Ionic interactions in solution: VI. The activity expansion and the association concept

The activity expansion equation which expresses the solute concentration as a series expansion of the activities of the solute species is used to reach a reformulation of the mean activity coefficient of a binary symmetrical electrolyte in solution. The result is displayed as the product of a shortrange term and a long-range term f_±=f _± ^S ·f^L _±, from which a straightforward derivation of the Bjerrum treatment is obtained. The analogy with an equivalent formulation for the molar conductance coefficient which results from the application of the echo-effect is emphasized. A simple formulation of the ion pair distribution function is proposed which is particularly powerful for ionic systems involving strong interactions. It is shown that the variable which controls the excess transport and thermodynamic quantities is not so much the stoichiometric concentration but rather the product of the concentration with the short-range factor f _± ^S of the activity coefficient product derived in the present work. In dilute solutions this factor becomes the so-called fraction of free ions originally introduced somewhat empirically by Bjerrum by means of a chemical model.Dedicated to Johannes Coetzee on the occasion of his 65th Birthday.     

Dilute Solution Properties of Styrene-N-Butyl Methacrylate (65:35) Copolymer: Short- and Long-Range Interaction of the Polymer Chain

Abstract

Viscosity and light-scattering data on styrene-n-butyl methacrylate (65:35) in chloroform are presented and tested by the two-parameter theoretical relations. The short-range interactions K and A and the long-range interaction parameter B have been calculated by different equations, using intrinsic viscosity and second virial coefficient data. These are then compared to the values of the homopolymer polystyrene. The conformation or the steric factor for the polymer chain has also been calculated. The excluded volume parameter Z, which is related to both the short- and long-range parameters, has been evaluated along with the expansion factor α _n . The higher value of the short-range parameters and the conformation factor compared to the parent styrene homopolymer is attributed to the effect of unlike monomer interactions causing extension of the polymer chain. An increase in the restriction of the internal rotation of side chains about the C-C bonds is also suggested. The excess interaction parameter has a negative value. The expansion factor α _n has been related to the excluded volume factor Z and the coefficient C is in close agreement with the theoretically calculated value of Yamakawa and Tanaka.     

Modeling solubility of acid gases in alkanolamines using the nonelectrolyte Wilson-nonrandom factor model

The nonelectrolyte Wilson-nonrandom factor local composition model (N-Wilson-NRF) by Haghtalab and Mazloumi is applied for modeling the vapor–liquid equilibrium of the acid gases (CO₂ and H₂S)–alkanolamine–water systems. The model is used to calculate the nonideality of species in liquid phase through the activity coefficient equations. In this work, we use the N-Wilson-NRF model for short-range forces in the aqueous electrolyte system of alkanolamines by using the concept of ion-pair. For the long-range interaction the Pitzer–Debye–Hückel theory is applied. The model is used to correlation of the solubility data of CO₂ and H₂S in aqueous monoethanolamine (MEA), diethanolamine (DEA), methyldiethanolamine (MDEA) and 2-amino-2methyl-1-propanol (AMP) systems over wide range of temperature (0–140 °C), partial pressure (0.001–1000 kPa) and acid gases loading (0.001–1.0 mol gas/mol amine). To show the predictability of the model, the interaction parameters without any additional adjustable parameters are used to predict the solubility of CO₂ in aqueous AMP solution at different conditions. The results of the model show a very good agreement with the experimental data.     

Long-Range van der Waals Interactions in Density Functional Theory

The early difficulties in accounting for long-range van der Waals interactions in the framework of density functional theory (DFT) have been overcome to a certain extent in recent works by several groups, and those interactions can be computed numerically. In this paper a derivation of the analytical form of the attractive van der Waals interaction between two neutral atoms with polarizabilities α₁ and α₂ at large distance R, namely E _int=−C ₆ α₁ α₂/R ⁶ is performed within the context of DFT. Use is made of the properties of the Coulomb correlation hole, and it is shown that nonlocal Coulomb correlations are responsible for long-range dispersion interactions.     

