Theoretical Modeling of pH-Sensitive Spontaneous Decay of Carbon Dots in Solution

Abstract

Since many biological and chemical processes strongly depend on pH, its precise detection is essential for a wide range of applications. Due to their distinct luminescence characteristics, carbon quantum dots, or CDs, have become attractive options for pH detection. In this thesis, fluorescence lifetime measurements of surface-functionalized CDs are investigated concerning their capability for pH monitoring. A detailed analysis is conducted of the theoretical understanding of the excitation lifetimes of these functional groups in response to variations of the surrounding medium's pH. The effects of protonation and deprotonation of the functional groups is the focus of these investigations. The pH-dependence of excitation lifetimes of functional groups, such as m-phenylenediamine, phloroglucinol, and disperse blue 1 attached to CDs, is modeled by utilising concepts from time-dependent density functional theory (TD-DFT) and macroscopic Quantum Electrodynamics. A mathematical relation between pH, pKa, and excitation lifetimes has been derived and applied to organic dye molecules functionalising a carbon dot. The obtained results manifest the intuition that the pKa determines the sensitive pH range and the pH sensitivity is proportional to the ratio of the fluorescence lifetimes of the protonated and deprotonated states. This model sheds light on the fundamental processes underpinning CDs' pH-dependent fluorescence and offers important insights into how they behave in different pH ranges. The theoretical framework developed within this thesis provides a comprehensive method for estimating and comprehending optical behaviour of pH sensitive materials.

Since many biological and chemical processes strongly depend on pH, its precise detection is essential for a wide range of applications. Due to their distinct luminescence characteristics, carbon quantum dots, or CDs, have become attractive options for pH detection. In this thesis, fluorescence lifetime measurements of surface-functionalized CDs are investigated concerning their capability for pH monitoring. A detailed analysis is conducted of the theoretical understanding of the excitation lifetimes of these functional groups in response to variations of the surrounding medium's pH. The effects of protonation and deprotonation of the functional groups is the focus of these investigations. The pH-dependence of excitation lifetimes of functional groups, such as m-phenylenediamine, phloroglucinol, and disperse blue 1 attached to CDs, is modeled by utilising concepts from time-dependent density functional theory (TD-DFT) and macroscopic Quantum Electrodynamics. A mathematical relation between pH, pKa, and excitation lifetimes has been derived and applied to organic dye molecules functionalising a carbon dot. The obtained results manifest the intuition that the pKa determines the sensitive pH range and the pH sensitivity is proportional to the ratio of the fluorescence lifetimes of the protonated and deprotonated states. This model sheds light on the fundamental processes underpinning CDs' pH-dependent fluorescence and offers important insights into how they behave in different pH ranges. The theoretical framework developed within this thesis provides a comprehensive method for estimating and comprehending optical behaviour of pH sensitive materials.