Ion pair, definition

A somewhat more subtle ion pair definition was introduced by Ebeling (Eb) [210-212]. Ebeling s definition of the association constant ensures consistency up to the level of the second ionic virial coefficient between the... 

We are dealing here with low-LET irradiation. There is definite evidence of multiple ion-pair involvement at higher LETs (Mozumder and Magee, 1967 Holroyd and Sham, 1985 Bartczak and Hummel, 1997). 

The chemical behavior of ions, ion pairs, and polarizable molecules partakes of the same indistinctness as the definitions of these species. Any attempt to make a complete catalog of the reactions of ions will almost certainly include borderline reactions whose intermediates are in fact ion-pairs or even covalent molecules. For many purposes the identification of a reaction as carbonium ion-like, or what the Germans would call Krypto-ionenreaktion, is as useful as the certain knowledge that the intermediate is actually a carbonium ion. Many of the ionic reaction mechanisms in the literature do not represent actual free ions and were not so intended by their authors. The ionic representation is often merely a convenient simplification if it is an oversimplification it is one that is easily rectified when the pertinent data become available. The value of such approximate mechanisms is that... 

In this first attempt at a systematic definition of the problem it is recognized explicitly that there may be a multiplicity of chemically distinct chain-carriers growing simultaneously in the same reaction mixture (enieidic polymerisation). The fact that these may include paired and unpaired ions is considered from the point of view of conventional ionic equilibria, and a warning is given that there may be tight and solvent-separated ion-pairs to be considered. This idea, taken over from the theory of anionic polymerisations, was shown much later to be inappropriate for cationic polymerisations 154. ... 

The question whether this reaction is monoeidic or enieidic was not discussed by that author, but in view of the low polarity of bulk THF it seems likely that the principal propagating species is ion-pairs but since there is no definite evidence we will denote the rate constant by kp, but write the equations in terms of x rather than Exr. For this equilibrium polymerisation therefore... 

The paired cation Pn+A The relative concentrations of the paired and unpaired cations are governed by an Ostwald-type equilibrium with dissociation constant KD. The magnitude of this is governed by the size and shape of the ions and the dielectric constant of the solvent. In contrast to anionic polymerisations, there is no definite evidence for distinguishing between tight and solvent-separated ion-pairs. 

It has been proposed to define a reduced temperature Tr for a solution of a single electrolyte as the ratio of kgT to the work required to separate a contact +- ion pair, and the reduced density pr as the fraction of the space occupied by the ions. (M+ ) The principal feature on the Tr,pr corresponding states diagram is a coexistence curve for two phases, with an upper critical point as for the liquid-vapor equilibrium of a simple fluid, but with a markedly lower reduced temperature at the critical point than for a simple fluid (with the corresponding definition of the reduced temperature, i.e. the ratio of kjjT to the work required to separate a van der Waals pair.) In the case of a plasma, an ionic fluid without a solvent, the coexistence curve is for the liquid-vapor equilibrium, while for solutions it corresponds to two solution phases of different concentrations in equilibrium. Some non-aqueous solutions are known which do unmix to form two liquid phases of slightly different concentrations. While no examples in aqueous solution are known, the corresponding... 

Studies of dimensiosolvatic effects have continued with an attempt to quantify them for solvolyses of 2-bromoadamantane in water-alcohol mixtures. Product selectivities S = fc(ether)/fc(alcohol) were measured at various concentrations of water in an alcohol and at various temperatures. The reciprocals of the averages of S values for 1.0 0.8 alcohol-water mixtures at all the experimental temperatures (120-150 °C) were proposed as measures D of dimensiosolvatic effects when a solvent molecule intervenes into contact ion pair to form solvent-separated ion pair. The scale runs from Z) = 1.0 (by definition) to D = 10.0 for r-butyl alcohol and is essentially a measure of the bulkiness of solvent molecules. 

The combining of two or more substances or molecular entities to yield a single substance or molecular entity, a process that involves either covalent or noncovalent bonding. Included in this definition is the formation of ion pairs from free ions, the noncovalent aggregation of monomers to form polymeric structures or complexes, as well as colligation. The opposite of association is dissociation. 

The mechanistic importance of the study of the temperature dependence of the rate constants is very clearly indicated in the study of the dynamics of fluorenyllithium in diethyl ether (5 , 3) Although the values of the rate constants fitted rather well with the values expected for a diffusional assocation-dissociation process at one temperature, the dissociation rate constant decreased with increasing temperature. This is a definite proof for the intervention of a solvent-separated ion-pair in the dissociation pathway. 

With accumulation of the experimental data, the field effects on polymerization reactions have become more and more definite. As the causes of the effects, we have suggested two factors, namely the field-facilitated dissociation of the ion-pair growing chain ends and the desolvation of the free-ion growing ends. Further detailed study is certainly required to determine unequivocally which of the above-mentioned factors is more influential. If the true cause or causes are discovered, we can be hopeful of finding much larger upgrading effects on polymerization reactions, which are interesting from the academic and practical points of view. 

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... 

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