Bjerrum concept

Several investigators (28, 29, 45, 94) criticized as energetically unfavorable the Bjerrum concept of a valence defect pair formed by rotation of a rigid molecule in an otherwise undisturbed lattice. Alternative mechanisms were proposed. 

Although acids and bases have been recognized since antiquity, our concepts of them are still the subject of debate and development (Walden, 1929 Hall, 1940 Bell, 1947, 1973 Luder, 1948 KolthofF, 1944 Bjerrum, 1951 Day Selbin, 1969 Jensen, 1978 Finston Rychtman, 1982). The history of these concepts is a long one and can be seen as a prolonged and continuous refinement of inexact and commonsense notions into precise scientific theories. It has been a long and difficult journey and one that is by no means ended. 

This concept is due to Bjerrum, who in 1926 suggested that in simple electrolytes ions of the opposite charge could associate to form ion-pairs (Szwarc, 1965 Robinson Stokes, 1959). This concept of Bjerrum arose from problems with the Debye-Huckel theory, when the assumption that the electrostatic interaction was small compared with IcTwas not justified. 

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... 

In 1941, J. Bjerrum [65] developed the useful concept of average ligand number, n, defined as the mean number of ligands per central atom ... 

Since Bjerrum s [7] introduction of the concept of ion pairing in 1926, a variety of analytical methods has been employed to study the structure and energetics of ion pairs. Szwarc s Book deals with the development of the ideas up to 1972 [3a]. It is also a guiding reference for the different spectroscopic methods that have been employed in the examination of ion pairs. 

Amphoteric — a substance that can act both as an acid and a base - acid-base theories, subentry - base-antibase concept, -r ampholyte, - Bjerrum, Niels Jan-niksen, - capillary isoelectric focusing (CIEF), -+ metals. 

The ion pair concept, introduced by Bjerrum [14], was critically reviewed by Szwarc [15] and definitions were given based on the mutual geometry of ions and solvent. The existence of loose and tight ion pairs was suggested by Winstein [16] and Sadek [17] and it is now common to speak about free ions (FI) as well as of solvent-separated ion pairs (SSIP) or contact ion pairs (CIP), having in mind the oversimplified picture ... 

Diamond was the first to focus on the concept of hydrophobic association and demonstrated that, at variance with the Bjerrum theory, ion-pairing of univalent organic electrolytes in water is possible [12]. He capitalized on the hydrophobic hydration concept [11,12] typical of large organic ions (yide supra) that increase the water structure via the formation of ice-like cages, thereby decreasing the system... 

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. 

In recent years, it has been found that the molar absorptivity of concentrated copper sulfate solutions does show a shght concentration dependence. This concentration dependence has been attributed to ion-pair formation occurring through the operation of Coulombic forces between the copper and sulfate ions. This is perhaps ironic because Bjerrum s concept of ion pairs is being used to contradict his conclusion that there are only free ions in copper sulfate solutions. Nevertheless, there is a fundamental difference between the erroneous idea that a copper sulfate crystal dissolves to give copper sulfate molecules, which then dissociate into free ions, and the modem point of view that the ions of an ionic crystal pass into solution as free solvated ions which, under certain conditions, associate into ion pairs. 

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 second golden time of solution chemistry staned by the work of Debye and Hiickel in 1923, which was based on statistical thermodynamics, one step further advanced from thermodynamics. This work was immediately followed by N. Bjerrum, whose idea of ion-pair formation was induced by the Debye-Hiickel theory. In these treatments they accepted the existence of ions and molecules with finite sizes as solutes, but solvent was regarded as a homogeneous continuum, and no molecular aspect was introduced in their concept. In this respect the second period can be said as the dawn of the molecular solution chemistry developed in the late 20th century. In this section, we have to mention the work by Bernal and Fowler (1933), which will be referred to again later. 

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. 

