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PUBLICATIONS

NBSIR 86-3355

Dielectric Phantoms for

Electromagnetic Radiation

NATL INST OF STANDARDS & TECH R.I.C.

All 102490853

Broadhurst, Martin G/Dlelectrlc phantoms QC100 .1156 NO.86-3355 V1986 C.1 NBS-PUBMartin G. Broadhurst, C. K. Chiang, and G. Thomas Davis

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Institute for Materials Science and Engineering

Gaithersburg, MD 20899

March 1986

Issued May 1986

Prepared for -QC~

100

- U 5 6

86-3355

1986

C. 2

Physical Sciences

:ience and Technology

)evices and Radiological Health

rug Administration

ibrook Parkway

ID 10857

NBSIR 86-3355

DIELECTRIC PHANTOMS FOR

ELECTROMAGNETIC RADIATION

Martin G. Broadhurst, C. K. Chiang, and G. Thomas Davis

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Gaithersburg, MD 20899

March 1986

Issued May 1986

Prepared for Division of Physical Sciences

Office of Science and Technology

Center for Devices and Radiological Health

Food and Drug Administration

12721 Twinbrook Parkway

Rockville, MD 10857

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

A DIELECTRIC PHANTOM MATERIAL FOR ELECTROMAGNETIC RADIATION

by

M . G . Broadhurs t , C.K.Chiang and G.T. Davis

Polymers Division

Institute for Materials Science and Engineering

National Bureau of Standards

a report for

Division of Medical Engineering

Center for Devices and Radiological Health

Food and Drug Administration
- 2

-

A DIELECTRIC PHANTOM MATERIAL FOR ELECTROMAGNETIC RADIATION

Abstract: This report describes the design and performance of a synthetic material that has the same dielectric heating

characteristics as living muscle in the 1-1000 MHz frequency

range. This dielectric phantom is a combination of four

components: 1) a 50/50 solution of ethylene carbonate and

propylene carbonate chosen to have the same dielectric constant

as water, 2) an organic salt to provide the same conductivity as

biological electrolytes, 3) flakes of polyethylene terephthalate

to provide the interfacial polarization that occurs at cell walls

in biological tissue and 4) an inorganic and a polymeric gelling

agents to provide mechanical rigidity. The resulting composite

material is more stable to biological attack and drying than are

existing aqueous based phantom materials, and its dielectric

properties are more closely matched to those of natural tissues

over most of the frequency range of interest.

Disclaimer: Certain commercial materials and equipment are

identified in this report in order to adequately specify the

experimental procedure. In no case does such identification imply

recommendation or endorsement by the National Bureau of

Standards, nor does it imply that the commercial materials or

equipment identified are necessarily the best available for the

purpose

.
-3-

INTRODUCTION

The development, testing and calibration of devices that

subject human tissue to the heating effects of high frequency

electromagnetic (EM) radiation [1] require a material (here

called a phantom) which duplicates the dielectric and thermal

properties of living tissue. Presently-used phantoms are gels

made of naturally occuring biological polymers swollen with a

large amount of water containing dissolved sodium chloride [2].

The dielectric constant is adjusted upward by adding aluminum

particles and downward by adding polyethylene particles. The

problems with the present phantoms are:

1. The gels are unstable because molds and bacteria attack

the biopolymers, the salt water reacts with the aluminum and the

gels dry to form hard surface layers as the water evaporates.

2. The changes in electrical properties with frequency are

different from those in living tissue, so that different

compositions are required for different frequencies.

3 . The thermal properties of the aluminium depart

significantly from those of living tissue.

It is desirable to find a new phantom material that

overcomes these deficiencies. The National Bureau of Standards

is helping the Food and Drug Administration's Center for Devices

and Radiological Health design and test such a material.

ANALYSIS OF THE PROBLEM

We can treat a material as a frequency dependent complex

admittance Y* in which the current leads the applied field by a

phase angle in the range of 0 to 90 degrees. If this phase angle
-4-

is near 0 degrees we generally consider the material an

electrical conductor and characterize its impedance as a complex

conductance, cr*. If the phase angle is nearer 90 degrees we

consider the material to be a dielectric and characterize its

impedance with a complex dielectric constant, k* . The

dielectric constant is defined here as the ratio of the

permittivity of the material to the permittivity of free space.

Biological tissues tend to give phase angles that vary over much

of the range of 0-90 degrees, and their electrical properties are

sometimes given as a complex dielectric constant, conductivity,

or as a combination involving the real parts of both the

dielectric constant and the conductivity. These representations

are equivalent, and a particular author usually chooses the

system he is used to. In this report we will give the electrical

properties in terms of the complex dielectric constant,

k* = k ' - ik" = k' + cr '/iweQ = cr */iweQ = Y*/iwC0 ,

where w is the angular frequency, eQ the permittivity of free

space, CQ is the empty specimen holder capacitance and i = 1.

The EM heating of a material results from that part of the

motion of the charges in the material that is in phase with the

sinusoidally alternating electric field, E. The heat generated

in the material per cycle is equal to k"e0E2. k' may be important

if it affects the magnitude of E^. if one matches k' and k" in

two homogeneous materials, one matches the electromagnetic

heating behavior also.
-5-

This criterion is not a sufficient one for composite

materials, because in these inhomogeneous systems, the electric

field can be localized in one part of the material and produce

localized heating. In two specimens with the same average complex

dielectric constants, one of them might heat uniformly and the

other nonuniformly . This situation is unacceptable for a phantom,

and a second criterion for matching heating behavior in

inhomogeneous materials must be that the distribution of electric

field be similar in the two materials.

Many of the properties of living biological tissues are based

on their high contents of salt water. This is true of the

electrical properties of tissues at frequencies above 100 MHz,

where the complex permittivity approaches that of the salt water

extracted from the tissues [3]. At lower frequencies the

electrical properties are extremely sensitive to the fact that

the salt water is confined to small inter- and intra-cellular

regions by cell membranes that partially block the ionic

conduction and produce high electrical polarization. The effects

of this charge blocking increase as the frequency decreases.

Interfacial polarization of this type is historically referred to

as Maxwell-Wagner [4] polarization and must be understood and

controlled in a material for it to be a successful phantom. If

the polarization mechanisms in living biological tissue can be

incorporated into a phantom, then one can expect the electric

field distribution and the dielectric constants to be the same.

When these conditions are met, one can expect the frequency and

temperature dependences of the dielectric constants to be the

same also.
- 6

-

The thermal properties of living tissue also are dominated by

the water. Few materials have as high a heat capacity as water,

unless undergoing a phase change. Since this property is hard to

match in non-aqueous systems, it is fortunate that heat capacity

differences can be accounted for computationally and that the

lower heat capacity of most common materials will actually

increase the sensitivity of the temperature measurements during

low-power EM exposure. For hyperthermia measurements, one would

like the thermal diffusivity-a measure of the rate of relaxation

of a non-equilibrium temperature distribution-to be as low as

possible, to provide sufficient time to measure temperature

distributions after EM exposure. Fortunately, organic materials

often have lower thermal dif fusivities than water. We can expect

then that thermal property requirements will be met easily in

a predominately organic phantom.

STATEMENT OF THE WORK TO BE DONE

In its original contract agreement with the FDA the NBS

agreed to:

1. Search for materials suitable for use as dielectric

phantoms over the frequency range of 10-100 MHz (of primary

importance is 10-50 MHz). The desired properties are in the

range 90 < k' < 120 and 0.65 < c' < 0.90 S/m at 27 MHz (25°C).

The materials should be commercially available or easily prepared

from commercial materials. The thermal diffusivity of the

material should be no larger than that of tissue.

2. Prepare samples as appropriate to evaluate types of

material

.
-7-

3. Measure electrical properties of candidate materials as

appropriate

.

4. Provide a report to the FDA's National Center for Devices

and Radiological Health on the results of the investigation which

will include recommendations for the direction of future work if

a phantom with satisfactory properties has not been developed or

identified.

EXPERIMENTAL MEASUREMENTS

Dielectric Specimen Holder

The dielectric measurements reported here were made using a

parallel plate specimen holder consisting of a cylinder cut from

standard polyethylene tubing nominally 1/4" (6.35mm) ID, and 3/8"

(9.52mm) OD. Polyethylene (PE) was chosen because of its low

complex dielectric constants and stability in the presence of

solvents. The electrodes consist of polished, gold-plated copper

disks of 9.52mm diameter. The specimens used in this work were

either liquids, gels or wet solids. The cell, with an electrode

at each end of the tube, was able to contain the specimens via

surface tension.

For some measurements the electrodes were secured to the PE

cylinder with parafilm [5] tape. The area and thickness of the

specimens were taken to equal the inner area and length of the PE

tube. These dimensions were carefully measured with a micrometer. This gave a sample area of A = 0.317cm2, thickness t

=0. 457cm, cell constant A/t = 0.694cm, and empty cell capacitance

C0= e0A/t = 0.0614pf. The sample capacitance, Cx and conductance,

Gx , were taken to be the difference in measured capacitance and
- 8 -

conductance of the cell with (Cmin and Gmin) and without (

C

mout

and Gmout) the specimen in place.

cx

= Cra in - Cmout + CQ , Gx ~ Gmin ~ Gmout

.

The real and imaginary parts of the dielectric constant are given

by.

k' — Cx /Cq,

k" = Gx/wC0 ,

This procedure eliminated the contributions from the fringing

fields and the walls of the PE tube. Care was taken not to allow

liquid from the specimen to enter the space between the parafilm

and PE, as this would change the fringing fields and introduce

error in the above procedure. The accuracy of the measurements

was checked using distilled water as a standard specimen, and

the measured k' was found to be within +/- 5% of the nominal

value of 78.5 from 1 to 1000 MHz [6]. The k" was sensitive to

ionic content of the water, as expected. We estimate that the

accuracy of the values of k' and k" reported here is +/- 5%

Impedance Measuring Instruments

The automated instruments used to measure and analyse the

impedance of the cell were the Hewlett Packard Impedance Analyser

model 4191A (10^ to 10^Hz)[7] and an HP Network Analyser model

3570A (50Hz to 1 . 3xl0 7 Hz ) [ 7

]

. The 4191A was used with the HP
-9-

16091A[ 7 ] coaxial fixture with the cell terminating the fixture.

The cell added an electrical length of 0.72cm to the fixture and

this length was automatically accounted for by the instrument.

The 3570A was used with the cell connected between the center

leads of 35cm long coax output and input cables in one channel

and a single cable of the same total length (acting as a short

circuit reference impedance) in the other channel. Data were

automatically recorded, processed and plotted with an HP 9845B

computer [ 7 ]

.

MECHANISM OF DIELECTRIC HEATING IN LIVING BIOLOGICAL TISSUE

A basic assumption of this work is that we should make a dielectric material that will simulate the mechanism of EM

heating in biological tissue. The first step is to thoroughly

understand what this mechanism is. For convenience we chose to

measure the leaves of the jade plant (Crassula portulacea) as a

representative biological material. These leaves have the same

dielectric behavior as muscle [3] and were much easier for us to

acquire, form into dielectric specimens, and replace with fresh

specimens than were muscle samples. Much of the published

dielectric data on animal tissues is for 37°C [3,8], some is

extrapolated to room temperature for comparisons with room

temperature data [9,10] and some data is taken at room

temperature [9,11]. The dielectric constant will decrease with

temperature because of the 1/temperature dependence of the static

k' of dipolar liquids and cr ’or k” will increase with temperature

because ionic transport is a thermally activated process. These

differences are important only in the selection of a final data
- 10 -

set for duplication by the phantom. Our data are for temperatures

around 25°C.

Optical micrographs of a cross section of a leaf like those

used in our measurements are shown in figures la and lb.

Typical curves of k' and k" are shown in figure 2 for a wide

range of frequencies. These data have been carefully analysed in

a recent preprint [ 12 ], and details of measurement procedures and

calculations will be found there. The results are summarized in

this report.

The leaf specimen can be considered for our present purpose

as a series combination of three parallel resistor-capacitor

pairs as shown in figure 3. These represent the bulk properties

of the salt/water electrolyte (denoted with subscript 3), the

resistance and capacitance of the cell walls (denoted with

subscript 2 ) and the resistance and capacitance of the ionic

double layer at the interface between the specimen and electrodes

(denoted with subscript 1). The inequalities hold that

c l >>c 2 >>c 3 an<^ R1 >>R2 >>R3* Thus the high frequency region in

figure 1 is dominated by R 3 and 03 , the mid frequency region by

R2 and C 2 and the low frequency region by R 3 and C]_.

