Page 41 - Book Hosokawa Nanoparticle Technology Handbook

FUNDAMENTALS CH. 1 BASIC PROPERTIES AND MEASURING METHODS OF NANOPARTICLES
1.5 Melting point, surface tension, 1.0
wettability

It is well known that melting point and surface ten- .95
sion, which are the physical properties of materials,
and wettability (contact angle), which is the intrinsic
value between liquid and solid, depend on particle Tm/To .90 In
size when the size is nano-meter order.
Pb
1.5.1 Melting point .85 Bi

A proportion of number of surface atoms to that of Sn
bulk atoms increases with decrease in particle size.
Accordingly, the melting point of nanoparticle falls as .80 0 0.05 0.10 0.15 0.20 0.25
much as corresponding surface energy.
Many researchers have reported melting points of Inverse of particle size (nm )
-1
nanoparticles [1–21] and some examples are shown
in Figs. 1.5.1 and 1.5.2. A melting point of Au Figure 1.5.2
declines suddenly when a particle size is less than Relationship between inverse of particle size of various
15 nm and a decrease of almost 200 K can be metal and T /T [19]. T , measured melting point; T ,
o
m
m
o
observed at about 6nm. As shown in Fig. 1.5.2, it has melting point of bulk material.
been reported that there is a linear relationship
between a ratio of a melting point of nanoparticle 3.0
(T ) to that of bulk material (T ) and a reciprocal
m
o
number of a particle diameter.
1.5.2 Surface tension
Morokhov [22] calculated a change in liquid drop Au (1348K)
diameter with an evaporation of a liquid drop at a
constant temperature based on a molecular dynamics
Logarithm of time change of particle size
and obtained an equation (1.5.1). 2.0

ln(dr dt lnA B ( r ) (1.5.1)
)
1350
Melting point
Melting point
1336K
1336K
1300 1.0 Pb (734K)
Melting point (K) Melting point (K) 1250

1200

0 10 20 30 40 0 0.05 0.10
-1
Particle size (nm)
Particle size (nm) Inverse of particle size (A )
Figure 1.5.1 Figure 1.5.3
Relationship between melting point of gold and its particle Relationship between particle size change of evaporating
size [8]. metal drop and particle size.

18