Page 150 - Environmental Nanotechnology Applications and Impacts of Nanomaterials

136 Principles and Methods

transmission obtained by dividing the measured transmitted intensity
I by the incident beam intensity I with the result of Eq. 22 using
∗/ =
O
2 3
15.9cm /g and = 1.06 g cm .
The scattered intensity as a function of the scattering vector q
obtained for this NPs solution is shown in Figure 4.17. The plain line
in this curve is a fit using Eq. 24 of the scattering intensity using the
form factor of an ellipsoid of revolution.

2
Isqd 5 fV r Psqd (24)
where P(q) is the form factor of an ellipsoid, V is the volume of the ellip-
soid,
is the volumetric fraction of the ellipsoid in solution, and is
the scattering length density contrast between CeO 2 and water ( 4.26
11
10 cm 2 ). The form factor of the ellipsoid is calculated according to the
following expression:

e
e
e
p>2 3[ sin sqR d 2 qR cos sqR d]
sin sadda (25)
e 3
3 sqR d
0
2
2
e
where R 5 R 2sin a 1 eps cos a and R, R and R are the semi-axes
of the ellipsoid.
Figure 4.17 clearly shows a very good agreement with the experi-
mental data. The model is very sensitive to variation in size, aspect

Figure 4.17 Scattering intensity measured for a 38 g/l suspension of CeO 2 nanoparticles.
The red line is the best fit using an ellipsoid model with the parameters: R 3.5 nm,
3
0.26 and NP 7.13 g/cm .