ECEN 5031/4031 Spring 2019 Lecture 6 -7

1. . ECEN 5031/4031 Spring 2019Lecture 6 -7 Dielectric constants of Biological Materials. Basic Shape of Dielectric constants Meaning of dielectric constants Dielectric Mixtures Water and Structure of Water Characteristics of Some Biological Materials

2. Dielectric Properties of Muscle

3. Capacitive Model • Consider  case of two capacitors in series as shown in the figure where W is the width of a perfectly conducting metal plate that inserted between the two plates of a parallel plate capacitor separated by a space d with a dielectric constant for the material between the plates. When the width w = 0 then

4. Further discussion of Model Now look at the case of a single capacitor with a plate of width w inserted between the plates as shown. The following equations apply where The individual capacitors are described by the following equations and so and then

5. Taking a step back we look at the dielectric constant again in terms of εo. The relationship is which plugs back into the equation for the capacitance as shown in the following equations.

6. Charge flow in Cells Charge flows back and forth inside the cell and along the surface • E ++++ E ------- • ------- ++++ • ++++ ------- • ------- ++++ • ++++++

7. Lecture 7 • Assignment for Monday February 4. • 1. Read chapter 4 and write a brief summary of what you extract from the first 40 of the 60 pages. • 2. Write a one page summary on a paper related to Chapter 4 and one on a topic of interest to you.

8. Some Basic Equations Maxwell’s Equations Two approaches 1. From Field theory 2From a sum of the dipole moments Electronic Atomic Molecular For N dipoles For a dilute gas as E=E1

9. Characterization of the Polarization and Dielectric ConstantsP∞and P0 are the instantaneous and steady-state polarization • 1 • Single Relaxation with conductivity, Debye Equation

10. Dielectric Constants Is the static value of the dielectric constant Is the dielectric constant at very high frequency µ is the point dipole moment and g is the Kirkwood Factor The time constant For a sphere of radius a in a fluid of viscosity The Current Density and Conductivity

11. Real Systems

12. Complex Conductivity • An alternate way to express the complex material properties. • σ= σ’ + jσ” σ‘= ωεoε’’ • σ“ = ωεo(ε’- ε∞)

13. Dielectric constant of Water

14. Experimental data for water : ε’ ε” as a function of temperature at five frequencies (34). Figure 8. Experimental data for water : ε’ ε” as a function of temperature at five frequencies (34 Figure 9. Experimental data for water: Water permitivity at 25oC, frequency from static to the far infrared (34).

15. Figure. 10. (a) The spectra of water at 25 oC. (b) The spectra of water at 25 oC, See following text for explanation of I, II, III,IV (37).

17. β dispersion for protein γdispersion for water

18. Structure of Hemoglobin

19. Dispersion For Hemoglobin

20. Dielectric Properties of Muscle

21. Different Dispersion Regions. • 1 Cole-Cole Description

22. Water has different properties in different tissues.

23. 1 v1is the volume fraction of the material with dielectric constant ε1 v2is the volume fraction of the material with dielectric constant ε2

24. Mixtures and Boundaries 1

25. Boundary Condition • 1. At the boundary ε1E1 =ε2E2 • for surface charge case • 2. Charging Currents • 3. Relaxation times thicknesses d1 and d2 = εo

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

27. Equivalent Circuit Two Layers

28. Two Layers

29. Dipole Relaxation

30. Dielectric Properties of Gray Matter as a Function of Frequency

31. Lecture 7 • February 1,2019

32. Dielectric Properties of Liver

33. Dielectric Properties of Gray Matter • 1

34. Dielectric Properties of White Matter

35. Dielectric Properties of Skin Forearm

36. Dielectric Properties of Skin • 1

37. Dielectric Properties of Skin

38. Palm Skin

39. Conductivity of Whole Body Parts.

40. Tissue Conductivity

41. Magnetic Field Effects Spin Alignment for Paramagnetic Materials