This term applies broadly to variations of quantum yield of photophysical processes (e.g. fluorescence or phosphorescence) or photochemical reaction (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 \(\frac{\mathit{\Phi}^{0}}{\mathit{\Phi}}\) (or \(\frac{M^{0}}{M}\) for emission) vs. concentration of quencher, \(\ce{[Q]}\), is linear obeying the equation: \[\frac{\mathit{\Phi}^{0}}{\mathit{\Phi}} \quad {\rm{or}} \quad \frac{M^{0}}{M} = 1 + K_{\rm{sv}} [\rm{Q}]\] In equation (1) \(K_{\rm{sv}}\) 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. \(\mathit{\Phi}^{0}\) and \(M^{0}\) are the quantum yield and emission intensity radiant exitance, respectively, in the absence of the quencher Q, while \(\mathit{\Phi}\) and \(M\) are the same quantities in the presence of the different concentrations of Q. In the case of dynamic quenching the constant \(K_{\rm{sv}}\) is the product of the true quenching constant \(k_{\rm{q}}\) and the excited state lifetime, \(\tau^{0}\), in the absence of quencher. \(k_{\rm{q}}\) 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): \[\frac{\mathit{\Phi}^{0}}{\mathit{\Phi}} \quad {\rm{or}} \quad \frac{M^{0}}{M} = 1 + k_{\rm{q}} \tau^{0} [{\rm{Q}}]\] When an excited state undergoes a bimolecular reaction with rate constant \(k_{\rm{r}}\) to form a product, a double-reciprocal relationship is observed according to the equation: \[\frac{1}{\mathit{\Phi}_{\rm{p}}} = \left(1 + \frac{1}{k_{\rm{r}} \tau^{0} [{\ce{S}}]}\right) \frac{1}{A \cdot B}\] where \(\mathit{\Phi}_{\rm{p}}\) 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 \(\ce{[S]}\) is the concentration of reactive ground-state substrate. The intercept/slope ratio gives \(k_{\rm{r}} \tau ^{0}\). If \(\ce{[S]} = \ce{[Q]}\), and if a photophysical process is monitored, plots of equations (2) and (3) should provide independent determinations of the product-forming rate constant \(k_{\rm{r}}\). 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: \[\frac{\tau^{0}}{\tau} = 1 + k_{\rm{q}} \tau^{0} [\ce{Q}]\] where \(\tau^{0}\) is the lifetime of the excited state in the absence of the quencher Q.