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Electrical Engineering Qualifying Exam Written Requirement James C. Stephenson April 7th, 2004 1. Abstract I have reviewed three technical papers for the purpose of establishing relevance to my own research area. The particular areas of research defined by these different efforts have nothing in common with each other than their applicability to my own work. White et al. have demonstrated that paramagnetic molecules can be contained within small spatial regions by the magnetic gradient force that exists near ferromagnetic microelectrodes immersed in a homogeneous magnetic field. Furse et al. reports their Plasma Fluid Finite Difference Time Domain formulation as a valid alternative to analytical methods when complex antenna shapes, or plasma dynamics need to be modeled. The third paper I reviewed was related to an investigation of the dielectric properties of laminate materials. 2. Introduction My own research interest is in the electromagnetic fingerprinting of molecules or particles in solution. I propose the development of a micro Nuclear Magnetic Resonance imaging cell that does not require an expensive cryogenically cooled electromagnet. Through simulation I have demonstrated that field strengths of 1 – 3 Tesla are possible with rare earth magnets combined with high permeability flux guiding features. Coils will be used to alter the magnetic field within this range. After a brief description of each of the three papers I will present the results obtained and establish relevance within the context of my own research interest. White et al. in “Microscale Confinement of Paramagnetic Molecules in Magnetic Field Gradients Surrounding Ferromagnetic Microelectrodes” demonstrated that paramagnetic molecules (electrogenerated in this case) could be confined to regions in close proximity to a ferromagnetic microelectrode for tens of seconds. Additionally, this work demonstrated that the magnetic gradient forces on a charged paramagnetic molecule are larger than the Lorentz or gravity driven convective forces within an electrochemical cell at or near the surface of the ferromagnetic microelectrode. Furse et al. in “The Response of a Short Dipole Antenna in a Plasma Via a Finite Difference Time Domain Model” demonstrated the validity of the approach as an alternative to the analytical model. The use of this approach would be indicated when complex antenna shapes need to be analyzed or when ion kinetics cannot be ignored. The results showed a qualitative agreement with the analytical model for various orderings of the gyration and plasma frequencies. Simulations were performed for plasma magnetization parallel and normal to the length of the antenna. Sharma et al. in “Laminate Materials with Low Dielectric Properties” discusses the resin structure and its effect on electrical properties of thermo set polymeric resins. The motivation behind the effort was based on the need for low loss substrates in highspeed digital, RF and microwave applications. While the efforts presented in this paper have no direct connection with my own efforts, the electromagnetic characterization of materials or media is of great interest. 3. Molecular Confinement White et al. constructed an electrochemical cell using a typical two-chamber configuration. Ag (reference) Fe or Pt (-q) Auxiliary B Electrolyte figure 2. Electrochemical cell schematic showing working (Fe/Pt), the Ag reference, and the platinum auxiliary electrodes. The working electrode materials (Fe, Pt) were chosen based on their nearly identical electrical properties and because iron is ferromagnetic, while platinum is weakly paramagnetic (~10-5). The magnetic field represented by horizontal arrows in figure (2) will spatially orient to accommodate a highly susceptible material, while no reorientation will occur for low susceptibility materials. magnetic gradient forces. It is clear that the I/V characteristics for the iron and platinum electrodes are very different. The results are presented relative to the no-field (B=0) voltammetric response of each electrode separately. There is a decrease in the current at the iron electrode when the electrode surface normal is parallel to the direction of the magnetic field, while an increase in the current at the platinum electrode is observed under the same conditions. The decrease in the cathode current at the iron electrode is due to the retention of NB- molecules after reduction, thus creating a barrier for the incoming NB molecules. This was visually explained via the use of video microscopy, as can be seen below1. Figure 1. Ferromagnetic (left) and weakly paramagnetic (right) objects immersed in a uniform magnetic field. This spatial gradient in the magnetic field will result in forces when a magnetic dipole is present. F (m B) (1) Where m is the magnetic moment vector and B is the magnetic flux density vector. In this paper the paramagnetic molecule was electrogenerated through the reduction of Nitro Benzene at the platinum or iron electrodes (negative potential) during voltammetric measurements. Voltammetric measurements are basically an I/V characterization of the electrochemical cell (sweep the voltage and measure the current). White et al. analyzed the voltammetric responses of both the platinum and iron electrodes with respect to the angle between the electrode surface normal and the background magnetic field vector. The goal of this approach was to separate the effects of the Lorentz, the gravity driven convection, and the Figure 3. Voltammetric measurement results for both the iron (A) and platinum (B) electrodes for zero-field, 0 degrees, and 90 degree electrode surface normal rotation with respect to the background magnetic field1. Figure 3. Video microscopic images taken during the voltammetric measurements for both the iron and platinum microelectrodes. Top panels (no-magnetic field), middle panels (electrode surface normal parallel to magnetic field), bottom panels (electrode normal at 90 degrees with respect to magnetic field)1. When Nitro Benzene is reduced in to the paramagnetic radical NB- its color is bright red as can be seen in figure (3). According to White et al. there is a slight decrease in mass density for the newly reduced NB molecule, such that gravity will cause an upward migration of the NB- molecule being replaced by the slightly denser NB molecule. The top panels in figure (3) indicate this upward flow. The middle panels illustrate the magnetic forces involved, i.e. the Lorentz and magnetic gradient forces. As the charge molecules leave the electrode they will experience the Lorentz force causing a vortex flow (see the right middle panel). It can be seen that this Lorentz force driven flow is inhibited by the large spatial gradient in the magnetic field near the iron electrode (left middle panel). This explains graphically the decrease in the voltammetric current for the iron electrode oriented parallel to the magnetic field presented in figure (3). The edge-on view given in the bottom panels of figure (3) explain qualitatively the increase of voltammetric current for both the iron and platinum microelectrodes. The results of these experiments can be summarized graphically with the inclusion of the normalized current versus orientation angle data obtained by White et al. channel, possibly altering the particle or molecular path as these molecules traverse the microsystem. t=0 t=36 sec Figure 5. Video images showing the behavior of paramagnetic NB- in regions close to the ferromagnetic microelectrode after the electrode current is shut off. Top panels show the retention of molecules after 36 seconds (magnetic field on). The bottom panels show the dispersive nature of the molecules when the magnetic field is turned off with the electrode current. Figure 4. Plots of the normalized currents for both the platinum (solid) and iron (dashed) electrodes as a function of electrode rotation angle with respect to the magnetic field1. This graph demonstrates some interesting dynamics related to the electrochemical cell. The Lorentz force direction will be upward for the 90 electrode orientation and downward for the 270 orientation. At 270 the Lorentz force is in direct competition with the mass density change driven flow discussed above. The fact that the magnitudes of the currents are essentially the same for both angles demonstrates that the Lorentz force is larger than the gravity driven force1. Further, This work has demonstrated the ability to confine paramagnetic particles for tens of seconds, see figure (5). The implications resulting from this investigation demonstrate phenomena that I will need to consider. Lorentz forces will be present in any permutation of my system (NMR, magnetic separation, etc.). I have also indicated the use of high permeability materials as a means to guide flux. These materials will be in close proximity to the NMR microchannel. Large gradients will exist near the inner surfaces of this 3.1 Additional Research Needs Of particular interest to me would be the relationship between retention times as a function of field strength. Pure iron saturates at much higher flux densities than were used in these experiments, leaving room for further investigation. I am also prepared to research the magnetic moment formulation described in this paper. In other words, under what circumstances can the Bohr magneton be used? A personal study of chemistry is unavoidable because I intend to use molecular magnetic properties for identification, and therefore need an accurate representation of the magnitude of the moment associated with the molecules of interest. 4. Numerical Modeling Furse et al. demonstrated in their work that an FDTD simulation could model an antenna immersed in magnetized plasmas. It is understood that my own work has nothing in common with space plasmas, but the formulations are just as applicable. I will therefore present these formulations in some detail and show relevance along the way. Additionally, I will indicate where the assumptions are not applicable to my system and/or describe how the model must be changed to capture the dynamics associated with a microfluidic analysis cell. From the outset, a numerical model is indicated in my work because of the complexity of the antenna or probe I intend to use (helix). One of the motivations for this PF-FDTD model was that it could be used to model arbitrarily shaped antennas. 