## Stern–Volmer kinetic relationships

https://doi.org/10.1351/goldbook.S06004
This term applies broadly to variations of @[email protected] of @[email protected] (e.g. @[email protected] or @[email protected]) or @[email protected] (usually reaction @[email protected]) with the concentration of a given @[email protected] which may be a substrate or a @[email protected] In the simplest case, a plot of $$\frac{\mathit{\Phi }^{0}}{\mathit{\Phi }}$$ (or $$\frac{M^{0}}{M}$$ for emission) vs. concentration of @[email protected], $$\text{[Q]}$$, 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) $$K_{\text{sv}}$$ is referred to as the Stern–Volmer constant. Equation (1) applies when a @[email protected] inhibits either a @[email protected] or a photophysical process by a single reaction. $$\mathit{\Phi} ^{0}$$ and $$M^{0}$$ are the @[email protected] and emission intensity @[email protected], respectively, in the absence of the @[email protected] Q, while $$\mathit{\Phi}$$ and $$M$$ are the same quantities in the presence of the different concentrations of Q. In the case of @[email protected] the constant $$K_{\text{sv}}$$ is the product of the true @[email protected] $$k_{\text{q}}$$ and the @[email protected] @[email protected], $$\tau ^{0}$$, in the absence of @[email protected] $$k_{\text{q}}$$ is the @[email protected] reaction @[email protected] for the @[email protected] of the @[email protected] with the particular @[email protected] 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 @[email protected] undergoes a @[email protected] reaction with @[email protected] $$k_{\text{r}}$$ 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 $$\mathit{\Phi} _{\text{p}}$$ is the @[email protected] of product formation, $$A$$ the efficiency of forming the reactive @[email protected], $$B$$ the fraction of reactions of the @[email protected] with substrate S which leads to product, and $$\text{[S]}$$ is the concentration of reactive ground-state substrate. The intercept/slope ratio gives $$k_{\text{r}}\ \tau ^{0}$$. If $$\text{[S]}=\text{[Q]}$$, and if a photophysical process is monitored, plots of equations (2) and (3) should provide independent determinations of the product-forming @[email protected] $$k_{\text{r}}$$. When the @[email protected] of an @[email protected] 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 $$\tau ^{0}$$ is the @[email protected] of the @[email protected] in the absence of the @[email protected] Q.