Ion-association concept

Abstract Analytical solution of the associative mean spherical approximation (AMSA) and the modified version of the mean spherical approximation - the mass action law (MSA-MAL) approach for ion and ion-dipole models are used to revise the concept of ion association in the theory of electrolyte solutions. In the considered approach in contrast to the traditional one both free and associated ion electrostatic contributions are taken into account and therefore the revised version of ion association concept is correct for weak and strong regimes of ion association. It is shown that AMSA theory is more preferable for the description of thermodynamic properties while the modified version of the MSA-MAL theory is more useful for the description of electrical properties. The capabilities of the developed approaches are illustrated by the description of thermodynamic and transport properties of electrolyte solutions in weakly polar solvents. The proposed theory is applied to explain the anomalous properties of electrical double layer in a low temperature region and for the treatment of the effect of electrolyte on the rate of intramolecular electron transfer. The revised concept of ion association is also used to describe the concentration dependence of dielectric constant in electrolyte solutions. 

In this section we consider the possibility of applying the ion association concept to the description of the properties of electrolyte solutions in the ion-molecular or Born-Oppenheimer level approach. The simplest ion-molecular model for electrolyte solution can be represented by the mixture of charged hard spheres and hard spheres with embedded dipoles, the so-called ion-dipolar model. For simplification we consider that ions and solvent molecules are characterized by diameters R and Rs, correspondingly. The model is given by the pair potentials,... 

The ion-association concept relies on the use of Debye-Huckel based activity coefficients to calculate aqueous activities and is one that is employed most frequently in the models used today. A primary assumption of this approach is the use of the Macinnes convention such that for an aqueous solution containing equimolal concentrations of and Cl, their activities and hence activity coefficients are equivalent. This approach and convention were reexamined by Parkhurst in this volume, who explored the issue of mean salt based activity coefficients and the apparent... 

For strong electrolytes, the activity of molecules cannot be considered, as no molecules are present, and thus the concept of the dissociation constant loses its meaning. However, the experimentally determined values of the dissociation constant are finite and the values of the degree of dissociation differ from unity. This is not the result of incomplete dissociation, but is rather connected with non-ideal behaviour (Section 1.3) and with ion association occurring in these solutions (see Section 1.2.4). 

J. Bjerrum (1926) first developed the theory of ion association. He introduced the concept of a certain critical distance between the cation and the anion at which the electrostatic attractive force is balanced by the mean force corresponding to thermal motion. The energy of the ion is at a minimum at this distance. The method of calculation is analogous to that of Debye and Hiickel in the theory of activity coefficients (see Section 1.3.1). The probability Pt dr has to be found for the ith ion species to be present in a volume element in the shape of a spherical shell with thickness dr at a sufficiently small distance r from the central ion (index k). 

Although the Bjerrum theory is thus not in general quantitatively applicable, the concept of ion association is very useful. It has assisted in an explanation of various phenomena observed in the study of homogeneous... 

Fig. 3 Concept of the ion-association method for fabricating ion-based organic dye nanoparticles in pure aqueous media. The approach is based on ion-pair formation between the ionic dye (for example, cationic dye) and the hydrophobic counterion that is soluble in water [for example, tetraphenylborate (TPB) or its derivative anion], which gives rise to a hydrophobic phase in water. For preparation, organic cosolvent is unnecessary. The size of the dye nanoparticles can be controlled by adjusting the interionic interaction between the dye cation and the associative hydrophobic counteranion...

The best-known of these current programs is French Creek Water Cycle, which uses the concept of Ion Association Model in the calculation of saturation level indices. This software series is available in a range of editions suitable for research laboratories, product managers, or field water treaters and operators with access to a laptop computer. 

In the same way as the electron transfer is mapped by the band diagram, the ion transfer of the ion-ion associates can be represented by an ionic level diagram (see Fig. 18 center, bottom).75,77 Figure 18 indicates that, in particular by comparison with the situation of water, the ionic associates play the role of internal acids and bases. It is even possible to transform the Brpnsted-concept in its ionotropic generalization to solids by using the point defect concept. In the same way as the numbers of H+ and OH" reflect the acidity and basicity in water, the numbers of v Ag and Agj reflect the (ionotropic) acidity and basicity in AgCl. An acidity function based on 2. which is identical... 

A critical review of the history of the ion-pair concept indicates that considerations other than electrostatic were scarcely provided by model makers. Clearly, for chromatography, solvophobic interactions usually neglected by ion-pair model makers are aucial. Chromatographers involved in ion-pair strategies realized that the theoretical description of the ion-pair was critical at the time of the ion-pair chromatography introduction in the late 1970s and subsequently, the electrostatic model of ion association dominated scientific debate. 

Section 2.5.3 in Chapter 2 expounded upon the hydrophobic ion-pair concept The peculiarities of this association mode, not even likely in the Bjerrum s model, were elucidated. Electrostatic attraction is only part of the story and solvophobic interactions are crucial to rationalize experimental evidence that often runs counter to the pristine electrostatic description of the process. 

