Page 233 - Book Hosokawa Nanoparticle Technology Handbook

4.4 NANOCOMPOSITE STRUCTURE FUNDAMENTALS

10 7
percolation threshold
(0.552) z =1.764
ii
Maximum active area (m 2 /m 3 ) 10 5 closest packing
6

(0.26) z =6
ii
10
electronic conductor
size : 0.1 μm
volume fraction : 0.5
10 4
0.2 0.3 0.4 0.5 0.6 0.7
Void fraction (−)

Figure 4.4.11
Effect of the void fraction on the maximum active contact area.

1.0 1.0 10 6
Conductivity
(Ni) α=1 α=1/2
Percolation probability (−) 0.5 0.5 Conductivity (a.u.) Effective conductivity (S/m) 10 0 Conductivity
α=2
3

(YSZ)
10

0.0 0.0
0.0 2.0 4.0 6.0 10 -3
0.0 0.2 0.4 0.6 0.8 1.0
Coordination number (−)
Volume fraction of electronic conductor (−)
Figure 4.4.12 Figure 4.4.13
Percolation probability and conductivity of a system as a Estimation of the effective conductivity of Ni/YSZ
function of the coordination number.
electrode.

that the two quantities are not proportional. The con- where
is the conductivity of i-component, n the
i
ductivity curve seems to end at the threshold with zero fraction number of particles of either the electronic or
slope although the percolation probability curve has ionic conductor, and n the percolation threshold. The
c
ff
infinite slope there, because most of the infinite net- value is an adjustable parameter so that

i
ie
work at the threshold belong to “dangling” or “dead when n 1, taking into account the effect of the necks
ends”, not to the “backbone”. Thus most of the clusters between the particles on the conductivity. Some
make no contribution to the conductivity of a system, results for an electrode formed by a mixture of Ni
6
and therefore the critical exponent for conductivity (
2 10 S/m) and YSZ (
15 S/m) at 1273 K
io
el
differs from that for the percolation probability. This are shown in Fig. 4.4.13, in which the adjustable
means we have to estimate the conductivity under the parameter is 0.5. The two conductivities
Ni and
various conditions on the coordination number.
YSZ are almost equal for a composition near to the
The effective conductivity can be calculated by [3] percolation threshold of the electronic conductor
phase. However, the estimation of anode performance

n ( n c ) 2 requires exact calculation of the conductivity because

eff i 2 (4.4.4) of sudden changes in the conductivity at the percola-
i
( 1 n c ) tion threshold. It should also be noted that the
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