4.1 The Equations The following analysis assumes measurements within several Debye lengths and ions are assumed stationary. The simplest model then becomes the fivemoment Maxwellian plasma fluid system2 taken from this article. The first equation used is the relationship between time the derivative of charge to the divergence of the current density. n nU 0 t (2) U mn nq(E U B) P nmv(U V ) (3) t The divergence of U is assumed to be zero here by assuming subsonic incompressible flows. The variables m, n, v, q are respectively the mass, density, electron-neutral collision frequency, and charge. P nkT U m U e m B (5) p E (6) Where n and U are the density and electron velocity respectively. The momentum equation basically relates the forces and mass transport of the system. general be present in the system (equation 3 does not account for these). Equations 2-4 must be modified to accommodate these system dynamics. The velocity term U in equations (2) and (3) will have a background DC component due to the fluid flow through the channel. The momentum equation given in (3) will need the addition of the dipole gradient forces, as well as an alteration of the electric field term to account for the polarization of the water in the channel. The energy terms for both electric and magnetic dipoles can be found in any electrodynamics text4. The negative gradient of these potentials will define the force. (4) P is the simplified energy equation with k and T equal to Boltzmann’s constant and the kinetic temperature of electrons respectively. The micro NMR system would require a fundamentally different set of equations representing the fluid dynamics for the following reasons. (1) The system consists of a background solution (water) and particles, which may or may not carry a net charge. (2) If charge particles are present in the fluid, the velocity of these particles will have two components, the fluid velocity in the channel, and the RF velocity due to EM wave interaction. (3) The polar nature of water will require an accounting of the RF polarization. (4) Electric and magnetic dipoles will in White et al. presented an average dipole moment formulation in their paper that would apply here. Since force densities are considered in (3), (5) and (6) would need to be multiplied by the density n. It should not be assumed that I understand completely the dynamics of my own system, however these arguments are correct in that these additional dynamics must be accounted for, but there are perhaps many others. In addition to the equations describing the mass flow of the plasma (2–4), Maxwell’s equations were included to complete the set of equations needed to solve for the ten unknowns, i.e. N, Ux, Uy, Uz, Ex, Ey, Ez, Bx, By, and Bz, where N is the charge species density, U, E, and B are the three spatial coordinate vectors for the velocity, electric, and magnetic fields respectively. This set of equations was then discretized in both space and time according to the temporal rules indicated by each equation and the standard Yee cell as can be found in any FDTD text. I will not include the details of the discretization here for the sake of brevity, but will move directly into the results obtained from the simulation. 4.2 Results & Discussion The simulations were setup to explore the behavior of the antenna impedance with three different orderings of the gyration frequency relative to the plasma frequency, i.e. p > , p = , p < . The antenna is expected to exhibit resonance properties at these different frequencies. Each of these orderings was simulated with a background magnetic field oriented parallel and then normal to the length of the antenna. The simulations were compared with Balmain’s analytical model. Figure 6. Magnitude of the impedance plotted against the normalized frequency. This plot represents the result for the magnetic field parallel to antenna length and p > . Balmain’s analytical data is plotted for comparison2. The impedance plot in figure 6 shows a good qualitative agreement with the analytical model. Differences at low frequencies are explained as originating from numerical errors and the lack of data points2. All of the simulations show similar qualitative agreement with theory and will therefore be omitted in this report. In the context of my work I would like to comment on why these results directly apply. In order to perform an NMR experiment, the interrogating radio frequency must be efficiently coupled to the medium under test. Therefore, the ability to calculate the expected impedance based on antenna geometry and liquid dynamics is essential. The interrogating frequency in NMR is determined by the DC magnetic field strength and the gyromagnetic ratio for a particular element (gyromagnetic data can be found in tables). f B (7) In Magnetic Resonance Imaging this frequency is called the Larmor frequency. A nuclear magnetic moment can occupy one of two states in the context of NMR, corresponding to the moment parallel to the DC magnetic field and the other to anti-parallel orientation. The nuclear moment can either give up energy (transition from anti-parallel to parallel), or absorb energy (transition from parallel to antiparallel). The NMR signal is basically the difference between the absorbed and emitted energy. Given that my device will be characterized by very small dimensions, the inductance and capacitance values associated with the helix antenna will be quite small making the antenna’s self resonance frequency very high. The largest efficiency in the RF energy transmission into the medium will occur at this frequency. Larmor frequencies are typically within the range of 15 and 80 MHz for hydrogen imaging, well below the expected helix resonance frequency (~ GHz). Using a model such as that described by Furse et al. will enable me to determine the energy transmission characteristics of my helical antenna at the Larmor frequency. Another contribution made by the authors if this paper relates to the FDTD simulation itself. The solution region must be truncated in order to accommodate the finite nature of computer memory, and as such must contain boundaries. These boundaries must approximate infinity in order for the solution to be at all accurate (conservation of energy). The trick is to simulate the propagation of EM waves (plasma waves) at the boundary as if the spatial distance between the boundary