Ionic interactions in solutions. I. The association concepts and the McMillan-Mayer theory

A review is given of the most common models of ionic-pair association used by Bjerrum, Fuoss, and Eigen to supplement the breakdown of the Debye-Hückel law for the mean activity coefficient of symmetrical electrolytes in lower-dielectric-constant solvents. The compressibility and pressure equations of Rasaiah and Friedman and the virial equation are used to rederive the activity coefficients from the distribution functions of Meeron and of Debye and Hückel. The results are compared to the well-known results of Debye and Hückel and that of Bjerrum. In each case the anion-cation pair association concept of Bjerrum is verified. Finally, a discussion is included on the best evaluation of the critical distance which distinguishes between free and associated ions. The activity equation is easily generalized to any short-range Hamiltonian model.This paper is based in part on the thesis of M.-C. Justice, Université Pierre et Marie Curie (Paris VI), in June 1974, in partial fulfillment of the requirements for the degree of Docteur d'Etat.     

Ionic interactions in solutions. III. Derivation of the ″associated″ electrolyte formulation from the Onsager treatment of conductance

The system of equations of the Onsager treatment of conductance is rederived in a systematic way by the use of several sets of hierarchy equations generalizing to other quantities the classical Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy of internal force. The monitoring term of the Onsager continuity equation obtained is compared to former theoretical studies. It is inferred in particular that the perturbation on the anion-cation pair distribution for a symmetrical binary electrolyte is proportional not only to the external fieldX but also to the conductance coefficientf _A=1+X/X+ _el/ ₀. This result, called the echo effect, leads to a new formulation of molar conductance which shows a great similarity to the empirical conductance function obtained by grafting the chemical model of Bjerrum onto the conductance equations derived on the basis of the Debye approximations as proposed formerly by the author from experimental observations. The result allows a simple generalization of the conductance equation to any direct short-range anion-cation energy-potential model.     

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.     

Luminescence kinetic and association equilibria of lanthanide ions in aqueous solutions. II. Determination of the formation constant of Tb acetato complex by means of luminescence lifetime measurement

The association constant K of mono-acetato complex of Tb³⁺ has been determined at normal p and T conditions by measurement of its luminescence lifetime in aqueous solution containing increasing concentrations of acetate. Two experimental arrangements used for the measurement are described.     

Fluorescence study of the interaction between metal ions and methyl methacrylate–methacrylic acid copolymers in aqueous solutions: thallium(I), calcium(II), and terbium(III)

 The binding of the cations thallium(I), calcium(II) and terbium(III) to methyl methacrylate– methacrylic acid copolymers with different fractions of acid groups (x) has been studied in aqueous solution at various pH values using the fluorescence of covalently bonded 9-vinyl anthracene as a probe. In all cases, the extent of binding increases as a function of the charge of the polymer with either increasing fraction of carboxylic acids or of pH. However, differences are observed in the behavior of the three cations. With Tl(I), quenching of the anthracene group fluorescence is observed, indicating that the thallium(I) approaches the probe and suggesting that the alkylanthracene is probably in a relatively polar region. Binding constants have been determined from anthracene quenching data and from studies with the fluo-rescent-probe sodium pyrenetetra-sulfonate. Good agreement is obtained between the two methods, and values for the binding constants increase from 250 to 950 M^-1 as x increases from 0.39 to 1. It is suggested that the cation is held in the polyelectrolyte domain, partly by Debye–Hückel effects and partly by more specific interactions. Stronger binding is found with calcium(II) and terbium(III), and in this case increases in fluorescence intensity are observed on complexation due to the anthracene group being in a more hydrophobic region, probably as a result of conformational changes in the polymer chain. In the former case the stoichiometry of the interaction was determined from the fluorescence data to involve two carboxylate groups bound per calcium. Association constants were found using murexide as an indicator of free calcium to vary from 8400 to 37 000 M^-1 as x increases from 0.39 to 1. It is suggested that in this case specific calcium(II)–carboxylate interactions contribute to the binding. With terbium(III), a greater increase in the probe fluorescence intensity was observed than with calcium, and it is suggested that the interaction with the polymer is even stronger, leading to a more pronounced conformational change in the polymer. It is proposed that the terbium(III) interacts with six carboxylic groups on the polymer chain, with three being coordinated and three attracted by electrostatic interactions. Received: 10 June 1997 Accepted: 24 October 1997     

