## Stern–Volmer kinetic relationships

https://doi.org/10.1351/goldbook.S06004
This term applies broadly to variations of quantum yields of photophysical processes (e.g. fluorescence or phosphorescence) or photochemical reactions (usually reaction quantum yields) 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: $\frac{\mathit{\Phi }^{0}}{\mathit{\Phi }}\quad \text{or}\quad \frac{M^{0}}{M}=1+K_{\text{sv}}\ [\text{Q}]$ In equation (1) Ksv is referred to as the Stern–Volmer constant. Equation (1) applies when a quencher inhibits either a photochemical reactions or a photophysical process by a single reaction. Φ 0 and M 0 are the quantum yields 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 Ksv is the product of the true quenching constant kq and the excited state lifetime, τ 0, in the absence of quencher. kq 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): $\frac{\mathit{\Phi }^{0}}{\mathit{\Phi }}\quad \text{or}\quad \frac{M^{0}}{M}=1+k_{\text{q}}\ \tau ^{0}\ \left[\text{Q}\right]$ When an excited state undergoes a bimolecular reaction with rate constant kr to form a product, a double-reciprocal relationship is observed according to the equation: $\frac{1}{\mathit{\Phi }_{\text{p}}} = (1+\frac{1}{k_{\text{r}}\ \tau ^{0}\ \text{[S]}})\ \frac{1}{A\cdot B}$ 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 kr.τ0. 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 constant kr. 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: $\frac{\tau ^{0}}{\tau} = 1+k_{\text{q}}\ \tau ^{0}\ [\text{Q}]$ where τ 0 is the lifetime of the excited state in the absence of the quencher Q.