Environmental Engineering Reference
In-Depth Information
molecular motion, leading to concentration or polar-
ization of local fl uctuations in the scattering volume.
Unlike SLS, DLS does take account of the small
fl uctuations in signal intensity arising by Brownian
motion of the particles. Such illuminated molecules
are in stochastic movement; that is, their degrees of
liberty, translation, rotation, and vibration are con-
stantly changing so the light-scattering intensity at
the detector fl uctuates in time. These temporal fl uc-
tuations are related and can be analyzed by a digital
correlator. Such a device determines the intensity
autocorrelation function,
G
(2)
(
example, when
is 0.775, 1.0, and 1.9, particles are
spherical, spherical shells, and rod-like respectively.
Light scattering is one of the few non-destructive
techniques that allow estimation of particle size
involving minimum sample handling. Another
important advantage of this technique is the speed
of measurement typically from a few seconds up to
900 s. In fact,
I
(
ρ
) is the factor that determines exper-
imental duration and is proportional to concentra-
tion, weight-average molecular mass and the form
factor,
P
(
θ
), of the colloidal particle. The major limi-
tation in light-scattering measurements is the pres-
ence of dust in the sample. Dust increases the level
of background noise, decreasing accuracy, which
limits reproducibility, leading to larger sized particles
and broadening size distribution. In general, a high
signal-to-noise ratio is required to analyze accurately
a sample with a variable size distribution. Currently,
the lowest particle size measured by light scattering
is 0.6 nm and the upper size limit is sample density-
dependent because DLS requires particles to diffuse
stochastically rather than to be sedimenting.
Light-scattering techniques have been used to
investigate the behavior of colloids extracted from
soil (Kammer & Forstner 1998; Baalousha
et al.
2005a) and sediment (Effl er
et al.
2006; Li
et al.
2007). The colloidal surface area and consequently
particle size, size distribution and shape, play an
important role in the aquatic environment owing to
their impact on contaminant adsorption and sedi-
mentation properties. Baalousha
et al.
(2006) applied
FIFFF and light-scattering techniques to characterize
colloids extracted from soil and to explain the role
of carbonates in the formation of colloidal dispersion
and sedimentation processes. Results from examina-
tion of silt samples showed that calcium carbonate
acted as a cement between colloidal particles. This
modifi es particle shape and changes sedimentation
behavior, as spherical particles settle faster than
platy ones. Kammer
et al.
(2005) also analyzed
natural colloidal suspensions from different soils
using FIFFF-light scattering and the ZIMM fi t algo-
rithm for particle sizes up to 500 nm in diameter. The
results indicated that, after hydrodynamic fractiona-
tion, static light-scattering techniques could be
applied to determine the radius of gyration (
R
g
) of
the particles. The results for soil colloids worked well
because the function
Kc
/
R
(
θ
), which can be
described as the average of
I
(
t
), with
I
(
t
+
τ
τ
) (Pecora
1985):
T
1
2
∫
G
()
2
()=
τ
I t I t
()
(
+
τ
) =
lim
ItIt
()
(
+
τ
)
d
(6)
t
T
T
→∞
−
T
where
I
(
t
) and
I
(
t
+
) are the intensities of light
scattering at some arbitrary time,
t
, and
t
+
τ
τ
,
respectively,
being the time delay between two
counts, and 2
T
the total time over which it is
averaged.
Modern devices can measure over a delay range of
100 ns to several seconds. At short time delays, cor-
relation is high and, over time as the particles are
moving, correlation diminishes to zero and the expo-
nential decay of the correlation function becomes
characteristic of the decay frequencies,
τ
(s
−1
). Several
methods to analyze the autocorrelation function and
obtain the distribution of
Γ
(s
−1
) are used today, cumu-
latively (Pecora 1985), non-negatively constrained
least squares (NNLS) (Stock & Ray 1985) and
constrained regularization (CONTIN) (Provencher
1982a,b).
Γ
(s
−1
) is related to the translational diffu-
sion coeffi cient,
D
, of the particles by the relation:
Γ
(
)
=
Γ
s
−
1
2
Dq
(7)
The hydrodynamic radius,
R
h
, of the particles may
be calculated using
D
in the Stokes-Einstein
equation
kT
D
B
R
=
6
(8)
h
πη
where
k
B
T
is the Boltzmann energy and
the viscos-
ity of the medium. Natural colloidal dispersions can
exhibit different shapes where the ratio
R
g
/
R
h
(the
shape form,
η
) is an unambiguous test for particle
shape (Schurtenberger & Newman 1993). For
ρ
) was found to be linear
against the scattering vector (
q
). The particle shape
θ
