indeed it is correct, that the force a magnetic field gradient can induce on a single 10 nm particle is too small to achieve substantial motion. However, induced by an external magnetic field, (an well chosen surface chemistry) the superparamagnetic nanoparticles can aggregate. These larger aggregate particles (usually in chain-like aggregates) can be large enough for rapid motion.

While it is possible to calculate the magnetic force on an individual particle, the dynamics of aggregation and aggregate motion make the calculation of particle collection highly laborious (or near to impossible).

Additional complication comes from the fact, that the magnetic field around a magnetic particle is not only governed by the external field, but also by the magnetic field induced by the particle itself.

indeed it is correct, that the force a magnetic field gradient can induce on a single 10 nm particle is too small to achieve substantial motion. However, induced by an external magnetic field, (an well chosen surface chemistry) the superparamagnetic nanoparticles can aggregate. These larger aggregate particles (usually in chain-like aggregates) can be large enough for rapid motion.

While it is possible to calculate the magnetic force on an individual particle, the dynamics of aggregation and aggregate motion make the calculation of particle collection highly laborious (or near to impossible).

Additional complication comes from the fact, that the magnetic field around a magnetic particle is not only governed by the external field, but also by the magnetic field induced by the particle itself.

Dear Mathias Brust,

I have worked with magnetic nanoparticles including superparamagnetic iron oxide (SPIO) as T2 contrast agent of MRI for a few years. It’s absolutely possible, and I see this phenomenon everyday in my works. The point is that motion of object actually is to overcome the object weight. Now for a good synthesis SPIO saturation magnetization is about 100 emu/g, but each 10 nm particle has about 10^-23 gram weight. Regarding to this superfine size, dragging nanoparticles with small hand held magnet will be possible.

Magnetic nanoparticles in a nanocolloidal system have a tendency to agglomeration even without an external magnetic field due to huge magnetic and gravity (F=M1*M2/r^2)attraction force. Addition to magnetic force, gravity is gigantic force for nanosize materials because distance (r) will be so small. We usually use organic coats like dextran and PEG with high Dalton number to increase distance between particles. In this situation hydrophilic coat helps to the stability of particles, and Brownian motion will be dominant parameter. Therefore, the vital point in nanocolloids is the coating agents and ligands which surrounded nanoparticles.

Sure, hydrodynamic drag can be overcome but through the formation of assemblies like in biogenic magnetosomes... I suggest these papers and refereces therein http://pubs.acs.org/doi/abs/10.1021/jp0755286

Zubarev &kostenko, colloid j. 75,66 (2013)

It all comes down to the product of the particle moment and the field gradient. Thus, particle material, its SD volume (or wall energies if MD), magnetic field (i.e the susceptibility too) and field gradient and kB/kT, KV/kT are all relevant.

So you need to be more explicit about the magnetic material of the nanoparticle. Pure Fe or Co have high MS values, for example, that make extraction (especially after aggregation) much easier.

You will find plenty of calculations relating to this in the Magnetic Fluid / Ferrofluids (magnetic colloid) literature stretching back to the 1970s and 80s, also in the metallic ESD (elongated single domain particle) electrodeposited literature of the 60s. A magnetic slurry is a complete no-no to Magnetic Fluids specialists! Also look at magnetotactic (magnetosome) bio-particle literature where the bacterium and its (nanoparticulate) magnetosomes are easily extracted by small magnets due to a combination of larger hydrodynamic volume and particle chaining.

You are right- in “good” colloid it is not possible to separate a single “superparamagnetic nanoparticle” from fluid with a magnet. In colloid the magnetic core of a nanoparticle is coated with the organic molecules, and there is “strong” attraction van-der Waals forces between ”the superparamagnetic nanoparticle” and molecules of the liquid.

If the definition of superparamagnetic particles means < 30 nm,then a hand held magnet will not collect all particles unless they occupy a small volume. Magnetic field strength falls off as a function of distance [1/d2]. If you have a great distance to overcome then magnetic induction is required.

@Henri: superparamagnetic means superparamagnetic: moment orientation fluctuates. At what size this happens depends on the material.

And I do not want to leave the gravitation remark brought up by Hamed above uncommented: gravitation is not an issue. No way. In case you're not convinced - feel free to check the attachment.

Note: in case I were wrong I'd apologize for the strong words above, of course.