and infinity is represented at this boundary. Absorbing boundary methods have been developed for FDTD simulations such retarded time absorbing, and perfectly matched layer boundary conditions. These methods assume propagation at the speed of light, which would suffice in simulations if plasma waves were not considered. However, the underlying goal of this work was to more accurately represent dynamics associated with time varying plasma conditions, which propagate at slower velocities. Furse et al. argued that since plasma exhibits quasineutral behavior, the variations in density would not be visible beyond a couple of Debye lengths from the antenna. They further reasoned that since the antenna was electrically short, the energy coupling into the far field would be poor. With these two assumptions, the inclusion of the time varying plasma density and velocity near the solution boundaries was gradually removed from the FDTD loop and considered constant. The method is graphically demonstrated in figure 7, which was taken from the article. function of relationship. density described the following 2 e n m 2 (9) e p o e Where e, epsilon, and m are the electronic charge, permittivity of free space, and electronic mass respectively. Looking at the plot in figure 8, results in the conclusion that altering the simulation size and time iterations may not fully correct the instabilities in the solution. 4.3 Additional Work Figure 7. Representation of the simulation near the boundary, illustrating the relationship between the fields at different spatial locations. The density N was assumed constant within a few cells from the boundary, followed by the removal of the plasma velocity prior to the simulation edge2. This approach worked well for the EM fields traveling at the speed of light, but was not completely effective in the representation of the slower moving plasma waves. This problem was overcome under certain conditions by altering the plasma parameters and simulation size. This is illustrated in figure 8. During my own analysis of the boundary condition development presented in this article, the complexity of my own system became more apparent. As was mentioned in the article, the PF-FDTD boundary conditions deal well with the radiation propagating at the speed of light, but were unable to accurately absorb the slower moving plasma waves. My analysis will be conducted in the liquid phase, thus reducing the speed of particle density propagation even further. Additionally, the lateral boundaries of my system will include a dU/dt = 0 relationship due to the constant fluid flow through the channel. However, the NMR analysis will occur in the brief moment of time when the particles/molecules are positioned within the helix (~ milliseconds). The quasi-stationary nature of the carrier fluid within the time scale of the NMR experiment would allow the removal of the background constant velocity fluid velocity. With respect to the article described in this section, the need for further work related to the boundary conditions seems necessary due to the properties of the plot in figure 8. Instability in any FDTD simulation refers to an increase in the magnitude of the solution caused by the spatial grid as time increases6. This paper reports that certain plasma conditions result in instability at the simulation edge. Consider the curve for a plasma frequency of 15 MHz in figure 8. Figure 8. Plot showing the relationship between three different plasma parameters (plasma frequency) and the number of plasma cycles needed versus simulation time2. The plasma parameters are altered via the plasma frequency. Remember that the plasma frequency is a 5. Dielectric Properties of Laminate Materials Sharma et al. used the Bereskin test method to characterize the dielectric properties of various materials including resins and laminates. This method involves the use of stripline conductors in contact with the material of interest. Microwave propagation along stripline conductors is treated in detail in any microwave engineering text6. The test setup would look something like the following. Dielectric material Stripline conductor Ground plane Figure 9. Graphic illustration of a possible Bereskin stripline test setup. Two control materials were chosen based on their respective dielectric loss coefficients being in the region of interest, i.e. polytetrafluoroethylene (PTFE) and polyethersulphone (PES). The loss coefficients for these materials are reported as being 0.002 for PTFE and 0.007 for PES. The dielectric thicknesses given in the article for the two materials were 0.060” 0.002” for PTFE and 0.080” 0.002” for PES. The conductor length for each of the two experiments was 3.5” and 3” respectively. The remaining details of the experimental setup are missing from the article. At this point I need to bring up a number of concerns I have about the quality of this report. (1) The lack of theoretical background and/or information related to the experimental method, (2) the uncertainty in the dielectric control film thicknesses was on the order of a few percent, (3) there is no description of how the stripline foil was mounted on the control films, and (4) an analysis of the experimental data suggests only error and uncertainty in what the dielectric properties actually are. I am left with a number of questions related to these concerns. First, was the 2-mil thickness variation seen across on film, or was this a sample-tosample variation? Second, what experimental deficiency caused the large variations in the measured dielectric properties? Given that the information presented in this article was at best inconclusive, I will give a brief description of how this experiment might be carried out such that useful information could be obtained. There is nothing fundamentally wrong with the Bereskin test method proposed by these authors so I will continue assuming the test setup depicted in figure 9. 