Introduction to Nanotechnology

266 SELF-ASSEMBLY AND CATALYSIS
351 .I I I I I I
0' ' I ' ' I
' I ' I ' I
m
....
methanol
2.6WoRh -
0
1.3 WoRh
0 -
ethanol
2.6 WoRh
+ -
1.3wYoRh -
0
I-propanol -
2.6WoRh
1.3 w%Rh -
0
1-butanol
2.6 w%Rh -
I ' I ' ' ' I
1 2 3 4 5 6 7
average particle size (nm)
Figure 10.6. Activity of cyclohexene hydrogenation, measured by the turnover frequency (TOF)
or rate of conversion of cyclohexene to cyclohexane, plotted as a function of the rhodium (Rh)
metal particle size on the surface. The inset gives the alcohols (alkanols) used for the
preparation of each particle size. [From G. W. Busser, J. G. van Ommen, and J. A. Lercher,
"Preparation and Characterization of Polymer-Stabilized Rhodium Particles", in Moser (1 996),
Chapter 9, p. 225.1
diameter d and length L has the volume V = zd2L/4. The limit L > d
has A - 2zrL, and A/ V - 4/d. Figure 9.2 provides sketches of these figures. Using
the units square meters per gram, m2/g, for these various geometries we obtain the
expressions
S(r) = ~ sphere
S(r) = ~ cube
S(r) - ~ thin
S(r) - ~ long
6 x lo3
Pd
6 x lo3
Pa
2 103
PL
4 x 103
Pd
of diameter d
m
(10.6a)
of side a (10.6b)
disk, L