基于四态动力学模型的氮掺杂碳点表面Cu<sup>2+</sup>/Fe<sup>3+</sup>竞争猝灭机制研究

韩泽玉; 徐达; 牛鹤桐; 刘琼; 高丽丽

doi:10.37188/CO.2026-0060

基于四态动力学模型的氮掺杂碳点表面Cu²⁺/Fe³⁺竞争猝灭机制研究

doi: 10.37188/CO.2026-0060

cstr: 32171.14.CO.2026-0060

北华大学理学院, 吉林吉林, 132013

基金项目: 北华大学研究生创新项目：研创合字【2024】008

详细信息

作者简介:
韩泽玉（2000—），男，吉林白山人，硕士研究生，2022年于北华大学大学获得学士学位，主要从事碳量子点光学性质研究。E-mail：2209157337@qq.com

刘　琼（1983—），男，吉林省吉林市人，博士，讲师，2011 年于吉林大学获得博士学位，主要从事复杂发光体系的统计物理建模、碳纳米点发光微观机理及多变量传感应用等方面的研究。E-mail：liuqiong@beihua.edu.cn

高丽丽（1972—），女，吉林省吉林市人，博士，教授，2011 年于吉林大学获得博士学位，主要从事半导体材料与器件的制备与物性研究、发光碳纳米点机理及其应用等方面的研究。E-mail：gaolili@beihua.edu.cn

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出版历程
- 网络出版日期: 2026-05-27

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

Department of Physics, School of Sciences, Beihua University, Jilin 132013, China

Funds: Supported by Research and Innovation Collaboration Document [2024] No. 008

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Corresponding author: liuqiong@beihua.edu.cn; gaolili@beihua.edu.cn

摘要

摘要:
由于实际水环境中多离子共存时的原位拮抗与位点竞争导致传统线性传感模型失效，本文以一步水热法合成的氮掺杂碳点（N-CDs）为平台，通过构建二维交叉荧光响应矩阵，研究了Cu²⁺与Fe³⁺共存体系下的微观响应机制。首先，实验观测了不同干扰背景下的荧光猝灭演化规律。结果显示，在高浓度Cu²⁺背景下，Fe³⁺诱导的荧光响应表现出显著的非线性偏移与猝灭阻滞，证实两种离子在纳米界面存在激烈的排他性抢夺。随后，为解析该非线性过程，基于细致平衡原理构建了“四态物理动力学模型”，并推导出内含热力学协同因子($ \alpha $)的全局响应解析式。最后，利用理论模型对实验响应矩阵进行了全局曲面拟合。结果表明，理论拟合与实验数据高度吻合，提取出协同因子$ \alpha $ ≈ 0.015。该极低数值定量证实了由高价态离子构筑的极端物理屏蔽与静电排斥效应。本研究将交叉干扰转化为可量化的本征热力学参数，为复杂体系非线性信号解码及界面动力学研究提供了坚实的理论基础。
- 氮掺杂碳点 /
- 荧光猝灭 /
- 交叉干扰 /
- 非平衡统计
Abstract:
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.
- nitrogen-doped carbon dots /
- Fluorescence quenching /
- Cross-interference /
- Non-equilibrium statistics

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图 1 碳点的TEM图片, 插图为粒径分布直方图

Figure 1. Transmission electron microscopy (TEM) image of the nitrogen-doped carbon dots (N-CDs). The inset shows the corresponding particle size distribution histogram.

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图 2 氮掺杂碳点（N-CDs）的X射线衍射（XRD）图谱，插图为氮掺杂碳点（N-CDs）的红外光谱

Figure 2. X-ray diffraction (XRD) pattern of the nitrogen-doped carbon dots (N-CDs). The inset shows the corresponding Fourier transform infrared (FTIR) spectrum.

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图 3 N-CDs 对单组分金属离子的定量猝灭响应。 (a) 体系相对荧光强度 (F/F0) 随Cu2+浓度的线性响应及检出限拟合曲线；(b) 体系相对荧光强度(F/F0)随Fe3+浓度的线性响应及检出限拟合曲线。

Figure 3. Quantitative quenching response of N-CDs to individual metal ions. Linear fitting curves of the relative fluorescence intensity (F/F0) versus the concentration of (a) Cu2+ and (b) Fe3+ for the determination of limits of detection (LOD).

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图 4 (a) N-CDs 荧光发射光谱的高斯分峰拟合图(展示了465 nm与500 nm两个发射通道)；(b) 固定Cu²⁺(200 μM) 背景下，Fe³⁺滴定过程中的荧光光谱演化图

Figure 4. (a) Gaussian peak-fitting of the N-CDs fluorescence emission spectrum, showing the two emission channels at 465 nm and 500 nm; (b) Evolution of fluorescence spectra during Fe3+ titration under a fixed Cu2+ (200 μM) background.

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图 5 (a)无干扰背景与(b) 600 μM Cu²⁺ 强背景下Fe³⁺ 的荧光猝灭响应曲线

Figure 5. Fluorescence quenching response curves of Fe³⁺ in (a) an unspiked background and (b) a strong 600 μM Cu²⁺ background

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图 6 四种微观状态的空间构型及其稳态分布示意图

Figure 6. Schematic diagram illustrating the spatial configurations and steady-state distributions of the four microscopic states

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图 7 (a) 实验测得的二维交叉干扰响应矩阵与(b) 基于四态模型的理论拟合曲面

Figure 7. (a) The experimentally measured two-dimensional cross-interference response matrix and (b) the theoretical fit based on the four-state model

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