Dear Binota,

I couldn't see the graph. You ought to express for which phenomena that you want to determine the CRITICAL particle size. Critical monodomain size above which nanoparticles tends to be multidomain, or Critical superparamgnetic diameter below which particles lacks anisotropic magnetization direction at RT. However, the saturation magnetization per unit mass of a magnetic material is an intrinsic property. It also depends on temperature and mean-size of the nanoparticles.

If you want to relate the mean-size of your sample with the saturation, you still need some measurement data other than magnetization such as from SEM, or XRD, or mass-density data if there is any technique for that, of course.

All the best,

Brook 

Hi, this is the formula that you have to use:

Considering the effect of thermal fluctuations, the coercivity as a function of particle size D, approximately follows the relation

HC(D)= 0.5Hk[1-(Dp/D)3/2]

where Hk is the anisotropy field of the material in question, D is the measured particle size and Dp is the superparamagnetic particle size. Therefor if you know the coercive field, the particle size and the anisotropy field you can calculate the critical diameter.

You can use the graph and the formula similar to that used in this article (Eq3 and fig 13)

Article Spherical magnetic nanoparticles fabricated by laser target ...

 Thank you brook, sayani and sergey. 

 @brook, sayani, sergey: i want to measure size of Fe3O4 sphere below which the particle will fail to be attracted towards a magnet bar (Fe3O4 here is used as catalyst for water treatment and at the end i need to  separate it from water). i have SEM, XRD data too, but am unable to find an equation serving my particular purpose). 

sayani: how can i know anistropy field? i have coercive field and measured particle size. 

@Binota,

Thanks.

For your intended application,  in principle there is no particle size limit for the partcle to be attracted. In other words, be It superparamagnetic, monodomain or multidomain magnetic nanoparticle, it should be attracted by a magnet. Nonetheless, from practical point of view, effective separation of the magnetic bead may depend upon the water's viscosity, flow rate and other engineering aspects the treatment plant, hence require some critical size for effective separation. If you mayn't get research paper on this specific case, a similar physical system would be in-vivo 'magnetic separation', 'magnetic swimmers' and so on. 

This reference might of help: 

1) Snezhko A, Belkin M, Aranson I S and Kwok W-K 2009 Phys. Rev. Lett. 102 118103

2) Nacev A, Komaee A, Sarwar A, Probst R, Kim S H, Emmert-Buck M and Shapiro B 2012 IEEE Control Systems 32 32–74

Nice weekend,

Brook

thank you so much brook. I will go through the papers.