Investigation into the competitive quenching mechanism of Cu²⁺ and Fe³⁺ on nitrogen-doped carbon dots based on a four-state kinetic model

Due to the in-situ antagonism and site competition during multi-ion coexistence in real water environments, traditional linear sensing models often fail. In this study, nitrogen-doped carbon dots (N-CDs) synthesized via a one-step hydrothermal method were used as a platform to investigate the microscopic response mechanism in Cu²⁺ and Fe³⁺ coexisting systems by constructing a 2D cross-fluorescence response matrix. Firstly, the fluorescence quenching evolution under different interference backgrounds was experimentally observed. The results showed that under a high concentration Cu²⁺ background, the fluorescence response induced by Fe³⁺ exhibited significant nonlinear shifts and quenching stagnation, confirming the intense exclusive competition between the two ions at the nano-interface. Subsequently, to analyze this nonlinear process, a "four-state physical kinetic model" was constructed based on the principle of detailed balance, and a global response analytical expression containing the thermodynamic synergy factor ($ \alpha $) was derived. Finally, a global surface fitting was performed on the experimental response matrix using the theoretical model. The results demonstrated a high degree of agreement between the theoretical fit and experimental data, yielding a synergy factor of $ \alpha $ ≈ 0.015. This extremely low value quantitatively confirms the extreme physical shielding and electrostatic repulsion effects constructed by high-valent ions. This study transforms cross-interference into quantifiable intrinsic thermodynamic parameters providing a solid theoretical foundation for nonlinear signal decoding and interface kinetics research in complex systems.