I have use for my first experience planetary ball mill PM400 (Retsch), and now I want to do another experience with the same condition (same energy of milling) but the PM400 is not functional so I am obliged to use the PM200 (Retsch)
Is there any equation or method to calculate the energy of milling and adjust the parameter between the two ball mills?
Best regards.
There is no equation for the comparison of milling energies. But if you are using the same milling container you can them going out that the milling result will be approximately equal at the same acceleration.
According Retsch manuals delivers PM 200 slightly higher maximal accelerator than PM 400 (37.1 g to 26.8 g). This means that you do not have to go to full speed with PM200.
You might measure the temperature increase filling only with balls, at least sould work theoretically.
Vadim is right, unfortunately there is no comprehensive equation to compare the power (W/g) or energy (J/g) passed to the milled material. In general these depend on the milling regime: milling time (seconds), centripetal acceleration (g), powder to balls mass ratio (%), grinding jar and balls diameter (mm) as well as type of treated powder.
First of all you should decide what power (or energy) you want to measure. Total energy passed to the jar with balls and powder can be estimated as dE= Cm*dT, where Cm –heat capacity of jar+balls+powder, dT – temperature rise at initial (linear) period of operation. But typically around 95% of the power goes to a simple heat loss and is not accumulated in the milled powder. Measuring temperature without any powder load doesn’t seem right as an established balls temperature strongly depends on the loaded powder mass. It can drop from 600-800C (without powder) to around 200C (at 1:100 powder to balls mass ratio).
One most common way to measure energy (J/g) passed exactly to the material is to control its specific surface S (m2/g, e.g. via gas sorbtion): dE= k*A*dS, where A – surface energy (J/m2), k – empiric constant (5-10). This approach works only while the material keeps refining (S rises) during treatment time, usually until particle size of several nm. In this way you can compare the effect of milling duration at two different devices (or two different regimes) simply by measuring dependance S(t). You can get an estimate of absolute value of E if you’ll find data on A for your material. Value of 1/k is a portion of energy spent on refinement of material (the rest is spent on its heating). But you should keep in mind that all the measured values correspond to certain investigated regime.
If you investigate milling of material which will be used as a reagent in some kind of exothermal reaction, you can measure insrease in heat effect instead of increase of specific surface.
Thank you for your response, but i am looking for a practical method.
you said me that i should calculate the surface energy of my material, please can you give me more clarification if it is possible.
best regards
Hi, maybe it's too late to be of help. Please, take a look to this work I published recentely:
DOI: 10.1016/j.cej.2016.01.079
I calculated the energy dose (according the definition of P. Butyagin) for different models of PBM. It is amply proved that the energy dose is an invariant quantity for MC transformations. In other words, providing the same energy dose (with different mills or milling parameters) you can obtain the same degree of refinement or conversion (if we are talking of MC reactions). The procedure is quite simple but you first need to calculate average ball velocity using the mathematical model of Chatthopadyhay (I used Excel for all calculations). All details and references are in the paper.
I hope it is useful. Regards.
Mr Giovanni Cagnetta,
please can you re-poste the link or the title of the publication.
Best regards.
Here there is the link:
http://dx.doi.org/10.1016%2Fj.cej.2016.01.079
I also attached the publication
http://dx.doi.org/10.1016%2Fj.cej.2016.01.079
Article A comprehensive kinetic model for mechanochemical destructio...
You could just ask the supplier of the machines, maybe they have got the right answer ,-)
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