both the stationary as well as the mobile phase. Therefore the main problem in LC results in selecting an appropriate phase system for the given separation problem. The selectivity factorα _ijis defined as the ratio of the capacity factors k′ _i k′_jof two solutes, which corresponds to the ratio of their distribution coefficients ^c K _i, ^cK_j. In LLC α _ijis determined by the relative solubility of the solutes in the two immiscible phases, which were prepared from binary or ternary liquid-liquid-systems. Secondary effects on retention are caused by the support. Two variations exist (LLC, Reverse-Phase-LLC) which differ in whether the polar phase is used as stationary or mobile phase, resp. In LSC the same phase variation is possible. Using a polar support and an unpolar solvent α _ijis governed by the relative strength of interactions between the solute molecules and the surface of the support. In Reverse-Phase-LSC, however, using an unpolar support and a polar solvent, these interactions are very weak and α _ijis mainly determined by the solubility of the solutes in the mobile phase. In IEC α _ijdepends on a set of parameters such as the type of ion-exchange matrix, its pore structure and its degree of crosslinking, resp., the type, surface concentration and distribution of functional groups, the type of the eluent ion, its concentration, the ionic strength and pH-value of the eluent, the temperature. Different methods have been developed in order to calculate the distribution coefficients of solutes for a given phase system.     

Solution structure and Kirkwood-Buff theory: Informativity and sensitivity to specific interactions

A comparative significance of the contribution from density and excess Gibbs energy into Kirkwood-Buff integrals G _ij has been considered exemplified by H₂O-sulfolane, H₂O-THF and model mixtures. It is shown that some salient features of the volume properties which are generally thought to be the sign of strongly hydrophobic behavior of solutes, do not clearly manifest themselves in the concentration dependences of these integrals. Literature data for G _ij have been analyzed and the structural information inherent to G _ij is assessed. Contributions from the first and the following solvation spheres to G _ij have been evaluated from the distribution functions of model mixtures computed by the Born-Green equation and it is shown that with no new chemical bonds, the contribution from the first solvation sphere does not govern the whole of G _ij and, consequently, G _ij as calculated from the thermodynamic properties contain no direct information as far as the details of short-range interactions are concerned.     

Evaluation of Multivariate Calibration Using a Tikhonov Regularization Approach and the Generalized Pair‐Correlation Method with Nonlinear Data

Abstract

In order to reduce data nonlinearity and overfitting with the multivariate calibration model y=Xb, a modified Tikhonov regularization (TR) algorithm is evaluated for selecting key variables from an X augmented with extra columns that contain the original measured variables (x _ij ) as squared terms (x _ij ²) and other orders. The TR approach simultaneously develops the multivariate calibration model. The new generalized pair‐correlation method (GPCM) is also studied for variable selection followed by partial least squares (PLS) for multivariate calibration. Results from synthetic spectral data are compared when using the modified TR approach, GPCM, and PLS without variable selection. The GPCM usually performs slightly better than the TR approach for tabulated bias and variance measures and in some cases, at a sacrifice to parsimony. The method of PLS without variable selection performs the worst. By using synthetic spectral data sets, how the methods work could be studied. Thus, results from this study will aid investigators of real spectral data sets exhibiting nonlinear behavior.     

Infrared band intensities: a comparative study of the transition moment matrix elements for the fundamental and overtones: Part II. Application to CO,HCl and OH

The various expressions considered in Part I for the transition moment matrix elements of fundamental and first two overtones are applied to carbon monoxide. The coefficients a_ij in the expressions R^io = Σa_ijp_j (where R^io is the transition moment integral for the O → i vibrational transition and p_j is the dipole moment derivative ?^jP/?XXX^j, XXX = (r — r_e)/r_e, r_e is equilibrium bond distance) are reported for i,j = 1, 2, 3. It is found that these coefficients do not vary by more than 5% when compared for the same i,j values in various expressions irrespective of the most exhaustive treatments used in deriving the original expressions. On the basis of the values of the coefficients obtained for CO, generalisations have been suggested on the effects of inclusion of mechanical and electrical anharmonicity to the intensities of fundamental and first two overtones. It is generally observed that the contribution of p'₁, is about 100 fold more than the contribution of p'₂, for R¹⁰. On the other hand the contributions of p'₁, and p, for R²⁰ and R³⁰ are of nearly equal magnitude but opposite in sign. The contribution of p'₁ to R¹⁰ is much higher than its contribution to R²⁰ and R²⁰. The various observations lead us to conclude that, whereas the effect of inclusion of mechanical anharmonicity on the intensity of the fundamental band is negligible, this effect is almost comparable to the effect of inclusion of electrical anharmonicity for the first two overtones. Simple forms of the a_ij expressions are applied to HC1 and OH to demonstrate the effect of variation of molecular constants on the a_ij values. On the basis of the observed trend in the values of these coefficients for CO, HCl and OH general remarks on the effects of hydrogen bonding on IR band intensities are given.     

Effects of different sized concentration differences across free diffusion boundaries and comparison of Gouy and Rrayleigh diffusion measurements using NaCl−KCl−H2O

Diffusion was systematically studied in the ternary system NaCl (0.5M)–KCl (0.5M)–H₂O at 25°C. There were four purposes. First, current methods to extractD _ij from Gouy and Rayleigh interferometry data depend on treating theD _ij as effectively constant. If concentration differences C _i across the boundary are large, this may not be true. To explore this issue, four sets of experiments were performed. Each set had four experiments with approximately the same total number of fringesJ. Each set also had the same corresponding C ₁/C ₂ ratios as the other three, but the C _i were adjusted such that the four sets hadJ30, 60, 90, and 120, respectively. Noclear dependence of theD _ij on C _i was found within their realistic errors. Second, the Gosting diffusiometer can yield both Rayleigh and Gouy fringe patterns during the same experiment. Therefore, theD _ij from both methods were compared, and agree well. Third, a new method for analyzing Gouy fringe positions (Miller; program TNY) can be compared to the classical one (Fujita-Gosting; program RFG). TheD _ij from both analyses agree well. Fourth, we compared results from the Gosting diffusiometer with those at the same composition from other diffusiometers: one data set by O[Donnell and Gosting from an older Gouy apparatus, and three Rayleigh sets at differentJ values from our older Model H diffusiometer. Results from older diffusiometers were more scattered, but correspondingD _ij agree within realistic errors. As reported previously, realistic errors are approximately four times the statistical errors obtained by least squares. Recommended Rayleigh and GouyD _ij are presented for this composition.     

Intradiffusion coefficients in perchloric acid solutions: Water at 5°C; water and perchlorate ion at 25°C

Intradiffusion coefficients for tritiated water (³HHO) and perchlorate ion (³⁶ClO ₄ ^- ) were measured in perchloric acid solutions. At 5°C the diffusion coefficient measured for the tritiated species increases to a maximum near 1.3 mol-dm^–3. The data at 25°C have been used to calculate distinct diffusion coefficients, D _ij ^d . As a precursor for those calculations, new estimates were made of the Onsager phenomenological coefficients, l _ij . The l _ij and D _ij ^d are similar to the respective coefficients in hydrochloric acid solutions.