Bjerrum potential

In Eq. (15) 2 qB/r is the coulombic part of the mean force potential, and Wjj is the noncoulombic part. The earlier association constants of Fuoss, Prue, and Bjerrum are special cases of this general chemical model [15]. The importance of noncoulombic interactions is proved [ 16] by ... 

Bjerrum and coworkers have assigned the three rate maxima shown in Figs. 10.7 and 10.8 to (starting from the negative potential) (a) destruction of vanadium polymeric chains (b) electric double layer effect at gold working electrode (c) stabilization of V (V) vs V (IV). These explanations are very plausible. 

Skibsted, L.FI. and Bjerrum, J. (1977) The standard electrode potentials of aqua gold ions. Acta Chemica Scandinavica Series A Physical and Inorganic Chemistry, 31, 155-156. 

Diffusion or liquid junctions are thus not clearly defined since the potential difference is dependent on the sharpness of the junction. Uniformly sharp junctions have been obtained by Lamb and Larson J.A.G.k XLii. 229,1920) by allowing one liquid to flow against the other, whilst Bjerrum f. Elektroohem. Liii. 428, 1906), has obtained a relatively diffuse junction by the insertion of a sand diaphragm between the two electrolytes. 

Bearing in mind these limitations on the Debye—Hiickel model of electrolytes, the influence of ionic concentration on the rate coefficient for reaction of ions was solved numerically by Logan [54, 93] who evaluated the integral of eqn. (56) with the potential of eqn. (55). He compared these numerical values with the predictions of the Bronsted— Bjerrum correction to the rate of a reaction occurring between ions surrounded by equilibrated ionic atmospheres, where the reaction of encounter pairs is rate-limiting... 

Potential functions based on the sp3-hybrid tetrahedral structure model of water molecules in which two positive and two negative charges are placed at the tetrahedral positions in the molecule have been proposed by Bjerrum 1), Ben-Naim and Stillinger (BNS model) (2), and Stillinger-Rahman (ST2) (3). 

Fig. 3 Effective potential between two counterions (left) and two monomers (right), respectively for various Bjerrum lengths /B. The chain length is N= 80 and the density 77= 1(T2...

The theory of ion-pair formation in nonaqueous solutions has been substantially advanced by the work of Barthel, who demonstrated how important it is to take into account the non-Coulombic forces at small ionic distances in addition to the Coulom-bic ones used by Bjerrum. These non-Coulombic forces are represented by the mean force potential W (r) in the region a[Pg.551]

The Bjerrum Model. Bjerrum (see Robinson and Stokes (19)) defined an "ion pair" as existing when two ions of opposite charge approached such that the mutual potential energy between them equalled 2kT (k is the Boltzman constant). At 25 C, this means that an "ion pair" exists if the ion separation distance is equal... 

Instead of characterizing deviations from ideality of the solvent by its activity coefficient y, it is often advantageous to introduce the osmotic coefficient ( ) of Bjerrum and Guggenheim, and to write the chemical potential in the form... 

The first three inter commands instruct ESPResSo to use the same purely repulsive Lennard-Jones potential for the interaction between all combinations of the two particle types 0 and 1 by using different parameters for different combinations, one could simulate differently sized particles. The last line sets the Bjerrum length to the value 10, and then instructs ESPResSo to use P M for the Coulombic interaction and to try to find suitable parameters for an rms force error below 10 , with a fixed mesh size of 32. The mesh is fixed here to speed up the tuning for a real simulation, one will also tune this parameter. 

Even though from the conceptual point of view the role of Bjerrum defects is well established", their molecular structure and energetics, remains a subject of debate. Recent atomistic studies based on empirical water potentials have provided important qualitative insight into the structure and dynamics of Bjerrum defects, although they have not yet attempted to make direct contact with experimental conductivity data. Furthermore, the few ab initio studies " involve clusters that are too small to reliably capture the properties of a defect embedded in bulk crystal. 

When treating the association of counterions one may also apply the association statistics (AS) model which is equivalent to the Bjerrum theory for ion pairing in an electrolyte solution [29,30]. However, in the case of surface association spaee is available only on the side of the liquid. Another difference is due to the critical distance which depends on direction and is a function of the surface potential. This theory explains why two ionic species may associate at the surface despite the fact that they do not undergo ion pairing in the bulk of solution. According to the Bjerrum theory, ions of large effective size cannot approach the critical distance and such an electrolyte is completely dissociated. At the surface the critical distance extends by increasing surface potential and once the surface potential exceeds the critical value, at which the critical distance matches the minimum separation, association at the interface proceeds. 

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... 

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 counts the number of unit charges on the rod per Bjerrum length. In the following the main focus will be on the strongly charged case characterized by > 1. A reduced electrostatic potential y and a screening constant k > 0 are defined as... 

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