The effects of steric aliphatic–aliphatic interactions in the coordination polymer of bis(N,N-diethylglycinato)copper(II): Experimental evidence and theoretical modeling

New coordination polymer catena-poly[(N,N-diethylglycinato-κO,κN)copper(II)-μ-[N,N-diethylglycinato-κO¹,κN:O²]] has been obtained by single-crystal X-ray diffraction. The copper(II) was surrounded with two amino N and two carboxyl O atoms in trans position in the coordination plane. Discrete polymeric chains were produced by axial coordinative bonding between copper(II) and carbonyl oxygen atom from adjacent asymmetric unit. Molecular mechanics (MM) force field developed to study the properties of copper(II) amino acid complexes reproduced well intermolecular aliphatic–aliphatic interactions between ethyl chains and C–H?O hydrogen bonding. The relative unit cell volume reproduction was 0.3%. Theoretical conformational analysis showed that experimentally obtained conformer was not the most stable in vacuo. The calculations of the unit cell packings and intermolecular interactions for a series of conformers elucidated the reasons that governed the experimentally obtained conformer to appear in the real crystal structure. MM results suggest that intermolecular aliphatic–aliphatic interactions between ethyl groups affected a conformational change concurrent with the change in the copper(II) coordination sphere upon crystallization.     

Organic acid solutions in the chromatography of inorganic ions VIII. Cation-exchange of Mn(II), Cd(II), Co(II), Ni(II), Zn(II), Cu(II), Fe(III), Sc(III), Y(III), Eu(III), Dy(III), Ho(III), Yb(III), Ti(IV) and Nb(V) in malate media

Summary The cation-exchange behaviour of Mn(II), Cd(II), Co(II), Ni(II), Zn(II), Cu(II), Fe(III), Sc(III), Y(III), Eu(III), Dy(III), Ho(III), Yb(III), Ti(IV) and Nb(V) in malate media at various concentrations and pH, was studied with Dowex 50 WX8 resin (200–400 mesh) in the ammonium form. Separation of Fe(III)/Cu(II), Fe(III)/Cu(II)/Zn(II), Fe(III)/Co(II)/Mn(II), Cu(II)/Ni(II)/Mn(II), Fe(III)/Cu(II)/Co(II)/Mn(II), Fe(III)/Cu(II)/Ni(II)/Cd(II), Yb(III)/Eu(III), Sc(III)/Y(III),Sc(III)/Yb(III)/Dy(III) and Nb(V)/Yb(III)/Ho(III) has been achieved, among others.This work was supported by C.N.R. of Italy.     

Application of the Bjerrum Association Model to Electrolyte Solutions. II. Enthalpies of Dilution in Water and Nonaqueous Solvents

The association theory based on the Bjerrum model, which had been developed for the treatment of apparent and partial molar volumes of electrolyte solutions, is extended to apparent molar relative enthalpies L _2,. Experimental enthalpies of dilution for tetrabutylammonium bromide in acetonitrile, propylene carbonate, and -butyrolactone and for lithium perchlorate and sodium thiocyanate in acetonitrile were obtained and analyzed with this model. Literature data for various electrolytes in water, acetonitrile, and n-propanol were also reanalyzed. Through the Bjerrum equations, enthalpies of dilution can be extrapolated to infinite dilution and reliable L _2, obtained for associated electrolytes. The model can be used to estimate the association constant K _A of the electrolyte and these K _A are compared with literature values (generally obtained from conductivity). Considering the difference in the concentration ranges investigated in L _2, and measurements, K _A extracted from L _2, generally fall within an expected range of deviation from the ones obtained by conductivity, provided that no specific interactions are present in solution.