Bjerrum ion pair

There is also a further crucial change to the model. Up to this time the free ions were taken to be the only species able to conduct the current. Contact ion pairs, Bjerrum ion pairs and early Fuoss ion pairs do not conduct the current. But now Fuoss allows solvent separated ion pairs as well as free ions to conduct the current. 

A criterion for the presence of associated ion pairs was suggested by Bjerrum. This at first appeared to be somewhat arbitrary. An investigation by Fuoss,2 however, threw light on the details of the problem and set up a criterion that was the same as that suggested by Bjerrum. According to this criterion, atomic ions and small molecular ions will not behave as strong electrolytes in any solvent that has a dielectric constant less than about 40. Furthermore, di-divalent solutes will not behave as strong electrolytes even in aqueous solution.2 Both these predictions are borne out by the experimental data. 

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. 

The first ideas concerning a role of pairwise electrostatic interaction between ions were advanced in 1924 by Vladimir K. Semenchenko. A quantitative theory of the formation of ion pairs was formulated in 1926 by Niels Bjerrum. 

Bjerrum s theory of ion pairs qualitatively correctly explains a number of experimental data, but cannot be used to the full extent in quantitative calculations, particularly because of the provisional character of quantities a and (the integration limits). 

Bjerrum s theory includes approximations that are not fully justified the ions are considered to be spheres, the dielectric constant in the vicinity of the ion is considered to be equal to that in the pure solvent, the possibility of interactions between ions other than pair formation (e.g. the formation of hydrogen bonds) is neglected and the effect of ion solvation during formation of ion pairs is not considered (the effect of the solvation on ion-pair structure is illustrated in Fig. 1.7). 

In solution theory the specialized distribution functions of this kind should appear in the theory of ion pairs in ionic solutions, and a form of the Bjerrum-Fuoss ionic association theory adapted to a discrete lattice is generally used for the treatment of the complexes in ionic crystals mentioned above. In fact, the above equation is not used in this treatment. Comparison of the two procedures is made in Section VI-D. 

In the present context P+n A might be poly(iso-butyl)+ A1C14". For the simple case of spherical ions, the dissociation constant, KD, of ion-pairs is governed by the Bjerrum-Fuoss Equation (13) ... 

In order for a solvated ion to migrate under an electric field, it must be prevented from forming close ion pairs with its counterions by the solvating solvent. The effectiveness of the solvent molecule in shielding the interionic Coulombic attraction is closely related with its dielectric constant. The critical distance for the ion pair formation q is given by eq 4 according to Bjerrum s treatment, with the hypothesis that ion-pair formation occurs if the interionic distance is smaller than... 

There is some arbitrariness in the definition of the ion pair, and hence the association constant. Often a structural definition of the ion pairs is preferred—for example, by adopting a cutoff distance such as rc = 2a [141, 207] or similar choices [208, 209]. In contrast, Bjerrum (Bj) theory [140] uses an energetic criterion by defining ions as being associated, when their interaction energy is twice the thermal energy kBT. Bjerrum theory yields... 

Solvent effects in electrochemistry are relevant to those solvents that permit at least some ionic dissociation of electrolytes, hence conductivities and electrode reactions. Certain electrolytes, such as tetraalkylammonium salts with large hydrophobic anions, can be dissolved in non-polar solvents, but they are hardly dissociated to ions in the solution. In solvents with relative permittivities (see Table 3.5) s < 10 little ionic dissociation takes place and ions tend to pair to neutral species, whereas in solvents with 8 > 30 little ion pairing occurs, and electrolytes, at least those with univalent cations and anions, are dissociated to a large or full extent. The Bjerrum theory of ion association, that considers the solvent surrounding an ion as a continuum characterized by its relative permittivity, can be invoked for this purpose. It considers ions to be paired and not contributing to conductivity and to effects of charges on thermodynamic properties even when separated by one or several solvent molecules, provided that the mutual electrostatic interaction energy is < 2 kBT. For ions with a diameter of a nm, the parameter b is of prime importance ... 

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. 

If the association of ions to ion pairs is solely due to electrostatic forces, then there should be a correlation between the association constant KA and the dielectric constant of the solvent. The relation proposed by Bjerrum [35] has been found to describe satisfactorily ion association in solvents of low dielectric constants [36], In the case of solvents of moderate to high dielectric constants, the electrostatic theory of association leads to the equation [34,37]... 

The best-developed way to measure the association of ions is through the measurement of electrical conductance of dilute solutions. As mentioned, this realization occurred in the nineteenth century to Arrhenius and Ostwald. An elaborate development of conductance equations suitable to a range of ion concentrations of millimolar and lower by many authors (see Refs. 5, 33 and 34 for critical reviews) has made the determination of association constants common. Unfortunately, in dealing with solutions this dilute, the presence of impurities becomes very difficult to control and experimenters should exercise due caution, since this has been the source of many incorrect results. For example, 20 ppm water corresponds to 1 mM water in PC solution, so the effect of even small contaminants can be profound, especially if they upset the acid-base chemistry of association. The interpretation of these conductance measurements leads, by least squares analysis of the measurements, to a determination of the equivalent conductance at infinite dilution, Ao, the association constant for a positively and negatively charged ion pair, KA, and a distance of close approach, d, using a conductance equation of choice. One alternative is to choose the Bjerrum parameter for the distance, which is defined by... 

Dissociation of a salt in a solvent can similarly be treated taking into account ion pair formation. An ion association constant associated with the equilibrium established between ion pairs and dissociated ions is derived in the -> Bjerrum theory of ion pairs. 

From the conductivity in solutions which are not extremely dilute, it appears that in numerous other cases also ion pairs are formed (Bjerrum), that is to say, combinations of ions, each still with its hydration sheath and which thus do not correspond with molecules. It is especially the higher valency ions from the nature of things which exhibit this phenomenon thus this pair formation occurs, for example, in the alkali sulphates, alkaline earth nitrates and barium hydroxide through the formation of [MS04], [MN03]+ and [Ba(OH)] ions, furthermore [Ce4+(OH)-]3+, [Fe3+(OH)-]2+. 

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 ... 

Justice and Justice [61] founded their theoretical description of ion-pairing on the Rasaiah and Friedman formulation of the concentration dependence of the activity coefficient. They took into account both a short-range interaction energy and a long-range coulombic term and a many-body interaction was considered. Their final expression is in agreement with that of Bjerrnm, since E = oo for r < fl and E = 0 for r>a, and the result [65] is comparable to Bjerrum s. 

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... 

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