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. ECEN 5031/4031 Spring 2014 Lecture 6 . Dielectric constants of Biological Materials. Review Dielectric Mixtures Characteristics of Some Biological Materials. Capacitive Model.
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. ECEN 5031/4031 Spring 2014Lecture 6 Dielectric constants of Biological Materials. Review Dielectric Mixtures 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 to the left. 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 which was shown and illustrated in the class.
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 Constants
Dielectric Constants Is the static value of the dielectric constant Is the dielectric constant very high frequency µ is the point dipole moment and g is the Kirkwood Factor The time constant τ For a sphere of radius a in a fluid of viscosity The Current Density and Conductivity
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 = εo
Polarization Mechanism • 1. Interface Polarization • Charging Interfaces • 2. Dipole Relaxation • 3. Counter Ions in the Debye Layer • 4. Surface Conductivity Changes
Water Dipoles brid orbitals of oxygen (14) brid orbitals of oxygen (14) Figure 2 Two descriptions of bonding in H2O. The observed angle between the two O—H bonds is 105o (a) H2O based on s, px, py and pz orbitals oxygen (b) H2O based on sp3hy
Water Clusters • Figure 3 An expanded icosahedral water cluster consisting of 280 water molecules with a central dodecahedron (left) and the same structure collapsed into a puckered central dodecahedron (right). (16; 17) .
Figure 5 Theoretical predictions of the stabilities of the five lowest-energy water hexamer structures. Values of De (lower line – lowest equilibrium dissociation energy) and Do (upper line – quantum vibrational zero-point energy) are shown. The zero-point energy is equal to Do-De (18)
Figure 6. Structures for the putative global minimum: (a) Na+(H2O)20, (b) Cl-(H2O)17, and (c) Na+(H2O)100. (25)
Table 1 Ionic mobilities in water at 298 K, u/(108 m2 s-1V-1) (12).
Table 2 Limiting ionic conductivities in water at 298 K, /(S cm2 mol-1) where is molar conductivity (12)
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).
Dielectric Properties of Gray Matter as a Function of Frequency
Magnetic Field Effects Spin Alignment for Paramagnetic Materials
