Stern–Volmer kinetic relationships
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.
See also:
PAC, 1996, 68, 2223. (Glossary of terms used in photochemistry (IUPAC Recommendations 1996)) on page 2277 [Terms] [Paper]