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Learn about the basics and characteristics of dielectric constants in biological materials, including water structure, muscle properties, and capacitive models. Explore relevant equations and data for better understanding. Lectures cover topics such as polarization, conductivity, relaxation processes, and dispersion in biological tissues.
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. 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
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
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
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.
Charge flow in Cells Charge flows back and forth inside the cell and along the surface • E ++++ E ------- • ------- ++++ • ++++ ------- • ------- ++++ • ++++++
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.
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
Characterization of the Polarization and Dielectric ConstantsP∞and P0 are the instantaneous and steady-state polarization • 1 • Single Relaxation with conductivity, Debye Equation
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
Complex Conductivity • An alternate way to express the complex material properties. • σ= σ’ + jσ” σ‘= ωεoε’’ • σ“ = ωεo(ε’- ε∞)
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).
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).
Different Dispersion Regions. • 1 Cole-Cole Description
1 v1is the volume fraction of the material with dielectric constant ε1 v2is the volume fraction of the material with dielectric constant ε2
Boundary Condition • 1. At the boundary ε1E1 =ε2E2 • for surface charge case • 2. Charging Currents • 3. Relaxation times thicknesses d1 and d2 = εo
Polarization Mechanism • 1. Interface Polarization • Charging Interfaces • 2. Dipole Relaxation • 3. Counter Ions in the Debye Layer • 4. Surface Conductivity Changes
Dielectric Properties of Gray Matter as a Function of Frequency
Lecture 7 • February 1,2019
Magnetic Field Effects Spin Alignment for Paramagnetic Materials
