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The trajectories are similar to those observed in case of a MBM, although the
degree of freedom regarding the oscillation is increased by at least a factor of
two (two-dimensional oscillation). Displacement in the x-, y-, and z-plane
would increase the degree of freedom threefold compared to an oscillation
in the horizontal plane. Owing to different directional vectors including their
tangential displacement vectors the trajectory of the milling containment
including the grinding bodies is complicated. The wear mechanisms are
similar to MBM and PBM.
10.3.1.3 Effect of the Ball Mill type on the Synthesis
The literature reports many examples of chemical reactions performed in
one of these ball mills.
10,48,57-59
However, studies comparing the effective-
ness of the ball mill types in a similar reaction are seldom. Up to now,
such comparative studies have been disclosed for the Zn/ZnCl
2
-mediated
Pinacol coupling of aromatic ketones and aldehydes,
60
Suzuki-Miyaura
cross-coupling with KF-Al
2
O
3
,
29
Knoevenagel condensation of aromatic al-
dehydes,
61
the oxidative homo-coupling of anilines,
62
and the CuI-catalyzed
Glaser reaction of phenylacetylene.
63
Most of the publications compare ac-
complishment of the respective reactions in a MBM and a PBM.
29,61-63
Experimental results for a Suzuki-Miyaura cross-coupling reaction
(Scheme 10.2) indicate that there is no difference between the reactions
carried out with respect to yield and selectivity if reaction time and scale are
on a comparable level. The only difference is the changed operating fre-
quency (Figure 10.6).
29
Whereas the PBM is often operated at its maximal
rpm of 800 min
1
(equal to n
rot
¼
13.3 Hz), reaction at similar frequency in a
MBM resulted in significantly lower yields.
29
Owing to the different torques
of the machines the peripheral velocities (v
p
) and g-forces are not compar-
able. Thus, the energy density at the same frequency is different, resulting in
different stress energies transferred to the mill feed (Eq. 10.1):
64,65
E
stress,feed
¼
d
3
MB
v
p
r
MB
K
1
with K
¼
f (E
Y,i
)
(10.1)
where
E
stress,feed
(J) is the stress energy transferred to the feed material,
d
MB
(m): diameter of the milling balls,
v
p
(m s
1
): peripheral velocity,
r
MB
(kg m
3
): density of the milling balls,
E
Y,i
(Pa): Young's modulus.
KF/Al
2
O
3
Pd(OAc
2
)
Br
B(OH
2
)
Ac
+
MV = stainless steel
MB = agate
Ac
Scheme 10.2
Suzuki-Miyaura cross coupling used as model reaction for the investi-
gation of parameter effects.
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