The equivalent series resistance and capacitance of the

circuit in figure 3 are given by,

3 c s = {

f

[C i (l+Q1 2)/Qi 2]-1)-1

3

t=l Rs =1 [Ri/(1+Qi 2

) ] \-i

Qi = wRiCi
- 11 -

Figure 1. Electron micrographs of a cross section of Crassula

portulacea leaf showing cell structure. The leaf (figure la) is

about 4mm thick and the scale in figure 3’ , showing the cell

detail, is 100 um long.
<7>

LO

co

CO

<J) h- LO CO

( m

h) 6on 6on

Figure

2.

Real

and

imaginary

parts

of

the

complex

dielectric

constant

of

a

Crassula

portulacea

leaf

with

the

epidermus
-13-

C

1

> > c 2 HH

ww-

> >

R

1

> > R 2 >> R 3

Ion Double Layer

at Electrode

Cell

Walls

Bulk

Water/Salt

O

Figure 3. Model circuit for the dielectric properties of

biological tissue.
-14-

To illustrate the degree of approximation involved in this

model we have calculated the apparent k' and k" of the circuit

in figure 3 assuming that the empty cell capacitance, Co=0.0614

Pf . .

k' — C s Qg2/ [

C

Q ( l+Qs^ )

]

,

k" = 1 /[wRs C0 (1+Qs 2)],

Qs = l/(wRs C s

).

The results are shown in figure 4. Note that the calculated

(figure 4) and measured (figure 2) data are quite similar in

shape at the highest frequencies. That is, the highest frequency

relaxation in the leaf acts much like the relaxation of an RC

circuit. The relaxations become relatively broader in the

experimental data the lower the frequency. This result is to be

expected since the lowest frequency relaxation involves charging

of the ionic double layer. Double layer charging is known to

involve a diffusion process [13]. Such a process results in

the k' and k" being equal in magnitude and with a slope of -0.5

on the log(k*) vs log(f) plot [14]. It is reasonable to

expect that ionic charging of an interface will be intermediate

between diffusion and RC relaxation. The data in figure 2 show

this trend from nearly ideal RC relaxation at the highest

frequency to nearly ideal diffusion at the lowest frequency.

We can compare the expected values of the cell wall and

double layer capacitances with the observed C 2 and C 3 in figure

3. If the cell wall thickness=0 . 1 jim, k'=10 and the electrode

area is 0.32 cm^ then Cw=30 nf. The series combination of
10

j

Figure 4. Real and imaginary parts of the complex dielectric

constant for the model circuit of figure 3, using the resistance

and capacitance values shown in the insert, and assuming an empty

holder capacitance of 0.062 pf.
-16-

several cell walls would give a value near C2=10 nf. The double

layer capacitance [13], for perfectly smooth electrodes, is

calculated to be about 30 V

f, in reasonable accord with C 3=100

jjf. These comparisons show that our model and the data are self

consistent.

We can be confident then that at 100 MHz the k' is

essentially that of bulk water mixed with low dielectric constant

solids (see below for mixing rules) , and the k" is due to the

conductivity of the ions of dissolved salt. Below 100 MHz the

increase in k' and concomitant change in k" is due to interfacial

polarization of the cell walls by the ions and partial blocking

of the ionic transport by the cell walls. The frequency and

magnitude of this increase in k' above its value at 100 MHz

depends on the capacitance and concentration of the biological

cell walls.

It is important to understand how the biological tissue is

heated by the electromagnetic field. We can calculate the

heating of the model circuit in figure 4, using the values given

in the figure for the circuit elements, as an excellent

approximation to the heating of biological tissue above 1 MHz.

With an applied voltage, V, the rate of heat generation in each

of the three circuits is given by.

Hi = Riv2/[Rs 2(i +Qi 2

) (1 +qs

2)

.

Figure 5 shows the total rate of heating in the circuit H x for v

= 1 volt, and figure 6 shows the fraction of this total power

• • dissipated in each of the three RC pairs, HiAEHi It is apparent
(/)

cz

U)

o

-3 -1 1 3 5 7 9

Log (Frequency)

Figure 5. Rate of dielectric heating in watts of the model

circuit of figure 4 as a function of frequency for an applied

potential of 1 volt.
Fraction

of

Total

Heat

Log (Frequency)

Figure 6. Fraction of total heating in each of the three par

of the circuit in figures 3 and 4. The symbols are for circui

circuit 2 , ; circuit 3 , A. .
-19-

from these results that the heating will be essentially

independent of frequency above 1 MHz independent of changes in

k' and that over 99% of the heat is dissipated in the bulk

electrolyte. However the coupling of the applied electric field

to the dielectric may cause the potential applied to the material

to change with k'(see a later section on the use of the phantom).

DESIGN OF A PHANTOM MATERIAL

We chose to build a material using synthetic components to

match the function (component for component) of the natural

components in biological tissue. This approach allowed

a systematic selection of components one at a time and removed

the complexity of evaluating a large number of mixtures of

components by trial and error.

The natural components of biological tissue and their

functions are 1) water which gives a k'=79, 2) dissolved salt,

mostly sodium chloride, that determines the conductivity and k

M

,

3 ) cell walls that partially block the ionic transport and

increase the k' by interfacial polarization, and 4) the

connective solid tissue that gives mechanical stability. We

discuss substitutes for each of these components below.

1) Dielectric liquid

There are very few dielectric liquids that have as high a dielectric constant as water. The one we have selected is a

mixture of ethylene carbonate (EC) and propylene carbonate (PC).

This mixture has low toxicity and is commonly used as a gel base

in cosmetics [15]. It is also used as an electrolyte in
- 20 -

batteries and capacitors-an application related to the present

application [15]. EC and PC have a much lower vapor pressure

than water, as shown in figure 7 [15], and a convienient freezing

point as shown in figure 8 [15]. The static k's of EC, PC [15]

and water [6] are shown in figure 9 as a function of temperature,

and of PC/EC mixtures as a function of concentration [15] in

figure 10. The orientational relaxation of the dipoles of water,

PC and EC are all nearly Debye in shape [6,16], so that we can

calculate the high frequency k' and k" as [14],

k' = k00+(ks -k00 )/[l+(f/fc ) 2

] , and

k" = (

k

s -k00 )f/fc /[l+(f/fc ) 2 ]

.

The kGO are 5.2 for water [6] and 2.6 for the EC/PC

mixture [16], and ks = 79. The critical frequencies, f c , for

molecular relaxation of water [6] and PC and EC [16] are given

as a function of temperature in figure 11. The calculated

frequency dependence of the k' is shown in figure 12 for these

two materials. The fact that the relaxation frequencies are

lower in PC/EC than for water means that its k' and k" depart

significantly from those of water above 1 GHz, as shown in figure

12 . Some of the important physical properties of PC and EC [15]

are summarized in Table 1. A heat capacity, thermal

conductivity and density of about 1.4 J/gmK (one third that of
Vapor

Pressure,

mm

Hg

- 21 -

Figure 7. Vapor pressure of propylene carbonate and ethylene

carbonate as a function of temperature, (from reference [15]).
- 22 -

% Ethylene Carbonate

Figure 8. Freezing points of ethylene carbonate/ propyie.

carbonate mixtures as a function of composition (f: >rr. reference

[ 15 ]).
Static

Dielectric

Constant

-23-

Figure 9. Static dielectric constants of ethylene carbonate,

A

and propylene carbonate,® preference [15]) and water, X / (reference [6]) as a function of temperature.
-24-

% Ethylene Carbonate in

Propylene Carbonate

Figure 10. Static dielectric constants of mixtures of propylene^ carbonate and ethylene carbonate as a function of concentration

at 25°C (from reference [15]).
Log

(Critical

Frequency)

(Hz)

-25-

Figure 11. Critical frequencies for molecular dipole relaxation

of ethylene carbonate , A , propylene carbonate,#, (reference [16])

and water

,

X ,( reference [6]) as a function of temperature.
-26-

Log (Frequency)(Hz)

Figure 12. Calculated high frequency dielectric behavior of

water and a 50/50 mixture of ethylene carbonate and propylene

carbonate as a function of frequency. The dashed curve is th

contribution to k" expected from a conductivity of 0.7 s m. relaxations are the orientational relaxations of the molecular

dipoles and are essentially single relaxation time processes.

These calculated curves do not take into account the effects f low dielectric constant additives.

<UH
- 27 -

Table 1. Physical data on ethylene carbonate and propylene

carbonate tt

Boiling point, °C(760 mm)

Ethylene

Carbonate

238

Propylene

Carbonate

241 .7

Coefficient of expansion, cc/cc/°C - 0.096

Dielectric constant, 25°C esu 95.3* 64.9+

36°C 90.8 62.4 + 40°C 89.1 61 .4 + 50°C 85.1 59.2 + 60°C 81 .0 56.9 +

Dipole moment, 25°C, Debye units 4.60 4.94 +

Fire point, °F - - 280

Flash point (PMCC),°F 305 275

Freezing point, °C 36.4 (melting point) -49.2

Heat of fusion, cal/g 34 18

Heat of combustion, cal/g 2,662 3,396

Kcal/mol 234 347

Heat of vaporization, cal/mol, 150°C 13,500 13,200

1 75°C - 12,600

200°C 13,000 12,200

230°C 12,400 - 240°C - 11,900

248°C 12,200* -

Pour point, °F - -100**

Refractive index 1.4158 (nD

50

) 1 .4210 (n

D 20

) Specific gravity 1.3218 (39/4°C) 1 ,2057 ( 20/4 °C

)

Specific heat, cal/g, 15°C 0.321 - 50°C 0.363 0.375 (25°C)

100°C 0.461 0.438

1 50°C 0.479 0.480

Thermal conductivity at 41 °C, BTU/(hr) (ft 2

) (°F/ft) 0.12 0.12

cal/ ( sec) (cm 2

) (°C/cm) 49.3 x 10" 5 49.6 x 10“ 5

Viscosity, cs. , -65°F Solid 57.6*

-40°F Solid 19.4

o

o Solid 6.64

1 00 °F 0.90 1.67

21 0°F 0.42 0.78

* Extrapolated.

** Propylene Carbonate supercools easily and has remained liquid at temperatures as low

as -80°C for a period of several months.

+t Ref. 15

tRef. 16
-28-

water), 2 mJ/sec/cm/K and 1.2 gm/cm3 respectively [15], give a thermal diffusivity of 0.0012 cm2 /sec. This value is less

than the corresponding value for water (0.0014 cm2 /sec) [17].

This means that non-equilibrium temperature distributions will be

slower to relax in the PC/EC mixture than in water and thus

easier to measure. The lower heat capacity of the PC/EC mixture

will also increase the temperature rise for a given input of

power and aid the measurement of temperature changes.

Propylene carbonate and ethylene carbonate are available in

drum quantities for around $0. 90/lb. or a little less than

$500/drum [15]. While toxicity of these materials is low, we

understand that new information about trace impurities is being

incorporated into a new product brochure.

2) Organic salts

A large variety of organic and inorganic salts were mixed

with a 50/50 mixture of PC/EC and the conductivities were

measured at 1, 10, 100, and 1000 MHz, using equipment described

earlier in this report. Generally the conductivities reported in

table II were the ones measured at 10 MHz since they were

reasonably free of interfacial polarization present at lower

frequencies and dipolar relaxation effects at higher frequencies.

The initial screening was done by adding an excess of salt to

the solvent and mixing to obtain a roughly saturated solution at

room temperature. The salts were not specially dried for these

measurements and probably contained some water. The salts tested

in this way and the maximum resulting conductivities obtained arc

listed in table 2. In general, the inorganic salts provided
-29-

conductivities at or below the required levels of 0.7 S/m. In

some cases the conductivities were limited by low solubility as

with NaCl while in other cases the salts seemed quite soluble but

had limited dissociation, as with mercuric chloride and the

lithium salts in general.

The organic salts were generally easier to dissolve and

provided conductivities above 0.7 S/m. Tetraethyl ammonium tetra

fluoroborate ( TEATFB ) is a conveniently available [18] organic

salt that we chose for use in the phantom because it provides a

reasonably linear conductivity with concentrations up to about 2

S/m, or 3 times the conductivities needed. The conductivity vs

concentration of TEATFB in a 50/50 mixture of PC/EC is shown in

figure 13. These data show that the conductivity of PC/EC with

this salt can be adjusted well beyond the 0.65 to 0.9 S/m range

of current interest. A 0.28 mol/litre solution of TEATFB gives a conductivity of about 0.7 S/m in PC/EC while only 0.06 mol/litre

of NaCl in water gives the same conductivity, as shown in figure

13. This difference is presumably due to the lower mobility of

the organic ions in PC/EC relative to NaCl in water, possibly

because of their larger size and the greater viscosity of the

solvent. Also, we do not know the degree of association of the

organic salt.

