Technical Implications of Organic Syntheses in Ball Mills - Ball Milling Towards Green Synthesis: Applications, Projects, Challenges - page 259

Figure 10.10 Influence of milling ball filling degree, F MB,packing , and milling ball

diameter, d MB , on the yield of the Knoevenagel condensation of vanillin
and barbituric acid (equimolar ratio; Scheme 10.4). PBM Fritsch P6
(V MV ¼ 0.25 L, n ¼ 100 mmol, rpm ¼ 650 min 1 , t reaction ¼ 12 min).
For further experimental conditions see Table 1 in the respective
reference 79.
Reproduced with permission of the Royal Society of Chemistry.

Figure 10.10 visualizes the influence of F MB,packing on the yield of the
model reaction for different d MB . Experiments have been conducted in the
large PBM in 250 mL milling beakers at a constant reaction time of 12 min
and rpm ¼ 650 min 1 , which are the optimal conditions already outlined for
F MB,packing ¼ 0.28-0.30 in Figure 10.10. The results strikingly indicate the
importance of this parameter, since independent from d MB the curves pass
through a maximum, which is in the range of 0.43 r F MB,packing r 0.50. 79
According to Eqs (10.1) and (10.7) the overall stress energy depends on SE
and SF.IfF MB,packing is o 0.4 the number of stress events, SN, and therefore
also SF and the medium SE are reduced, which leads to the observed effect
regarding the yield. Although the movement of the milling balls inside the
beakers is not distorted, for an ecient energy transfer the grinding bodies
need space for acceleration and movement through the milling beaker. In
case of F MB,packing 40.5 the free space for the trajectories is restricted or
completely blocked and the milling balls cannot be accelerated, make their
way through the vessel, and cause impacts (Figure 10.4). 9,20,31,53 Manu-
facturers of PBMs generally advise their customers to leave at least 33% of
V VM for the trajectories of the milling balls and the geometrical volume,
V MB,material , of the milling balls should not exceed 33%. 31 Based on par-
ameters like d MB , n MB and r MB , the value of F MB,material can be estimated
(Eq. 10.10). Recalculation of the optimal values for F MB,packing from
Figure 10.10 results in F MB,material of 0.26, 0.27, and 0.28 for d MB ¼ 10, 20,
and 30 mm, respectively. This is roughly in accordance with the manu-
facturers' advice.
Beside the volume of milling balls the volume of reagents also influences
F total . Changing this value would consequently result in different conditions