  Carbon quantum dots have become attractive in various applications, such as
drug delivery, biological sensing, photocatalysis, and solar cells. Among
these, pH sensing via luminescence lifetime measurements of
surface-functionalised carbon dots is one application currently investigated
for their long lifetime and autonomous operation. In this manuscript, we
explore the theoretical connection between excitation lifetimes and the pH
value of the surrounding liquid via the protonation and deprotonation of
functional groups. Example calculations applied to m-phenylenediamine,
phloroglucinol and tethered disperse blue 1 are shown by applying a separation
approach treating the electronic wavefunction of functional groups separately
from the internal electronic structure of the (large) carbon dot. The bulk of
the carbon dot is treated as an environment characterised by its optical
spectrum that shifts the transition rates of the functional group. A simple
relationship between pH, pKa and mixed fluorescence lifetime is derived from
transition rates of the protonated and deprotonated states. pH sensitivity
improves when the difference in transition rates is greatest between protonated
and deprotonated species, with the greatest sensitivity found where the pKa is
close to the pH region of interest. The introduced model can directly be
extended to consider multicomponent liquids and multiple protonation states.