In subsequent sections of this report we will refer to

PC/EC/salt meaning a mixture of 50% propylene and 50% ethylene

carbonate with about 0.28 mol/litre of TEATFB. It should be

clear that the k' and the k" of this mixture will vary

with the concentrations of the three components in a

controllable way as shown in figures 10 and 13, and can be easily
- 30 -

Table 2. Conductivities of satuarated solutions of various salts

in a mixture of equal parts of ethylene carbonate and

propylene carbonate.

Salt Conductivity at Saturation (S

KI 0.52

L1CF

3 S03 0.22

SrCl 2 .6H2 0 0.12

KC1 0.13

NapSOn ' 0.01

Zn(00CCH

3

) 2

< 0.01

FeSOn • (NHij) 2

S0ij • 6H20 <0.01

LiBr 0.36

KN0

3 0.35

CsCI 0.03

CsSCN 1.07

KSCN 1.08

CoC1 2 -6H2 0 0.15

Co(N0 3

) 2 0.70

Tetrabutylammoniumbromide 0.7^

Tetrabutylammoniumnitrate 0.97

Tetraethylammoniumtetrafluoroborate (TEATFB) >1 .7

The following organic salts gave conductivities similar to TEAT E I Jt . less conductivity per unit molarity.

Tetra (n-butyl )ammoniumtetraphenylborate

Tetrae thylammoniumtoluenesulfonate

Tetraethylammoniumhexaf luorophosphate

Dodecyltrimethylammoniumchloride
Bulk

Conductivity

(S/m)

at

10

MHz

-31-

Molarity (moie/litre)

Figure 13. Conductivities and static dielectric constants of

solutions of tetraethylammonium tetraf luoroborate in a 50/50

mixture of ethyene carbonate and propylene carbonate. The dashed

line gives the conductivities of sodium chloride in water for

comparison. Biological electrolytes have about 0.14 molar NaCl.

k'

at

10

MHz
-32-

ad justed over the range of values of interest. We have observed

no changes in the conductivity of the initial mixture of

PC/EC/salt during several months of use. TEATFB is commonly

available from chemical supply companies [18].

3) Films for interfacial polarization

The most difficult component to simulate was the cell walls

which encapsulate the salt water in biological tissues. Presently

used aqueous phantoms either do not attempt to incorporate this

feature, or use aluminum particles to achieve the effect. It is

known to be difficult to obtain interfacial polarization with low

k' particles in a material of high k' and k" as, for instance,

oil droplets in water [19]. This is because the ion transport

is not effectively blocked by spherical particles, as it is by an

encapsulating structure like a cell wall.

Ideally we want the liquid to be in the form of droplets and

the films to encapsulate these droplets. Encapsulation

techniques are commonly developed for aqueous solutions but the

techniques developed for aqueous media are not directly

transferrable to other solvent systems. Liposome technology

[20] provides a means of making phospholipid bilayers that

encapsulate droplets of water in oil or oil in water. We

attempted to incorporate liposomes produced in water into the

PC/EC/salt solution, but were unable to obtain structures that

provided interfacial polarization.

We contacted one company [21] with experience in

encapsulation of ink. One of their researchers tried

unsuccessfully to encapsulate PC using simple techniques. An
-33-

expert in the use of microencapsulation [22] said he could apply

other standard technologies to PC/EC/salt if requested. Another

technology that might be useable [23] involves atomizing the

solvent, freezing it into fine solid particles and then coating

these frozen particles with sub micrometer thick films of

poly-p-xylylene. While this process should lead to an easily

handled powder, and it might be possible to develop the process

[24]

, it could be quite expensive for the production of large

quantities of material.

The simplest adequate solution is to use thin flakes of a

barrier material in the solvent. We tried several different

sources of ready-made flakes with the general guidance that we

needed them to be as thin as possible to have a high capacitance

and with a large area so as to more effectively block the

transport of ions. We tried paper and found it was too thick.

However, the ashes of burnt paper were thinner and showed some of

the desired effect. Flakes of glass from bubbles that had been

blown thin enough to show interference colors (about 3 jam thick)

were found to support some interfacial polarization. We then

tried single crystals of polyethylene grown from solution that

were nominally 10 nm thick. These showed very little indication

of interfacial polarization. Mica was obtained in several sizes

[25] having thicknesses as low as 0.5 jam and aspect ratios of 25

to 1. These mixtures gave less interfacial polarization than

desired probably because the aspect ratios were too small. In

all of the above trials we thickened the PC/EC/salt with about 5

weight percent of cabosil [26] in order to make the solution

thick enough that the suspended flakes did not separate from the
-34-

solvent . By far the most successful interfaces were polymer films.

For example, polyethylene from grocery produce or dry cleaning

bags of 12 pm thickness can be drawn by hand to about 4 pm so

that it shows interference colors in white light. Both PE and 4

pm polyvinylidene fluoride (PVDF) were added to the PC/EC/salt.

Even though they increased k' by about 4 times at 1 MHz, they

also reduced the higher frequency values, indicating that the

film capacitances were lower than desired. In addition, PVDF is

soluble in PC at elevated temperatures.

The thinnest commercial film that we found was polyester

(PET) in 1.5 pm thickness [27]. When cut into flakes a few mm in

diameter this film gave an acceptable interfacial polarization

down to 4 MHz. At 1 MHz these flakes could increase k' by 10

times which approaches the increases found for biological tissue

(40 times). For high electrical capacitance one would prefer a thinner film and for sufficient stiffness to ensure that the film

will remain extended when mixed into the PC/EC/salt one would

prefer a thicker film. As a compromise the 1.5 pm film is

adequate for our purposes.

The optimum concentration of 1.5 pm thick PET films in the

PC/EC/salt can be calculated for an ideal case. Assume that the

films lie parallel to the electrodes (perpendicular to the

electric field) with an kf'=3.2 [28] and thickness tf=1.5 pm.

The desired apparent kc

' for the combination of fully polarized

film and bulk material between films is about 8xl0 4 . To provide

such an kc

'

,

the films will have to be spaced kc 'tf/kf'= 4 cm

apart. This gives a relaxation time, R]_C 2 = 10 -6 sec as desired.
-35-

If the films are stirred into the PC/EC/salt only 1/3 of them on

average will have the proper orientation (perpendicular to the

electric field). Thus for each (4cm) 3 of phantom we need

3x(4cm) 2 of film. This calculation is completely valid only

when the film completely blocks all liquid paths for ion

transport from one electrode to the other. Film pieces mixed

into the conductive electrolyte will be subject to a low

resistance path around the flakes of film which will reduce their

charge storage ability and lower the maximum interfacial

polarization they can support.

A comparison of the effect of the film geometry on its

charging characteristics is shown in figures 14-17. Our

measurements show that a 1.5 pm film mixed in the bulk gives good

results down to 4 MHz but gives less polarization than biological

cell walls at 1 MHz. Heterogeneities on the scale of 4 cm in the

phantom should not cause heterogenieties in the heating. As shown

in figure 6 for frequencies above 1 MHz the heating is entirely

in the bulk and not affected by the presence of the films.

The specimen holder we used for these measurements was too

small (thickness = 0.457 cm and area = 0.317 cm2

) to measure the

formulation suggested above. With PC/EC/salt and a single film of

area 0.32 cm2 in the holder we obtained the results shown in

figure 14. These data are compared to the results using the same

PC/EC/salt mixture without a film present in the holder. The data

are in reasonable agreement with expectations. The mean frequency

for charging the film is 8 MHz rather than the desired 1 MHz

because the holder is 1/8 as thick as desired. And the value of

log ( k

’

)

is about 0.5 decades too low because the conduction
-36-

Figure 14. Dielectric properties of a 50/50 mixture of ethylene

carbonate and propylene carbonate with 0.28 molar

tetraethylammonium tetraf luoroborate . A single film of 1.5 pr

thick PET the same diameter as the specimen holder is used for

the "with" data.
-37-

Figure 15. Dielectric properties of the synthetic phantom material with 4.5 weight% of silica thickener and a single film
DIELECTRIC

CONSTRNTS

-38-

FREQUENCY (Hz)

Figure 16. Dielectric properties of the synthetic phantom

material containing 3mm x 3mm flakes of PET film.
-39-

FREQUENCY (Hz)

Figure 17. Dielectric properties of the synthetic phantom

material with a single film of PET completely covering one

electrode

.
-40-

around the edge of the film limits the charge that can be placed

on the film.

4 ) Thickeners

Two types of thickener are of potential use in the phantom.

Fumed silica [26] can be stirred in the PC/EC/salt to increase

its viscosity and keep the polymer flakes suspended, or a soluble polymer can be cross-linked chemically to give a more

permanent gel. Both types provide a network which gives the

PC/EC/salt increased mechanical stability. We found that about

4.5% by weight of fumed silica yielded a gel that is thick enough

to suspend the polymer flakes without being so thick that air

bubbles are suspended in the mixture. Air bubbles must be avoided

if the dielectric properties of the unthickened PC/EC/salt are to

be preserved. Gels can be formed also by mixing into the

PC/EC/salt a soluble polymer like polyethylene glycol 600

dimethacrylate (PEG) [29], and cross linking it with a photo

initiator like benzoin methyl ether [30]. We used 7% of the

polymer and 0.5% of the initiator to produce a clear gel which

showed no signs of exuding the solvent. The PEG 400

dimethacrylate on the other hand partially separated from the

liquid phase when crosslinked. PEG of higher molecular weight

(1000 or 2000 for example) can be used at higher concentrations

than the 400 without increasing the crosslink density and the

tendency for the solvent to separate from the network.

Figure 15 shows data for PC/EC/salt thickened with 4.5 % by

weight of fumed silica, and with a single 1.5 pm thick film of

PET. For comparison, figure 16 shows data for the same material
-41-

but with 0.96 cm^ of film cut into about 3 mm x 3 mm squares and

mixed into the specimen.

The system that gave the most interfacial polarization was

the one giving the data of figure 17 with one thickness of film

covering one electrode so that a conduction path around the film

was eliminated. These data were quite close to a recent set of

Jade plant leaf data as shown in figure 18 over the whole

frequency range from 100 Hz to 1 GHz. We expect the differences

between the data in figures 2 and 18, are due to how tightly the

specimen fits in the polyethylene tube of the specimen holder,

but these differences are not significant for present purposes.

Even the phantom with flakes (figure 16) follows well the

increase in dielectric properties of the leaf down to 4 MHz.

For a more careful analysis of the dielectric data than the

graphs allow we have included tabulated data in tables 3-9. Table

3 is the data for the empty holder to be used to correct the data

given in tables 4-9. This correction is made by subtracting the

k' and k" given in table 3 from the values given in the other

tables at corresponding frequencies. This correction is

significant only at the highest frequencies. The tables 4-9 are

for figures 15-20 respectively.

These results confirm that the basic concepts described above

are correct and that commercially available 1.5 )im thick PET film

can provide adequate interfacial polarization to mimic that

provided by biological cell walls.
DIELECTRIC

CONST

PINTS

-42-

FREQUENCY (Hz)

Figure 18. Dielectric properties of a jade plant leaf measured

under the same conditions as was the synthetic phantom.
-43-

DIELECTRIC CONSTANTS OF MIXTURES

It is important to be able to calculate the decrease in k'

of the PC/EC/salt when we add thickeners and other materials.

A useful additivity rule for dilute mixtures is that the cube

roots of the components are additive [30]. The k' of a mixture is

given by;

k’ = ( Jifiki' 1 / 3

) 3

,

i

where and kj_

'

are the volume fraction and k' of component i.

A more accurate mixing rule is the one given by Bruggeman

[32] for concentrated mixtures of spherical particles of

dielectric constant, k

p

’ and volume fraction, (j), in a medium of

dielectric constant, km . The dielectric constant of the mixture

is given by,

[(k’-kp' )/<kra '-kp

' )](kra '/k' ) 1/3 =

A useful approximation [19] to this rule for our present case

of km '>>kp' is.

k' = km

' ( 1 - (|> ) 3 / 2

, or

k' = km

' ( 1 — 3(j)/2 ) , for ^)<<1.

The fumed silica has a k* = 3.8 [28] and a density of 2.2 [26].

Five percent by weight of SiC>2 is equivalent to 3 percent by

volume in the PC/EC/salt. This should decrease the dielectric

constant from 79 to 75. This is about the same decrease as we
-44-

measured directly for different concentrations of fumed silica in

PC/EC/salt. The addition of 7% by weight of polyethylene glycol

with a density of 1.1 and an k'=8 [28] reduces the k' of the

mixture from 79 to 70, and 5% by volume of air reduces the k'

from 79 to 73. Note that the last equation above does not require

knowledge of the k* of the particles as long as it is small. For

muscle, 25% organic material of k'=3 in water should lower the k'

from 79 to 49 according to the last equation given above. The

unsimplified Bruggeman equation gives 53. This prediction agrees

with k'= 50-60 reported for muscle around 1 GHz [3]. We use these

mixing rules only at higher frequencies where interfacial

polarization is not important. It has been suggested that the

Bruggeman equation can be used also to calculate k" of a mixture

[19]. That is, we can substitute cr* or k" for k' in the previous

three equations as long as there is no interfacial polarization.

