Technical Implications of Organic Syntheses in Ball Mills - Ball Milling Towards Green Synthesis: Applications, Projects, Challenges - page 261

induce chemical transformation, particle refinement, or heat dissipation
to the mill feed. The impact intensity of the milling balls correlates strictly
with the impulse and the kinetic energy. As previous considerations regarding
the kinetic energy of a rotating or oscillating system (E kin ) (Eq. 10.3) as well
as the stress energy transferred to the feed material (E stress,feed ) (Eq. 10.1)
indicate, the correlation with the rotation, n rot ((Hz) or rpm (min 1 )), or
oscillation frequency, n osc (Hz s 1 1/60 min 1 ), is of a quadratic
nature. 10,29,75 In combination with the moving mass the operating frequency
determines the energy amount that can be transferred into heat or chemical
energy. Therefore, a strong correlation is reasonable for the influence of n on
resulting variables describing the characteristics of a product or the
performance of a chemical reaction. Beside reaction time (t), it has been
shown that the influence of n on a chemical reaction in ball mills is the most
important. 72 Several examples described in the literature indicate this
mathematical correlation between, for example, yield or conversion and the
frequency a ball mill is operated with. Generally, higher frequencies result
in an increase of those variables. Examples regarding organic synthesis
are very widespread, resembling many fields of synthesis chemistry: cross-
coupling, 29,72 redox chemistry, 73,77,80 synthesis of heterocycles, 81 organocata-
lytic enantioselective aldol-type reactions, 82 condensation reactions, 61,78,79,83,84
polymer grafting, 85 reactions of carbohydrates, 86 and further examples are
known dealing with these correlations. 87 The correlations are illustrated for the
KnoevenagelcondensationoutlinedinScheme10.4atdifferentreactionscales
(Figure 10.11). 79 It should be mentioned that similar operating frequencies for
different ball mills should not allow us to conclude that the stress energies are
similar (see also Section 10.3.1).
Many authors report that the target variable (yield, conversion or select-
ivity) reaches a static relation or they observe a decrease after passing

Figure 10.11 Influence of milling time, t reaction , and rotation frequency, rpm, on the

yield of the Knoevenagel condensation of vanillin and barbituric acid
(equimolar ratio; Scheme 10.4). Left: PBM Fritsch P7 premium line
(V MV ¼ 0.045 L, n ¼ 20 mmol, d MB ¼ 10 mm). Right: PBM Fritsch P6
(V MV ¼ 0.25 L, n ¼ 100 mmol, d MB ¼ 20 mm). For further experimental
conditions see Table 1 in the respective reference 79.
Reproduced with permission of the Royal Society of Chemistry.