Stem-Volmer constants

If A is a thexi state, its reactions should obey conventional chemical kinetics, and we can examine several simple, important cases. Suppose firstly that A is produced by a flash or laser pulse technique in a time short compared to the time scale of the other processes. The produced A will disappear with a rate constant k which is the sum of the rate constants for all applicable processes. In the absence of quencher, we write k° = knr + kT + kcr the time for [A ] to decrease by a factor of e, r°, is just jk°. With quencher present, we have k = knr + kT + kCT + fcq[Q] and i = 1 jk. The ratio of lifetimes in the absence and presence of quencher is given by equation (10). A plot of t°/t versus [Q] should thus be linear, with slope kqr° this product is often designated as Kgy and called the Stem—Volmer constant. 

The participation of the singlet states of dyes such as rose bengal (RB, tetraiodotetrachlorofluorescein, sodium salt) and MB during the sensitized oxygenation of amines was demonstrated by Davidson (40). Fluorescence quenching Stem-Volmer constants were reported for several amines, halide anions, and for 3-carotene and were consistent with charge transfer stabilization of an exciplex quenching intermediate. 

Stem-Volmer constant for quenching inside MIP cavities Potentiometric selectivity coefficients... 

If the quenching is expressed in terms of the analytical quencher concentration, the Stem-Volmer constant becomes... 

The emission spectrum of Ru(bpy)21 in HZrP and HexA-ZrP had maxima at 620-625 nm. In both cases, quenching by ferricyanide was used to distinguish between the Ru(bpy)2+ adsorbed on the outer surface and in the interlamellar regions. For HexA-ZrP, the Stern-Volmer plot was nonlinear and this nonlinearity was interpreted as due to the adsorption of Ru(bpy) + at two different places. The Stem-Volmer constant (KSv) for the major component was estimated to be 7200 M 1 and this value is of the same order of magnitude as that of Ru(bpy)f1 -kaolin [85], in which Ru(bpy)21 is known to bind on the external surface, and both values are much smaller than that observed in aqueous solution (23,000 M1) [75b],... 

On the contrary, under diffusion control the nonstationary quenching lasts almost the whole lifetime and its contribution into quantum yield is dominant at least for large concentrations. Some insights into the concentration dependence of the corresponding Stem-Volmer constant, k(c), one can obtain, using in Eqs. (3.10) and (3.4), the simplest Smoluchowski expression (3.23), which is valid at any time in a limit of diffusional control (when ko ko). For this limit the analytic solution was given in Ref. [54]... 

For exponential W(r) this serves as an alternative to the contact estimate of Ko at slow diffusion given in Eq. (3.65). The latter tends to zero as /T) > 0 while Ko from (3.67) approaches the lowest but finite static value, lini/j, oKo(/J) / 0. The Stem-Volmer constant increases monotonously with diffusion from this value up to the kinetic rate constant ko = linio Xl Ko(D). As shows Figure 3.10, at the same ko the more efficient the remote transfer is, the greater the tunneling length l. 

From Eqs. (3.178) and (3.179) it is inferred that the Stem-Volmer constants for the reversible and effective irreversible reactions are related to each other as follows ... 

A different situation arises if one calculates the same constant in the superposition approximation (SA) competing with encounter theory. This approximation was first employed in Refs. 139 and 140 and then applied to a number of particular problems [141-145], However, the present problem is an exceptional one because it has an exact solution that allows the examination of all others. To make this possible, the original SA was employed for this very problem in Ref. 136, and the following Stem-Volmer constant was obtained ... 

The divergency of KB with c —> 0 is astonishing, but this does not complicate calculation of the Stem-Volmer constant (3.183) since it contains only the... 

