\[\frac{I_0}{I} = \frac{\tau_0}{\tau} = 1 + k_q\tau_0[\mathrm Q] = 1 + K_\mathrm{SV}[\mathrm Q]\]
含义Meaning
猝灭剂 Q 与激发态碰撞使其非辐射失活，荧光强度和寿命随 [Q] 下降；I₀/I 对 [Q] 为直线（动态猝灭）。用于测氧传感器、蛋白质中色氨酸的可及性等。
A quencher Q deactivates excited states by collision, lowering fluorescence intensity and lifetime; I₀/I is linear in [Q] (dynamic quenching). Used in oxygen sensors and tryptophan-accessibility studies.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(I_0, I\) | 无 / 有猝灭剂时的荧光强度intensity without / with quencher | |
| \(k_q\) | 双分子猝灭速率常数bimolecular quenching constant | L·mol⁻¹·s⁻¹ |
| \(\tau_0\) | 无猝灭时寿命unquenched lifetime | s |
| \(K_\mathrm{SV}\) | 斯特恩–福尔默常数Stern–Volmer constant | L·mol⁻¹ |
推导Derivation
激发态 M* 衰减：\(k_r + k_{nr} + k_q[\mathrm Q]\)；荧光量子产率 \(\Phi = k_r/(k_r + k_{nr} + k_q[\mathrm Q])\)。
M* decays by k_r + k_nr + k_q[Q].
无猝灭剂时 \(\Phi_0 = k_r\tau_0\)，相除得 \(\Phi_0/\Phi = 1 + k_q\tau_0[\mathrm Q]\)。
Dividing by the unquenched yield gives the result.
\(k_q\) 接近扩散控制（约 10¹⁰ L·mol⁻¹·s⁻¹）说明每次碰撞都猝灭。
k_q near 10¹⁰ means quenching on every encounter.
适用条件与局限Assumptions & limitations
静态猝灭（基态络合）只降低强度不改变寿命，图线上弯；同时存在两种猝灭时需二次式。
Static quenching lowers intensity but not lifetime and bends the plot upward.