Environmental Engineering Reference
In-Depth Information
scattering, where size related properties are derived from the intensity variations
with detection angle (Schurtenberger and Newman, 1993; Wyatt, 1993).
The full light scattering theory is quite complex but simplifi cations based on
certain approximations have been developed. In its simplest forms, according to
the Rayleigh- Gans -Debye and Guinier approximations, where it is assumed that
the particles are much smaller than the incident lights wavelength, the refractive
index is similar to that of the solvent and no light absorption occurs. Light scatter-
ing can be formulated as:
Kc
R
*
1
( ) +
2
Ac
(6.3)
2
MP
θ
θ
w
2
16
3
π
λ
n
P
0
(6.4)
θ ( ) ≈−
θ
1
r g
2
sin
2
(
θ
2
)
2
0
0
(
)
2
4 , R θ the excess Rayleigh
ratio (scattered intensity in excess of the scattering from pure solvent), M w the
molar mass of the particle/polymer, A 2 the second virial coeffi cient, P(
(
)
2
where K* is the material constant 4
π
dn dc
n
N a
λ
0
) the par-
ticle form factor, n 0 the refractive index of the solvent, dn/dc the refractive index
increment of the particles,
θ
λ
0 the vacuum laser wavelength and
θ
the scattering
angle (Schurtenberger and Newman, 1993;Wyatt, 1993).
On plotting K * c/R θ against sin 2 (
/2) in a double extrapolation plot (or Zimm-
plot) the intercept yields molecular weight ( M w ) at the zero concentration ( c ) and
zero angle, and from the two slopes the root mean square radius of gyration r g 2
θ
and the second viral coeffi cient can be derived. The molar mass and second viral
coeffi cient are mainly relevant for studies of polymers or proteins while r g 2 is
mainly relevant for NPs. r g 2 describes how the mass of a particle is distributed
from the centre of mass (Table 6.2).
The sensitivity of light scattering is dependent on laser wavelength, particle
refractive index increment and particle size. The sensitivity is inversely proportional
to
4 , and inversely proportional to the d 2 for larger particles and d 6 for particles
much smaller than the laser wavelength (Filella et al. , 1997 ; Schurtenberger and
Newman, 1993). This strong size dependency has major implication for character-
ization of NPs, since the detection limit increases to above the mg l − 1 level for NPs
below
λ
50 nm. This means that the light scattering method has to be used in particle
concentrations that may not be environmentally relevant. Even more important is
that the strong sensitivity dependence on particle size means that a few larger
components in the sample often completely skew the measured size.
6.2.3.3
Laser Diffraction
Laser diffraction methods build on the analysis of the diffraction patterns gener-
ated when a laser beam is interfered with by a particle (Figure 6.3). The understand-
ing of laser diffraction is explained by the Mie theory, and mainly applicable to
micron size particles (the Mie size region above the laser wavelength), but some
manufacturers have incorporated backscatter detectors and multiple lasers in order
to cover the submicron size range. Thus, the technique can be used in the size range
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