荧光光谱

荧光光谱原理

${\displaystyle n_{b}/n_{a}=e^{-(E_{b}-E_{a})}=e^{-h\nu /kT}}$

${\displaystyle -{\frac {dn_{a}}{dt}}=I(\nu )n_{a}B_{ab}-I(\nu )n_{b}B_{ba}-n_{b}A_{ba}}$

${\displaystyle B_{ab}=B_{ba}={\frac {2\pi }{3\hbar ^{2}}}D_{ab}}$

${\displaystyle D_{ab}=\mid <\psi _{b}\mid {\underline {\mu }}\mid \psi _{a}>\mid }$

${\displaystyle I(\nu )={\frac {8{\pi }h{\nu ^{3}}}{c^{3}(e^{h{\nu }/kT}-1)}}}$

${\displaystyle A_{ba}=({\frac {32{\pi ^{3}}{\nu ^{3}}}{3c^{3}\hbar }})\mid <\psi _{b}\mid {\underline {\mu }}\mid \psi _{a}>\mid }$

Sb上的分子去激发速率

${\displaystyle {\frac {dn_{b}}{dt}}=-A_{ba}n_{b}}$

${\displaystyle n_{b}(t)=n_{b}(0)e^{-A_{ba}t}}$

${\displaystyle \tau _{R}={\frac {1}{A_{ba}}}}$

Sb通过发出荧光回到Sa的过程的反应速率，即固有荧光速率常数 kF

${\displaystyle k_{F}=A_{ba}={\frac {1}{\tau _{R}}}}$

Sb回到Sa的其他非辐射途径包括内转变，系统间转变，猝熄作用，其速率常数分别为kIC,kIS,kQ[Q] 则Sb总的去激化（熄灭）常数为kF+kIC+kIS+kQ[Q]

${\displaystyle \phi _{F}={\frac {k_{F}}{k_{F}+k_{I}C+k_{I}S+k_{Q}[Q]}}}$

${\displaystyle -{\frac {d[S_{b}]}{dt}}=(k_{F}+k_{I}C+k_{I}S+k_{Q}[Q])[S_{b}]}$

${\displaystyle S_{b}(t)=S_{b}(0)e^{-t/\tau _{F}}}$

Sb是激发态上的分子数

荧光强度

${\displaystyle A=\epsilon cl=lg{\frac {I_{0}}{I}}}$

${\displaystyle I=I_{0}e^{-2.303\epsilon cl}}$

${\displaystyle F(\lambda )=2.303\epsilon clI_{0}\phi _{F}f(\lambda )d=\epsilon \phi _{F}f(\lambda )cI_{0}k}$

k=2.303ld

${\displaystyle I(t)={\frac {dS_{b}}{dt}}\phi _{F}=S_{b}(0)({\frac {\phi _{F}}{\tau _{F}}}e^{-t/\tau _{F}}=k_{F}S_{b}(0)e^{-t/\tau _{F}}}$

${\displaystyle E_{m}(t)=Ae^{-t/\tau _{F}}}$

${\displaystyle E_{m}(t)=A_{1}e^{-t/\tau _{1F}}+A_{2}e^{-t/\tau _{2F}}}$

Em是荧光强度，上述公式为荧光衰减（decay）公式

外环境影响

${\displaystyle {\frac {F_{0}}{F}}={\frac {\phi _{0}}{\phi }}={\frac {k_{F}+k_{I}C+k_{I}S+k_{Q}[Q]}{k_{F}+k_{I}C+k_{I}S}}=1+k_{Q}[Q]}$

τ0可测，以F0/F对[Q]作图求得kQ

荧光共振能量迁移

${\displaystyle E={\frac {k_{T}}{k_{T}+k_{F}^{D}<+k_{I}C^{D}<+k_{I}S^{D}}}}$

${\displaystyle k_{T}={\frac {1}{\tau _{0}}}{\frac {R_{0}}{R}}}$
${\displaystyle R_{0}=9.7*10^{3}(J\kappa ^{2}n^{-4}\phi _{D})^{\frac {1}{6}}cm}$
${\displaystyle J=\int \epsilon (\nu )f_{D}(\nu )\nu ^{-4}\,d\nu }$

${\displaystyle E={\frac {R_{0}^{6}}{R_{0}^{6}+R^{6}}}}$

${\displaystyle {\frac {\phi _{D+A}}{\phi _{D}}}=1-E}$
${\displaystyle {\frac {F_{D+A}}{F_{A}}}=1+{\frac {\epsilon _{D}c_{D}}{\epsilon _{A}c_{A}}}E}$
${\displaystyle {\frac {\tau _{D,A}}{\tau _{D}}}=1-E}$

参考文献

• C.P Cantor & P.R. Schimmel, BIOPHYSICAL CHEMISTRY, Part II. Techniques for the study of biological structure and function. Page 433-465.