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

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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.
V
d
w
When the width w = 0 then
0 A
C0 
d
2
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.
1 1
1
The following equations apply   where C  A
C
C1
C2
d
The individual capacitors are described by the following
 A
0 A
C1  0
equations
and
C

2
d w
so
1 d w 1


C1
2A C2
2
and then
d w
2
1 d w

C
A
d
w
3
Taking a step back we look at the dielectric constant
again in terms of εo.

0
w
The relationship is
(1  ) which plugs back into the
d
equation for the capacitance as shown in the following
equations.


0 A
0 A  1 
C0


C


(d  w)
d  1  w  (1  w )


d
 d
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
Maxwell’s Equations
xH  i 
xE  
D
t
B
t

0
1
B  o H  mh 
w
d
Two approaches
1. From Field theory
2 From a sum of the dipole moments
T  e  a  m
   1
For N dipoles
Electronic Atomic Molecular
For a dilute gas as E=E1
6
Characterization of the Polarization and Dielectric
Constants

 o i
i
7
Dielectric Constants
 s 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
8
Real Systems
9
Dielectric Properties of Muscle
10
Different Dispersion Regions.
1
Cole-Cole Description
11
1
v1 is the volume fraction of the material with dielectric constant ε 1
v2 is the volume fraction of the material with dielectric constant ε2
12
Mixtures and Boundaries
13
Boundary Condition
 1. At the boundary
ε1E1 =ε2E2
 for surface charge case
 2. Charging Currents
𝐽1
𝐽2

=
σ1𝐸2
σ2𝐸1
 3. Relaxation times

=
ε1𝑑2+ε2𝑑1
εo
σ1𝑑2+σ2𝑑1
14
Polarization Mechanism
 1. Interface Polarization

Charging Interfaces
 2. Dipole Relaxation
 3. Counter Ions in the Debye Layer
 4. Surface Conductivity Changes
15
Equivalent Circuit Two Layers
16
Two Layers
17
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 sp3 hy
18
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
Figure 4 Some of the many water
molecule clusters (15).
20
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+(H2O)20, (b) Cl-(H2O)17, and (c) Na+(H2O)100. (25)
22
Figure 7. Water molecules next to a
nonpolar solute (16)
23
Table 1 Ionic mobilities in water at 298 K,
u/(108 m2 s-1V-1) (12).
24
Table 2 Limiting ionic conductivities in water at 298 K, /(S cm2
mol-1) where  is molar conductivity (12)
25
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,
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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).
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Dielectric Properties of Gray Matter as a Function of Frequency
28
Dielectric Properties of Liver
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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
Spin Alignment for Paramagnetic Materials
37