Stern-Volmer relationship

The Stern-Volmer relationship, named after Otto Stern and Max Volmer, [ O. Stern and M. Volmer "Über die Abklingzeit der Fluoreszenz", "Physik. Zeitschr." 20 183-188 (1919) as cited in Mehra and Rechenberg, Volume 1, Part 2, 2001, 849.] allows us to explore the kinetics of a photophysical "intermolecular" deactivation process.

Processes such as fluorescence and phosphorescence are examples of "intramolecular" deactivation (quenching) processes. An "intermolecular" deactivation is where the presence of another chemical species can accelerate the decay rate of a chemical in its excited state. In general, this process can be represented by a simple equation:

:$mathrm\{A\}^*\; +\; mathrm\{Q\}\; ightarrow\; mathrm\{A\}\; +\; mathrm\{Q\}$

or

:$mathrm\{A\}^*\; +\; mathrm\{Q\}\; ightarrow\; mathrm\{A\}\; +\; mathrm\{Q\}^*$

where A is one chemical species, Q is another (known as a quencher) and * designates an excited state.

The kinetics of this process follows the Stern-Volmer relationship::$frac\{I\_f^0\}\{I\_f\}\; =\; 1+k\_q\; au\_0cdot\; [mathrm\{Q\}]$Where $I\_f^0$ is the intensity, or rate of fluorescence, without a quencher, $I\_f$ is the intensity, or rate of fluorescence, with a quencher, $k\_q$ is the quencher rate co-efficient, $au\_0$ is the fluorescence lifetime of A, without a quencher present and $[mathrm\{Q\}]$ is the concentration of the quencher.Permyakov, Eugene A.. [Luminescent Spectroscopy of Proteins] , CRC Press, 1993.]

For "diffusion-limited" quenching ("i.e.", quenching in which the time for quencher particles to diffuse toward and collide with excited particles is the limiting factor, and almost all such collisions are effective), the quenching rate coefficient is given by $k\_q\; =\; frac\{8RT\}\{3eta\}$, where $R$ is the ideal gas constant, $T$ is temperature in Kelvin and $eta$ is the viscosity of the solution. This formula is derived from the Stokes-Einstein relation. In reality, only a fraction of the collisions with the quencher are effective at quenching, so the true quenching rate coefficient must be determined experimentally. [ [http://www.stetson.edu/~wgrubbs/datadriven/quenching/quenchingwtg.html Fluorescence lifetimes and dynamic quenching] ]

See also

Optode, a chemical sensor that makes use of this relationship

Sources and notes