Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 2A / Section A / 16

Let $s=[S_1]$ and treat the quencher concentration as a constant reservoir. Weak steady excitation, one emitting population, and the three specified processes giveDividing the fluorescence photon-production rate by the absorbed photon rate therefore givesThis assumes no saturation, photochemical loss, reabsorption, static association or additional excited-state decay, and that each counted absorbed photon reaches the stated $S_1$ population. In this restricted scheme ${\varphi }_0=1$ and the unquenched lifetime is ${\tau }_0=1/k_F$.

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.