BJerrum distance

Here q is the Bjerrum-distance ( -efe /2DkT), the Boltzmann Constance, to the mechanical mobility of an ion Kd(E=0) the equilibrium constant in the absence of electric field and D and dielectric constant of the medium. From these expressions we see that the shift in dissociation constant upon the application of an electric field is given by ... 

On the basis of tois model, Lee and Wheaton arrived at an equation for in terms of q, the Bjerrum distance. The equation is several lines long and clearly only fit for use in appropriate software. The application of experimental data of to the equation allows one to find values of and the co-sphere radius R. These values... 

The value of the Bjerrum distance depends on the ionic charges, the nature of the solvent and the temperature but not on electrolyte concentration. For aqueous solutions of 1-1 electrolytes at 25°C, it is equal to 357 pm. Bjerrum proposed that all ions contained in a sphere with this radius are paired. This is a reasonable proposal for aqueous systems, since ions of typical size would be close to contact at such small separations. However, if the solvent has a lower dielectric permittivity, the distance over which ions are considered to be paired increases and the assumption that they are in contact is more diiScult to accept. For example, when the solvent s relative permittivity is 10, the Bjerrum distance r-Q increases to 2800 pm. 

This minimum value of r is frequently referred to as the Bjerrum distance and given, as shown, the symbol q. Bjerrum makes the arbitrary assumption that ions inside the sphere with radius q are associated, and that those outside this sphere are free. The value of q evidently depends upon the ratio of the electrostatic potential energy of an ion pair, t2/Dr, to the thermal kinetic energy of an ion, which is 3... 

It is evidently of interest to obtain an expression for computing the extent of association of free ions into ion pairs as a function of the concentration, the distance of closest approach, the dielectric constant, etc. The following discussion will be restricted to uni-univalent electrolytes for which 01 = — 02 = 1. To obtain the time average number of ion pairs for each ion of opposite charge it is necessary to integrate through the volume between spheres with radii, at, the distance of closest approach, and the Bjerrum distance, q. For this purpose it is... 

This value of r at which the minimum occurs is given the symbol, q, and the name, the Bjerrum distance , and takes a value ... 

Values in parentheses correspond to b equal to the Bjerrum distance (see p. 564). 

Fig. 5.3.2. Distance at which 9/10 and 3/4 of the associated ions lie from a central ion = 3 A) against the Bjerrum distance /. The vertical bars denote the values of / for a (1 1) electrolyte in W = water, D = dimethylformamide, A = acetone, P = pyridine, C = < -dichIorobenzene. In the top of the graph values of Ka corresponding to some / values are given.

It is possible to reduce the number of free parameters by replacing a by the Bjerrum distance of the closest approach of free ions given by... 

Wood and co-workers (Sharygin et al., 2001) have compared the FHFP and TBBK equations for associated electrolytes using conductivity data for aqueous NaCl at high temperature and pressure (623.9 K, 19.79 MPa and p = 0.596 g cm ). The FHFP equation for associated electrolyte was used witii the distance of closest approach fixed at the Bjerrum distance, d. 

The semidiluted phase is not necessarily the most complicated to be depicted. For instance for our copolymers with a content in ionic units of a few percent and a weight concentration of 5-10% it can be easily calculated, that the distance between ionic sites on a given chain is always smaller than the Bjerrum distance. Similarly in these conditions the electrostatic contribution to the persistence length [38-39] remains very small. 

The behavior of three sorts of ions has been explored elementary (spherical), tetrahedral, and planar. Equilibrium constants of iono-phores composed of spherical or tetrahedral ions, Bjerrum distances of... 

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