The signal can be interpreted using an autocorrelation function. Incoming data
is processed in real time with a digital signal processing device known as a
correlator and
the autocorrelation function, shown in Figure 26 as a function of
delay time, Τ, is extracted.
The autocorrelation function from dynamic light scattering in Figure 26 shows a
sample where all of the particles are the same size, the baseline subtracted auto-
correlation function, C, is simply an exponential decay of the following form:
EQUATION 1
C
= exp(-2
Γ)
Γ
is readily derived from experimental data by a curve fit.
The diffusion coefficient
is obtained from the relation
Γ=D
t
q
2
where q is the scattering vector, given by
q=
(4
πn/λ)
sin
(
θ/2).
The refractive index of the liquid is n. The wavelength of the
laser
light is
λ,
and scattering angle
,
θ.
Inserting D
t
into the Stokes-Einstein equa-
tion then solves for particle size D
h
is the final step.
EQUATION 2
D
h
=
k
B
T
Where:
D
h
= the hydrodynamic diameter
D
t
= the translational
diffusion coefficient
k
B
= Boltzmann’s constant
T = temperature
η = dynamic viscosity
figure 25
|
Chia sẻ với bạn bè của bạn: