Bjerrum formation function

Which of the following denotes Bjerrum formation function ... 

Another useful function for the analysis of binding is the Bjerrum complex formation function n, which gi es an average number of ligand molecules bound per receptor ... 

Once such functions are obtained, they can be used for the calculation of equilibrium constants of Eqs. (2.1), (2.4), and (2.5). As one can see, Eqs. (2.9) and (2.10) are quite similar to the functions widely used in Bjerrum s theory of stepwise complex formation in solutions (Leden s and Bjerrum s functions accordingly) [5,6]. Thus, the mathematical analysis and calculation of the constants become well-elaborated routine. Some examples of such calculations are given below. 

When the concentration of ligand is L is measured, the formation function (n) of a metal ligand system defined following Bjerrum is applied ... 

Uij = Rij/Rij. Similarly, Ga[(ljp u /) + 1] attains its maximum value whenever the direction of the acceptor arm Ij is in the direction -u//. Thus, the product of these three functions attains a value close to unity only if, simultaneously, Rij is about Rh, the direction of Hia is about that of Xij, and the direction of jp is about that of -u /. Such a configuration is said to be favorable for HB formation. Clearly, if all of the above three conditions are fulfilled, then the interaction energy is about sub- The sum of the various terms in the curly brackets of (2.7.8) arises from the total of eight possible favorable directions for HB formation (four when molecule i is a donor and four when molecule i is an acceptor). The variances a and a are considered as adjustable parameters. Note that of the eight terms in the curly brackets, only one may be appreciably different from zero at any given configuration X Xy. Clearly, the HB part of the potential in (2.7.8) does not suffer from a possible divergence as in the Bjerrum model, and clearly does not allow two bonds to be formed by a pair of water molecules (Fig. 2.48b). 

The diagram n as a function of the decimal antilogarithm of the ligand activity (concentration) of the free ligand after complexation (here pCl) is known as the formation curve. The mathematical study of the formation curve permits us to determine the equilibrium constants, A l, K2, K3, K4, etc. (see Sect. 24.3). The formation curve concept is due to J. Bjerrum. It can be extended to other phenomena in solution. 

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