266
SELF-ASSEMBLY AND CATALYSIS
351 . I I
I
I
I
I
methanol
0
1.3 WoRh
0
ethanol
2.6 WoRh
2.6WoRh -
-
+
0
-
1.3wYoRh -
I-propanol -
2.6WoRh
0
1-butanol
m
1.3 w%Rh -
2.6 w%Rh -
'
I
'
I
'
I
m
....
0 ' '
I
' ' I 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 corresponds
to the shape of a disk with the area A - zd2/2, including both sides, to give
A / V - 2/d. In like manner, a long cylinder or wire of diameter d and length 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
6 x lo3
S(r) = ~
sphere of diameter d
Pd
(10.6a)
6 x lo3
Pa
S(r) = ~
cube of side a
(10.6b)
2 103
PL
S(r) - ~
thin disk, L << d
(10.6~)
4 x 103
Pd
S(r) - ~
long cylinder or wire d << L
(10.6d)
SELF-ASSEMBLY AND CATALYSIS
351 . I I
I
I
I
I
methanol
0
1.3 WoRh
0
ethanol
2.6 WoRh
2.6WoRh -
-
+
0
-
1.3wYoRh -
I-propanol -
2.6WoRh
0
1-butanol
m
1.3 w%Rh -
2.6 w%Rh -
'
I
'
I
'
I
m
....
0 ' '
I
' ' I 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 corresponds
to the shape of a disk with the area A - zd2/2, including both sides, to give
A / V - 2/d. In like manner, a long cylinder or wire of diameter d and length 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
6 x lo3
S(r) = ~
sphere of diameter d
Pd
(10.6a)
6 x lo3
Pa
S(r) = ~
cube of side a
(10.6b)
2 103
PL
S(r) - ~
thin disk, L << d
(10.6~)
4 x 103
Pd
S(r) - ~
long cylinder or wire d << L
(10.6d)