Abstract
Mechanochemistry (MC) exerts extraordinary degradation and decomposition effects on many chlorinated, brominated, and even fluorinated persistent organic pollutants (POPs). However, its application is still limited by inadequate study of its reaction kinetic aspects. In the present work, the ball motion and energy transfer in planetary ball mill are investigated in some detail. Almost all milling parameters are summarised in a single factor—total effective impact energy. Furthermore, the MC kinetic between calcium oxide/Al and hexachlorobenzene is well established and modelled. The results indicate that total effective impact energy and reagent ratio are the two factors sufficient for describing the MC degradation degree of POPs. The reaction rate constant only depends on the chemical properties of reactants, so it could be used as an important index to appraise the quality of MC additives. This model successfully predicts the reaction rate for different operating conditions, indicating that it could be suitably applied for conducting MC reactions in other reactors.
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Abbreviations
- C 0 :
-
Original concentration of HCBz, mg g−1
- C t :
-
Concentration of HCBz after a certain time of milling, mg g−1
- C R :
-
Charge ratio (ball to sample ratio in w/w)
- D 0 :
-
Total energy supplied to the powder being milled (total effective impact energy), J g−1
- E t :
-
Ball impact energy, J
- E e :
-
Ball effective impact energy, J
- E eff :
-
Effective flexibility modulus of the collision media, GPa
- f :
-
Ball hitting frequency, Hz
- g r :
-
Geometrical constant
- g p :
-
Geometrical constant
- h 0 :
-
Thickness of the powder layer, m
- K 1 :
-
Rate constant of Delogu’s model, mg J−1
- K :
-
Rate constant of the model used in the present work, mg J−1
- m b :
-
Mass of a single ball, g
- m p :
-
Mass of pollutants, g
- n B :
-
Number of balls
- P t :
-
Ball impact power, W
- P e :
-
Ball effective impact power, W
- P 0 e :
-
Ball effective impact power per mass unit, W g−1
- P n :
-
Normal impact pressure, Pa
- R :
-
Reagent to pollutant ratio
- RSS:
-
Root-sum square deviation
- r d :
-
Distance between the centre of disk and pot, m
- r v :
-
Radius of pot, m
- r h :
-
Impact radius, m
- r b :
-
Radius of balls, m
- t :
-
Milling time, s
- t 1 :
-
Time of ball detachment, s
- t 2 :
-
Time of ball flight, s
- t 3 :
-
Time of ball returning to the starting position, s
- v :
-
Moving velocity of balls, m s−1
- v x :
-
Component velocity of v in x axis, m s−1
- v y :
-
Component velocity of v in y axis, m s−1
- v n :
-
Ball normal impact relative velocity, m s−1
- v r :
-
Radial velocity component of balls, m s−1
- v v :
-
Linear velocity of hitting point on pot, m s−1
- v vr :
-
Radial velocity component of v v , m s−1
- χ:
-
Fractional conversion degree
- χ i cal :
-
Conversion efficiency calculated by the model
- χ i xp :
-
Conversion efficiency obtained from the experiments
- X 2 :
-
x value of hitting point, m
- X c2 :
-
x value of pot centre at hitting moment, m
- Y 2 :
-
y value of hitting point, m
- Y c2 :
-
y value of pot centre at hitting moment, m
- Ω:
-
Rotation speed of the disk, rad s−1
- ω :
-
Rotation speed of the pot, rad s−1
- γ :
-
Ball impact angle, rad
- θ 2 :
-
Rotation angle of disk, rad
- ϕ 1 :
-
Rotation angle of pot, rad
- δ max :
-
Deformation of the ball at maximum compression, m
- θ 2 :
-
Rotation angle of disk, rad
- ρ B :
-
Density of the balls, kg/m3
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Acknowledgements
This project was supported by the National Natural Science Foundation of China (No. 51676172, No. 51706201), the National Key Research and Development Program of China (2017YFC0703101), the Zhejiang Provincial Natural Science Foundation of China (R14E060001), the Zhejiang University’s Pao Yu-Kong International Fund, and the Program of Introducing Talents of Discipline to University (B08026).
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Chen, Z., Lu, S., Mao, Q. et al. Energy transfer and kinetics in mechanochemistry. Environ Sci Pollut Res 24, 24562–24571 (2017). https://doi.org/10.1007/s11356-017-0028-9
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DOI: https://doi.org/10.1007/s11356-017-0028-9