Stern–Volmer relationship

The Stern–Volmer relationship, named after Otto Stern and Max Volmer,[1] 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:

${\displaystyle \mathrm {A} ^{*}+\mathrm {Q} \rightarrow \mathrm {A} +\mathrm {Q} }$

or

${\displaystyle \mathrm {A} ^{*}+\mathrm {Q} \rightarrow \mathrm {A} +\mathrm {Q} ^{*}}$

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:

${\displaystyle {\frac {I_{f}^{0}}{I_{f}}}=1+k_{q}\tau _{0}\cdot [\mathrm {Q} ]}$

Where ${\displaystyle I_{f}^{0}}$ is the intensity, or rate of fluorescence, without a quencher, ${\displaystyle I_{f}}$ is the intensity, or rate of fluorescence, with a quencher, ${\displaystyle k_{q}}$ is the quencher rate coefficient, ${\displaystyle \tau _{0}}$ is the lifetime of the emissive excited state of A, without a quencher present and ${\displaystyle [\mathrm {Q} ]}$ is the concentration of the quencher.[2]

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 ${\displaystyle k_{q}={8RT}/{3\eta }}$, where ${\displaystyle R}$ is the ideal gas constant, ${\displaystyle T}$ is temperature in Kelvins and ${\displaystyle \eta }$ 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.[3]