Page 44 - Book Hosokawa Nanoparticle Technology Handbook

1.6 SPECIFIC SURFACE AREA AND PORE FUNDAMENTALS
by the specific surface area and the true density of the
particle. Although the particle shape was supposed to A B C
be cubic in the derivation above, the relationship
between specific surface area and particle diameter
for a perfect sphere can also be given by equation
(1.6.1). Thus, the coefficient 6 in the equation is the
shape factor for a particle with cubic or spherical
shapes. For particles with other shapes, similar rela-
tionships can be obtained by using an appropriate Number of particles
shape factor. There are a number of definitions for
shape factors [1, 2], whereas the details cannot be
described here due to limitation of space. The particle
size calculated from equation (1.6.1) is normally used
as an equivalent specific surface diameter for practi-
cal convenience.
In general, it is very rare to deal with the ideal par-
ticle shown above. Actual particle has usually irregu-
lar shapes and a size distribution. In the following
part, how particle size distribution and particle shape small Particle size large
give effects for analyzing particle size from specific : Characteristic diameter obtained from number-size distribution
surface area will be discussed, and then points to be
considered will be given. : Equivalent diameter obtained from specific surface area
If particles have ideal spherical or cubic shape with
a mono-dispersed size distribution, the specific sur- Figure 1.6.2
face area can be related to the particle size as shown Relationship between particle size distribution and specific
in equation (1.6.1). When a sample powder has a par- surface area.
ticle size distribution, relationship between specific
surface area and the size distribution can be addressed has a good symmetry as shown in Fig. 1.6.2, the coef-
as follows. Supposing that the spherical particles with ficient f is 1 and hence an equivalent specific surface
a true density and a diameter l exist n per unit diameter obtained from equation 1.6.1 is equal to a
i
i
mass, the specific surface area can be given by the characteristic diameter obtained from number-size
following: distribution. On the other hand, if the size distribution
is not symmetric, the coefficient f is not equal to 1.
3
2
S 6 [( n l ) [( n l )] (1.6.2) For the distribution A shown in Fig. 1.6.2, the coeffi-

i
i
i
i
cient f 1 and hence the equivalent specific surface
diameter becomes smaller than the characteristic
For taking account of correspondence to particle size diameter obtained from number-size distribution. In
distribution, n is expressed here with a ratio to the contrast, for the distribution C shown in Fig. 1.6.2, the
i
i
total number of particles N.
coefficient f 1 and hence the equivalent diameter
becomes larger than the characteristic diameter.
n i N (1.6.3) As described above, for a good symmetric size dis-
i
tribution, an equivalent diameter estimated by the
The particle diameter l is also expressed with a ratio measurement of specific surface area can be a char-
i
to the mode particle size L. acteristic diameter of a particle size distribution, but
i
for an asymmetric size distribution the equivalent
l i L (1.6.4) diameter is not always equal to the characteristic
i
diameter. These points have to be considered thor-
Substituting equations 1.6.3 and 1.6.4 into equa- oughly for estimating the equivalent diameter from
tion 1.6.2 gives the following:
specific surface area. As the measurement of specific
surface area cannot give particle size distribution,
S f 6 ( L) (1.6.5) concomitant use of an electron microscopic observa-
Where tion or other particle size measurements is necessary
for more detailed discussions.
∑ 2 3 The particle shape has been supposed to be spheri-
f [( i ) ( i )] (1.6.6) cal or cubic in the discussions so far. However, it is
i
i
very rare in practice to deal with such ideal shaped
and can be obtained from data of particle size dis- particles. In general, if primary particle has pores,
i
i
tribution, and f is a coefficient depending on shape of specific surface area increases and a resultant equiva-
the size distribution. If the particle size distribution lent diameter decreases apparently. Therefore, it is
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