Thus a water-salt solution of biological concentration and cr' =1.4

S/m, when mixed with 25 volume % of solids of low conductivity

gives cr' =0.9 S/m, in fair agreement with muscle data at about 100

MHz [3]. Mixing material of a low k* such as a thickening agent

is a useful way (in addition to changing the relative

concentrations of the PC and EC) of adjusting the high frequency

k' of PC/EC/salt.

There is a detectable decrease in k' due to the addition

of 0.28 mol/litre of TEA TFB. Assuming a density of 1.1 gm/cm^

for the salt (217 is the formula weight), we have 5 volume % of

salt in the phantom. The mixing equations give an expected

decrease in the k' of 6 which is close to the change found in

figure 13.
-45-

STABILITY

We did not study stability of the phantom but observed no

changes in our PC/EC/salt solution during the six months we have

been using it. The product brochure [15] warns that "If an acid,

base or salt is present in the aqueous solutions of these

products, decomposition will occur." Water is soluble to the

extent of 8.3gm/100gm of PC and highly soluble in EC [15]. We

have taken no precautions to avoid water in our samples. While

evaporation of PC is much slower than evaporation of water,

drying will still occur. The long term stability and useful

lifetime of this synthetic electrolyte should be determined

before compositions are standardized.

THE USE OF THE TISSUE PHANTOM

The phantom is usually placed in a mold. In a common version,

the mold material is made with the same electrical properties

as fat. A plastic film may cover the ends of the mold. In these

cases the covering acts as a relatively small capacitance in

series with the phantom. This is equivalent to placing an

additional capacitance in series with the circuit of figure 3.

The impedance of this capacitor can easily dominate the circuit

impedance and reduce the electric field in the phantom and reduce

the bulk heating. The effect increases as the frequency is

lowered. A 25 pm (1 mil) thick coating on the surface of a 1

meter long specimen of phantom will have the same effect on the

interfacial polarization as 1.5 pm thick films spaced 6 cm apart

within the bulk of the phantom. A much thicker surface coating

can greatly modify the electrical response.
-46-

We caution that if a parallel plate specimen holder is not

used for measuring the phantom, care must be taken to assure that

a sufficiently large volume of material is sampled. For example,

the fringing field from a small open-terminated coaxial probe is

sometimes used to measure the impedance of a material. Used with

this phantom it can give a wide variation in properties depending

on the proximity and orientation of pieces of film in the phantom

with respect to the end of the probe. The electrical properties

of the phantom containing dispersed films will be isotropic but

only when sampled over distances of several centimeters.

For comparison with our results, we include data from

aqueous muscle and brain phantoms currently in use at the FDA

(figures 19 and 20). The brain phantom values are probably too

low because we had trouble removing all air from the holder.

Note that these data have the same form as our data for the

synthetic phantom without film added (figure 14). This means that

this new phantom can be used in place of the aqueous phantom

without the film component, for use over small frequency ranges.

The formulation given in this report is not intended as

the optimum for a particular use. It is proposed as a close

approximation to the required material to illustrate the

important design factors involved and the way in which the

electric properties can be easily manipulated to give desired

magnitudes and shapes to the k' and k" curves.
DIELECTRIC

CONSTRNTS

-47-

Figure 19. Dielectric properties of an aqueous brain phantom in

current use at the Center for Devices and Radiological Health.
DIELECTRIC

CONSTANTS

-48-

FREQUENCY (Hz)

Figure 20. Dielectric properties of an aqueous muscle phantom in

current use at the Center for Devices and Radiological Health.
-49-

Table 3. Calibration data for k' and k" obtained with an empty

specimen holder. To correct the measured values

reported in the other data tables subtract these values

of k' and k" and o' from the values reported in the

other tables at the corresponding frequencies. The

differences will be important only for the higher

frequency data.

No. f (Hz) G (S) C (pF) 0 (S/cm) k' k" No.

1 5. 600E+01 8.404E-07 -9. 000E+02 1 . 212E-06 -1 . 465E+04 3. 891E+04 1 2 1 . 000E + 02 3. 966E-07 7. 4 1 5E+02 5. 71SE-07 1 . 207E+04 1 . 028E + 04 2

3 1 . 780E + 02 1 . 471E-07 1 . 396E + 02 2. 121E-07 3. 088E+03 2. 143E + 03 3

4 3. 160E+02 1 . 352E-07 4. 937E+01 1 . 949E-07 8. 039E+02 1 . 109E+03 4 5 5. 620E+02 1 . 219E-07 1 . 900E + 01 1 . 758E-07 3. 093E+02 5. 625E+02 5

6 1 . 000E + 03 1 . 340E-07 7. 970E+00 1 . 931E-07 1 . 298E+02 3. 473E+32 6

7 1 . 730E+03 1 . 507E-07 6. 149E+00 2. 172E-07 1 . 001E + 02 2. 195E+02 7

8 3. 160E+03 1 . 571E-07 4 . 1 08E+00 2. 264E-07 6. 689E+01 1 . 2S9E+02 8

9 5. 620E+03 1 . 733E-07 3. 657E+00 2. 499E-07 5. 954E+01 7. 995E+0

1

9

10 1 . 000E + 04 1 . 966E-07 3. 247E+00 2. 834E-07 5. 287E+01 5. 096E+01 10

1 1 1 . 780E+04 2. 348E-07 2. 673E+00 3. 384E-07 4. 360E+01 3. 419E+01 1 1 12 3. 160E+04 2. 735E-07 2. 256E+00 4. 015E-07 3. 674E+01 2. 285E+01 12

13 5. 620E+04 3. 4S4E-07 1 . 941E + 00 5. 022E-07 3. 160E + 01 1 . 607E+01 13

14 1 . 000E+05 4 . 393E-07 1 . 661E + 00 6. 333E-07 2. 704E+0

1

1 . 139E+01 14

15 1 . 780E + 05 5. 525E-07 1 . 535E+00 7. 965E-07 2. 499E+01 8. 047E+00 15

16 3. 160E + 05 7. 001E-07 1 . 416E + 00 1 . 009E-06 2. 305E+01 5. 744E+00 16

17 5. 620E+05 8. 899E-07 1 . 339E+00 1 . 283E-06 2. 180E+01 4. 105E+00 17

18 1 . 000E+06 1 . 1 18E-06 1 . 257E + 00 1 . 612E-06 2. 047E+01 2. 899E+00 18

19 1 . 780E + 06 1 . 404E-06 1 . 214E+00 2. 024E-06 1 . 977E + 01 2. 045E+00 19

20 3. 160E + 06 1 . 762E-06 1 . 168E + 00 2. 540E-06 1 . 901E+01 1 . 445E+00 20

21 5. 620E+06 2. 306E-06 1 . 147E+00 3. 324E-06 1 . 868E+01 1 . 064E+00 21

22 1 . 000E+07 3. 394E-06 1 . 1 16E + 00 4. 893E-06 1 . 817E+01 8. 800E-01 22

23 1 . 299E+07 4 . 004E— 06 1.101 E+00 5. 772E-06 1 . 793E+01 7. 991E-01 23

Sample flrea= 3.170E-01 cm A 2

Measured with HP3570A

Th i c k ness = 4 . 570E-0 1 cm fl/d= 6.937E:-01 cm

No

.

f ( Hz ) - G <S> C (pF) o (S/cm) k' k" No

1 1 . 000E + 06 5. 000E-06 1 . 75 1 E + 00 7. 208E-06 2. 851E+01 1 . 296E + 01 1 2 1.31 3E + 06 6 . 000E-06 1 . 690E + 00 8. 650E-06 2. 752E+01 1 . 179E+01 2 3 1 . 738E + 06 7 . 000E-06 1 . 649E + 00 1 . 009E-05 2. 684E+01 1 . 044E+O1 O

4 2. 291E+06 7. 000E-06 1 . 667E + 00 1 . 009E-05 2. 715E+01 7. 913E+00 4

5 3. 020E+06 9 . 000E-06 1 . 634E+00 1 . 297E-05 2. 660E+01 7. 723E+00 5 6 3., 98 1 E + 06 1 . 100E-05 1 . 599E + 00 1 . 536E-05 2. 604E+01 7. 160E+00 6

7 5. 248E+06 1 . 300E-05 1 . 547E + 00 1 . 874E-05 2. 518E+01 6. 419E+00 7

3 6. 913E+06 1 . 700E-05 1 . 51SE + 00 2. 451E-05 2. 472E+01 6 . 368E+00 8

9 9. 120E+06 2. 100E-05 1 . 466E + 00 3. 027E-05 2. 337E+01 5. 967E+00 q 10 1 . 202E+07 2. 6O0E-05 1 . 416E + 00 3. 748E-05 2. 306E+01 5. 604E+00 10

1 1 1 . 535E + 07 3. 100E-05 1 . 366E + 00 4. 469E-05 2. 224E+01 5. 069E+00 1 1 12 2. 0S9E+07 3. 900E-05 1 . 313E+00 5. 622E-05 2. 146E + 01 4. 837E+00 12

13 2. 754E+07 4. 70OE-05 1 . 277E + 00 6. 776E-05 2. 079E+01 4. 422E+00 13

14 3. 631E+07 5. 800E-05 1 . 227E + 00 8. 362E-05 1 . 993E+01 4. 14OE+00 14

15 4. 786E+07 7. 000E-05 1 . 184E + 00 1 . 009E-04 1 . 927E+01 3. 790E+00 15

16 6.310E+07 8. 300E-05 1 . 143E+00 1 . 197E-04 1 . S61E+01 3. 409E+00 16

17 8. 313E+07 9. 700E-05 1 . 1 12E + 00 1 . 398E-04 1 . 810E + O1 3 . 022E+00 17

13 1 . 096E + 08 1 . 100E-04 1 . 03 1 E + 00 1 . 586E-04 1 . 761E+01 2 . 6 0 0 E + 0 O 13

19 1 . 445E+08 1 . 240E-04 1 . 058E + 00 1 . 788E-04 1 . 723E+01 2. 223E+00 19

20 1 . 905E+03 1 . 350E-04 1 . 042E + 00 1 . 946E-04 1 . 696E + 01 1 . 836E+0O 20

21 2. 512E+08 1 . 550E-04 1 . 02SE+00 2. 235E-04 1 . 674E+01 1 . 599E+00 21

22 3. 31 1E+03 1 . 740E-04 1 . 017E + 00 2. 508E-04 1 . 655E+01 1 . 362E+0O OC- i

23 4 . 365E+03 2. 15OE-04 1 . 006E + 00 3. 100E-04 1 . 637E+01 1 . 276E+0O 23

24 5. 754E+08 2. 570E-04 9. 893E-01 3. 705E-04 1.61 1E+01 1 . 157E+O0 24

2 5 7. 5S6E+03 3. 360E-04 9. 653E-01 4 . 344E-04 1 . 572E + 01 1 . 143E+0O 25

26 1 . 0O0E+09 4. 210E-04 9. 360E-01 6 . 069E-04 1 . 524E+01 1 . 09 1 E+00 2 *5 Samp 1 e flrea= 3. 170E-O1 cm A 2 Thi c k n e s s = 4 . 570E-0 1 cm A / d = 6.93 7 E - O 1 cm Measured with HP4191A
-50-

Table 4. Data for figure 15, phantom with a single film of PET.

No. f <Hz> G <S> C < pF ) ° (S/cm) k" k" No.