Solubility and Ionic Interaction of the CaF<Subscript>2</Subscript>–CaSO<Subscript>4</Subscript>–H<Subscript>2</Subscript>O System at 298.1 K

Solubility isotherms of the sparingly soluble salts CaF_2(s) and CaSO₄·2H₂O_(s) in their mixed aqueous solutions have been measured at 298.1 K. It was found that the CaF_2(s) solubility decreases with increasing CaSO₄ concentration in the solution and reaches about 1/3 of the CaF_2(s) solubility in pure water in the CaSO₄·2H₂O_(S) saturated solution. A thermodynamic model was developed to predict the CaF_2(s) solubility isotherm in this system, in which the short range interactions of the species in the aqueous solution are represented by ion-association constants reported in literature, and the long range interaction, i.e., the electrostatic term, is represented by the well known Davies equation. The predicted solubility isotherm reasonably agrees with the experimental results. The contributions of the long-range term and the short-range term to the calculated solubility isotherm were investigated. It was concluded that the ionic association combining with the Davies equation is sufficient to represent the excess interaction of the CaF₂ + CaSO₄ aqueous solution at 298.15 K. This model approach could be applicable for other dilute mixed electrolyte systems in which component activity coefficients are lacking and model parameters are difficult to determine.     

Current developments in CO2 hydrogenation towards methanol: A review related to industrial application

Regarding the still increasing CO₂ emissions and the accompanied imminent climate change, utilization of CO₂-containing exhaust gases is one of the major opportunities to lower CO₂ emissions while obtaining valuable products in parallel. Methanol as one of today's key platform chemicals can be industrially produced from these exhaust gases by heterogeneously catalyzed CO₂ hydrogenation. This review elaborates why the Cu/ZnO/Al₂O₃ catalyst is still the most promising candidate to catalyze CO₂ hydrogenation from exhaust gases to reduce CO₂ emissions in the short term. It emphasizes catalyst lifetime and deactivation as well as catalyst poisoning, which are significant factors considering the use of impurity-containing exhaust gases. Besides modifications of the Cu/ZnO system, completely different catalysts are discussed regarding their usability and comparability to the conventional Cu/ZnO/Al₂O₃ catalyst.     

Delicate Balance of Non-Covalent Forces Govern the Biocompatibility of Graphitic Carbon Nitride towards Genetic Materials

Despite a plethora of suggested technological and biomedical applications, the nanotoxicity of two-dimensional (2D) graphitic carbon nitride (g-C₃N₄) towards biomolecules remains elusive. To address this issue, we employ all-atom classical molecular dynamics simulations and investigate the interactions between nucleic acids and g-C₃N₄. It is revealed that, toxicity is modulated through a subtle balance between electrostatic and van der Waals interactions. When the exposed nucleobases interact through predominantly short-ranged van der Waals and π–π stacking interactions, they get deviated from their native disposition and adsorb on the surface, leading to loss of self-stacking and intra-quartet H-bonding along with partial disruption of the native structure. In contrast, for the interaction with double-stranded structures of both DNA and RNA, long-range electrostatics govern the adsorption phenomena since the constituent nucleobases are relatively concealed and wrapped, thereby resulting in almost complete preservation of the nucleic acid structures. Construction of free energy landscapes for lateral translation of adsorbed nucleic acids suggests decent targeting specificity owing to their restricted movement on g-C₃N₄. The release times of nucleic acids adsorbed through predominant electrostatics are significantly less than those adsorbed through stacking with the surface. It is therefore proposed that g-C₃N₄ would induce toxicity towards any biomolecule having bare residues available for strong van der Waals and π–π stacking interactions relative to those predominantly interacting through electrostatics.     

