Flourence polarization(荧光偏振)

2 3 cos2 a 1 r0 5 2
Polarization of 2-photon fluorescence
Molecules can be excited by a simultaneous absorption of 2 photons. The molecule is excited by energy 2 hnexc. The process is nonlinear – probability of excitation is proportional to Iexc2.
Let us consider random orientation of dipole moments – we have to average over q
The probability density function of finding an excited molecule with a dipole under the angle q:
Polarization in a fluorescence experiment
Z
excitation
X
I
I detection Y
The polarization state of fluorescence is described by: Polarization
Ill I P Ill I Ill I Ill I r IT Ill 2I
and viscosity on the observed polarization. Wiegert discovered that
polarization increased with the size of the dye molecule and the viscosity of the solvent, yet decreased as the temperature increased.
excitation I detection I Y
X
Why is the total intensity IT equal to I + 2 I ???
For the reason of symmetry the component polarized in the X direction and Y direction have the same intensity I, but in the given geometry we detect only the one polarized in X direction. Note: anistropy of a mixture of fluorophores fi – fraction of i-th fluorophore
2 0
2
2

p(q ) dq
0
0 2
4 cos q sinq dq 2 cos q sinq dq 0

3 5
Polarization in a fluorescence experiment
Da
De Z
q
r
Ill I Ill 2I
r0 0.4 0 -0.2 P0 0.5 0 -0.333
I0 Polarizer Unpolarized (random) light
I = I0/2 Linear polarized light
Common polarizers:
• double refracting (birefrigent) calcite (CaCO3) crystals- which refract components of light polarized in two perpendicular planes under different angles • filters, which effectively absorb one plane of polarization (e.g., Polaroid type-H sheets based on stretched polyvinyl alcohol impregnated with iodine)
Averaging over f:
sin2 f 1 2
I≈ 1/2 sin2q
Polarization in a fluorescence experiment
Z D
q
Ill I 3 cos2 q 1 r Ill 2I 2
excitation
X
I
f
I Y
detection
He recognized that all of these considerations meant that fluorescence
polarization increased decreased. as the mobility of the emitting species
Βιβλιοθήκη Baidu
Polarization and dipole transitions
B
B
E
n E c
I E2
Natural light contains randomly all possible orientations of electric vector
Unpolarized (random) light
Polarizer
an optical component that selects from passing light only the component polarized in a given direction
Polarization of multiphoton fluorescence
Anisotropy and molecular motion
So far we have considered “frozen” molecules. However, in reality the molecules are mobile and their rotation changes the orientation of the dipole q. Changes in q are reducing the anisotropy caused by photoselection.
I
excitation
X
f
I Y
detection
p(q ) sinq cos2 q
Let us consider random orientation of dipole moments – we have to average over q
2
cos2 q
cos q p(q ) dq
r
f
i
i
ri
Polarization in a fluorescence experiment
Z D
q
Ill I 3 cos2 q 1 r Ill 2I 2
excitation
X
I
I ≈ cos2q
detection
f
I Y
I≈ sin2f sin2q
First we consider the simplest case – a single fluorophore with a fixed position of its transition dipole moment Next we take an ensemble of molecules with random values of f
p(q ) sinq cos2 q
size of the “cone” for given q
photoselection
Polarization in a fluorescence experiment
Z D
q
Ill I 3 cos2 q 1 r Ill 2I 2
r0 = 0.4
r(t ) r0 exp( t )
Where is the rotational correlation time (Debye rotational relaxation time) which is the time for a given orientation to rotate through an angle given by the arccos e-1 (68.42o). For a spherical molecule:
Fluorescence Polarization
Polarization
Light is a harmonic electromagnetic wave. When considering its interaction with matter we can in most cases neglect the magnetic part. The plain in which the electric vector E oscillates defines the polarization of light.
excitation
a
I
a
0 54.7 90
I detection Y
X
f
The derivation was true for molecules with collinear transition dipole moments of absorption and emission, that is however not a general situation. Let us consider an angle a between the two dipoles
hnexc hnexc
hnem
hnem > hnexc
The excitation probability is proportional to cos4q – different photoselection
p2p(q ) sinq cos4 q
cos2 q 5 7
r2 p
3 cos2 q 1 4 2 7
Anisotropy is preferred because it contains the total intensity IT
Anisotropy
Polarization in a fluorescence experiment
Z
Ill I Ill I r IT Ill 2I
In 1920, F. Weigert discovered that the fluorescence from solutions of dyes was polarized. Specifically, he looked at solutions of fluorescein, eosin, rhodamine and other dyes and noted the effect of temperature
+
-
potential dipole orientation probability of excitation Photoselection: The phenomenon of anisotropic distribution of orientation of molecules in excited state in the sample caused by the properties of excitation light. Emission of a point dipole is polarized in the direction of the dipole The emitted intensity is proportional to sin2x, where x is the angle between the dipole and the direction of propagation of the emitted light
Absorption: The probability of a transition of a molecule between two energetic levels (for example S0 S1) is proportional to cos2f, where f is the angle between the dipole moment of the transition and the direction of polarization of the excitation light.