1 5. 600E+01 8. 370E-04 2. 303E+06 1 . 207E-03 3. 758E+07 3. 375E+87 1 2 1 . 000E + 02 1 . 235E-03 1 . 440E + 06 1 . 731E-03 2. 344E+07 3.202E+07 £. 3 1 . 780E+02 1 . 649E-03 7. 724E+05 2. 373E-03 1 . 258E+07 2. 402E+07 3

4 3. 160E + 82 1 . 9S9E-03 3. 643E+05 2. 367E-03 5. 932E+06 1 . 632E+07 4

5 5. 620E+02 2 . 220E-03 1 o 566E + 05 3. 200E-03 2. 550E+06 1 . 024E+07 5

6 1 . 0 0 0 E + 0 3 2 . 366E-03 6. 3S3E+04 3. 41 IE-03 1 . 040E+06 6. 1 3 4 E + 8 6 6

7 1 . 73OE + 03 2. 455E-03 2. 527E+04 3. 539E-03 4. 1 15E+05 3. 576E+06 7 S 3. 160E+03 2. 506E-03 9. 931E+03 3. 613E-03 1 . 617E+05 2. 056E+06 8

9 5. 620E+03 2. 534E-03 3. 949E+03 3. 654E-03 6. 430E+04 1. 1 69E+06 9

10 1 . 000E + 04 2. 543E-03 1 . 652E+03 3. 674E-03 2. 6 9 0 E + 0 4 6. 606E+05 10

1

1

1 . 730E + 04 2. 553E-03 7. 623E+02 3. 638E-03 1 . 241E+04 3. 726E+05 1 1 12 3. 160E + 04 2. 564E-03 4. 136E+02 3. 696E-03 6. 735E+03 2. 1 04E + 05 12

13 5. 620E+04 2. 567E-03 2. 692E+02 3. 701E-03 4. 383E+03 1 . 1S4E+05 13

14 1 . 000E+05 2. 569E-03 1.991E+02 3. 704E-03 3. 241E+03 6. 66 1 E+84 14

15 1 . 730E+05 2. 582E-03 1 . 777E+02 3 . 722E-03 2. 894E+03 3. 761E+04 15

16 3. 160E+05 2. 606E-03 1 . 615E+02 3. 757E-03 2. 629E+03 2. 138E + 04 16

17 5. 620E+05 2 . 675E-03 1 . 479E+02 3. 856E-03 2. 407E+03 1 . 234E+04 17

13 1 . 000E + 06 2. 867E-03 1 . 301E+02 4. 133E-03 2. 1 18E+03 7. 433E+03 18

19 1 . 7S0E+06 3. 286E-03 1 . 004E+02 4. 737E-03 1 . 634E+03 4. 736E+03 19

20 3.1 60E + 06 3. 893E-03 6. 171E+01 5. 612E-03 1 . 005E+03 3. 1 94E+03 20

21 5 o 620E + 06 4 . 4 1 0E-03 3. 074E+01 6. 35SE-03 5. 005E+02 2. 035E+03 21

22 1 . 000E + 07 4. 691E-03 1.483E+01 6. 763E-03 2. 415E+02 1 . 216E+03 22

23 1 . 299E+07 4. 749E-03 1. 135E+01 6. 846E-03 1 . 849E+02 9. 478E+02 23

Sample flrea= 3.170E-01 cm A 2

Measured with HP3570R

Th i c k ness = 4.570E-01 cm R/d= 6.937E>01 cm

No f < Hz > G <S> C ( pF ) 0 (S/cm) k' k" No.

1 1 . 000E + 06 2 . 960E-03 1 . 261E+02 4 . 2 6 7 E

_ 0 3 2. 052E+03 7 . 67 1 E+03 1 2 1.31 3E + 06 3. 129E-03 1 . 149E+02 4. 51 IE-03 1 . 87 1 E+03 6. 1 5 1 E + 03 2

3 1 . 73SE+06 3. 359E-03 1 . 007E+02 4. 842E-03 1 . 639E+03 5. 009E+03 3

4 2. 291E+06 3. 642E-03 8. 323E+01 5. 250E-03 1 . 355E+03 4. 120E + 03 4

5 3. 020E+06 3. 949E-03 6.466E+01 5. 693E-03 1 . 053E+03 3. 389E+03 5

6 3. 931E+06 4. 239E-03 4. 749E+01 6.11 IE-03 7. 733E+02 2. 759E+03 6

7 5 . 248E+06 4. 480E-03 3. 34SE+01 6. 459E-03 5. 451E+02 2. 212E+03 7

3 6. 918E+06 4. 662E-03 2. 321E+0L 6. 721E-03 3. 779E+02 1 . 746E+03 8

9 9. 120E+06 4. 789E-03 1 . 623E+01 6 . 904E-03 2. 643E+02 1 . 36

1

E+03 9

1 0 1 . 202E + 07 4. 373E-03 1 . 176E+01 7. 025E-03 1 . 914E+02 1 . 050E+O3 10

1 1 1 . 5S5E + 07 4. 928E-03 8. 973E+00 7. 104E-03 1 . 462E+02 8. 053E+O2 1 1 12 2. 039E+07 4. 964E-03 7. 290E+00 7. 156E-03 1 . 1 87E+02 6. 157E + 02 12

13 2. 754E+07 4. 990E-03 6. 281E+00 7. 194E-03 1 . 023E+02 4. 695E+02 13

14 3. 631E+07 5. 010E-03 5. 690E+00 7. 223E-03 9. 264E+01 3. 576E+02 14

15 4. 786E+07 5. 029E-03 5. 334E+00 7. 250E-03 8. 634E+01 2. 723E+02 15

1 6 6. 310E+07 5. 051E-03 5. 1 13E+00 7. 282E-03 8 . 325E+0

1

2. 075E+02 16

17 8. 313E+07 5. 079E-03 4. 981E+00 7. 322E-03 8. 1 10E+01 1

.

532E + 02 1 7 13 1 . 096E+08 5. 1 19E-03 4. 893E+00 7. 3S0E-03 7. 967E+01 1 . 210E + 02 18

19 1 . 445E+03 5. 180E-03 4. 833E+00 7. 463E-03 7. S69E+01 9. 287E+01 19

20 1 . 905E+03 5. 271E-03 4. 739E+00 7. 599E-03 7. 798E-01 7. 169E + 01 20

21 2. 512E+08 5. 436E-03 4. 755E+00 7. 837E-03 7. 743E+01 5. 603E+01 21

22 3.31 1E + 08 5. 702E-03 4. 719E+00 8. 220E-03 7. 684E+01 4

.

432E+0

1

& 2

23 4. 365E+08 6. 157E-03 4. 675E+00 8. 876E-03 7. 61 lE-t-01 3. 655E+01 23

24 5. 754E+03 6. 901E-03 4. 613E+00 9. 949E-03 7.51 1E + 01 3 . 1 08E +0 1 24

2 j 7. 536E+03 8.11 IE-03 4. 519E+00 1 . 169E-02 7 . 358E+0

1

2. 771E+01 & J 26 1 . Q00E+09 1 . 014E-02 4. 396E+00 1 . 462E-02 7. 1 5SE+0

1

2. 629E+01 26

Saini p 1 e R r e a= 3 . 170E-01 cm A 2 Thickness= 4.570E-01 cm R/d= 6.93 7E-0 1 cm Measured with HP4191R
-51-

Table 5. Data for figure 16, flakes of film of PET mixed into

the phantom.

No. f (Hz) G (S) C ( pF

)

n (S/cm) k

" k" No

.

1 5. 600E+01 6 . 173E-04 2. 447E+06 8 . 399E-04 3. 984E+07 2. 858E-07 1 2 1 . 000 E + 02 1 . 016E-03 1 . 786E+06 1 . 465E-03 2. 909E+07 2. 635E+07 2

3 1 . 730E + 02 1. 566E-03 1 . 153E + 06 2. 258E-03 1 . 386E+07 2. 232E+07 3

4 3. 160E + 02 2. 177E-03 6. 481E+05 3. 133E-03 1 . 055E + 07 1 . 78bE-f-07 4 5 5. 620E+02 2. 716E-03 3. 138E + 05 3. 916E-03 5. 109E+06 1 . 253E + 07 C

sj 6 1 . 000E + 03 3. 101E-03 1.351E+85 4. 471E-03 2. 200E+06 8 . 040E*0d e

7 1 . 730E + 03 3. 336E-03 5. 350E+04 4. 809E-03 8. 71 1E+05 4. 859E+0S 7

3 3. 160E + 03 3. 467E-03 2. 023E+04 4. 998E-03 3 . 294E+05 2. 845E+06 8

9 5. 620E+03 3. 533E-03 7. 453E+03 5. 094E-03 1 . 214E + 05 1 . 630E+06 9

10 1 . 000E + 04 3. 568E-03 2. 752E+03 5. 143E-03 4. 482E+04 9. 249E+05 1 0

1 1 1 . 730E + 04 3. 532E-03 1 . 043E + 03 5. 164E-03 1 . 707E+04 5. 218E+05 1 1 12 3 . 1 60E+04 3. 591E-03 4. 295E+02 5. 176E-03 6. 993E+03 2. 946E+05 12

13 5. 620E+04 3. 596E-03 1 . 963E+02 5. 184E-03 3. 204E+03 1 . 659E+05 13

14 1 . 000E + 05 3 . 596E-03 1. 163E+02 5. 183E-03 1 . 902E+03 9. 322E+04 14

15 1 . 730E+05 3. 601E-03 6. 567E+01 5. 192E-03 1 . 069E+03 5. 245E+04 15

Id 3. 160E+05 3. 604E-03 4. 756E+01 5. 196E-03 7. 744E+02 2. 957E+04 16

17 5. S20E+05 3 . 6 1 7E-03 3. 794E+01 5. 214E-03 6. 178E+02 1 . 663E+04 17

13 1 . 000E + 06 3. 639E-03 3. 196E+01 5. 247E-03 5 . 205E+02 9. 436E+03 13

19 1 . 730E+06 3. 691E-03 2. 679E+01 5. 321E-03 4. 361E+02 5. 375E+03 19

20 3. 1 60E+06 3. 796E-03 2. 1 16E+01 5. 472E-03 3. 445E+02 3. 1 14E+03 20

21 5. 620E+06 3. 950E-03 1 . 523E + 0 1 5. 695E-03 2 . 489E+02 1 . 822E+03 21

22 1 . 000E+07 4. 120E-03 1 . 033E+0 1 5. 940E-93 1 . 690E+02 1 . 063E+03 22

23 1 . 299E + 07 4. 183E-03 8. 903E+00 6. 030E-03 1 . 450E+02 8 . 343E+02 23

Sample flrea= 3.170E-01 cra A 2

Measured with HP3570A

Th i c k ness = 4.570E-01 cm fl/d= 6.937E>01 cm

No . f (Hz) G (S) C (pF) Q (S/cm) k

" k" No .

1 1 . 000E + 06 4. 010E-03 2. 722E+01 5. 731E-03 4. 431E+02 1 . 039E + 04 1 2 1 . 31SE + 06 4. 030E-03 2. 584E+01 5. 810E-03 4 . 207E+02 7. 922E+03 2

3 1 . 733E + 06 4. 059E-03 2. 454E+01 5. 852E-03 3. 996E+02 6. 053E+03 3

4 2. 291E+06 4. 100E-03 2. 286E+0

1

5. 91 IE-03 3 . 722E+02 4. 638E+03 4

5 3. 020E+06 4. 156E-03 2.071E+01 5. 991E-03 3. 372E+02 3. 566E+03 5

6 3. 981E+06 4. 229E-03 1 . 827E+0

1

6. 097E-03 2. 975E+02 2. 753E+03 6

7 5'. 243E + 06 4. 313E-03 1 . 580E + 01 6. 218E-03 2. 573E+02 2. 130E + 03 7

8 6. 918E+06 4. 403E-03 1 . 327E + 0 1 6. 348E-03 2. 161E + 02 1 . 649E + 03 8

9 9. 120E + 06 4. 494E-03 1. 108E+01 6. 479E-03 1 . 804E + 02 1 . 277E+03 9

10 1 . 202E+07 4. 577E-03 9. 214E+00 6. 598E-03 1 . 500E+02 9 . 866E+02 10

1 1 1 . 585E + 07 4. 647E-03 7. 773E+00 6. 699E-03 1 . 266E + 02 7. 598E+02 1 1 12 2. 089E+07 4. 706E-03 6. 71 1E + 00 6. 734E-03 1 . 093E+02 5. 837E+02 12

13 2. 754E+07 4. 752E-03 5. 987E+00 6. 851E-03 9. 748E+01 4. 471E+02 13

14 3. 631E+07 4. 783E-03 5. 497E+00 6. 903E-03 8. 950E+01 3. 417E+02 14

15 4. 736E+07 4. 819E-03 5. 1S4E + 00 6. 947E-03 8. 441E+01 2. 609E+02 15

16 6. 310E+07 4. 843E-03 4. 982E+00 6. 989E-03 8 . 1 12E + 01 1 . 991 E+02 16

17 8. 313E+07 4. 832E-03 4. 853E + 00 7. 033E-03 7. 901E+01 1 . 521E+02 17

13 1 . 096E+03 4. 924E-03 4. 764E+00 7. 099E-03 7. 757E+01 1 . 164E+02 13

19 1 . 445E + 03 4. 933E-03 4. 705E+00 7. 134E-03 7. 661E+01 8 . 934E + 0 1 19

20 1 . 905E + 08 5. 071E-03 4. 661E+00 7.31 IE-03 7. 5S9E+01 6 . S 9 7 E + 9 1 20

21 2. 512E+03 5. 228E-03 4. 62SE+0O 7. 537E-03 7. 536E+01 5. 394E+01 21

22 3.31 1E + 03 5. 4S0E-03 4.593E+00 7. 900E-03 7. 47SE+01 4. 289E+01 CL C. 2 3 4. 365E+03 5. 913E-03 4. 551E+00 8. 524E-03 7. 409E+01 3. 510E+01 2 3 24 5. 754E+03 6.621E-03 4. 493E+00 9. 545E-03 7. 315E+01 2. 9S2E+01 24

25 7. 536E+03 7. 787E-03 4. 404E + 00 1 . 123E-02 7. 171E+91 2. 66OE+01 25

26 1 . 0O0E + 09 9. 736E-03 4. 28SE + 00 1 . 404E-02 6.981 E + 0 1 2. 523E+01 26

Sample firea= 3

.

