PHYS01200704032 Debes Ray - Homi Bhabha National Institute

Chapter 3: Multi-Technique Approach for Characterization of Gold Nanoparticles
(v) Gaussian Coil
The form factor of Gaussian chain coils with the radius of gyration R g is given by [176-181]
2( e
x1)
P Q x Q R
x
x
2 2
( ) ,
(3.15)
2
g
Determination of Inter-Particle Structure Factor
When the concentration of particles is high they start interacting with each other. The nature
of S(Q) depends on the structure and the organization of the particles and the type of
interactions between the particles. In general, S(Q) shows several maxima and minima of
decreasing amplitude. The first peak in S(Q) occurs at Q max ≈ 2π/d, where d is the average
distance between the particles.
The expression for S(Q) depends on the relative positions of the particles. For an
isotropic system, S(Q) can be written as
sin Qr
S Q n
g r r dr
Qr
2
( ) 1
4 ( ( ) 1) (3.16)
where g(r) is the radial distribution function. g(r) is the probability of finding another particle
at a distance r from a reference particle centered at the origin. The details of g(r) depend on
the interaction potential U(r) between the particles [181-185]. Thus, one has to have the
knowledge of U(r) for calculating S(Q). This in turn implies that measured S(Q) can be used
to obtain information about the interaction potential U(r).
3.5.2. Small-Angle X-Ray vs. Neutron Scattering
The fundamental difference between X-rays and neutrons is the mechanism by which the
incident radiation interacts with matter. X-rays are scattered by electrons surrounding atomic
nuclei whereas neutrons by the nuclei. It is seen that as one goes across the periodic table, the
X-ray scattering lengths increase with the atomic number of the atom, whereas the neutron
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