11 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Electrophoretic light scattering | 2/3 | https://en.wikipedia.org/wiki/Electrophoretic_light_scattering | reference | science, encyclopedia | 2026-05-05T10:04:29.562309+00:00 | kb-cron |
|
q
|
=
4
π
n
λ
0
sin
(
θ
2
)
(
5
)
{\displaystyle \ |q|={\frac {4\pi n}{\lambda _{0}}}\sin \left({\frac {\theta }{2}}\right)\qquad (5)}
Since velocity
V
{\displaystyle \ V\,}
is proportional to the applied electric field,
E
{\displaystyle \ E\,}
, the apparent electrophoretic mobility
μ
o
b
s
{\displaystyle \ \mu _{obs}\,}
is define by the equation
V
→
=
μ
o
b
s
E
→
(
6
)
{\displaystyle \ {\vec {V}}=\mu _{obs}{\vec {E}}\qquad (6)}
Finally, the relation between the Doppler shift frequency and mobility is given for the case of the optical configuration of Fig. 3 by the equation
υ
D
=
μ
o
b
s
n
E
λ
0
sin
θ
(
7
)
{\displaystyle \upsilon _{D}=\mu _{obs}{\frac {nE}{\lambda _{0}}}\sin \theta \qquad (7)}
where
E
{\displaystyle \ E\,}
is the strength of the electric field,
n
{\displaystyle \ n\,}
the refractive index of the medium,
λ
0
{\displaystyle \ \lambda _{0}\,}
, the wavelength of the incident light in vacuum, and
θ
{\displaystyle \ \theta \,}
the scattering angle.
The sign of
v
D
{\displaystyle \ v_{D}\,}
is a result of vector calculation and depends on the geometry of the optics. The spectral frequency can be obtained according to Eq. (2). When
|
υ
M
|
>
|
υ
D
|
{\displaystyle \ |\upsilon _{M}|>|\upsilon _{D}|\,}
, Eq. (2) is modified and expressed as
υ
p
=
υ
o
=
±
(
υ
D
−
|
υ
M
|
)
(
8
)
{\displaystyle \upsilon _{p}=\upsilon _{o}=\pm (\upsilon _{D}-|\upsilon _{M}|)\qquad (8)}
The modulation frequency
υ
M
{\displaystyle \upsilon _{M}\,}
can be obtained as the damping frequency without an electric field applied. The particle diameter is obtained by assuming that the particle is spherical. This is called the hydrodynamic diameter,
d
H
{\displaystyle \ d_{H}\,}
.
d
H
=
k
B
T
3
π
η
D
(
10
)
{\displaystyle \ d_{H}={\frac {k_{B}T}{3\pi \eta D}}\qquad (10)}
where
k
B
{\displaystyle \ k_{B}\,}
is Boltzmann coefficient,
T
{\displaystyle \ T\,}
is the absolute temperature, and
η
{\displaystyle \ \eta \,}
the dynamic viscosity of the surrounding fluid.
== Profile of electro-osmotic flow == Figure 4 shows two examples of heterodyne autocorrelation functions of scattered light from sodium polystyrene sulfate solution (NaPSS; MW 400,000; 4 mg/mL in 10 mM NaCl). The oscillating correlation function shown by Fig. 4a is a result of interference between the scattered light and the modulated reference light. The beat of Fig. 4b includes additionally the contribution from the frequency changes of light scattered by PSS molecules under an electrical field of 40 V/cm. Figure 5 shows heterodyne power spectra obtained by Fourier transform of the autocorrelation functions shown in Fig. 4. Figure 6 shows plots of Doppler shift frequencies measured at various cell depth and electric field strengths, where a sample is the NaPSS solution. These parabolic curves are called profiles of electro-osmotic flow and indicate that the velocity of the particles changed at different depth. The surface potential of the cell wall produces electro-osmotic flow. Since the electrophoresis chamber is a closed system, backward flow is produced at the center of the cell. Then the observed mobility or velocity from Eq. (7) is a result of the combination of osmotic flow and electrophoretic movement. Electrophoretic mobility analysis has been studied by Mori and Okamoto [16], who have taken into account the effect of electro-osmotic flow at the side wall. The profile of velocity or mobility at the center of the cell is given approximately by Eq. (11) for the case where k>5.
U
a
(
z
)
=
A
U
0
(
z
/
b
)
2
+
Δ
U
0
(
z
/
b
)
+
(
1
−
A
)
U
0
+
U
p
(
11
)
{\displaystyle \ U_{a}(z)=AU_{0}(z/b)^{2}+\Delta U_{0}(z/b)+(1-A)U_{0}+U_{p}\qquad (11)}
where
z
=
{\displaystyle \ z=\,}
cell depth
U
a
(
z
)
=
{\displaystyle \ U_{a}(z)=\,}
apparent electrophoretic velocity of particle at position z.
U
p
=
{\displaystyle \ U_{p}=\,}
true electrophoretic velocity of the particles.
z
/
b
=
{\displaystyle \ z/b=\,}
thickness of the cell
U
0
=
{\displaystyle \ U_{0}=\,}
average velocity of osmotic flow at upper and lower cell wall.
Δ
U
0
=
{\displaystyle \Delta U_{0}=\,}
difference between velocities of osmotic flow at upper and lower cell wall.
A
=
1
(
2
/
3
)
−
(
0.420166
/
k
)
(
12
)
{\displaystyle \ A={\frac {1}{(2/3)-(0.420166/k)}}\qquad (12)}
k
=
a
/
b
{\displaystyle \ k=a/b\,}
, a ratio between two side lengths of the rectangular cross section. The parabolic curve of frequency shift caused by electro-osmotic flow shown in Fig. 6 fits with Eq. (11) with application of the least squares method. Since the mobility is proportional to a frequency shift of the light scattered by a particle and the migrating velocity of a particle as indicated by Eq. (7), all the velocity, mobility, and frequency shifts are expressed by parabolic equations. Then the true electrophoretic mobility of a particle, the electro-osmotic mobility at the upper and lower cell walls, ware obtained. The frequency shift caused only by the electrophoresis of particles is equal to the apparent mobility at the stationary layer. The velocity of the electrophoretic migration thus obtained is proportional to the electric field as shown in Fig. 7. The frequency shift increases with increase of the scattering angle as shown in Fig. 8. This result is in agreement with the theoretical Eq. (7).
== Applications == Electrophoretic light scattering (ELS) is primarily used for characterizing the surface charges of colloidal particles like macromolecules or synthetic polymers (ex. polystyrene) in liquid media in an electric field. In addition to information about surface charges, ELS can also measure the particle size of proteins and determine the zeta potential distribution.