Stern-Volmer relationship

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The Stern-Volmer relationship 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:

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

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

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:

$\frac{I_f^0}{I_f} = 1+k_q\tau_f\cdot[\mathrm{Q}]$

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, $τ 0$ is the fluorescence lifetime of A, without a quencher present and $[Q]$ is the concentration of the quencher.^[1]

It is from this relationship that the rate co-efficient of the quencher can be calculated as $k_q = \frac{8RT}{3\eta}$ , where $R$ is the ideal gas constant, $T$ is temperature in Kelvin and $η$ is the viscosity of the solution.