Probably the best known and most investigated reaction of a ligand at the coordinated atom is the acidic nature of various coordinated ligands. This concept of proton dissociation from a coordinated ligand is not a recent one, for very early in this century Bjerrum determined the j)Ka of [Cr(H20)6] to be 4.05 at 25°C. (4), a value later refined by Lamb and Fonda to 3.8. Of greater interest, however, is the acidic behavior of protons on coordinated atoms other than oxygen. 

Surveys of the influence of master variables, such as pH, and the rapid solution of even complicated equilibria can be accomplished with relative facility by graphic representation of equilibrium data. The concepts of graphical repre -sentation of equilibrium relationships were first introduced by Bjerrum (1914) and have more recently been developed and popularized by Silldn (1959). 

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-... 

Bjerrum (Bj) combined the Arrhenius and DH approaches by assuming a chemical equilibrium between ion-pairs and free ions [27], This concept takes into account interactions of ions at short range, which are not adequately described in DH theory. It also includes a theory for the mass action constant as a function of the dielectric constant e of the solvent. Many experimental investigations of the electrical conductance A, e.g. reviewed by Kraus [36], have confirmed Bjerrum s concept, which is the basic concept of many modern approaches. 

Soon after the development of the quantum mechanical model of the atom, physicists such as John H. van Vleck (1928) began to investigate a wave-mechanical concept of the chemical bond. The electronic theories of valency, polarity, quantum numbers, and electron distributions in atoms were described, and the valence bond approximation, which depicts covalent bonding in molecules, was built upon these principles. In 1939, Linus Pauling s Nature of the Chemical Bond offered valence bond theory (VBT) as a plausible explanation for bonding in transition metal complexes. His application of VBT to transition metal complexes was supported by Bjerrum s work on stability that suggested electrostatics alone could not account for all bonding characteristics. 

Considerable effort has been made to develop a model for the parameter on the basis of statistical theories using simple electrostatic concepts. The first of these was proposed by Bjerrum [25]. It contains important ideas which are worth reviewing. He assumed that all oppositely charge ions within a certain distance of a central ion are paired. The major concept in this model is that there is a critical distance from the central ion over which ion association occurs. Obviously, it must be sufficiently small that the attractive Coulombic forces are stronger than thermal randomizing effects. Bjerrum assumed that at such short distances there is no ionic atmosphere between the central ion and a counter ion so that the electrostatic potential due to the central ion may be calculated directly from Coulomb s law. The value of this potential at a distance r is... 

Although the concept of outer sphere complexation was introduced by Werner (1) in 1913 and the theory first given a mathematical base by Bjerrum (2) in 1926, progress in understanding the factors involved in the competition between inner and outer sphere complexation has been very slow. 

Bjerrum s concept of an ion pair and his theoretical development is the most successful treatment used in conjunction with the Debye-Hiickel theory for analysing experimental data, despite all the ambiguities in deciding at what stage to introduce the cut-off distance between ion pairs and free ions. His theory was basically a device to account for the short range electrostatic interactions not included in the Debye-Hiickel theory (see Guggenheim s treatment, Section 10.13.1). 

Various explanations have been given for deviations from the Debye-Hiickel-Onsager equations. A common type of behavior is for the negative slopes of the A versus /c plots to be greater than predicted by the equation that is, the experimental conductivities are lower than predicted by the theory. This has been explained in terms of ion pairing, a concept which was developed by the Danish physical chemist Niels Bjerrum (1879-1958) in 1926. Although most salts, such as sodium chloride, are present in the solid state and in solution as ions and not as covalent species, there is a tendency for them to come together from time to time to form ion pairs. 

The experimental data discussed above do not confirm in every case the assumptions of McBryde et al, which are otherwise based to some extent on the earlier concept of Bjerrum and Jorgensen [Bj 53] nevertheless, it appears beyond doubt that the interpretation of the solvent effect in solvent mixtures should be soluble with the aid of equilibrium constants which also include the solvent... 

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