## Stern–Volmer kinetic relationships

https://doi.org/10.1351/goldbook.S06004
This term applies broadly to variations of @Q04991@ of @P04647@ (e.g. @F02453@ or @P04569@) or @P04585@ (usually reaction @Q04991@) with the concentration of a given @R05190@ which may be a substrate or a @Q05006@. In the simplest case, a plot of $$\frac{\mathit{\Phi }^{0}}{\mathit{\Phi }}$$ (or $$\frac{M^{0}}{M}$$ for emission) vs. concentration of @Q05006@, $$\text{[Q]}$$, 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 @Q05006@ inhibits either a @P04585@ or a photophysical process by a single reaction. $$\mathit{\Phi} ^{0}$$ and $$M^{0}$$ are the @Q04991@ and emission intensity @R05041@, respectively, in the absence of the @Q05006@ Q, while $$\mathit{\Phi}$$ and $$M$$ are the same quantities in the presence of the different concentrations of Q. In the case of @Q05007@ the constant $$K_{\text{sv}}$$ is the product of the true @Q05008@ $$k_{\text{q}}$$ and the @E02257@ @L03515@, $$\tau ^{0}$$, in the absence of @Q05006@. $$k_{\text{q}}$$ is the @M03989@ reaction @O04322@ for the @E02035@ of the @E02257@ with the particular @Q05006@ 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 @E02257@ undergoes a @M03989@ reaction with @O04322@ $$k_{\text{r}}$$ 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 @Q04988@ of product formation, $$A$$ the efficiency of forming the reactive @E02257@, $$B$$ the fraction of reactions of the @E02257@ 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 @O04322@ $$k_{\text{r}}$$. When the @L03515@ of an @E02257@ 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 @L03515@ of the @E02257@ in the absence of the @Q05006@ Q.