Stern–Volmer kinetic relationships

This term applies broadly to variations of quantum yields of photophysical processes (e.g. fluorescence or phosphorescence ) or photochemical reactions (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 $Φ 0 Φ$ (or $M 0 M$ for emission) vs. concentration of quencher, $[Q]$ , is linear obeying the equation:

$Φ 0 Φ or M 0 M = 1 + K sv Q$

In equation (1) $K sv$ 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. $Φ 0$ and $M 0$ are the quantum yield 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 $K sv$ is the product of the true quenching constant $k q$ and the excited state lifetime, $τ 0$ , in the absence of quencher. $k q$ 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):

$Φ 0 Φ or M 0 M = 1 + k q τ 0 Q$

When an excited state undergoes a bimolecular reaction with rate constant $k r$ to form a product, a double-reciprocal relationship is observed according to the equation:

$1 Φ p = ( 1 + 1 k r τ 0 [S] ) 1 A · B$

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 $k r τ 0$ . 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 $k r$ . 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:

$τ 0 τ = 1 + k q τ 0 [Q]$

where $τ 0$ is the lifetime of the excited state in the absence of the quencher Q.