Technical Implications of Organic Syntheses in Ball Mills - Ball Milling Towards Green Synthesis: Applications, Projects, Challenges - page 252

For rotation (i ¼ rot) or oscillation (i ¼ osc) processes Eq. (10.2) can be
transformed into Eq. (10.3) with substitution of m and v by the moment of
inertia I and the angular velocity o or frequency n (o ¼ 2pn), respectively: 10
E kin,i pIo i pIv i (10.3)
where I (kg m 2 ) is the moment of inertia, o (s 1 ) is the angular velocity and
n (s 1 ) is the rotation or oscillation frequency.
On substitution of n by the peripheral velocity (v p ) of a punctual mass that
rotates at the distance r from the rotation axis and the general definition for
the moment of inertia of a complex body, Eq. (10.3) can be transformed into
Eq. (10.4), demonstrating the importance of the grinding body density for
the kinetic energy of the system: 54,68
E kin,rot ¼ 6mv p (10.4)
where v p (m s 1 ) is the peripheral velocity and m (kg) is the mass of the
rotating body.
The kinetic energy that originates from the torque of the propulsion unit
of the ball mill is transformed through friction and impact processes into
either chemical or thermal energy. If the mechanical action of the milling
balls directly induce a chemical reaction, a mechanochemical reaction takes
place. 17 On the other hand, frictional heat induces an increase of the local or
bulk temperature of the mill feed and can speed up chemical reactions by
providing the required activation energy. Although the kinetic energy pro-
vided by the propulsion system cannot be used completely as (thermal) ac-
tivation energy due to dissipative losses, a correlation between the mass of
the grinding bodies (m MB B r MB ) and the chemical yield has been described

for some organic reactions in ball mills. 10,62,69-71 In several cases a signifi-
cant increase of yield was observed when the material is changed, e.g. from
light-weight natural mineral agate (r ¼ 2.7 g cm 3 ) to the heavier ZrO 2
(r ¼ 5.7 g cm 3 ). 62,70 However, there are also examples from the field of
organic synthesis in which no influence was observed, which seems to in-
dicate a product decomposition due to high energy. 60,66,72,73
Table 10.1 provides an overview of the materials for milling balls and
milling vessels applicable for mechanochemical syntheses. Beside material
density, the chemical resistance is also important for organic syntheses. From
the available materials, tungsten carbide and stabilized zirconia are the
materials of choice. Although they are very expensive, they proved to be
chemically inert towards most reagents and in case of zirconia the abrasive
resistance is also high. Other materials available for grinding bodies or
milling containment have a high porosity (agate or steel) and, therefore,
memory effects might occur if the tools are not properly cleaned after the
reaction.
During ball milling, abrasion of particles from the surface of the milling
tools may occur and can interact with the mill feed (Table 10.1). For metal-
catalyzed reactions this might be a problem due to contamination with other
catalytically active elements. However, it is also possible to take advantage of