170E-01 cm A 2 Th i c k ness = 4.570E-01 cm fl/d= 6.93 7 E -

0

1 cm Measured with HP4191P
-52-

Table 6. Data for figure 17, phantom with a single film

of PET covering one electrode.

No

.

f (Hz) G (S) C (pF) a (S/cm) k

" k" No

1

' 5. 609E+01 2. 359E-04 2. 497E+05 3. 401E-04 4. 066E+06 1.092E+07 1 2 1 . 000E+02 2. 643E-04 1 . 354E+05 3. 817E-04 2. 204E+06 6. S63E+06

3 1 . 730E + 02 2. 951E-04 7. 609E+04 4. 255E-04 1 . 239E+06 4. 298E+06 3

4 3. 160E + 02 3 . 265E-04 4 . 224E+04 4. 70SE-04 6. 87SE+05 2. 679E+06 4

5 5. 620E+02 3. 533E-04 2.254E+04 5. 166E-04 3. 670E+05 1 . 653E->-06 5

6 1 . 000E+03 3. 366E-04 1 . 1 40E+-04 5. 573E-04 1 . 856E+05 1 . 002E + 06 6

7 1 . 730E + 03 4. 091E-04 5. 606E+03 5. 897E-04 9. 128E+04 5. 953E+05 r 3 3. 160E + 03 4. 250E-04 2. 330E+03 6. 127E-04 4. 609E+04 3. 437E+05 8

9 5. 620E+03 4. 356E-04 1 . 536E + 03 6. 280E-04 2. 583E+04 2. 010E+05 9

10 1 . 000E+04 4. 436E-04 1 . 050E + 03 6. 395E-04 1 . 709E+04 1 . 150E+05 10

1 1 1 . 730E + 04 4. 515E-04 8. 194E+02 6. 509E-04 1 . 334E+04 6. 576E+04 1 1 12 3 . 1 60E+04 4. 640E-04 7. 044E+02 6. 690E-04 1 . 147E+04 3. 807E+04 12

13 5. 620E+04 4. 862E-04 6. 250E+02 7. 010E-04 1 . 013E+04 2. 243E+04 13

14 1 . 000E + 05 5. 240E-04 5. 581E+02 7. 554E-04 9. 086E+03 1 . 353E+04 14

15 1 . 730E + 05 5. 945E-04 5. 057E+02 8. 570E-04 8. 234E+03 8. 659E+03 15

16 3. 160E+05 7 . 608E-04 4. 573E+02 1 . 097E-03 7. 454E+03 6. 242E+03 16

17 5 . 620E+05 1 . 142E-03 3. 925E+02 1 . 647E-03 6. 390E+03 5. 270E+03 17

13 1 . 000E + 06 1 . 867E-03 2.919E+02 2. 691E-03 4. 752E+03 4. 839E+03 13

19 1 . 780E+06 2 . 870E-03 1 . 755E + 02 4. 138E-03 2 . 857E+03 4. 1 80E + 03 19

20 3. 160E+06 3. 757E-03 8. 427E+01 5. 416E-03 1 . 372E + 03 3. 082E+03 20

21 5. 620E+06 4. 286E-03 3. 574E+01 6. 179E-03 5. 820E+02 1 . 977E+03 21

22 1 . 000E + 07 4 . 520E-03 1 . 575E + 01 6. 517E-03 2. 565E+02 1 . 1 72E+03 22

23 1 . 299E + 07 4 . 568E-03 1 . 174E + 01 6. 586E-03 1 . 91 1E+02 9. 1 18E + 02 23

Samp 1 e Rrea= 3 . 170E-01 cm-2 Thick ness= 4.570E-01 cm R/d= 6.937E[-01 cm Measured with H P 3 5 7 0 R

No . f (Hz) G (S) C (pF) a (S/cm) k

" k" No

1 1 . 000E + 06 1.901E-03 2. 971E+02 2. 741E-03 4. 833E+03 4. 926E+03 1 2 1 . 31SE + 06 2. 385E-03 2. 429E+02 3. 438E-03 3. 955E+03 4. 638E+03 2

3 1 . 738E + 06 2. 908E-03 1.876E+02 4. 192E-03 3. 054E+03 4. 336E+03 3

4 2. 291E+06 3. 412E-03 1 . 363E+02 4. 919E-03 2.21 9E + 03 3. 860E+03 4

5 3. 020E+06 3. 844E-03 9. 423E+01 - 5 . 542E-03 1 . 534E+03 3. 299E-*-03 5 6 3'„ 98 1 E + 06 4. 1S0E-03 6. 277E+01 6. 026E-03 1 . 022E+03 2.721E+03 6

7 5. 248E+06 4. 421E-03 4. 106E + 01 6. 373E-03 6. 686E+02 2. 1 33E + 0 3 7 8 6. 91SE+06 4. 585E-03 2 . 692E + 0 f 6.61 0E-03 4. 383E+02 1 . 717E + 03 8

9 9. 120E + 06 4. 693E-03 1 . 808E + 0

1

6. 766E-03 2. 944E+02 1 . 333E+03 9

10 1 . 202E + 07 4. 762E-03 1 . 267E + 01 6. 865E-03 2. 063E+02 1 . 026E + O 3 10

1 1 1 . 535E + 07 4. 807E-03 9. 429E+00 6. 930E-03 1 . 535E+02 7. 860E-02 1 1 12 2. 089E+07 4. 336E-03 7. 51 1E + 00 6. 972E-03 1 . 223E + 02 5. 998E-02 12

13 2. 754E+07 4. 857E-03 6. 3S0E+00 7. 002E-03 1 . 039E+02 4 . 570E+02 1 3 14 3. 631E+07 4. 374E-03 5. 716E+00 7. 027E-03 9. 307E+01 3. 479E+02 14

15 4. 786E+07 4. 891E-03 5 . 320E+00 7. 051E-03 8. 663E+0

1

2. 648E+02 15

16 6. 310E+07 4. 912E-03 5. 035E+00 7. 0S1E-03 8. 280E + 0 1 2.017E 16

17 8 . 318E+07 4. 939E-03 4. 941E+00 7. 120E-03 8.044E+01 1 . 539E+02 17

13 1 . 096E + 03 4. 9S0E-03 4. 843E+00 7. 179E-03 7 . 894E+0

1

1 . 177E+02 13

19 1 . 445E+03 5. 040E-03 4. 785E+00 7. 266E-03 7. 792E+01 9.03 6

E

0

1

19

20 1 . 903E + 03 5. 131E-03 4. 741E+00 7. 397E-03 7. 719E+01 6 . 978E+01 20

21 2. 512E+03 5. 295E-03 T 0 9 E + 0

0

7. 6 3 3

E

- 0

3

7 . 667E+0

1

5. 463E+01 21

•“< •-> 3. 31 lE+08 5 . 562E-03 4. 674E+00 8. 0 13E-03 7.61 1E+01 4. 353E+01 £ 4, 23 4. 3 6 5 E + 0

3

6. 020E-03 4. 633E+00 8. 679E-03 7. 543E+01 3. 574E+0

1

23

24 5. 754E + 03 6. 77OE-03 4. 577E+00 9. 76OE-03 7 . 452E + 0 1 3. 049E O

1

24

25 7. 5S6E+03 8. 008E-03 4. 492E+00 1 . 154E-02 7. 314E+01 2. ?36E*01 25

26 1 . 000E+09 1 . 009E-02 4. 3S0E+00 1 . 454E-02 7. 132E+01 2. 614E+01 2 b

Samp 1 e Rrea= 3. 170E-01 cm A 2 Th i c k ness = 4.570E-01 cm R/d= 6.93 7E-01 cm Measured with HF4191R
-53-

Table 7. Data for figure 18, jade plant leaf.

No

.

f <Hz) G <S> C <cF> a (S/cm) k - k" No

.

1

• 5. 60OE+01 2. 774E-04 2. 470E+05 3. 999E-04 4. 022E+06 1 . 284E+07 1 2 1 . 00QE + 02 3. 053E-04 1 . 171E + 05 4. 401E-04 1 . 906E+36 7. 915E+06 2 3 1.780E+02 3. 271E-04 5. 540E+04 4. 716E-04 9. 021E+05 4. 763E->-06

4 3. 160E+02 3. 442E-04 2. 667E+04 4. 962E-04 4. 342E+05 2. S24E+06 4 5 5. 620E+02 3. 571E-04 1 . 354E+04 5 . 1 47E-04 2. 204E+05 1 . 647E*06 5 6 1 . 000E+03 3. 672E-04 7. 619E+03 5. 294E-04 1 . 241E+05 9. 520E+05 6 7 1 . 730E+03 3. 761E-04 4. 946E+03 5. 423E-04 8. 052E+04 5. 478E+05 7 8 3. 160E+03 3. 362E-04 3. 660E+03 5. 563E-04 5. 960E+04 3. 169E + 05 3 9 5. 620E+03 3. 996E-04 2 . 952E+03 5. 761E-04 4 . 806E+04 1 . 844E+05 9 10 1 . 000E+04 4. 208E-04 2. 494E+03 6. 066E-04 4.061 E+04 1 . 09 1 E + 05 10

1 1 1 . 780E + 04 4. 554E-04 2. 146E+03 6. 566E-04 3. 494E+04 6 . 634E+04 1 1 12 3. 160E + 04 5. 151E-04 1 . 846E+03 7.425E-04 3. 006E+04 4. 226E+04 12

13 5. 620E+04 6. 192E-04 1 . 559E+03 8. 927E-04 2. 538E+04 2. 857E+04 1

3

14 1 . 000E + 05 8. I40E-04 1 . 292E + 03 1 . 174E-03 2. 103E-r04 2. 1 10E+04 14

15 1 . 780E + 05 1 . 167E-03 1 . 01 1E+03 1 . 632E-03 1 . 647E + 04 1 . 699E+04 15

16 3. 160E+05 1 . 714E-03 7. 1 13E+02 2. 472E-03 1 . 159E + 04 1 . 407E+04 16

17 5. 620E+05 2. 414E-03 4. 284E+02 3. 431E-03 6. 976E+03 1 . 1 14E+04 17

13 1 . 000E+06 3. 092E-03 2. 201E+02 4. 457E-03 3. 584E+03 8. 016E+03 13

19 1 . 7S0E+06 3. 591E-03 1. 005E+02 5. 177E-03 1 . 636E+03 5. 231E+03 19

20 3. 160E+06 3. 904E-03 4. 422E+01 5. 628E-03 7. 201E+02 3. 203E+03 20

21 5. 620E+06 4. 086E-03 2. 045E+01 5. 891E-03 3 . 329E+02 1 . 835E+03 21

22 1 . 000E+07 4. 197E-03 1 . 097E + 01 6. 050E-03 1 . 787E+02 1 . 08SE+03 22

23 1 .299E + 07 4. 223E-03 9. 027E+00 6. 095E-03 1 . 470E+02 8. 438E+02 23

Sample flrea= 3. 170E-01 c m^2 Thi ckness= 4.570E-01 cm fl/d = 6.937E -01 cm Measured with HP3570R

No. f(Hz) G <S> C < pF ) o ( S/cm

)

k' k" No

1 1 . 000E + 06 3. 263E-03 2. 253E+02 4 . 704E-03 3. 677E+03 8. 456E+03 1 2 1 . 318E + 06 3. 541E-03 1 . 562E+02 5. 105E-03 2. 544E+03 6. 961E+G3 2 3 1 . 733E+06 3. 771E-03 1 . 059E + 02 5. 436E-03 1 . 724E+03 5. 623E+03 3

4 2. 291E+06 3. 952E-03 7. 100E+01 5. 697E-03 1 . 156E + 03 4. 470E+03 4

5 3 . 020E+06 4. 094E-03 4. 743E+01 5. 902E-03 7. 723E+02 3. 513E+03 5 6 3-. 931E + 06 4. 205E-03 3. 202E+01 6. 062E-03 5. 214E+02 2. 737E+03 6

“7

i 5. 243E+06 4. 239E-03 2. 205E+01 6. 133E-03 3. 590E+02 2. 1 18E + 03 7

8 6. 91SE+06 4. 354E-03 1 . 5 6 9 E + 0 f 6. 277E-03 2. 555E+02 1 . 63 1 E + 03 8

9 9. 120E + 06 4. 405E-03 1 . 16 9E + 01 6. 350E-03 1 . 904E+02 1 . 252E+03 9 10 1 . 202E+07 4. 446E-03 9. 161E+00 6. 410E-03 1 . 492E+02 9. 583E+02 10

