Chemistry Reference
In-Depth Information
d
n
3
r
4
n
g
|
7
Figure 2.1 Experimental (dots) and theoretical (solid line) values of the melting
point temperature of gold particles. Note that the melting point of bulk
gold is 1337 K and decreases rapidly for nanoparticles with diameters
below 5 nm.
Reproduced with permission from ref. 21.
nanomaterials: (i) the disappearance of the state of order in the solid, (ii) the
sharp variation of some physical properties, such as evaporation rate, and
(iii) the sudden change in particle shape. Bulk gold has a melting point of
1337 K and it decreases rapidly for nanoparticles with sizes below 5 nm as
shown in Figure 2.1. Such size dependence has also been found in other
materials such as copper,
22
.
tin,
23
indium,
24
lead and bismuth,
25
barium
titanate (BaTiO
3
),
26
lead titanate (PbTiO
3
)
27
in the forms of particles
and films.
Various theories have been proposed to explain the size-dependent
melting temperature drop of nanomaterials. A classical thermodynamics
theory, such as the Gibbs model to account surface area, can be exploited to
explain this phenomenon to in the nanosystems as follows (eqn (2.1)):
21,28
2
=
3
2T
b
DHr
s
g
s
r
s
r
l
T
b
T
m
ΒΌ
g
s
g
l
(2
:
1)
where T
b
and T
m
are the melting points of a bulk material and a nanoparticle
respectively, g
s
is the radius of the particle, DH is the molar latent heat of
fusion, and g and p are surface energy and density respectively. This simple
relationship (eqn (2.1)) is based on many assumptions to explain the
size-dependent melting temperature drop in nanoparticles. Besides nano-
particles, the size-dependent melting temperature drop has been observed in
nanowires including gold nanorods
29
and Ge nanowires.
30,31
After melting,
nanowires may spontaneously break up into smaller and shorter segments
and finally form small micro/nano beads due to Rayleigh instability
32
to
reduce the high surface energy of nanowires or nanorods, when their
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