The long-range non-additive three-body dispersion interactions for the rare gases, alkali, and alkaline-earth atoms

The long-range non-additive three-body dispersion interaction coefficients Z(111), Z(112), Z(113), and Z(122) are computed for many atomic combinations using standard expressions. The atoms considered include hydrogen, the rare gases, the alkali atoms (up to Rb), and the alkaline-earth atoms (up to Sr). The term Z(111) arising from three mutual dipole interactions is known as the Axilrod-Teller-Muto coefficient or the DDD (dipole-dipole-dipole) coefficient. Similarly, the terms Z(112), Z(113), and Z(122) arise from the mutual combinations of dipole (1), quadrupole (2), and octupole (3) interactions between atoms and they are sometimes known, respectively, as dipole-dipole-quadrupole, dipole-dipole-octupole, and dipole-quadrupole-quadrupole coefficients. Results for the four Z coefficients are given for the homonuclear trimers, for the trimers involving two like-rare-gas atoms, and for the trimers with all combinations of the H, He, and Li atoms. An exhaustive compilation of all coefficients between all possible atomic combinations is presented as supplementary data.     

Structural and calorimetric studies of order-disorder in CdMg(CO3)2

The disordering of CdMg(CO₃)₂ was studied near room temperature by powder X-ray diffraction and solution calorimetry using samples quenched from 600 to 850°C. The long-range order parameter changes from unity to zero in this range and the enthalpy of disordering is 13.7 ± 0.8 kJ/mole. The enthalpy of formation of ordered CdMg(CO₃)₂ from CdCO₃ and MgCO₃ is −5.6 ± 0.8 kJ/mole; that of the disordered phase is +8.1 ± 0.8 kJ/mole. These data support energetic models which assume positive interactions of Cd and Mg within cation layers and negative interactions (leading to ordering) between layers. A reasonable fit to the observed phase relations is achieved using either the point approximation (PA) of the generalized Bragg-Williams model or the tetrahedron approximation (TA) of the cluster variation method (CVM). These models however, do not give a quantitative fit to the variation of enthalpy and long-range order parameter with temperature. In particular, the observed order-disorder transition occurs more sharply over a smaller temperature range than predicted, perhaps because of more strongly cooperative behavior in which the carbonate groups as well as the divalent cations play a role.     

Effet de Solvant en RMN du Carbone-13. III—Cas d'un Soluté Polaire: l'Acétone dans Divers Solvants et en Phase Gazeuse

The chemical shifts of acetone carbons are measured in the gas phase and in nineteen solvents, thus allowing the separation of the screening constant terms arising from the different kinds of solute–solvent interactions. It is shown that for methyl carbons the van der Waals term σ_w, interpreted using Rummens's theory, is more important than the specific solute–solvent interaction term σ_H. In contrast, for the carbonyl carbon, the term σ_H, which is eight times greater than for the methyl carbons, dominates when dipole–dipole interactions and hydrogen bonding occur. No evidence for an electric field term proportional to the Onsager reaction field is found. But when there are dipole–dipole interactions, σ_H is proportional to the electric field of the dipole of a solvent molecule interacting with the dipole of a solute molecule, the two dipoles being antiparallel. The variation of σ_H with the acetone concentration in a non-associating solvent is interpreted as a consequence of the displacement of the acetone in self-association equilibrium, leading to the determination of the equilibrium constant.     

The effect of pressure on gas permeation through semicrystalline polymers above the glass transition temperature

A method is proposed to analyze the effect of pressure on permeation of gases through semicrystalline polymers above the glass transition temperature. The method utilizes similarities in molecular diameters of the gases and differences in their solubilities. Two polymers, polyethylene and polypropylene, and a series of gases are chosen for an application of the method, and the effect of pressure on the permeabilities for 10 gases is measured in the pressure range 1–130 atm at 25°C. For polymers, the logarithm of the permeability coefficient is linear in the pressure for each gas, with negative slope for slightly soluble gases (He, Ne, H₂, N₂, O₂, and Ar) and positive slope for highly soluble gases (CH₄, Kr, CO₂, and N₂O). Analyzing these slopes by the method proposed permits contributions of hydrostatic pressure and concentration to the pressure dependence of permeation to be evaluated. On the basis of the results, the mechanism of gas permeation in rubbery films under high pressures is discussed.     

