pH-sensitive spontaneous decay of functionalised carbon dots in solutions

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.