.
Dielectric constants of Biological Materials.
1. Basic Shape of Dielectric constants
2. Meaning of dielectric constants
3. Dielectric Mixtures
4. Water and Structure of Water
5. Characteristics of Some Biological Materials
6.
1
Dielectric Properties of Muscle
2
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
3
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.
1
1
1
The following equations apply   where C  A
C
C1
C2
d
The individual capacitors are described by the following
0 A
0 A
C

C

equations 1 d  w and 2 d  w
2
so
1 d w 1


C1
2A C2
d w

C
A
2
d
w
and then 1
4
Taking a step back we look at the dielectric constant
again in terms of εo.

0
(1 
w
)
d
The relationship is
which plugs back into the
equation for the capacitance as shown in the following
equations.


0 A
0 A  1 
C0
A


C



( d  w)
d  1  w  (1  w ) d


d
d

5
Charge flow in Cells
Charge flows back and forth inside the cell and along the
surface
E
++++
E
------
------++++

++++
------
------++++


++++++
6
Some Basic Equations
Maxwell’s Equations
xH  i 
xE  
D
t
B
t

B  o H  mh 
0
w
1
d
A
C   r o
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
7
Characterization of the Polarization and Dielectric
Constants
1
 Single Relaxation with conductivity, Debye Equation

 o i
i
8
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
9
10
Real Systems
11
Dielectric Properties of Muscle
12
Different Dispersion Regions.
1
Cole-Cole Description
13
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
14
Mixtures and Boundaries
1
15
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
16
Polarization Mechanism
 1. Interface Polarization

Charging Interfaces
 2. Dipole Relaxation
 3. Counter Ions in the Debye Layer
 4. Surface Conductivity Changes
17
Equivalent Circuit Two Layers
18
Two Layers
19
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
20
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) .
21
Figure 4 Some of the many water
molecule clusters (15).
22
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)
23
Figure 6. Structures for the putative global minimum:
(a) Na+(H2O)20, (b) Cl-(H2O)17, and (c) Na+(H2O)100. (25)
24
Figure 7. Water molecules next to a
nonpolar solute (16)
25
Table 1 Ionic mobilities in water at 298 K,
u/(108 m2 s-1V-1) (12).
26
Table 2 Limiting ionic conductivities in water at 298 K, /(S cm2
mol-1) where  is molar conductivity (12)
27
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).
28
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).
29
Dispersion of NaCl in H2O
30
Structure of Hemoglobin
31
Dispersion For Hemoglobin
32
Dielectric Properties of Gray Matter as a Function of Frequency
33
Dielectric Properties of Liver
34
Dielectric Properties of Gray Matter
1
35
Dielectric Properties of White Matter
36
Dielectric Properties of Skin Forearm
37
Dielectric Properties of Skin
1
38
Dielectric Properties of Skin
39
Palm Skin
40
Conductivity of Whole Body Parts.
41
Magnetic Field Effects
Spin Alignment for Paramagnetic Materials
42