5.1 Experimental Methods In any experiment great care must be taken to remove as many variables and process parameter variations as possible. The process parameters for this characterization effort will include, stripline dimensions (length, width, thickness), dielectric film thickness and processing conditions, and the wire bonding required for electrical connection. Variables in this experiment would include temperature and humidity. Humidity was mentioned in this article as a main contributor to dielectric property variation (water absorption into the polymer matrix). The experimental method is presented in bulleted form below. 1. Spin or spray coating techniques can be used to obtain repeatable film thicknesses on top of a conducting substrate. Thickness of the film can be determined within 100 angstroms with a surface profiler. 2. Sputter deposit the stripline conductor on top of the dielectric film and pattern the desired feature with lift-off lithography to avoid polymer damage with etching. Use the surface profiler tool to obtain actual dimensions. 3. In order to remove variation in experiments, a custom test fixture can be machined from aluminum with appropriate network analyzer couplers mounted on the ends (typical two port network analysis). 4. The ends of the stripline would then be wire bonded to the couplers in the test fixture. The conducting substrate is electrically coupled to the test fixture with conductive epoxy. Only after a procedure such as this is followed can any conclusions about dielectric properties be made. Once the experimental setup is proved with control materials (PTFE or PES), process parameters related to the polymer can be varied in order to correlate polymer structure with dielectric properties. I believe the significance of this article is in the stated intent. It is clear that dielectric properties of materials will be dictated by the internal structure of these materials and the polar nature of polymeric chains that make up the film. Additionally, water uptake or absorption is of great concern because of its polar nature. The lack of conclusive evidence or clear definition of methods does not detract from the value of the intent. My own experiments will require the characterization of the electronic double layer that is present at any electrode/solution interface. This is actually why I chose to review this paper in the first place. The composition of this double layer capacitance will be a function of the ion and/or molecular concentration within the NMR cell. Understanding how these molecules affect the polarization dynamics will be essential. 6. Conclusion Several forces exist within an electrochemical cell immersed in a background magnetic field. White et al. was able to show through experiment that electrochemical currents could be altered based on the interaction of these forces. The most significant finding was that paramagnetic molecules could be retained for tens of seconds within a 1-millimeter diameter of the ferromagnetic microelectrode. While I am not immediately interested in the confinement of molecules, this finding does provide an additional tool for particle manipulation. I was able to establish a connection with these results due to the similar nature of my device with electrochemical cell. The review of the PF-FDTD article has led me to some conclusions about the complexity of my own numerical modeling efforts. An understanding of the antenna impedance immersed in an isotropic medium as a function of frequency was the underlying theme of this paper, which directly impacts my own work. Furse et al. were able to show qualitative agreement with the analytical method. The significance of this is in the full-wave nature of the PF-FDTD solution and in its ability to accommodate complex antenna geometries. Further, this FDTD method has opened the door for the addition of more plasma parameters allowing the more accurate description of the dynamics and associated impact on antenna impedance. The third paper was actually quite valuable in the sense that critical thinking is essential in any development work. I gained additional respect for the difficulty in obtaining meaningful results. 7. References [1] Micah D. Pullins, Kyle M. Grant, and Henry S. White*, “Microscale confinement of Paramagnetic Molecules in Magnetic Field Gradients Surrounding Ferromagnetic Microelectrodes”, J. Phys. Chem. B 2001, 105, 8989-8994. [2] Jeffrey Ward, Charles Swenson, and Cynthia Furse, “The Response of a Short Dipole Antenna in a Plasma Via a Finite Difference Time Domain Model”, January 15, 2004 [3] Jyoti Sharma, Marty Choate, and Steve Peters, “Laminate Materials with Low Dielectric Properties”, presented at IPC Printed Circuits Expo, 2002 [4] John David Jackson, “Classical Electrodynamics, third edition”, pages 146-190 “review of the dynamics of electric and magnetic dipoles and their energies within EM fields”, John Wiley & Sons, Inc., 1999 [5] David M. Pozar, “Microwave Engineering, second edition”, pages 153-166 “approximate representation of the stripline impedance”, John Wiley & Sons, Inc., 1998 [6] Matthew N. O. Sadiku, “Numerical Techniques in Electromagnetics”, pages 161-165, “Stability and accuracy, and description of the techniques used to control these”, CRC Press, Inc. 1992