Benesi-Hildebrand treatment

Calculated from IJV/VIS spectrophotometric analyses by Benesi-Hildebrand treatment. Range of A values used in the determination from 410 to 450 nm In parentheses values calculated from kinetic data. 

A similar effect of the CDs on the fluorescence of 2-(p-toluidinyl)naph-thalene-6-sulfonate (2) was reported by Kondo and co-workers [55], who demonstrated the existence of complexes with different stoichiometry by applying the Benesi-Hildebrand treatment to the fluorescence variations of 2 as a function of CD concentration. For a-CD, the Benesi-Hildebrand plot—reciprocal fluorescence intensity versus reciprocal CD concentration—was a straight line, whereas for / - and y-CD it deviated from the linearity at high CD concentrations. This indicates that a 1 1 complex is formed between a-CD and 2, while / - and y- CD also form 2 1 (host guest) complexes. It was suggested that CD complexes 2 by including the toluidinyl moiety of the probe. In complexes with 2 1 stoichiometry, the CDs include the naphthalene moiety as well as the toluidinyl part of 2. This mode of complexation for 2 with a- and /S-CD was confirmed in reference 56. The fluorescence quantum yields for 1 1 and 2 1 complexes are reported in Table 1. 

The quantitative (Benesi-Hildebrand) treatment of the spectral data indicated that the equilibrium constants /Cda for the formation of these inter-molecular (1 1) complexes ... 

The hyperbolic direct plot can easily be straightened out, as analogies from classical enzymology teach us. The most popular data treatment for yielding straight lines is the double reciprocal plot, also known as the Lineweaver-Burke or Benesi-Hildebrand plot. Here, we take the reciprocal of equation (2.24) ... 

Some data treatment methods are general, some rely on approximations and thus are subject to some premises, and some are just regression methods. Typical examples of the approximate methods are the Benesi-Hildebrand [12], Ketelaar [13], Nagakura-Baba [14], Scott [15], Scatchard, and Hammond [16] methods which approximate [G] by [G]o. 

An equilibrium is established between the probe in its ground state and the supramolecular system. Equilibrium constants and complexation stoichiometries are established with a variety of techniques, including absorption and fluorescence measurements. Examples of these methodologies are the Benesi-Hildebrand [52] and Job plot [53,54] treatments. Equilibrium constants for the ground state molecules are established in order to know the fraction of probes... 

Experimental data may be treated according to Scott s modification [207] of the Benesi-Hildebrand equation [221], Technically easier and more exact may appear other methods described especially for the treatment of NMR data [222]. The known stoichiometry of the complex is a prerequisite for obtaining correct binding data. Almost all techniques described in the literature are suitable for 1 1 complexes. The formation of complexes of other stoichiometry may significantly complicate the treatment of the data or introduce a significant source of error in the calculations. Nonlinear curve-fitting techniques may avoid the problems of this kind. 

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