I work with dispersions of maghemite nanoparticles (7-12 nm diameter, superparamagnetic) in different solvents and with different coatings, also known as ferrofluids, and I can assure you that in a stable dispersion you cannot separate your particles from the bulk solvent. When you approach a hand magnet, you'll have different effects depending on the nanoparticle concentration of your sample: nothing happens if it's dilute; the fluid (or part of it) moves as a whole towards the magnet in the case of concentration around 1-5% (volume fraction in water); when vol fract >= 8% you get the famous peaks. If the repulsive part of the pair potential is strong enough to stabilize the dispersion, in no way will you be able to separate the particles. Stability can be achieved not only by coating the nanoparticles surface with long chain molecules but also just thanks to electrostatic repulsion. For example positively (acid) or negatively (basic) charged maghemite nanoparticles dispersed in water are stable for years, and the only way (that I know of) to separate the particles from the solvent without forming aggregates is to centrifuge the ferrofluid in a filter centrifugal unit.

Respected Mathias Brust

I worked on SPION, and also observe aforementioned phenomenon. I support the view of Dr. R. Grass and Mr. Hamed. I think this is happing due to the agglomeration of the nanoparticles. If the magnetic field applied is constant than, force of attraction between the nanoparticles is directly proportional to the size of the nanoparticles.

Dear Deepak Jha,

are you sure of your statements in the last sentence?

What is the significance of a "constant magnetic field"? Do you mean a homogeneous field? (-> a homogeneous field does not exerce force on magnetic objects, only a gradient field does).

What dou you mean by "size" of the nanoparticles (diameter, volume)? How do you conclude on the forces between particles to be proportional to that size parameter? And what role does the (constant) magnetic field play in this?

Sorry, but I cannot understand you at all.

Here is a bit more food for thought -- not just so called SPION or magnetic nanoparticles, magnetic ionic liquids, which are molecular in nature (although some of them are known to form small nano domains in liquid) and paramagnetic (super-para in some cases) do move towards an external magnet. As for magnetic nanoparticles, even a single 4nm particle can be moved under magnetic field (J. Am. Chem. Soc. 2008, 130, 3710–3711) -- for additional reference please look up magnetophoresis. There are different forces at play when you drag a single particle inside a stable dispersion. Magnetic force applied on the particles is proportional to the volume of the magnetic core, to the gradient of the magnetic field multiplied by the saturation magnetization of the particle. Keep it in mind this is vectorial in nature. Next comes viscous drag -- which scales with solvodynamic diameter, it's harder to move a smaller particle, harder more so as Brownian motion impacts smaller particles more -- hence the "even" before 4nm particle in my earlier sentence. Here is a paper that offers comprehensive discussion on the topic ACS Nano, 2011, 5 (1), pp 217–226.

@ Robert Grass:

referring to the last paragraph of your comment, what is the implication of your thought? Do you think about some kind of self-interaction for a single particle (role of dipolar interactions within each single particle, with resulting demagnetizing fields) or is it about interaction between particles on top of the external field (and gradient). I have the impression to miss your point.

Can you help?

Mathias Brust:"Is there an easy way to calculate the magnetic field gradient needed for separation from dispersion?"

You have to compare the magnetic force on the particle and the gravitation force (the weight of the particle). But this comparison has to be performed for for this particular substance, because you have to take into account both the density of the particles, and the fraction of the magnetic core inside the particle, and the properties of the solvent (surface tension)... A good challenge for the graduate student! :-)

Dear Kai Fauth,

what I meant is that the magnetic field is disturbed by the presence of the nanoparticles - even in a homogeneous magnetic field, every individual particle will be surrounded by a magnetic field gradient. This is best understood in high gradient magnetic separation (HGMS) where a wire mesh (soft magnetic) is added to the liquid volume. The wire is magnetized by the external magnetic field and generates strong field gradients around every wire. Very similar to this, if a magnetic nanoparticle is magnetized in a magnetic field, the original field is distorted and high field gradients are generated surrounding the particle. This is the main reason, why magnetic nanoparticles also aggregate in homogeneous fields (although there is no movement, (magnetophoresis), of the aggregates).

Please watch the excellent movie from Juan Camacho and Jordi Faraudo (although for much larger particles). http://www.youtube.com/watch?v=MyTXF0SPWTU

There are also other movies similar to this one on the web somewhere, but at the moment I can not find them.

Some literature (not mine): http://www.sciencedirect.com/science/article/pii/S0021979709000356

http://pubs.rsc.org/en/content/articlelanding/2011/sm/c0sm01424a

Robert

They can but the amount of time it would take for the particles to move to the magnet would probably be longer than for, say, a 100nm superparamagnetic particle.