An understanding of the concentration dependence of activity coefficients required the postulation of the concepts of ion-pair formation and complex formation. Certain structural questions, however, could not be answered unequivocally by these considerations alone. For instance, it was not possible to decide whether pure Cou-lombic or chemical forces were involved in the process of ion association, i.e., whether the associated entities were ion pairs or complexes. The approach has been to postulate one of these types of association, then to work out the effect of such an association on the value of the activity coefficient, and finally to compare the observed and calculated values. Proceeding on this basis, it is inevitable that the postulate will always stand in need of confirmation because the path from postulate to fact is indirect. 

In 1926, Bjerrum [137] used Debye-Hiickel theory to describe ion association and took into account the interaction of ions within a short range. He introduced an ion-pair concept, gave a definition of ion pairs as neutral species formed by electrostatic attraction between oppositely charged ions in solution, and showed how ion-pair formation was dependent on the ions size (radius of ions), solvent (dielectric constant), and temperature. 

Ion-Association.—A device, proposed by Bjerrum, for avoiding the difliculty of integrating the Poisson equation when it is not justifiable to assume that Ziep/kT is much smaller than unity, involves the concept of the association of ions to form ion-pairs (cf. p. 96). It may be remarked that, in a sense, a solution, such as that of Gronwall, Sandved and LaMer, of the differential equation resulting from the use of the complete expression for the electrical density, makes the Bjerrum treatment unnecessary. The results obtained are, nevertheless, of interest, especially in connection with their application to media of low dielectric constant. 

The concept of coordination in the second sphere was introduced by Werner. All authors agree that such outer-sphere association exists in solution, hut they disagree about the kind and the extent of this association. Some advocate a second-sphere coordination which is closely analogous to the inner-sphere coordination. The data which support this hypothesis are not very convincing and can be criticized in various ways. The present author finds that the electrostatic theories of N. Bjerrum, Fuoss, and Kraus, according to which the formation of the ion-associates is a result of coulombic attraction, both qualitatively and quantitatively, give the most trustworthy picture of the outer-sphere association. However, this does not exclude the fact that some preferred mutual orientation exists in the ion pairs. 

For some strongly associated species, ion association can be measured directly, for example, by spectroscopic means (Byrne and Millero, 1985). Because there is no method by which unequivocal structures of the species present may be obtained, ion association is a phenomenological concept. Ion-pair formation is involved in explaining deviations from normal behavior. However, the impossibility of knowing unambiguously the relevant activity coefficients in seawater implies that the concept of normal behavior is not clearly defined. 

A concept of ion association in electrolyte solutions was introduced about eighty years ago by Bjerrum [1] in order to improve the Debye-Hiickel (DH) theory [2], In accordance with this concept an electrolyte solution is considered to be a mixture of free ions and ion clusters (usually ion pairs and some-... 

The DH and MSA theory, that are linear in charge can be considered in the framework of linearized Poisson-Boltzmann (PB) equation. The concept of ion association entails nonlinearity in the treatment of electrostatic interactions by the formulation of appropriate thermodynamic equilibrium constants between free ions and ion clusters [14], In general, this formulation can be considered as the division of ion-ion interaction potentials into an associative part responsible for the ion association, and nonassociative part which is more or less arbitrary. In order to optimize this division in the framework of associative hypernetted chain approximation (AHNC), the division of energy and distance were considered [17] with the parameters calculated from the condition of sta-... 

In this chapter some aspects of the present state of the concept of ion association in the theory of electrolyte solutions will be reviewed. For simplification our consideration will be restricted to a symmetrical electrolyte. It will be demonstrated that the concept of ion association is useful not only to describe such properties as osmotic and activity coefficients, electroconductivity and dielectric constant of nonaqueous electrolyte solutions, which traditionally are explained using the ion association ideas, but also for the treatment of electrolyte contributions to the intramolecular electron transfer in weakly polar solvents [21, 22] and for the interpretation of specific anomalous properties of electrical double layer in low temperature region [23, 24], The majority of these properties can be described within the McMillan-Mayer or ion approach when the solvent is considered as a dielectric continuum and only ions are treated explicitly. However, the description of dielectric properties also requires the solvent molecules being explicitly taken into account which can be done at the Born-Oppenheimer or ion-molecular approach. This approach also leads to the correct description of different solvation effects. We should also note that effects of ion association require a different treatment of the thermodynamic and electrical properties. For the thermodynamic properties such as the osmotic and activity coefficients or the adsorption coefficient of electrical double layer, the ion pairs give a direct contribution and these properties are described correctly in the framework of AMSA theory. Since the ion pairs have no free electric charges, they give polarization effects only for such electrical properties as electroconductivity, dielectric constant or capacitance of electrical double layer. Hence, to describe the electrical properties, it is more convenient to modify MSA-MAL approach by including the ion pairs as new polar entities. 

In this section we consider the application of the concept of ion association to describe the properties of electrolyte solutions within the ion or McMillan-Mayer level approach. In this approach the effects of solvent molecules are taken into account by introducing the dielectric constant into Coulomb interaction law and by appropriately choosing the short-range part of ion-ion interactions. To simplify, we consider here the restrictive primitive model (RPM)... 

Concept of ion association is also important in explaining the specific properties of the electrical double layer, especially in the regime of strong ion-ion interaction when ion clusterization occurs. For the sake of simplicity, we consider here the RPM model near a charged hard wall. The interaction between ions and surface is given by the potential,... 

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