Benesi-Hildebrand plot

Fig. 1 Charge-transfer absorption spectra of enol silyl ethers complexes with re-acceptors. (a) Spectral changes accompanying the incremental additions of cyclohexanone enol silyl ether [2] to chloranil in dichloromethane. Inset Benesi-Hildebrand plot, (b) Charge-transfer absorption spectra of chloranil complexes showing the red shift in the absorption maxima with decreasing IP of the enol silyl ethers, (c) Comparative charge-transfer spectra of EDA complexes of a-tetralone enol silyl ether [6] showing the red shift in the absorption maxima with increasing EAs of the acceptors tetracyanoben-zene (TCNB), 2,6-dichlorobenzoquinone (DCBQ), chloranil (CA), and tetracyanoqui-nodimethane (TCNQ). Reproduced with permission from Ref. 37.

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) ... 

The ground state complex formation between A + CC14 which may only be of contact type is indicated from changes in columns (4) and (5) for low and high concentrations of anthracene. A Benesi-Hildebrand plot for A + CC14 in cyclohexane gives the value of K, the equilibrium constant, for complex formation1 ... 

Construct a double reciprocal (Benesi-Hildebrand plot) plot l/AA60o vs l/[py]x-Do a linear regression and determine the y-intercept (1 /q). Determine K from the slope (1 /Kq), see equation (3.28). 

Figure 17 Absorption spectra of 21 (3 pM) in 2 3 CHjClj.CHjCN containing (a) 0, (b) 0.25, (c) 0.5, (d) 1, and (e) 2 mM of colloidal Ti02. The inset shows the fitting of the 670 nm absorption band to the Benesi-Hildebrand plot. (From Ref. 101.)...

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 sequential formation of 1 1 and 2 1 complexes was proposed based on the absorption spectral variations which occurred with an isosbestic point for [/ -CD] < 10 M above this concentration a new, red-shifted band appears, indicating the formation of higher complexes [101]. A Benesi-Hildebrand plot of reciprocal R versus reciprocal [/ -CD] is linear for [ -CD] < 10 M, indicating the formation of a 1 1 complex in this [/ -CD] range at [/ - CD] > 10 M, the plot is linear versus l/[/ -CD], indicating 2 1 complexation. 

The binding constants (K) of naphthalene, 1-methylnaphthalene, and acenaphthene with 3-CD and 3-CD-2 were determined by Benesi-Hildebrand plots for fluorescence intensities (5) ... 

Common titration plots use A as a convenient value for graphical interpretation of data. A direct plot or Langmuir isotherm is obtained as a plot of A versus [G] the concentration at which A = 0.5 is the dissociation constant for the system. A plot of A/[G] versus A is known as a Scatchard plot [100], and the slope of the line is equal to -VK. A plot of IIA versus 1/[G], also known as a double reciprocal plot or Benesi-Hildebrand plot gives directly from the magnitude of the slope of the line [101]. 

A foldamer-based molecular recognition system that has enantiomeric M and P helical conformation was also studied. The diastereoselective complexation of an achiral, amphiphilic, helical m-phenylene ethynylene dodecamer 13 with a chiral plant natural product a-pinene 14 was demonstrated by ICD studies (Figure 10). The stoichiometry of the complex was determined as 1 1 by CD titration measurements based on the linearity of a Benesi-Hildebrand plot and the slope of a Hill plot. The association constant was estimated to be = 6.83 x 10" indicating that 13 can capture 14 efficiently. The results suggested that the chiral guest can stabilize one of the oligomer s enantiomeric helical M or P conformations. 

Instead of a nonlinear fitting, (8) is often linearized. The linearized plot is known as a Scatchard or Benesi-Hildebrand plot. ... 

Deviations from COPS theory are easily detected. For exemple, neither the kinetic nor the NMR equations could be linearized for the solvent couples benzene(5 )-mesitylene(Z) and benzene(5 )-l-methylnaphthalene(Z). This is due to solute induced solvent-solvent interaction which becomes more evident in the case of stronger complexes (e.g., tetracyano-ethylene-anthracene [to be published]). This might also provide explanation to curved Benesi-Hildebrand plots [72]. 

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