Magnetically Controlled Reflection of a Ferrofluid Cell

Figure 2 – A 300x microscope picture of moving magnetic agglomerate clusters

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Figure 2 – A 300x microscope picture of moving magnetic agglomerate clusters
What happens is that the surfactant can only keep the nanoparticles apart in weaker magnetic fields. Once you exceed the abilities of the surfactant, the nanoparticles start clumping together and given enough time, they self assemble into micrometer long helical rods.

For many years I have looked at this precipitate and did not realized it's importance. The rods form within the liquid and if given enough time the rods stick to the glass windows. Often, I would disassemble the cells and would have to make a effort with acetone solvent to remove the precipitate.

I did not disregard the precipitate because it was a mystery; but I disregarded it because it was exactly not a mystery. You apply a magnetic field, of course some of the magnetite might come out of solution and stick to the glass. I started this work in 2007 and in 2015 I finally figured out my error when a meta-materials paper was published.
"For a nonmagnetic material, magnetic resonances can be created by resonating loops of displacement current. This can be achieved in closely packed subwavelength metallic nanoparticles. The boundary conditions at the surfaces of the nanoparticle dictate that the direction of the electric field should always be normal to the surface of the particle. Therefore, in circularly arranged nanoparticles, at each boundary the electric field rotates slightly, leading to a full circulation of the light's electric field at a resonance. ... Because the metal doesn’t touch the electrons can only oscillate within individual particles and can’t move from one nanoparticle to its neighbor. This is known as a displacement current. It’s like doing the wave in a stadium; no one fan is moving from their seat, but the wave moves around in a circle." - Nader Engheta - 2015
In Figure #2 I am showing the micrometer long helical rods precipitating out of a light oil and traveling to a permanent magnet chip. Notice how well ordered the self assembled magnetic agglomerate clusters are aligning themselves.
Once I had read Dr. Engheta's paper everything started making sense. I had assumed a precipitate of nanoparticles would have the same physical properties as the bulk material. Not once did I imagine that a agglomerate of nanoparticles could have physical properties that is different than the bulk material nor a solution of nanoparticles.
To be fair, Dr. Engheta works with metal nanoparticles and I work with magnetic metal-oxide nanoparticles but I believe his displacement current idea is correct. If we treat each nanoparticle as an isolated group of electrons and then an agglomerate of nanoparticles is treated as many groups of isolated groups of electrons, which are electromagnetically coupled each together; then my ferrofluid cells are showing optical resonances which corresponds to the magnetic agglomerate clusters resonating.
Another name for electrostatic neutral surfactant would be an insulating surfactant which means each nanoparticle has a small amount of capacitance. Referring to Figure #3, each ferrofluid particle has a magnetic moment which we could call inductance, and magnetite is known to have magnetoresistance. I have a background in electronics and can easily believe that each magnetic metal-oxide nanoparticle can be modeled as a RLC oscillator, and when you couple them together in an agglomerate, it is a large system of coupled oscillators. No wonder that I have photographs of optical resonances.

Figure 3 – Each metal-oxide nanoparticle can be modeled as a RLC oscillator
I claim that in Figure #1 and Figure #2 that we are looking at electromagnetic oscillators which are coupled to both electric and magnetic fields of their environment. Later in the document I will be flooding the ferrofluid cells with photons and measuring the back scatter at a 45 degree angle of incidence.
My point being that not only do we have a system of oscillators but we have a large amount of incoming high frequency energy in the form of photons that drives the system.
One problem is how are these micrometer sized structures oscillating at optical frequencies? One would not expect the large agglomerate clusters to have this ability. I believe the answer is that you have to remember that there's a large number of individual nanoparticles that are still in the solution.
I can imagine a system where the agglomerate clusters are oscillating at a lower primary frequency in the terahertz range, and the single nanoparticles in the solution are oscillating at a higher harmonic optical frequency.
In electronics we have the Skin Effect where the high frequencies travel on outside surface of copper wires. How do you define the surface of the agglomerate clusters? Do you include the ferrimagnetic nanoparticles that are magnetically bound, but are not physically touching it? What is the high frequency permeability of ferrimagnetic nanoparticles in general? Do the opposing magnetic moments produce a fractional Mu?

Clearly, I have more questions than answers but no one can be an expert at everything.

Figure 4 – A 100x microscope picture of millimeter sized agglomerate rods.
In Figure #4 we see in over 15 minutes that the magnetic agglomerate clusters have formed a network of millimeter sized rods aligned along the magnetic field lines. This leads to another question, is Figure #4 a picture of a metasurface?
In 2005, Dr. S. Y. Yang called his magnetic agglomerate clusters a photonic crystal with the ordered structures, that produces a refractive index that varies periodically over the film. In 2015, this sounds like the definition of metasurface. Just think, if Figure #4 shows helical rods of photonic crystal, that sounds useful for self assembled optics.
"Ordinary mirrors reflect light over a broad range of frequencies, but a new mirror design can reflect a single frequency while allowing all others through. This “metamirror,” an array of subwavelength pieces of shaped metal embedded in a transparent medium, can also be made to reflect light in a chosen direction or focus it like a curved mirror. The shape of the inclusion affects the phase of the scattered microwave light the timing of its wave crests in relation to the incoming light—and the net effect of the right combination of shapes is to reinforce one specific direction for the scattered waves. The team’s metasurface design includes a variety of inclusion shapes, placed in a two-dimensional geometric pattern. The inclusions all respond to the same frequency, allowing other frequencies to pass through unaffected. Using computer simulations, the researchers showed that they could design an array that completely reflected an incoming light wave at any angle they wished." V. S. Asadchy 2015

My understanding of a metamirror is that it uses oscillating dipoles to scatter photons. Later in this document I have page after page of magnetic dipoles that are scattering photons. The inventor of the Ferrofluid cell, Timm Vanderelli has been selling cells since 2004. As a physics undergrad I needed a senior final project and bought a cell. I think my words at the time about explaining how the cells work was,

"How hard could it be?"

Figure 5 – The frequency of harmonic oscillator is a function of the potential.
The last point of this section I wanted to address is the ferrofluid cells tend to show potential energy contours of the applied filed. In Figure #6 there is a small permanent magnet behind one of the ferrofluid cells with its perimeter leds turned on. The image itself is made of many ellipses of photon scatter but our minds tend to average out the ellipses into a system of concentric circles. Not surprisingly the potential energy of a magnetic pole is a system of concentric circles.
This is not an accident, I can show that if you average out the scatter lines in the ferrofluid cell photographs, it reduces to a potential energy plot of the applied field.

Which brings up the question, how does the ferrofluid cell show the potential energy levels of the applied field?

Unlike conventional magnetic fluid deformable mirror technology, the ferrofluid cells are sealed and there is no free surface other than the surfaces of the window and the mirror.

Instead I think the answer comes from first principles. We need to switch models from a RLC tank to a true harmonic oscillator. The simple pendulum seen in Figure #5 will do.

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