Stern–Volmer kinetic relationships

This term applies broadly to variations of quantum yields of photophysicalprocesses (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 (or for emission) vs. concentration of quencher, , is linear obeying the equation: In equation (1) 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. and are the quantum yield and emission intensity radiant exitance, respectively, in the absence of the quencher Q, while and are the same quantities in the presence of the different concentrations of Q. In the case of dynamic quenching the constant is the product of the true quenching constant and the excited statelifetime, , in the absence of quencher. 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): When an excited state undergoes a bimolecular reaction with rate constant to form a product, a double-reciprocal relationship is observed according to the equation: where is the quantum efficiency of product formation, the efficiency of forming the reactive excited state, the fraction of reactions of the excited state with substrate S which leads to product, and is the concentration of reactive ground-state substrate. The intercept/slope ratio gives . If , and if a photophysical process is monitored, plots of equations (2) and (3) should provide independent determinations of the product-forming rate constant. 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: where is the lifetime of the excited state in the absence of the quencher Q.