Dielectric constants of Biological Materials. 1. Review 2. Dielectric Mixtures 3. Characteristics of Some Biological Materials 4. 1.

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. 2 When the width w = 0 then

Further discussion of Model 3 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 equationsand so and then

Taking a step back we look at the dielectric constant again in terms of ε o. The relationship is which plugs back into the equation for the capacitance as shown in the following equations. 4

Charge flow in Cells Charge flows back and forth inside the cell which was shown and illustrated in the class. 5

Some Basic Equations 6 Maxwell’s Equations Two approaches 1. From Field theory 2 From a sum of the dipole moments Electronic Atomic Molecular For N dipoles For a dilute gas as E=E 1

Characterization of the Polarization and Dielectric Constants 7

Dielectric Constants 8 Is the static value of the dielectric constant Is the dielectric constant very high frequency For a sphere of radius a in a fluid of viscosity The Current Density and Conductivity The time constant τ µ is the point dipole moment and g is the Kirkwood Factor

Real Systems 9

Dielectric Properties of Muscle 10

Different Dispersion Regions. 11 Cole-Cole Description 1

1 12 v 1 is the volume fraction of the material with dielectric constant ε 1 v 2 is the volume fraction of the material with dielectric constant ε 2

Mixtures and Boundaries 13

Boundary Condition 14

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

Equivalent Circuit Two Layers 16

Two Layers 17

Water Dipoles 18 Figure 2 Two descriptions of bonding in H 2 O. The observed angle between the two O—H bonds is 105 o (a) H 2 O based on s, p x, p y and p z orbitals oxygen (b) H 2 O based on sp 3 hy brid orbitals of oxygen (14)

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). 19

20 Figure 4 Some of the many water molecule clusters (15).

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) 21

Figure 6. Structures for the putative global minimum: (a) Na + (H 2 O) 20, (b) Cl - (H 2 O) 17, and (c) Na + (H 2 O) 100. (25) 22

Figure 7. Water molecules next to a nonpolar solute (16) 23

Table 1 Ionic mobilities in water at 298 K, u/(10 8 m 2 s -1 V -1 ) (12). 24

Table 2 Limiting ionic conductivities in water at 298 K, /(S cm 2 mol -1 ) where is molar conductivity (12 ) 25

Experimental data for water : ε’ ε” as a function of temperature at five frequencies (34). 26 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 25 o C, frequency from static to the far infrared (34).

Figure. 10. (a) The spectra of water at 25 o C. (b) The spectra of water at 25 o C, See following text for explanation of I, II, III,IV (37). 27

Dielectric Properties of Gray Matter as a Function of Frequency 28

Dielectric Properties of Liver 29

Dielectric Properties of Gray Matter 1 30

Dielectric Properties of White Matter 31

Dielectric Properties of Skin Forearm 32

Dielectric Properties of Skin 1 33

Dielectric Properties of Skin 34

Palm Skin 35

Conductivity of Whole Body Parts. 36

Magnetic Field Effects 37 Spin Alignment for Paramagnetic Materials