1 1 1 . 5S5E + 07 4. 479E-03 7. 572E+00 6. 457E-03 1 . 233E+02 7. 324E+02 1 1 12 2. 089E+07 4. 507E-03 6. 582E+00 6. 497E-03 1'. 072E + 02 5. 590E+02 12

13 2. 754E+07 4. 533E-03 5. 952E+00 6. 535E-03 9. 691E+01 4. 265E+02 13

14 3. 631E+07 4. 557E-03 5. 550E+00 6. 570E-03 9. 036E+01 3. 253E+02 14

15 4. 736E+07 4. 583E-03 5. 294E+00 6. 607E-03 8. 619E+01 2. 431E+02 15

1 6 6. 310E+07 4. 61 IE-03 5. 1 1SE+00 6 . 647E-03 8. 333E+01 1 . 8S4E+02 16

17 8. 318E+07 4. 645E-03 4. 998E+00 6 . 696E-03 8. 138E + 01 1 . 447E+02 17

13 1 . 096E+03 4. 633E-03 4. 906E+00 6. 75SE-03 7. 938E+01 1 . 1 0SE-*-02 13

19 1 . 445E + 03 4. 739E-03 4. 837E+00 6. S32E-03 7. S76E + 01 8. 496E+01 19

20 1 . 905E+0S 4. 804E-03 4. 7S0E+00 6. 926E-03 7. 783E+01 6. 533E+0

1

20

21 2. 512E-r08 4. 907E-03 4. 736E+00 7. 074E-03 7. 712E+01 5. 062E+01 21

22 3.31 1E + 08 5. 049E-03 4. 692E+00 7. 279E-03 7. 640E+01 3.951E+01 22

23 4. 365E+08 5. 273E-03 4. 648E+00 7. 602E-03 7. 563E+01 3. 130E+01 2 3

24 5. 754E+03 5. 591E-03 4. 599E+00 8. 060E-03 7. 4S9E+01 2. 51SE+01 24

25 7. 5S6E+0S 6. 060E-03 4. 538E+O0 8. 736E-03 7. 389E+01 2. 070E + 0 1 25

26 1 . 000E + 09 6. 778E-03 4. 4S0E+O0 9. 771E-03 7. 295E+01 1.756E+01 26

Sample fire a= 3

.

170E-01 cm A 2 Thick ness = 4.570E-01 cm R/d= 6.93 7 E - 0 1 cm Measured with HP4191R
-54-

Table 8. Data for figure 19, aqueous brain phantom material from

the FDA.

No. f (Hz) G <S) C (pF) a (S/cm) k

" k" No

.

1 5. 600E+01 6. 919E-04 2. 912E+06 9. 974E-04 4. 741E+07 3 . 203E+07 1 2 1 . 000E+02 1 . 084E-03 2. 262E+06 1 . 562E-03 3. 6 8 2 E + 0

7

2. 809E+07 oc. 3 1 . 730E+02 1 . 6 3 1 E - 0 3 1 . 639E + 06 2. 423E-03 2. 669E+07 2. 448E+07 3

4 3 . 1 60E + 02 2 . 506E-03 1 . 094E+06 3.613E-03 1 . 731E+07 2. 056E+07 4

5 5. 620E+02 3. 514E-03 6 . 623E+05 5 . 066E-03 1 . 073E + 07 1 . 621E + 07 5 6 1 . 000E + 03 4. 569E-03 3. 605E+05 6. 536E-Q3 5 . S69E+06 1 . 184E + 07 6

7 1 . 730E+03 5. 496E-03 1 . 762E+05 7. 923E-03 2. 370E+06 8. 004E+06 7

8 3. 160E+03 6. 199E-03 7. 374E+04 3. 936E-03 1 . 232E+06 5. 036E+06 8

9 5 . 620E+03 6. 678E-03 3. 265E+04 9. 62SE-03 5. 3 1 6E+05 3. 081E + 06 9

10 1 . 000E+04 6. 972E-03 1 . 231E+04 1 . 005E-02 2.086E+05 1 . 807E+06 10

1 1 1 . 780E+04 7. 155E-03 4. 350E+03 1 . 032E-02 7. 896E+04 1 . 042E+06 1

1

12 3 . 1 60E+04 7.261E-03 1 . 799E+03 1 . 047E-02 2. 929E+04 5. 957E+05 12

13 5. 620E+04 7. 317E-03 6 . 56 1 E+02 1 . 055E-02 1 . 068E + 04 3. 376E+05 13

14 1 . 000E+05 7. 345E-03 2. 266E+02 1.059E-02 3. 639E+03 1 . 904E + 05 14

15 1 . 730E+05 7. 366E-03 3. 943E+01 1 . 062E-02 1 . 456E+03 1 . 073E+05 15

16 3. 160E+05 7. 378E-03 3. 494E+01 1 . 064E-02 5. 689E+02 6. 053E+04 16

17 5. 620E+05 7 o 373E-03 1 . 730E+01 1 . 064E-02 2. 817E+02 3. 404E+04 17

18 1 o 000E+06 7. 373E-03 1 . 004E+0

1

1 . 064E-02 1 . 635E+02 1 . 913E + 04 13

19 1 . 730E+06 7 . 376E-03 6. 521E+00 1 . 063E-02 1 . 062E + 02 1 . 074E+04 19

20 3. 160E+06 7 o 377E-03 5 . 049E+00 1 . 064E-02 8. 221E+01 6. 053E+O3 20

21 5. 620E+06 7 „ 379E-03 4. 197E+00 1 . 064E-02 6. 834E+01 3 . 404E+03 21

22 1 . 000E + 07 7. 378E-03 3. 899E+00 1 . 064E-02 6. 348E+01 1 . 913E + 03 22

23 1 . 299E + 07 7. 374E-03 4. 007E+00 1 . 063E-02 6. 524E+01 1 . 472E+03 23

Sample flrea= 3.170E-01 cm^

Measured with HP3570FI

Thi ckness= 4.570E-01 cm fl/d = 6.937E -01 cm

No. f (Hz) G <S) C (pF) a (S/cm) k

"* k" No.

1 1 . 000E + 06 7. 91 IE-03 9. 549E+00 1 . 140E-02 1 . 555E + 02 2 . 05QE+04 1 2 1 . 313E + 06 7. 904E-03 7. 244E+00 1 . 139E-02 1 . 179E + 02 1 . 554E + 04 O4m 3 1 . 738E+06 7. 895E-03 6 . 045E+00 1 . 138E-02 9. 842E+01 1 . 177E + 04 3

4 2. 291E+06 7. 890E— 03 5. 349E+00 1 . 137E-02 8. 710E+01 8 . 925E+03 4 5 3. 020E+06 7. 886E-03 4. 638E+00 1 . 137E-02 7. 551E+01 6.76 7E+03 5 6 ~3. 931E + 06 7o 881E-03 4. 318E+00 1 . 136E-02 7. 030E+01 5. 130E+03 6

7 5. 243E+06 7. 876E-03 4 o 064E+00 1 . 135E-02 6.617E+01 3 . 889E+03 7

8 6. 918E+06 7. 872E-03 3. 934E+00 1 . 135E-02 6. 405E+01 2 . 949E+03 8

9 9. 120E+06 7. 870E-03 3. 804E+00 1. 135E-02 6. 194E+01 2 . 236E+03 9

10 1 . 202E+07 7. 863E-03 3. 720E+00 1 . 134E-02 6. 057E+01 1 . 696E+03 10

1 1 1 . 585E+07 7. 867E-03 3. 655E+00 1 . 134E-02 5. 952E+0

1

1 . 286E+03 1 1 12 2. 039E+07 7. 865E-03 3. 61 1E+00 1 . 134E-02 5. 879E+01 9 . 755E+02 12

13 2. 754E+07 7. 866E-03 3. 565E+00 1 . 134E-02 5. 805E + 0 1 7. 401E+02 13

14 3. 631E+07 7. 863E-03 3. 537E+00 1 . 134E-02 5. 760E+0

1

5.61 6E + 02 14

15 4. 786E+07 7. 872E-03 3. 515E+0O 1 . 135E-02 5. 723E+01 4. 262E+02 15

1 6 6. 310E+07 7. 873E-03 3. 494E+00 1 . 136E-02 5. 683E+01 3. 236E+02 16

17 3. 313E+07 7.887E-03 3. 473E+00 1 . 137E-02 5 . 655E+0

1

2 . 457E + 02 17

IS 1 . 096E+08 7. 901E-03 3. 455E+00 1 . 139E-02 5. 625E+01 1 . 867E+02 18

19 1 . 445E+08 7. 919E-03 3. 436E+00 1 . 142E-02 5. 595E+01 1 . 420E + O2 1?

20 1 . 905E+08 7. 947E-03 3. 420E+00 1 . 1 46E-02 5. 568E+01 1 . 081E + O2 20

21 2. 512E+03 7. 999E-03 3. 404E+00 1 . 153E-02 5. 542E+0

1

8. 252E-01 21

22 3. 31 1E+0S 8. 077E-03 3. 3S2E+00 1 . 164E-02 5. 507E+01 6 . 32 1 E+0

1

2 & 23 4. 365E+03 8. 203E-03 3. 355E+00 1 . 133E-02 5. 463E+0

1

4. 870E+01 & J 24 5. 754E+03 8. 391E-03 3. 320E+0O 1 . 210E-O2 5. 406E+0

1

3 . 779E+0 1 24

25 7. 5S6E+03 8. 631E-03 3. 269E+0O 1 . 25 1 E -02 5. 323E+01 2 . 966E 0

1

m

c. J 26 1 . 000E+09 9. 143E-03 3. 209E+00 1 . 313E-02 5. 224E+01 2. 369E+01 ft w Samp 1 e flrea= 3. 170E-01 cm-2 Thi ckness= 4 . 570E-0 1 cm fl/d= 6.937E -01 cm

(leisured with HP4191R
-55-

Table 9. Data for figure 20, aqueous muscle phantom material from

the FDA.

No

.

f (Hz) G (S) C (pF) o (S/cm) k

" k" Ho

.

1 5. 600E+01 3. 636E-04 1 . 676E + 06 5. 270E-U4 2. 729E+07 1 . 692E + 07 1

1 . 000E+02 5. 522E-04 1 . 356E + 06 7. 961E-04 2. 207E+07 1 . 432E + 07 2

3 1 . 780E+02 8. 543E-04 1 . 030E + 06 1 . 232E-03 1 . 759E+07 1 . 244E + 07 O 4 3. 160E+02 1 . 330E-03 8. 259E+05 1 . 913E-03 1 . 345E+07 1 . 091E + 07 4

5 5. 620E+02 2. 056E-03 5. 881E+05 2. 964E-03 9. 576E+06 9. 434E+06 5 6 1 . 000E+03 3. 066E-03 3. 794E+05 4. 421E-03 6. 177E+06 7 . 950E+06 ' 6

7 1 . 730E+03 4. 236E-03 2. 134E+05 6. 107E-03 3. 474E+06 6. 170E+06 7 8 3. 160E+03 5. 272E-03 1 . 034E + 05 7. 600E-03 1 . 684E+06 4. 325E + 06 8

9 5. 620E+03 6. 009E-03 4 . 409E+04 8. 663E-03 7. 178E+05 2. 772E + 06 9

10 1 . 000E+04 6. 449E-03 1 . 722E+04 9. 297E-03 2. 804E+05 1 . 672E + 06 1 0

1 1 1 . 730E+04 6. 693E-03 6. 316E+03 9. 649E-03 1 . 023E+05 9. 748E + 05 1 1 12 3 . 1 60E+04 6. 823E-03 2. 261E+03 9. 336E-03 3. 682E+04 5. 598E+05 12

13 5. 620E+04 6. 892E-03 7. 821E+02 9 . 936E-03 1 . 273E+04 3. 179E + 05 13

14 1 . 000E+05 6. 933E-03 2. 445E+02 1 . 000E-02 3. 982E+03 1 . 799E + 05 14

15 1 . 730E+05 6. 936E-03 9. 351E+01 1.000E-02 1.523E+03 1 . 010E + 05 15

16 3. 160E+05 6 . 950E-03 3. 615E+01 1 . 002E-02 5. 885E+02 5. 702E+04 16

17 5. 620E+05 6. 949E-03 1 . 747E+01 1 . 002E-02 2. 844E+02 3 . 206E+04 17

13 1 . 000E+06 6. 949E-03 1 . 014E + 01 1 . 002E-02 1 . 652E+02 1 . 802E + 04 IS

19 1 . 780E+06 6. 948E-03 7. 736E+00 1 . 002E-02 1.260E+02 1 . 012E + 04 19

20 3. 160E+06 6. 949E-03 6. 369E+00 1 . 002E-02 1 . 037E+02 5. 702E+03 20

21 5. 620E+06 6. 947E-03 5. 664E+00 1 . 001E-02 9. 223E+01 3. 205E+03 21

22 1 . 000E+07 6. 950E-03 5. 370E+00 1 . 002E-02 8. 744E+01 1 . 802E + 03 22

23 1 .299E+07 6. 950E-03 5. 638E+00 1 . 002E-02 9. 168E+01 1 . 387E+03 23

Sample Rrea= 3.170E-01 cm A 2

Measured with HP3570R

Thi ckness= 4.570E-01 cm fl/d = 6.937E>01 cm

No

.

