Lecture 7 ECEN 5341 01-29-2014

1. Lecture 7 ECEN 5341 01-29-2014 Chapter 3 and 4 Frank Barnes

2. Two Layers in Series

3. Two Slabs • 1. At the boundary ε1E1 =ε2E2 • for surface charge case • 2. Charging Currents • 3. Relaxation times τ= εo

4. Two Layers

5. Two Layers • At high frequencies we have two capacitors in series • At low frequencies we have two resistors in series • Complex Dielectric Constant

6. Polarization Mechanism • 1. Interface Polarization • Charging Interfaces • 2. Dipole Relaxation • 3. Counter Ions in the Debye Layer • 4. Surface Conductivity Changes

7. Dipole Relaxation

8. Magnetic Materials • 1. Diamagnetic • 2. Paramagnetic • 3. Ferromagnetic • 4. Antiferromagnetic

9. Diamagnetic Materials • 1. Electron spins are paired one up, one down 2. The magnetic moments are from the orbital motion of the electrons. The sign of the magnetic moment is negative. 3.Most biological materials are diamagnetic and these materials are weakly repelled by in a magnetic field gradient. 4. Superconductors are diamagnetic and you can float a magnetic above a superconducting plate

10. A Superconductor is a perfect magnetic shield. • 1

11. The Moses Effect

12. Paramagnetic Materials • 1 Paramagnetic materials are attracted by a magnetic field gradient. • 2. These materials have net magnetic moments but on the average to zero as a result of the thermal energy. • 3. At low fields the net magnetic moment is proportional to the applied magnetic field. • 4. The magnetic moment saturates at high fields. • Pierre Curie and is known as Curie ’s law: • M =H ¼ x ¼ C =T • where M is the magnetization, H is the applied magnetic field, x is the magnetic susceptibility, • T is the temperature, and C is the Curie constant and is related to the magnetic proper ties of the material

13. Magnetic Field Effects Paramagnetic materials have permeate magnetic moments Spin Alignment for Paramagnetic Materials

14. Ferromagnetic Materials • 1 There are coupled spins in an inner shell of atoms such as iron. In Iron the exchange energy parallels four electron spins. This is a strong enough magnetic moment to align blocks of atoms. • 2. The magnetic susceptibility is positive. • 3. Ferromagnetic material have magnetic moments even after the field is removed and hysteresis below a given temperature.

15. Ferromagnetic Spins Align

16. Antiferromagnetic Material • These materials can have net magnetic moment.

17. Ferrimagnetic Materials • This the case for Fe3O4 which had Fe2+ and Fe3+ in the lattice. This is a bio manufactured material

18. Temperature Dependence of Ferromagnetic Materials • 1

20. Energy Barrier for Superparamagnetic Material • 1 Spins flip as a group with thermal energy ≈10-9seconds Remanent magnetic field

21. Biological Magnet • FIGURE 4.7 • Model of the ferritin protein showing the peptide subunits and iron transport channels. (From www.chemistry wustl.edu/edudev/LabTutorials/Ferritin/FerritinTutorial.html. With permission • .)

22. Iron in the Body • In organisms, iron is stored as the mineral ferrihydrite(5Fe2O39H2O) with in the iron storage protein ferritin. It consistsof a 12-nm hollow spherical protein shell made up of 24 subunits (Figure 4.7). The core of • ferritin protein is 8 nm in diameter, and it can hold up to 4500 iron atoms in the form of ferrihydrite. Iron is transported into and out of the core through three- and fourfoldchannel s in the shell. During trans port, highly toxic Fe(II ) is oxidized to Fe( III) for storage • as ferrihydrite(Harrison and Arosio, 1996). • Ferrihydriteis a superparamagneticantiferromagnet

23. Magnetite (Fe3O4)a ferromagnetic iron oxide • Transmission electron micrograph of the magnetotactic bacterium MS-1 (top). (From www.calpoly.edu/ • rfrankel/mtbphoto.html) • Biogenic magnetite extracted from the human hippocampus (bottom). (From Schultheiss-Grassi, PP, R Wessiken, and J Dobson (1999) Biochim. Biophys. Acta1426 : 212–216. With permission.)