E vdW ¼
A
12
d
2
t 2 À d 2 þ
d
2
t 2 þ 2 ln
t
2 À d
2
t 2
!
&
'
ð2Þ
E steric ¼
50dl
2
ðt À dÞps a
3
kTe
ÀpðtÀdÞ
ð3Þ
The van der Waals interaction due to the polarization of the metal cores constitutes
the attractive term and the steric interaction between the thiol molecules on the
two surfaces forms the repulsive term, where t is the interparticle distance. The
Hamaker constant, A, for Pd nanocrystals, in toluene for instance, has been estimated to be 1.95 eV [140]. The calculated diameter of the area occupied by the thiol
molecule (sa) on the particle surface is 4.3 A ˚ [112]. The total energy is attractive
Fig. 4.16. TEM micrographs showing hexagonal arrays of
hexanethiol capped PbS nanocrystals (unpublished results from
our laboratory).
4 Mesoscopic Assembly and Other Properties of Metal and Semiconductor Nanocrystals
70
A
12
d
2
t 2 À d 2 þ
d
2
t 2 þ 2 ln
t
2 À d
2
t 2
!
&
'
ð2Þ
E steric ¼
50dl
2
ðt À dÞps a
3
kTe
ÀpðtÀdÞ
ð3Þ
The van der Waals interaction due to the polarization of the metal cores constitutes
the attractive term and the steric interaction between the thiol molecules on the
two surfaces forms the repulsive term, where t is the interparticle distance. The
Hamaker constant, A, for Pd nanocrystals, in toluene for instance, has been estimated to be 1.95 eV [140]. The calculated diameter of the area occupied by the thiol
molecule (sa) on the particle surface is 4.3 A ˚ [112]. The total energy is attractive
Fig. 4.16. TEM micrographs showing hexagonal arrays of
hexanethiol capped PbS nanocrystals (unpublished results from
our laboratory).
4 Mesoscopic Assembly and Other Properties of Metal and Semiconductor Nanocrystals
70