Benesi-Hildebrand equation

Ideas very similar to those presented here were developed by Litt and Wellinghoff [19] with regard to the formation of D—A complexes and the involvement of competition of donors (D) and solvents in the solvation shell of the acceptors (A) and of the complexes. Their theory was used successfully to account for deviations from the Benesi-Hildebrand equation [20]. 

In addition, it is worthwhile noting that the use of the Benesi-Hildebrand equation provides only approximate Kf values, because more emphasis is placed on the lower concentration values than on the higher ones, and the data are not weighted properly [85,103,104], Therefore, a better estimation of Kf can be made by using Eq. 4 based on a non-linear regression (NLR) analysis [83,86] ... 

Molecular recognitions of amino acids. The binding constant is a measure of recognition interactions of different amino acids with metallohematoporphyrin. It can be estimated by Benesi-Hildebrand equation (the double-reciprocal method) ... 

Benesi and Hildebrand derived the equation for the calculation of association constants of iodine with aromatic hydrocarbons by spectrophotometry in 1949 [47]. At present, many techniques used for the determination of binding constants represent the various modifications of the Benesi-Hildebrand equation [47]. That commonly used in spectrometric techniques is Scott s modification of this technique [48]. 

Inserting Equation (22-67) and transforming leads to the Benesi-Hildebrand equation. 

A plot of the left-hand sides against 1 /[i)]o (Benesi-Hildebrand equation) or against [D]o (Scott equation) yields equilibrium constants and molar linear absorption coefficients from the slope and ordinate intercepts of the straight lines. The equilibrium constants obey the van t Hoff relationship as long as only one CT complex occurs. 

In a second study , again employing synthetic data, multiple equilibria were considered. The results indicate that the presence of some 1 2 complex may not be detected as a deviation of the data from a linear plot of the usual sort. Johnson and Bowen speeifieally considered the data plots obtained with eqn. (2) (the Benesi-Hildebrand equation), but the conclusions will presumably apply to all similar equations. 

Scott, R.L. (1956) Some comments on the Benesi-Hildebrand equation. Rec. Trav. Chim., 75,787-789. 

FIGURE 13.5 Double reciprocal plots of Benesi-Hildebrand equation for the determination of tbe stoichiometry of a host-guest system, Py = pyrene. (Reproduced from Ref. [40] with permission of American Chemical Society. Copyright 2008.)... 

A double reciprocal plot of 6/A/l versus I/cl should be a straight line with a slope of ll eK,cu and an intercept. of 1/Aecm- This equation is sometimes called the Benesi-Hildebrand equation. ... 

Charge transfer spectra of the carbazole polymer with TCNQ were measured in several solvents and compared to the model compound. The results are shown in Table 1. K and e were calculated using the Benesi-Hildebrand equation.is almost independent of whether the material is polymer or model compound, e is higher for the polymer while A max is unchanged. This is difficult to explain at present. One hypothesis is that the polymer may form a DDA complex, which will increase e and may not increase X max or K. 

A salient feature of the TNDCF monomer 50 is its fluorescence. When excited at X = 308 run an emission band centered around 520 nm is observed (cf. Fig. 12.39a). The fluorescence emission of 50 is quenched upon the addition of 42. For instance, the fluorescence emission intensity of a 23 pM solution of 50 in CH2CICH2CI is quenched by 53 % when 1 equivalent of 42 is added (cf. Fig. 12.39c). Likewise, the fluorescence emission of 50 is quenched by 97 % when 1 equivalent of 42 is added to a solution of 50 at 100 pM (cf. Fig. 12.39c). The quenching mechanism is assumed to reflect charge transfer interactions, as well as possibly competitive photon absorption by 42. Analyzing the fluorescence quenching (cf. Fig. 12.39b) by the Benesi-Hildebrand equation gave a complexation constant of 2.6 x 10" M [93]. 

The association constant (K ) of the FLZ P-CD complex were determined by using well known Scott s method [9] which is a modification of Benesi-Hildebrand equation [10]. Equation (1) refers the Scott s equation ... 

Scott R. L. Some comments on the Benesi-Hildebrand equation. 

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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