Page 42 - Book Hosokawa Nanoparticle Technology Handbook

1.5 MELTING POINT, SURFACE TENSION, WETTABILITY FUNDAMENTALS
where r is the radius of liquid drop, the surface between the drop and a solid surface under the action
tension, t the time, and A and B are constants. of three interfacial free energies.
As can be seen from equation (1.5.1), when the

surface tension value of liquid drop remains constant, cos SL (1.5.2)
L
S
Ln (dr/dt) should be proportional to (1/r). Fig. 1.5.3
shows changes of particle sizes of Au and Pb with where is the contact angle, the surface free
L
time by evaporation. It can be found that Ln (dr/dt) energy of liquid, the surface free energy of solid
S
and (1/r) does not show linear relationship when par- and SL the interface free energy between solid and
ticle sizes of Au and Pb drops are less than 2 and 5 liquid.
nm, respectively. Since the surface free energy (surface tension) of
Gladkikh et al. [21] performed theoretical and liquid depends on a liquid drop size as mentioned
experimental approach on surface energies of nano- above, the contact angle also depends on the liquid
particles of metals and reported the results of Au and drop size. Fig. 1.5.6 shows particle size dependence
Pb particles. As can be found from Fig. 1.5.4, of contact angles of various liquid metals on carbon
obtained result of Pb is fairly in good agreement with
that by Morokov [22].
1.5.3 Wettability
As shown in Fig. 1.5.5, a contact angle value is used
as a criterion for wettability of solid by liquid. In (a)
general, when a contact angle is larger than 90 degree
(cf. Fig. 1.5.5a), it is defined as “non-wetting sys-
tem” and when a contact angle is smaller than
90 degree(cf. Fig. 1.5.5b), it is defined as “wetting
system”.
Over 200 years ago, equation (1.5.2) was proposed
by treating the contact angle of a liquid drop as the
result of the equilibrium of mechanical energy (b)

Figure 1.5.5
1200 Liquid drop shape on solid.
Surface tension (mN/m) Surface tension (mN/m) 800 155 Sn

150

400 Au 1348K 145
Contact angle (°) 135 Au
0 2 4 6 8 10 140
1.0 Bi

σm/σb m/ 0.8 130

125
Pb 734K
120
0.6
0 2 4 6 8 10 115
Particle size (nm) 0 10 20 30 40 50
Particle size (nm)
Radius of particle (nm)
Figure 1.5.4
Effect of particle size of surface tension of Au and Pb. Figure 1.5.6
m, surface tension of nanoparticle; b, surface tension Relationship between contact angles of liquid metals on
of bulk metal. graphite and particle sizes.

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