f (Hz) G <S) C < pF ) ° (S/cm) k

" k" No

1 1 . 000E+06 6. 944E-03 9 . 549E+00 1 . 001E-02 1 . 555E+02 1 . 799E + 04 1 2 1 . 31SE+06 6. 943E-03 7. 848E+00 1 . 001E-02 1 . 273E + 02 1 . 365E + 04 2

3 1 . 733E+06 6. 942E-03 6.869E+00 . 1.001 E-02 1 . 1 13E+02 1 . 035E + 04 3

4 2. 291E+06 6. 941E-03 6 . 392E+00 1 . 001 E-02 1 . 041E+02 7. 852E+03 4 5 3. 020E+06 6. 941E-03 5. 903E+00 1 . 00 1 E-02 9. 61 1E+01 5. 956E+03 5

6 3. 981E+06 6. 940E-03 5. 637E+00 1 . 000E-02 9. 178E+01 4. 517E+03 6

7 5. 248E+06 6. 939E-03 5. 519E+00 1 . 000E-02 8. 987E+01 3. 426E+03 7

8 6. 913E+06 6. 938E-03 5. 429E+00 1 . 000E-02 8. 840E+01 2. 599E+03 8

9 9. 120E+06 6. 938E-03 5. 375E+00 1 . 000E-02 8. 752E+01 1 . 971E + 03 9

10 1 . 202E+07 6. 933E-03 5 . 335E+00 1 . 000E-02 8. 6S6E+01 1 . 495E + 03 10

1 1 1 . 535E+07 6. 937E-03 5. 292E+00 1 . 000E-02 8. 617E+01 1 . 134E + 03 1 1 12 2. 089E+07 6. 937E-03 5. 264E+00 1 . 000E-02 8. 571E+01 8. 604E+02 12

13 2. 754E+07 6. 938E-03 5. 247E+00 1 . 000E-02 8. 543E+01 6. 52SE+02 13

14 3. 631E+07 6 . 939E-03 5. 234E+00 1 . 000E-02 8. 522E+01 4. 953E+02 14

15 4. 786E+07 6. 945E-03 5. 224E+00 1 . 00 1 E-02 8 . 506E+0

1

3. 760E+02 15

16 6. 310E+07 6. 951E-03 5. 209E+00 1 . 002E-02 8. 481E+01 2. 855E+02 1 D 17 8. 313E+07 6. 962E-03 5. 199E + 00 1 . 004E-02 8. 465E+01 2. 169E+02 17

13 1 . 096E+03 6. 978E-03 5. 1S6E + 00 1 . 006E-02 8. 444E+01 1 . 649E+02 13

19 1 . 445E+08 7. 003E-03 5. 173E+00 1 . 010E-02 8. 423E+01 1 . 256E + 02 19

20 1 . 905E+03 7. 03SE-03 5. 161E + 00 1 . 015E-02 8. 403E+01 9. 572E+01 20

21 2. 512E+08 7. 1 10E-03 5. 152E+00 1 . 025E-02 8. 388E+01 7. 335E + 0 1 2 1 22 3.31 1E + 0S 7. 224E-03 5. 139E+00 1 . 04 1 E-02 8. 368E+01 5. 653E+01 22

23 4. 365E+08 7. 419E-03 5. 1 24E+00 1 . 070E-02 8. 343E+01 4 . 404E+0

1

^ •“> O 24 5. 754E+03 7. 725E-03 5. 105E+00 1 . 1 14E-02 8. 312E+01 3. 479E+01 24

25 7. 5S6E+0S 8. 21SE-03 5. 077E+00 1 . 185E-02 8. 267E+01 2. S07E + 01 25

26 1 . 000E + 09 9. 070E-03 5. 066E+00 1 . 308E-02 8. 24SE+01 2. 350E+O

1

26

Samp 1 e Rrea= 3. 170E-01 cm A 2 Thi ckness= 4. 570E-01 cm R/d= 6.93 7 E - 0 1 cm Measured with HP4191R
-56-

REFERENCES

Cl]. A recent popular article on the use of heat for cancer

treatment is in the Wall Street Journal, November 29,

page 15 ,

( 1985 ) .

[2]. A. Y. Cheung and D.W.Koopman, IEEE Transactions on

Microwave Theory and Technique, 24, 669, (1976).

A.W.Guy, "Analysis of Electromagnetic Fields Induced

in Biological Tissues by Thermographic Studies on

Equivalent Phantom Models." IEEE Microwave Theory and

Techniques, vol MTT-19, no. 2, (1971).

[3] R.Pethig, "Dielectric Properties of Biological

Materials: Biophysical and Medical Applications", IEEE

Transactions on Electrical Insulation, Vol EI-19, No.

5, Oct. (1984) pp. 453-474.

[4] J.C. Maxwell, "Electricity and Magnetism" Vol. I, p 452,

London ( 1892

)

. A.R.Von Hippie, "Dielectrics and Waves", John

Wiley & Sons, New York, (1954) p.228.

[5] Parafilm is a self sealing tape manufactured by the

American Can Company, Greenwich, CT 06830.

[6] F. Buckley and A.A.Maryott, "Tables of Dielectric

Dispersion Data for Pure Liquids and Dilute Solutions"

National Bureau of Standards Circular 589, Nov. 1,

( 1958) .

[7] Hewlett-Packard Company, Eastern Headquaters, 4 Choke

Cherry Road, Rockville, MD 20850, (301) 258-2000.
-57-

[ 8 ]

[9]

[ 10 ]

[ 11 ]

[ 12 ]

[13]

[14]

[15]

[16]

J.L.Schepps and K. R. Foster , "The UHF and Microwave

Dielectric Properties of Normal and Tumour Tissues:

Variations in the Dielectric Properties with Tissue

Water Content", Phys. Med. Biol., 25, 1149 (1980).

A.Surowiec, S.S.Stuchly and A. Swarup,

"Radiofrenquency Dielectric Properties of Animal

Tissues as a Function of Time Following Death" Phys.

Med. Biol., 30, 1131 (1985).

H.P.Schwan and K.R. Foster, Proc. IEEE 68, 104 (1980)

M.C. Steel and R.J. Sheppard, "Dielectric Properties of

Mammalian Brain Tissue Between 1 and 18 GHz", Phys.

Med. Biol., 30, 621 1985.

M.G.Broadhurst , C.K.Chaing, K. J. Wahls tr and, R.M.Hill,

L.A.Dissado and J.Pugh, "The Electrical Response of

Jade Leaves", submitted to the Journal of Colloid and

Interface Sciences.

J.D. Ferry, J. Chem. Phys. 16, 737, (1948).

A. K. Jonscher , "Dielectric Relaxation in Solids",

Chelsea Dielectrics Press, London (1983)

Texaco Chemical Company, 4800 Fournace Place,

Bellaire , TX 77401, (713) 432-3071, Robert E. Watson,

Jr., Product Supervisor. Mr. Watson said during a

phone conversation that a new product brochure was in

preparation and gave me permission to use data from

the old brochure in the interim.

R. Payne and I . E . Theodorou , "Dielectric Properties and

Relaxation in Ethylene and Propylene Carbonate". J.

Phys. Chem., 76 no. 2, 2892-2900, (1972).
-58-

[17]

[18]

[19]

[ 20 ]

[ 21 ]

[ 22 ]

[23]

H.S.Carslaw and J.C. Jaeger, "Conduction of Heat in

Solids", Clarendon Press, Oxford, (1947), Appendix VI.

For example, Aldrich Chemical Company, Inc. Catalog

no. 24 ,214-4

.

T.Hanai, N. Koizumi, T.Sugano and R.Gotoh,

"Dielectric Properties of Emulsions",

Kolloid-Zeitschrif t , 171, 20 (1960).

Liposome Technology volumes I, II and III, Edited by

Gregory Gregoriodis, CRC Press, Boca Raton, Florida

33431.

E.D.Eanes of the National Institute of Dental Research

provided Liposomes for our Exploratory Measurements.

Hung Chao, Moore Business Machines, Inc., Research

Division, 300 Long Blvd. , Grand Island, NY 14072.

Curt Thies, Professor of Chemical Engineering,

Washington University, Saint Louis, MO, (314)

889-6066.

W.M. Jayne, Jr., "Microencapsulation by Vapor

Deposition", in "Microencapsulation, Processes and

Applications", Jan E.Vandergaer , Ed., Plenum Press,

N.Y., (1973).

Dr. Jayne (reference 23) suggested that Dr. W. Beach of

Bound Brook R&D, (201) 563-5000, had used this

technology and might be able to apply it to

encapsulation of propylene carbonate.

[ 24 ]
-59-

[25]

[26]

[27]

[28]

[29]

[30]

Samples were supplied by The Mearl Corporation,

Franklin Mineral Products Div. , 41 East 42 n<^ Street,

New York, NY 10017, (Attn. Roger Hayden), and the

English Mica Co., Highway 2165, P.O.Box709, Kings

Mountain, N.C. 28086, (704) 739-1321.

Fumed Silica, M cab-o-sil" was obtained from Cabot

Corporation, 125 High Street, Boston, Mass. 02110,

(617) 423-6000. Density data were taken from their

product brochure.

Polyethylene terephthalate film in 6 guage was

supplied by the DuPont Company, Polymer Products

Dept., Chestnut Run Bldg. 712, Wilmington, DE 19898,

(800) 441-9494.

F.M. Clark, "Insulating Materials for Design and

Engineering Practice", John Wiley & Sons, New York,

(1962) . Polyethylene glycol dimethacrylate was obtained from

Ware Chemical Corp.

,

who no longer supply the

material. It can be purchased from Sartomer Company,

subsidiary of Atlantic Richfield Co.

,

Marshall Bldg.

,

West Chester Plaza, West Chester, PA 19380, (215)

692-8400, Nancy Dunn, Market Area Manager, Mid

Atlantic Reagion, (800)345-8247

Benzoin methyl ether was obtained from Polysciences,

Inc., 400 Vally Road, Warrington, PA 18976, (215)

343-6484.
-60-

[31]

[32]

L.D. Landau and E.M. Lif shitz , "Electrodynamics of

Continuous Media", Pergamon Press, Oxford, (1960)

p. 45

D.A.G.Bruggeman, Annalen der Physik, 24, 636 (1935).
NBS-114A irev. 2 -ac) U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report NoJ 3. Publication Date BIBLIOGRAPHIC DATA

REPORT NO.

MAY 1986

SHEET (See instructions) NBSIR 86-3355

4. TITLE AND SUBTITLE

Vielectric Phantoms for Electromagnetic Radiation

5. AUTHOR(S)

M.G. Eroadhurst, C. K. Chiang, and G 0 T. Davis

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

10. SUPPLEMENTARY NOTES

~1 Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bl iography or literature survey , mention it here)

This report describes the. design and testing of a synthetic electromagnetic

tissue, phantom (a material that has the. same, response, to electromagnetic fields as human tissue,). The. phantom overcomes some, of the. disadvantages of aqueous biopolymer

based phantoms. These disadvantages include instabilities from water evaporation,

biological attach. , and metal-salt-water reactions, and the need to use different

formulations for. different frequencies. The synthetic phantom uses a mixture of

ethylene and propylene carbonate with dissolved organic salt to provide permittivities

and conductivities that are adjustable over the range of values found for biological

electrolytes from 100 to 1000 MHz. Interfacial polarization that enhances the

permittivity and lowers the conductivity below 100 MHz is produced by the inclusion of

flakes of micrometer thick polymer film like Mylar or polyethylene. Flake size and

concentration regulate the dielectric properties and their frequency dependence below

100 MHz. The phantom was thickened to a gel without change in electrical properties

by addition of fumed silica or by polymerizing dissolved polyethylene glycol

dlmethacrylate into a swollen polymer network within the liquid. The permittivity

and conductivity of a sample formulation is shown to match those of biological tissue

from 1 to 1000 MHz „

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) dielectric, phantom, electromagnetic, microwave heating, propylene carbonate, ethylene

carbonate, interfaclal polarization, conductivity , jel, biological tissue, electrolyte

13. AVAILABILITY

ij

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