Crossover Sorption of C2H2/CO2 and C2H6/C2H4 in Soft Porous Coordination Networks

Porous sorbents are materials that are used for various applications, including storage and separation. Typically, the uptake of a single gas by a sorbent decreases with temperature, but the relative affinity for two similar gases does not change. However, in this study, we report a rare example of “crossover sorption,” in which the uptake capacity and apparent affinity for two similar gases reverse at different temperatures. We synthesized two soft porous coordination polymers (PCPs), [Zn₂(L1)(L2)₂]_n (PCP-1) and [Zn₂(L1)(L3)₂]_n (PCP-2) (L1= 1,4-bis(4-pyridyl)benzene, L2=5-methyl-1,3-di(4-carboxyphenyl)benzene, and L3=5-methoxy-1,3-di(4-carboxyphenyl)benzene). These PCPs exhibits structural changes upon gas sorption and show the crossover sorption for both C₂H₂/CO₂ and C₂H₆/C₂H₄, in which the apparent affinity reverse with temperature. We used in situ gas-loading single-crystal X-ray diffraction (SCXRD) analysis to reveal the guest inclusion structures of PCP-1 for C₂H₂, CO₂, C₂H₆, and C₂H₄ gases at various temperatures. Interestingly, we observed three-step single-crystal to single-crystal (sc-sc) transformations with the different loading phases under these gases, providing insight into guest binding positions, nature of host–guest or guest-guest interactions, and their phase transformations upon exposure to these gases. Combining with theoretical investigation, we have fully elucidated the crossover sorption in the flexible coordination networks, which involves a reversal of apparent affinity and uptake of similar gases at different temperatures. We discovered that this behaviour can be explained by the delicate balance between guest binding and host–guest and guest-guest interactions.     

Nonelectrolyte NRTL-NRF model to study thermodynamics of strong and weak electrolyte solutions

An electrolyte activity coefficient model is proposed by combining non-electrolyte NRTL-NRF local composition model and Pitzer–Debye–Hückel equation as short-range and long-range contributions, respectively. With two adjustable parameters per each electrolyte, the present model is applied to correlation of the mean activity coefficients of more than 150 strong aqueous electrolyte solutions at 298.15 K. Also the results of the present model are compared with the other local composition models such as electrolyte-NRTL, electrolyte-NRTL-NRF and electrolyte-Wilson-NRF models. Moreover, the present model is used for prediction of the osmotic coefficient of several aqueous binary electrolytes systems at 298.15 K. Also the present activity coefficient model is adopted for representation of nonideality of the acid gases, as weak gas electrolytes, soluble in alkanolamine solutions. The model is applied for calculation of solubility and heat of absorption (enthalpy of solution) of acid gas in the two {(H₂O + MDEA + CO₂) and (H₂O + MDEA + H₂S)} systems at different conditions. The results demonstrate that the present model can be successfully applied to study thermodynamic properties of both strong and weak electrolyte solutions.     

A fragment multipole approach to long-range Coulomb interactions in Hartree–Fock calculations on large systems

An efficient ab initio method for electronic structure calculations on extended molecular systems is presented, along with some illustrative applications. A division of the system into subunits allows the interactions to be separated into short- and long-range contributions, leading to a reduction of the computational effort from the original fourth-power size-dependence to one that is approximately quadratic. The short-range contributions to the Fock matrix are obtained in an essentially conventional fashion, while the long-range interactions are evaluated using a two-center multipole expansion formalism. The number of short-range contributions grows only linearly with the number of subunits, while the long-range contributions grow as N². Systematic studies of the computational efforts for systems of up to 99 water molecules organized as one-stranded chains, three-stranded chains, and three-dimensional clusters, as well as alkane chains with up to 69 carbon atoms, have been performed. In these model systems, the overall computational effort grows as N^K where 1 < K < 2.     

