Stern–Volmer kinetic relationships

This term applies broadly to variations of quantum yields of photophysicalprocesses (e.g. fluorescence or phosphorescence ) or photochemical reactions (usually reaction quantum yield) with the concentration of a given reagent which may be a substrate or a quencher. In the simplest case, a plot of Φ 0 Φ (or M 0 M for emission) vs. concentration of quencher, [Q], is linear obeying the equation:
Φ 0 Φ or M 0 M = 1 + K sv Q
In equation (1) K sv is referred to as the Stern–Volmer constant. Equation (1) applies when a quencher inhibits either a photochemical reaction or a photophysical process by a single reaction. Φ 0 and M 0 are the quantum yield and emission intensity radiant exitance, respectively, in the absence of the quencher Q, while Φ and M are the same quantities in the presence of the different concentrations of Q. In the case of dynamic quenching the constant K sv is the product of the true quenching constantk q and the excited statelifetime, τ 0, in the absence of quencher. k q is the bimolecular reaction rate constant for the elementary reaction of the excited state with the particular quencher Q. Equation (1) can therefore be replaced by the expression (2):
Φ 0 Φ or M 0 M = 1 + k q τ 0 Q
When an excited state undergoes a bimolecular reaction with rate constantk r to form a product, a double-reciprocal relationship is observed according to the equation:
1 Φ p = ( 1 + 1 k r τ 0 [S] ) 1 A · B
where Φ p is the quantum efficiency of product formation, A the efficiency of forming the reactive excited state, B the fraction of reactions of the excited state with substrate S which leads to product, and [S] is the concentration of reactive ground-state substrate. The intercept/slope ratio gives k r τ 0. If [S] = [Q], and if a photophysical process is monitored, plots of equations (2) and (3) should provide independent determinations of the product-forming rate constantk r. When the lifetime of an excited state is observed as a function of the concentration of S or Q, a linear relationship should be observed according to the equation:
τ 0 τ = 1 + k q τ 0 [Q]
where τ 0 is the lifetime of the excited state in the absence of the quencher Q.
See also: self-quenching
PAC, 1996, 68, 2223 (Glossary of terms used in photochemistry (IUPAC Recommendations 1996)) on page 2277