Stern-Volmer plots

Another useful technique for measuring the rates of certain reactions involves measuring the quantum yield as a function of quencher concentration. A plot of the inverse of the quantum yield versus quencher concentration is then made Stern-Volmer plot). Because the quantum yield indicates the fraction of excited molecules that go on to product, it is a function of the rates of the processes that result in other fates for the excited molecule. These processes are described by the rate constants (quenching) and k (other nonproductive decay to ground state). 

A plot of FJF vs. Cq is called a Stern-Volmer plot. From the slope, the quantity qTq is evaluated. This is a relative rate. 

Figure 10 illustrates Stern-Volmer plots for the fluorescence quenching of APh-x by MV2+ and SPV in aqueous solution [74]. With MV2+, the quenching is so effective that it occurs at very low quencher concentrations (in the range of 10 6 M), whereas with SPV, it proceeds to about the same extent at two-orders of magnitude higher quencher concentration (in the range of 10 4 M). 

Table 2 lists the apparent Stern-Volmer quenching constants (Ksv) for APh-x, estimated from the initial slopes of the Stern-Volmer plots, along with the... 

Figure 11 shows Stern-Volmer plots for fluorescence quenching of the amphiphilic cationic copolymer QPh-x [74]. The quenching of QPh-x with MV2+ is expected to be much less effective than that of APh-x. The quenching data for the QPh-x system are presented in Table 3. For comparison, the data for a related... 

Fig. 15. Stern-Volmer plots for (O) po-ly(A/St/Phen) (29) and ( ) APh-2 (8 with x = 2) with MV2+ in aqueous solution excitation wavelength, 297 nm [119]...

Fig. 1. a) UV-Vis absorption and fluorescence emission spectra of riboflavin (RF, 20 pM) and Gum Arabic aqueous solutions at pH 7 (phosphate buffer 100 mM). b) Transient absorption spectra of RF (35 pM) in N2-saturated MeOH-Water (1 1) solution. The insets show the transient decay at 720 nm for the RF species and the Stern-Volmer plot for the quenching of 3RF by GA, eqn 11. 

The Stern-Volmer plot is represented by the following equation ... 

Figure 3. Stern-Volmer plots for quenching of yellowing following photolysis of PVCa solutions in methylene chloride by (a) piperylene and (b) naphthalene. Yellowing is measured as the increase in absorption at 390 nm.

Measurements of the hydrocarbon fluorescence lifetimes provide important information which is useful in interpreting the Stern-Volmer plots. In cases where Equation 1 is valid, the hydrocarbon fluorescence decay profiles must be the same with and without DNA. In some cases, BP for example, this is not the case. For BP the observed decay profile changes significantly when DNA is added (72). 

Figure 4. Stern-Volmer plots and quenching constants derived from the fluorescence quenching of DMA (T), 1,2,3,4-tetra-hydro-BA ( ), 5,6-dihydro-BA (A), 8,9,10,11-tetrahydro-BA ( ) and anthracene ( ) by DNA in 15% methanol at 23° C. Emission and excitation wavelengths and details concerning the experimental conditions are given in refs. 12 and 14. The open symbols, o and V, show I /I for 1,2,3,4-tetrahydro-BA and DMA respectively in denatured DNA([P04"] 4.4 x 10 4 M).

Figure 6.7 Typical intensity-based Stern-Volmer plots for 3-month-old [Ru(dpp)3]2+-doped octyl-triEOS-TEOS composite xerogels. The solid lines represent the best lit to a Demas (TEOS) or Stern-Yolmer model (all others). (Reproduced from ref. 7, with permission.)...

If the fluorescence quantum yield is measured in the absence and presence of known concentrations of quencher, a Stern-Volmer plot of ( )f/Q( )f against [Q] will give a straight line of slope KQ and intercept 1 (Figure 6.1). 

Figure 6.1 A Stern-Volmer plot of fluorescence quenching...

Figure 10.3 Stern-Volmer plot for the quenching of the Norrish type 2 photoreaction of hexan-2-one by penta-1,3-diene...

It is possible to obtain a Stern-Volmer plot specifically for the triplet reaction from the equation ... 

Equation (4.18) can be compared to the Stern-Volmer relation (4.10). The multiplying factor Y-1 accounts for the transient term and leads to a slight upward curvature of the Stern-Volmer plot. 

In contrast to the Stern-Volmer equation (4.10), the ratio Io/I is not linear and shows an upward curvature at high quencher concentrations. At low concentrations, exp(VqNa[Q]) 1 + VqNa[Q], so that the concentration dependence is almost linear (as in the case of the Stern-Volmer plot). 

A linear relationship is thus obtained, as in the case of the Stern-Volmer plot (Eq. 4.10), but there is no change in excited-state lifetime for static quenching, whereas in the case of dynamic quenching the ratio I0/I is proportional to the ratio to/t of the lifetimes. 

Figure 4.2 summarizes the various cases of quenching, together with the possible origins of a departure from a linear Stern-Volmer plot. 

To test whether one can differentiate between a two-site discrete model and a dual distribution function, we calculated intensity Stern-Volmer plots for a two-component model as a function of R. These are also shown in Figure 4.13. What is remarkable is that even for the quite wide R = 0.25, there is no experimentally detectable difference between two discrete sites and two continuously variable distribution of sites. Only when one gets to R = 0.5 does the data deviate noticeably. However, even though the shape has changed, it is still well fit by a dual discrete site model with different parameters. 

However, for reasonably wide single distributions lifetime decays can provide a warning that a single discrete model is inappropriate even when the intensity Stern-Volmer plots give no warning of system complexity. 

Large differences in A sv s for a dual Gaussian distribution site model are required to produce nonlinear intensity Stern-Volmer plots. When the differences in /f.sv s are large enough to produce nonlinear intensity Stern-Volmer plots, wide ranges in the fractional contributions of the sites to the total intensity can yield detectable curvature. 

Figure 5.3. Simulated Stern-Volmer plots of the ratio of the initial fluorescence intensity F0 to the intensity Fin the presence of quencher of concentration [Q] showing (a)static quenching, (b) dynamic quenching (linear), and (c) binding and/or inaccessible quenchers.

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