Methods for Studying Ion Association

The Bjerrum theory of electrostatic ion pairing, as applied to conductivity data, has been well substantiated by Justice and Justice [36]. The interpretation of such data that have traditionally been one of the main methods for studying ion association according to Martell and Motekaitis [37] is according to the following expression by Femandez-Prini and Justice [38]  

Here Ag is the molar conductivity of the electrolyte, A is that quantity at infinite dilution, ac is, as above, the concentration of free ions, and S, E, 7, and are known explicit expressions, containing contributions from relaxation and electrophoretic effects. The latter two functions depend also on the ion distance parameters R and that are set equal to q according to the Bjemim theory. If the departure of y, from unity is ignored, only two parameters, A (yielding a from Eq. (7.23)) and Ag have to be modeled. 

Here is the infinite frequency permittivity (the square of the refractive index 

Here A. is a geometric factor reflecting the ellipsoid of rotation of the ion pair to be obtained from its dimensions and f. is the reaction field, expressions for which having been reported by Barthel et al. [39], / . and are the dipole moment and polarizability of the dipolar species, and g. is the dipole orientation correlation factor, generally set as = 1. Eventually the concentrations of the ion pair species, c., are used for the calculation of the partial association equilibrium quotients, K, K, and and the overall constant which may be compared with values obtained by other methods. 

Ultrasonic relaxation measurements have also been used for the study of stepwise ion association, but in contrast with the DRS method, it detects the ion pairing equilibria rather than the species formed, which must be assumed. NMR and Raman spectroscopy are sensitive only to CIPs and treat SIPs and 2SIPs, with solvent molecules intervening between the partner ions, as if they were free ions. A thorough treatment of the theories relating to ion association of strong electrolytes and the experimental methods used to study it are presented in the review by Marcus and Hefter [29], 

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The overall association constant is =K, +K,K.+K,K.K. Most methods for studying ion association (such as conductivity or potentiometry, see below) provide values only for or K, but some methods (Section 1.12 and volumetric data according to Hemmes [25]) are able to distinguish between the three kinds of ion pairs. 

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