Figure 3.47. The free-energy dependence of the stationary rate constant for irreversible ionization k = ki defined in Eq. (3.22) (thick line) and the Markovian Stem-Volmer constant for reversible ionization Ko fromEq. (3.85) (dashed line). The open circles represent the non-Markovian Stern-Volmer constant of irreversible ionization Ko = K, from Eq. (3.27) or (3.372) for r = Tj. The energy of the excited singlet state is = 3.5 c and Xc = 35T. (From Ref. 107.)...

Unlike Kg, the Stem-Volmer constant k0 from Eq. (3.373) turns to zero as kc > 0. If there is no recombination to the ground state, then all separated ions... 

Figure 3.62. The light dependence of the Stem—Volmer constant K, i (/, i for diffusional quenching with given exponential rate (Wq — 103 exp[—2(r — cr)/L] ns-1), but at different diffusion in pairs containing the excited molecules (a) D =0.1 Dd, (6) D = D= 10 5cm2/s (dashed line—the same, but in contact approximation), (c) D = WD. Other parameters a = 5A, L = 1.0 A, i = 10ns, ko = f Wq(r)d3r = 1.9 x 105 A3/ns. (From Ref. 200.)...

Although k, is exactly the same as in Eq. (3.492), the Stem-Volmer constant (3.529) differs from it because of the multiplier 0. Both Ko and K, shown by solid and dashed lines in Figure 3.63, increase with the light intensity and the difference between them is attributed to 0. 

Stem-Volmer constant responsible for the nonlinearity of the Stem-Volmer law predicted by DET and UT [see Eqs. (3.30)-(3.33) and Fig. 3.61]. All these drawbacks arise because of the limited validity of IET, which is merely the lowest-order approximation with respect to particle concentration c. 

Figure 3.85. The Stem—Volmer constant of reversible energy quenching at zB = oo, A -/ . related to its irreversible analog K as a function of backward energy transfer rate constant kb related to the forward one, ka. The thick line is an IET result, while the thin lines are obtained with MET at different concentrations of A 4na3NA/3 = 0.05,0.15,0.3 (from bottom to top). The remaining parameters are 47ia3Afi/3 = 0.15, = 2t(/, and kD

Using here Eq. (3.770), we obtain the Stem-Volmer constant... 

Even at large AG, > 0 where excitation of the triplets is practically irreversible (ko 0), the difference between Eqs. (3.828) and (3.831) does not disappear. The Stem-Volmer constants Kcb are identical to the kinetic rate constants kc b only when they both are smaller than ko- This is true near the point of inflection in the %r(AG,-) dependence, which is equally far from the maxima of both constants. Near this point kb kc -C ko, and there should be no difference between the fast and slow spin conversions. This is the point of intersection of all the curves shown in Figure 3.103. As can be seen from this figure, accounting for the spin state is not an essential factor in electrochemiluminescence. This is because the electrochemical preparation of ions is not spin-selective. 

However, at still larger concentrations only DET/UT is capable of reaching the kinetic limit of the Stem-Volmer constant and the static limit of the reaction product distribution. On the other hand, this theory is intended for only irreversible reactions and does not have the matrix form adapted for consideration of multistage reactions. The latter is also valid for competing theories based on the superposition approximation or nonequilibrium statistical mechanics. Moreover, most of them address only the contact reactions (either reversible or irreversible). These limitations strongly restrict their application to real transfer reactions, carried out by distant rates, depending on the reactant and solvent parameters. On the other hand, these theories can be applied to reactions in one- and two-dimensional spaces where binary approximation is impossible and encounter theories inapplicable. 

A sv The difference of the reciprocal of Stem-Volmer constants for monomer ( AT 60) and... 

Association constants (Ka), were determined by absorption spectroscopy and Stem-Volmer constants (Ksv) by fluorescence spectroscopy. 

TABLE 1 Emission lifetimes (in aerobic aqueous solution), Stem Volmer constants and rate constants for quenching by MV2+ of the excited [Ru(bpy3]2+—like centre of the N-ethylated vinylpyridine copolymer at various salt concentrations. 

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