Stem-Volmer modified plot

The plot of FJF against [Q does not follow the linear law and shows downward curvature toward the X-axis (Fig. 2a). Such behavior of the Stern-Volmer plot is the feature of two fluorophore populations, one of which is not accessible to a quencher [6]. In such case, the modified Stem-Volmer equation should be used ... 

Figure 2. (a) Stem-Volmer and (b) modified Stem-Volmer plots for amphi-PIC J-aggregate luminescence quenching by Sq-2Me... 

In equation 11, v=[ML]/Cl, and all other symbols used are the same as defined previously for nonlinear and modified Stem-Volmer models. Theoretically, a plot of v versus v/[L] should yield a straight line with K as the y intercept and -K as the slope. Algebraic manipulation of Cl and mass balance relationships (equations 4 and 5) and substitution into equation 11, yields equation 12. 

It is valuable to notice a difference in the method of data analysis for the modified Stem-Volmer plots (Section 8.8.A) and for the quenching-resi vedeiiussion spectra. In analyzing a modified Stem-Volmer plot, one assumes that a fraction of the fluorescence is totally inaccessible to quenchers. This may not be completely true because one component can be more weakly quenched, but still quenched to some extent. If possible, it is preferable to analyze the Stem-Volmer plots by nonlinear least-squares analysis when the/ and K/ values are variable. With this approach, one allows each component to contribute to the data according to its fractional accessibility, instead of forcing one component to be an inaccessible fraction. Of course, such an analysis is more complex, and the data may not be adequate to recover the values of fi and Kj at each wavelength. 

This expression for the intensity ratio or quantum yield is a modified form of the Stem-Volmer expression (Equation (6.19)) for the case where there is concurrent static quenching. It contains a term in [Q], like Equation (6.19), but also a term in [QJ, which predicts an upward curvature of the Stem-Volmer plot. The separate values of K and 3Tq can be obtained from the slope and intercept of a linear plot of [(/o//[Q]) — 1 ]/[Q] against [Q]. 

Inhomogeneous systems can give Stem-Volmer plots that curve downward with increasing [Q], as shown by the dashed curve in Fig. 5.7B. In this situation, a modified Stern-Volmer expression is useful [40]. Consider a protein in which a fraction da of the tryptophan residues is accessible to quenchers in the solvent and a fraction di is inaccessible. In the absence of external quenchers, the overall fluorescence yield will be... 

The modified Stem-Volmer expression (Eq. 5.58) also gives a straight line in the case of a homogeneous system with either purely dynamic or purely static quenching (Fig. 5.7C, solid line). A mixture of dynamic and dynamic quenching gives a nonlinear plot, but the curvature may be apparent only at high quencher concentrations (Fig. 5.7C, dotted line). The slope and abscissa intercept of such a plot must, therefore, be interpreted cautiously and with comparisons to the curvature of an ordinary Stem-Volmer plot. 

The ionic strength effect is not limited to fcsv variation as described by eq. (22). The addition of large amounts of electrolytes may also modify the quencher solubility and thus its efficiency. This effect has been used by some authors, in systems very different from those examined in this work, in order to determine the association constant of the inhibitor salt (Mac, 1997 Mac and Tokarczyk, 1999) as the electrolyte concentration is increased, the quencher ion associates, so that the effective concentration of the inhibitor ion decreases, leading to a downward curvature of the Stem-Volmer plot. Such a curvature can be quantitatively related... 

What is quite surprising in these plots is not the (solution-like) Stem-Volmer behavior that is found, but the diffusion coefficients which can be calculated for MV2+. From the luminescence lifetime of Ru(bpy)32+ in the absence of quencher, the kgv values can be converted to bimolecular quenching rate constants kq. The diffusion coefficient is derived from kq by means of a modified Smoluchowsky equation (equation 1), where Dq is the diffusion coefficient of MV2+, Rq is its radius (taken to be 6.7 A), R is the average... 

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