Chemistry Reference
In-Depth Information
lowered and so is the yield. This effect has been demonstrated for Pd(OAc)
2
-
catalyzed Suzuki-Miyaura reaction using KF/Al
2
O
3
as base and grinding
auxiliary: decreasing d
MB
from 15 to 10 mm with n
MB
¼
6 reduces the yield
from 92% to 6%.
72
10.3.5 Filling Degree
The filling degree of a milling vessel (F) is an important measure since it
influences the milling balls' trajectories in a ball mill (Figures 10.3, 10.4 and
10.9). If the milling vessel is completely filled with milling balls and sub-
strates no movement will be possible in general. As a consequence no energy
can be transferred to the system. Generally the total filling degree of the
vessel (F
total
) is calculated following Eq. (10.9) by adding up the volumetric
filling degrees for the milling balls (F
MB,material
) and the grinding stock
(F
GS,packing
). The values for the milling balls can be easily calculated con-
sidering basic parameters as outlined in Eq. (10.10). In addition to
F
MB,material
the milling balls' filling degree considering the milling balls'
packing volume (F
MB,packing
) might be of interest, especially for scale-up
purposes. Following Eq. (10.11) the filling degree for the grinding stock
(substrates in the case of mechanochemical syntheses) can be approximated
using basic material parameters as well:
F
total
¼
F
MB,material
þ
F
Gs,packing
(10.9)
¼
pd
3
MB
n
MB
6V
MV
F
MB
;
material
¼
V
MB
;
material
V
MV
(10
:
10)
D
F
MB
;
packing
1
e
ð
Þ
P
i
m
GS
;
i
r
GS
;
i
V
MV
F
GS
;
packing
D
(10
:
11)
where
F
total
(
) is the total filling degree,
F
MB,material
(
): volumetric filling degree of the milling balls,
F
GS;packing
(
): volumetric filling degree of the grinding stock,
V
MB,material
(cm
3
): overall milling ball volume,
V
MV
(cm
3
): total milling vessel volume,
F
MB,packing
(
): milling balls' filling degree regarding packing volume,
e (
): porosity of the milling balls' packing,
m
GS,i
(g): mass of individual substrate,
r
GS,i
(g cm
3
): density of individual substrate,
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