PHYS01200704032 Debes Ray - Homi Bhabha National Institute

Chapter 3: Multi-Technique Approach for Characterization of Gold Nanoparticles
3 j1 ( QR1 ) 3 j1 ( QR2
)
P( Q) ( c shell ) V1 ( shell m) V2
(3.12)
QR1 QR2
where c , shell and m are the scattering length densities of core, shell and solvent,
respectively, j 1 is first order Bessel function.
2
(iii) Prolate Ellipsoidal Particle
The expression for form factor of prolate ellipsoidal particle with semi-major axis a and
semi-minor axis b = c is given by [176-181]
1
2
( ) ( , )
(3.13)
P Q F Q d
0
where
F( Q, x)
2
1
3(sin x xcos x)
3
x
, x Q [ a 2
2 b
2 (1
2 )]
2
and μ is the cosine of
the angle between the direction of major axis and wave vector transfer Q.
(iv) Rod-like/Cylindrical Particle
The form factor of randomly oriented cylindrical particles with the radius R and
length L (= 2l) is given by [176-181]
/2 2 2
j1
QR Ql
2 2 2 2 2
Q R sin ( Ql) cos
0
4 ( sin ) sin [( )cos ]
P( Q)
sin d
(3.14)
where j 1 (x) is first order Bessel function and θ is the angle subtended by the principal axis of
the cylinder with Q.
P(Q) variation on log-log scale shows a linear region in the intermediate Q-range
1/l < Q < 1/R. The slope of the linear region is –1. On the other hand, P(Q) for a disc-like
particle having radius R and thickness t has a slope of –2 in the intermediate Q-range of
1/R < Q < 1/t.
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