Dipole, Bjerrum

Bjermm defects act as catalysts to promote dipole turns, with one fault for every 106 molecules, corresponding to a turn rate of 10-12 s-1 at an orientation fault site. Devlin and coworkers (Wooldridge et al 1987) suggested that Bjerrum defects are essential to the growth of hydrates from the vapor phase. 

Davidson and Ripmeester (1984) discuss the mobility of water molecules in the host lattices, on the basis of NMR and dielectric experiments. Water mobility comes from molecular reorientation and diffusion, with the former being substantially faster than the water mobility in ice. Dielectric relaxation data suggest that Bjerrum defects in the hydrate lattice, caused by guest dipoles, may enhance water diffusion rates. 

The need for an analytical expressions for the equation of state have led to a revival of the macroscopic electrostatic theory due to Debye, Hiickel and Bjerrum. DH theory becomes exact for large particles. In pilot work by Fisher and Levin (FL) [31], DH-Bj theory is extended by considering the interactions of the pairs with the free ions. Weiss and Schroer (WS) [32] have supplemented this theory accounting for dipole-dipole interactions between pairs and the e-dependence of the association constant. 

A particularly important question involves the understanding of the role of crystal defects in the peculiar electrical behaviour of ice 4. Upon the application of an electric field, the solid becomes polarized by the thermally activated reorientation of the molecular dipoles. Niels Bjerrum postulated the existence of orientational defects, which represent local disruptions of the hydrogen-bond network of ice 4, to explain the microscopic origin of this phenomenon. 

Bjerrum s equation can be extended to include dipolar substituents if the dipole moment (fi) of the substituent is treated as a point dipole located at a distance r from the acidic proton (see Fig. 2), The pKa difference between the unsubstituted and substituted acids is then given by... 

For a symmetrical electrolyte, the ion pair is taken to behave as though it were a neutral species. It is, however, a dipole and as such will interact with the other ions. Consideration of this would lead to an activity coefficient for the ion pair which is not unity. There is also the question as to whether the ions of the ion pair are in contact, or are separated by one or more water molecules. Bjerrum himself recognised these limitations to his treatment the distinction between free and associated ions is not a chemical one, but only a mathematical device . 

The essence of this treatment lies in considering a Bjerrum field effect term as a separate component of the Hammett equation. Wepster s paper occupies some 25 pages of the Journal of Organic Chemistry and contains extensive tabulation of experimental results (partly Wepster s own work, but mainly from the literature, with many references) and of the results of applying the new treatment. The experimental results are for the effects of both unipolar and dipolar substituents in a variety of reactions and they have been analysed in terms of the classical ideas developed by G. N. Lewis and Bjerrum and revived (now some 20 years ago) by Palm and his coworkers The outcome is that the Hammett equation needs only a simple extension to cover the effects of both dipoles and unipoles. The present author has previously written" a fairly lengthy summary of Wepster s paper, while recommending that seriously interested readers should consult the original paper. Here, however, only a brief summary will be attempted, with an indication of application to N2. ... 

Note that the value of 17 = 0.19 is slightly larger than the value of 17 = 0.17 chosen by Bjerrum to reproduce the dipole... 

The Bjerrum value oft = 0.17 corresponds to a dipole moment of = 1.87 D, whereas the value of ri = 0.19 corresponds to / = 2.1 D. Such an increase in the dipole moment is indeed expected for a water molecule in the condensed state (see also Section 6.3). 

There is also a more fundamental aspect of smeared-out charges a smeared-out point charge has no divergence. For the same-charged ions this eliminates effective excluded volume effects of a Coulomb potential and permits interpenetration of two or more charges. For opposite-charged ions it leads to a new type of a Bjerrum pair where two ions collapse into a neutral but polarizable entity [46-49]. The usual Bjerrum pair, formed between ions with hard-core interactions, is represented as a permanent dipole [50]. 

Solutions to the Poisson—Boltzmann equation in which the exponential charge distribution around a solute ion is not linearized [15] have shown additional terms, some of which are positive in value, not present in the linear Poisson—Boltzmann equation [28, 29]. From the form of Eq. (62) one can see that whenever the work, q yfy - yfy), of creating the electrostatic screening potential around an ion becomes positive, values in excess of unity are possible for the activity coefficient. Other methods that have been developed to extend the applicable concentration range of the Debye—Hiickel theory include mathematical modifications of the Debye—Hiickel equation [15, 26, 28, 29] and treating solution complexities such as (1) ionic association as proposed by Bjerrum [15,25], and(2) quadrupole and second-order dipole effects estimated by Onsager and Samaras [30], etc. 

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