Rotating Pulsed Magnetic Field Design and a Pulsed Field Study of Nanoparticle Phase Dynamics

by John N. Moore

moorejn@rose-hulman.edu

supervisor:  Dr. Viktor Chikan

Kansas State University Physics Department REU Program

This program is funded by the National Science Foundation through grant number PHY-1157044. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Introduction to Project 1: When nanoscale magnetic particles are delivered near tumor sites there are two mechanisms by which they can destroy cancerous cells. The first, called magnetic hyperthermia, results when the nanoparticles absorb energy via relaxation of their magnetic moments in the presence of an alternating magnetic field. The temperature increase caused by these relaxations is sufficient to kill surrounding cancerous cells (~44°C), however, until nanoparticle relaxation is better understood in biological systems the particle concentrations required for effective treatment (~5 mg/cm³) are not without unhealthy side effects. An alternative to magnetic hyperthermia would be to cut through the cancer cell membranes using the mechanical motion of nanoparticles. If rod-shaped nanoparticles are placed in a rapidly rotating magnetic field they will maintain their alignment with the field and spin like miniature drills. Using this method it would be possible to destroy cancer tissue at much lower particle concentrations than used for a heating method.

Unfortunately magnetic nanorods are still challenging to synthesize, and the rotating magnetic fields that one would use to study such nanorods are difficult to generate. I spent about seven weeks working to build a high-voltage experimental setup capable of producing a pulsed field that rotates in a single plane. The setup when complete will be useful for a host of optical experiments including measurements of Faraday rotation and Cotton-Mouton coefficients which provide important information about the magnetic environment of nanoparticle suspensions. Beyond nanoparticle magnetism, a rotating magnetic field might also be used to create molecules with dynamic chirality and materials with a negative refractive index.

A nested Helmholtz coil arrangement is used with the coil axes oriented perpendicular to each other. As the magnetic field produced by each coil adds as a linear combination, a resultant field can be produced in any direction within the plane of the coil axes.

To ensure that all of the nanorods in a solution are aligning with the magnetic field, fields on the order of a couple tesla are ideal. To achieve such fields, a pulsed RLC circuit is used. One branch of the circuit made up of a capacitor, inductor, and a resistor is shown here. After the capacitor is charged up to a voltage anywhere between 1kV and 10kV, a spark ionizes the gas between two electrodes, closing the circuit and allowing the capacitor to discharge through the Helmholtz coil.

The current pulse resulting from the above circuit is modeled as an under-damped sign wave (left). When one of these pulses is shifted by a phase of with respect to the other, the resultant field traces out an ellipse in space as it decays (right).

A major challenge is to reliably fire the capacitors with the correct phase delay. In our experiment this phase is about 21 microseconds. One spark gap the we use to give precise triggering of the pulse is a pressurized cavity that can be filled with either helium, argon, or air depending on the desired dielectric constant (left and bottom right). The spark comes from a box which receives an input signal from a timing box (bottom left). The timing box sends two output signals with delays that can be programmed with nanosecond precision.

Introduction to Project 2: During my last three weeks I studied the Faraday rotation of nanoparticle solutions using a different experimental setup which delivered a pulsed magnetic field of up to around 3.5 tesla. Faraday rotation is observed as the rotation of light’s axis of polarization as it propagates through a medium in which a magnetic field is present along the direction of propagation. The angle of rotation is given as the product of the magnetic field strength, the optical path length, and a material specific constant called the Verdet constant. Materials with a large Verdet constant are useful in the design of optical isolators, magneto-optic modulators and switches, and magnetic field sensors. These devices in their conventional bulk forms usually rely on materials like garnet crystals for their large rotations and fast response times, but as optical components continue to be miniaturized for applications to integrated optical systems, more compact designs demand new materials. Nanoparticle composites, because of their scalability and potential to deliver exceptionally large magneto-optic rotations, are a viable solution.

One limitation of the magneto-optic devices mentioned is the time that it takes the magnetic moments inside the material to respond to the external field. This can be seen our experiment as a delay in the Faraday rotation signal peaks with respect to the peaks in the pulsed field. Studying how these delays depend on factors such as the magnitude of the field, the duration of the pulse, and the concentration of the nanoparticle solution, we can gain a better understanding of nanoparticle dynamics and some the interactions that give rise to longer relaxation times in these solutions. Further, we may see that the puled field in out experiment can offer more useful information related to phase than a more conventional AC field technique.

Faraday rotation is observed as the rotation of light’s axis of polarization as it propagates through a medium in which a magnetic field is present along the direction of propagation. The angle of rotation is given as the product of the magnetic field strength (B), the optical path length (d), and a material specific constant called the Verdet constant ().

When the magnetic field pulse and Faraday rotation pulse are plotted together there are several points at which both the field and the rotation go to zero. At ten of these intersections I measured the relative delay of the rotation signal with respect to the field signal. I averaged these phases over three pulse captures to help cancel statistical variations, then I plotted the phase against the intersection number for five different concentrations of nanoparticle solution. This plot shows the phase decreasing over the duration of a pulse. The phase delay of each concentration averaged over the duration of a pulse shows a trend of increasing phase with increasing concentration.

Links: 

Chikan Group Webpage

Final Presentation