STD-w- -7

00

cv) THE ELECTRICAL PROPERTIES

OF SEAWATER (INCLUDING

CONDUCTIVITY RELAXATION)

JULY 1984

COASTAL SCIENCE PROGRAM

STD-R-1071

THE ELECTRICAL PROPERTIES

OF SEAWATER (INCLUDING

CONDUCTIVITY RELAXATION)

JULY 1984

-M. E. THOMAS

APPROVED FOR PUBLIC RELEASE,DISTRIBUTION UNLIMITED

"FINAL REPORTTASK - ZEDOCONTRACT -NOOO24-83-C-5O1

DTIC.MAR 1 8 198F

V BMARINE TECHNOLOGY DEPARTMENTThe Johns Hopkins University

Applied Physics Laboratory

This document has been apptovedfor public ieleas* and sale; its

distribution is un•imited.

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STD- R- 10 716a. 7AME 9F P E"RMING ORbANIZATION 6b OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION•Pie flySiCS Lab (N' spkable)

Johns Hopkins University Office of Naval Research, Code 422CS6c. ADDRESS (Clty. Stati...nd ZIP Code) 7b. ADDRESS (City. Stais. &W ZP Code)

Johns Hopkins Road Arlington, VA 22218Laurel, MD 20707

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11. TITLE (/nclude Security C0laficatlon)

The Electrical Properties of Seawater (Including Conductivity Relaxation)

12. PERSONAL AUTHOR(S) M. E. Thomas13a-TYPI Of REPORT 13b. TIME COVERED . 14. DATE OF REPORT (Yeor,A 7 hO ay) 5. PAGE COUNT

Technical Keport FROM 10/83 TO 1984, Jul~ 3416. SUPPLEMENTARY NOTATION

Approved for Public Release, Distribution Unlimited17. COSATI CODES IS. SUBJECT TERMS (ContnrWnu_ "everen if necenasy " idelntirfy blck nember)

FIELD GROUP SUB-GROUP (a) Dielectrical .rroperties Cc) Conductivity1ARabove one GHz> "'d- Relaxation(b Seawater W;" •d-Microwave

19. ABSTRACT (Continue on revere Nf necearjy and 1*ent/vy by block nunjber),-The electrical properties of seawater for ac currents or fields of 1 GHz or

higher frequencies are examined with particular emphasis-..oQn the effects of relaxatioof the charge carriers with the frequency of the applied field. Such effects havenot been definitively quantified either experimentally or theoretically. Newexperiments are conducted but are not conclusive. It is pos*ible that the conductiv-itv relaxation time is similar to the Debye relaxation time ,making direct observa-tions of this effect difficult. ,-

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22a NAME OF RESPONSIBLE INDIVIDUAL 22b. TELEPHONE (Include Area Code) 22c. OFFICE SYMBOLW. '1. Chambers ;n/93i 12 n/1DO FORM 1473, 64 MAR 53 APR edition may be used until exhausted, SECIURITY CLASSIFICATION OF THIS PAGE

All other editions are obsolete.

UNCLASSIFIED-iii-

STD-R-10?1The .Iehwm Iepkigm UAnwwelIt

APPLIED PHYSIC LAMORATORYLowed. Muy~en

TABLE OF CONTENTS

Chaptr/Sect ion e

LIST OF ILLUSTRATIONS Vi

LIST OF TABLES Vi

1. INTRODUCTION 1

2.ELECTRICAL IMPEDANCE MEASUREMENTS 4

21 Experimental Apparatus 5

2.2 Results 9

3. PRESENT UNDERSTANDING OF THE ELECTRICAL PROPERTIES 17OF SEAWATER

3.1 Microwave Electrical Properties 20

3.2 Anomalous Electrical Properties 28

4. CONCLUSIONS 31

REFERENCES R- 1

DISTRIBUTION LIST DL- 1

Accession ForNWTIS GGRA&IDTIC TABUniannouncedI JutifcentiorLn

By- .( *Distribution/ ~ env.

Availabi lity Co-les aAvail and/or-

Dist SpecialAk __

STD-R-1071The JuhIm eo~ Uakwv

APPLIED PI4Y2i1C LAUO. ATORYLa~w M

LIST OF ILLUSTRATIONS

Figure Page

1 Experimental Apparatus 6

2 Modified Jones Test Cell 73 LCR Meter Accuracy 8

4 Equivalent Electrical Circuit 11

5(a) Real Part of the Permittivity Versus Frequency 255(b) Imaginary Part of the Permittivity Versus Frequency 256(a) The Index of Refraction and Absorption Coefficient 26

"for Liquid Water as a Function of Linear Frequency6(b) Logarithmic Plot of c, e , and u/we 0 Against 27

