Page 43 - Book Hosokawa Nanoparticle Technology Handbook

FUNDAMENTALS CH. 1 BASIC PROPERTIES AND MEASURING METHODS OF NANOPARTICLES
substrate [23, 24]. It can be found that the contact 1.6 Specific surface area and pore
angles of all liquid metals decrease at less than 40nm
and a remarkable decrease of the contact angles is Nanoparticles have a large specific surface area, and
observed when particle radius is less than 10nm.
hence their properties are dominated by surfaces rather
than bulk. The specific surface area is often used as a
References basic unit for the particle properties of nanoparticles.
In this section, methodologies and things to be consid-
[1] M. Takagi: J. Phys. Soc. Jpn., 9, 359–363 (1954). ered for analyzing particle size from specific surface
[2] F.O. Jones, K.O. Wood: Brit J. Appl. Phys., 15, area will be discussed. The first half of this section will
185–187 (1964). describe requirements for measuring particle size dis-
[3] N.T. Gladkich, R. Niedermayer and K. Spiegel: Phys. tribution from specific surface area. In the second half,
pore size distribution will be reviewed as an applica-
Stat. Sol., 15, 181–192 (1966).
tion of the measurement of specific surface area.
[4] C.R.M. Wronski: Brit. J. Appl. Phys., 18, 1731–1737
It is important to access thoroughly the influence of
(1957).
particle shapes and particle size distribution for meas-
[5] B.T. Boiko, A.T. Pugachev and V.M. Bratsykhin: Sov.
uring particle size from specific surface area. For this
Phys. Solid State, 10, 2832–2834 (1969). reason, using electron microscopic observations or
[6] J.F. Pocza, A. Barna and P.B. Barna: J. Vac. Sci. Tech., other particle size measurements are preferable in
6, 472–475 (1969). combination with the measurement of specific sur-
[7] M. Blackman, J.R. Sambles: Nature, 226, 938 (2970). face area. Comprehensive analysis for these measure-
[8] M.J. Stowell, T.J. Law and J. Smart: Proc. Roy. Soc. ments would enable to estimate reasonable and
London A, 318, 231–241 (1970). meaningful particle size.
The relationship between specific surface area and
[9] J.R. Sambles: Proc. Roy. Soc. London A, 324,
particle size is described here with an ideal particle
339–351 (1970).
model. As shown in Fig. 1.6.1, ideal size reduction
[10] C.J. Coombes: J. Phys. F: Metal Phys., 2, 441–449
where a dense cube, 1 cm on a side, is divided into
(1972).
cubes, l cm on a side, is supposed. The surface area of
[11] M. Bkackman, S.J. Peppiatt and J.R. Sambles: Nature each divided cube is given as 6·l and the number of
2
Phys. Sci., 239, 61–62 (1972). divided cubes is given as 1/l . Therefore, the total sur-
3
[12] R.P. Berman, A.E. Curzon: Can. J. Phys., 52, 923–929 face area of all the divided cubes can be expressed as
2
3
(1974). (1/l )·( 6l ), thus 6/l. Supposing the true density of a
[13] S.J. Peppiat, J.R. Sambles: Proc. R. Soc. Lond. A, 345, particle , specific surface area S is given by
387–399 (1975).

l
S 6( ) (1.6.1)
[14] S.J. Peppiatt: Proc. R. Soc. London A, 345, 401–412
(1975). In contrast, supposing that the powder is composed of
[15] P. Buggst, J.P. Boreld: Phys. Rev. A, 13, 2287–2298 uniform cubic particles, the particle size can be given
(1976).
[16] G.L. Allen, W.W. Gile and W.A. Jesser: Acta Metall.,
28, 1695–1701 (1980).
[17] V.P. Skipov, V.P. Koverda and V.N. Skokov: Phys.
State. Sol., 66, 109–118 (1981).
[18] M.S. Rahman: Micron, 13, 273–274 (1982).
[19] G.L. Allen, R.A. Bayles, W.W. Gile and W.A. Jesser:
Thin Solid Films, 144, 297–308 (1986). S=6/d•l
[20] H. Saka. Y. Nishikawa and T. Imura: Phil, Mag. A, 57,
1 × 1 × 1 cm 3
895–906 (1988).
[21] N.T. Gladkikh, L.K. Grigoreva, S.V. Dukarov,
V.E. Zilbervarg, V.I. Larin, E.L. Nagaev and S.P.
Chizhik: Sov. Phys. Solid State, 31, 728–732 (1989).
[22] I.D. Morokhov, S.P. Chizhik, N.T. Gladkikh,
L.K. Grigoreva, S.V. Stepanova: Izv. Akad. Nauk SSSR
Metall., 6, 159–161 (1979). area : 6 • l 2
1/l
[23] N.T. Gladkikh: Fiz. Khim. Obrabot. Mater., 2, 96–102 number : (1/l) 3
division
(1979).
[24] S.P. Chizhik: Izv. Akad. Nauk SSSR Metall., 4, 73–79 Figure 1.6.1
(1981). Relationship between particle size and specific surface area.
20