Effect of long-range hydrodynamic and direct intermacromolecular forces on translational diffusion

Within the framework of recently formulated microscopic theories of macromolecular diffusion it is shown that hydrodynamic forces act always to diminish the influence of direct forces, but never to reverse the sign of the correction term due to direct forces alone. Although the correction term D(k) to the intrinsic diffusion coefficient may vary with scattering vector |k|, it is shown that a reversal in sigh of the correction term with increasing |k|, if it occurs, must be associated with an amplitude of less than 10% of the correction term at |k| = 0. At |k| = 0 direct repulsive forces are predicted to always increase the apparent diffusion constant, even after accounting for hydrodynamic interactions. Although experiments on polylysine (1 mg/ml) at salt concentrations above 0.01 M are in qualitative accord with the theory, below 10^?3 M salt the apparent diffusion coefficient is reduced by a factor of about 20, concomitant with a much reduced intensity of scattered light. The strong contradiction of the theory implied by this observation is attributed to a dramatic rise in Stokes friction arising from long-range interionic forces in the low-salt solutions.     

Solution properties of ultrahigh molecular weight polymers. VII. Conformational characteristics of poly(butyl methacrylate)

The paper is concerned with light scattering studies on solutions of ultrahigh molecular weight poly(butyl methacrylate). The dependence of the radius of gyration and of the second virial coefficient on the weight-average molecular weight of the polymers was established in methyl ethyl ketone, dimethylformamide, and CCl₄. Short-range and long-range interactions were discussed in terms of the steric factor σ, of the interaction parameter B, and of the interpenetration function ψ(z).     

Phase compositions,viscosities and densities of systems PPG425 + Na2SO4+H2O and PPG425 + (NH4)2SO4 + H2O at 298.15 K

Phase diagrams of PPG425+Na₂SO₄+H₂O and PPG425+(NH₄)₂SO₄+H₂O systems at 298.15 K were measured. The densities and viscosities of two-phase systems were also measured. The improved regular solution theory was used to correlate the equilibrium data. In this theory a mixing entropy term and the Fowler-Guggenheim long-range electrostatic term has been used.     

High-pressure calorimetric study of plasticization of poly(methyl methacrylate) by methane,ethylene, and carbon dioxide

Glass transition in the system poly(methyl methacrylate)/compressed gas was studied as a function of the gas pressure p using a high-pressure Tian-Calvet heat flow calorimeter. Measurements were made on PMMA-CH₄-C₂H₄, and ;-CO₂ at pressures to 200 atm. All three gases plasticize the polymer leading to depression of the glass transition temperature T_g. Trends in the T_g depression were the same as those reported for the solubility of these gases in PMMA; the higher the solubility the larger the depression in T_g. CO₂ was found to be the most effective plasticizer producing a depression of about 40°C at a pressure of about 37 atm. In the low-pressure limit, the pressure coefficient of the glass transition temperature (dT_g/dp) was found to be about −0.2°C atm^-1 for PMMA-CH₄, the same as that observed for polystyrene-CH₄. For PMMA-C₂H₄, the pressure coefficient was −0.7°C atm^-1, which is lower than the value of −0.9°C atm^-1 observed for PS-C₂H₄. The pressure coefficient for PMMA-CO₂ was found to be about −1.2°C atm^-1, which is larger than the value of −0.9°C atm^-1 observed for PS-CO₂. © 1996 John Wiley & Sons, Inc.     

Poly(amide-imide)/TiO2 nano-composite gas separation membranes: Fabrication and characterization

Nano-composite membranes based on a fluorinated poly(amide-imide) and TiO₂ were fabricated by a sol-gel method. Permeability data for gases such as O₂, N₂, CO₂, H₂ and CH₄ were collected as a function of pressure and temperature. With the exception of CO₂ and H₂, all other gases exhibited higher activation energies for the nano-composite membrane when compared with the pure poly(amide-mide), consistent with the picture of a more rigid or denser structure as suggested by the physical characterization data. The decrease in the activation energy for permeation in the case of CO₂ and H₂ has been attributed to specific interactions of these gases with the TiO₂ domains. Significant improvements in permselectivies of the poly(amide-imide) membrane have been observed in view of the volume percentage of the TiO₂ incorporated into the polymer matrix.