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Without quencher, ${\varphi }_{P,0}=k_P/(k_P+k_D)$. Taking the ratio gives the Stern-Volmer equationThus the plot has unit intercept and slope $k_Q{\tau }_0$. A triplet formation yield less than one would cancel from this ratio if it remained independent of quencher concentration. The result assumes dynamic triplet quenching and no additional quencher-induced absorption or singlet loss.^[ref]

Rearrangement gives the Stern-Volmer equationThus a straight-line plot against $[Q]$ has unit intercept and slope $K_{\mathrm{SV}}=k_Q{\tau }_0$. Determine $k_Q=K_{\mathrm{SV}}/{\tau }_0$ using an independently measured unquenched lifetime, or use known $k_F$ in the restricted model. Yield measurements alone do not separate two unknown rate constants. Equivalently the slope of $1/{\varphi }_Q$ is $k_Q/k_F$.

Use the absorbed intensity rather than incident intensity to normalize samples, and correct solvent/background signals, quencher absorption and fluorescence reabsorption. Under dynamic fluorescence quenching the lifetime ratio should follow the same straight line as the yield ratio. A reduced intensity without the corresponding lifetime change suggests static fluorescence quenching or an optical artefact; curvature can also indicate multiple populations or more complicated kinetics.

A quencher-independent intersystem-crossing rate adds to the unquenched decay rate:The normalized Stern-Volmer equation retains the same form, so intersystem crossing does not bias $k_Q$ if the actual unquenched lifetime is used. It reduces ${\varphi }_0$ below one and changes the slope through ${\tau }_0$; assuming ${\tau }_0=1/k_F$ would then give the wrong result. A quencher that itself changes intersystem crossing or returns triplet population to the singlet requires a larger kinetic scheme.

Official terminology entry S06004. Describes dependence of photophysical quantum yields on reagent concentration, including the linear dynamic-quenching relation underlying the Stern-Volmer equation.