Frequency v for 20 0 C and a = 5 S/m

7 Experimental Data for the VL and vT Band of Pure 29

D2 0 and D2 0 KC1 and NaCl Solutions at 4 m

8 Relaxation Time Spreading Parameter as a Function 31

of Temperatv-e and Concentration for a Water-

NaCI Solution

LIST OF TABLES

Table Page

1 228C CARBON COMPOSITION RESISTOR RESULTS 11

2 75701 CARBON COMPOSITION RESISTOR RESULTS 12

3 NaCI SOLUTION IMPEDANCE 14

4 NaCI SOLUTION IMPEDANCE 15

5 SIMULATED SEAWATER SOLUTION IMPEDANCE 16

6 KC1 SOLUTION IMPEDANCE 18

7 MgSO 4 SOLUTION IMPEDANCE 19

%-vi-

7Saf. o.........................*..........*.-

STD-R-1071The John H901 Uslive Un Wet

APPLIE PHYSICS LA3OAATOMYLUMr, MNyVWe

1. INTRODUCTION

A better understanding of the electromagnetic properties of aqueous

electrolytes has important implications for oceanography and biology. The

purpose of this study is to consider the conductivity relaxation time of sea-

water. Potentially, this phenomenon influences the electrical properties of

seawater above 5GHz. Also, the dielectric resonant bands in the far-infrared

affect the electrical properties beyond 5 GHz, and their effects are considered

based on available information in the literature.

"Although the study of aqueous electrolytic solutions has a long

history, much yet remains to be understood. Essentially, the electrical

properties of solutions of high concentration (>0.1 Molarity (M)] (i.e., sea-

water) are not completely understood and are typically represented by empir-

ical models. To improve the present understanding of seawater conductivity,

the determination of its relaxation time is important because it gives informa-

tion about the mobility of the charge carriers.

To see how the properties of mobility influence the impedance of

* electrolytes, consider the standard definition for conductivity (Reference 1)

" N N0=. (le+tin+tp+ + le_iln_;i_i); (e+in+i + e_in_) 0

. i l(1)

where n+,-i is the number density of the ith +, - charge carrier, e+,_t is the

charge of the ith +,- charge carrier, i+,_j Is the carrier mobility of the ith

. +,- charge carrier, and N is the number of solutes. Since most electrolytes

composing the ocean are 1:1, it is assumed that

le+iln+i le-iln-i P

-V

STD-R-1071The .Iuetf ""hkim Um"vu*t

APPLIED PHYSICS LAOtNATORY"•', LWVW. WIrfle"

The conductivity for a single 1:1 solute simplifies to

"P( + + /A-). (2)

A simple expression for the carrier mobility can be obtained from

the following equations (Reference 2)

S•- <v>

"and

i d~v>

m d•v + mg <v>= eE (3)

where <v> is the mean velocity of the charge carrier, m is the mass, g is the

damping constant, e is the charge of the charge carrier, and E Is the applied

electric field. Let <v> and E be time harmonic as ejft The solution of

Equation (3) results in the following

S- - e (4)1+ J 1

4'

59

Substituting this result Into Equation (2), the conductivity becomes

0 Ao- + A...(5)-'i i+ j i + j •g+ zrrIt is assumed that the damping forces will be similar for both the positive and

"negative charge carriers. Therefore,

A g÷ = g = g.

2-2

'-, w wr• r-,-, r' .�r ' r '-r rr ,.-� r r' r-z• .• ' '- w -. 1. .. .. I' - - W 6 w V-1., V- , - w, . ; yr nr Yr r b r

STD-R-1071The Jol,. H.opkim Univlu

APPLIED PHYSICS LADORATORY

The "g" parameter is the reciprocal of the conductivity relaxation time. Thisinterpretation is easily seen from Equation (3). When the applied E-field isturned off, the charge carriers relax back to equilibrium and the mean velo-city becomes

<v>= /v(t=O) > e-tg

The conductivity relaxation time, 1/g, is designated "r .,I Thus,

P /Ao++ 0- +

oo. 1j

:" - •,o 1-'- ' T

where r is the conductivity relaxation time related to mobility. The factor

a represents the conductivity according to the Debye-Falkenhagen theory(Reference 3) and the remaining factor represents the correction for inertia.

The impedance can now be determined for a parallel plate probe as

K7 '-C W 9 --T(7)

R + j (wL- ); L =0-0Ag g

-3-

,. -. , 1. . .- -- . I ,- .. * WF -

STD-R-1071Te Johns Hoo•ins Univerity

"APPLIED PHYSICS LABORATORYLalnf, Mm•land

where £ is the length of the sample and A Is the cross-sectional area of the

plate. R° is the DC resistance, L is the effective inductance, and C is the

capacitance of the solution between the plates. Since the ions cannot move

instantaneously with the applied field, the current will lag the voltage. The

conductivity relaxation time, Tc, Is determined by computing L/Ro.

Impedance measurements of this type should be used instead of

microwave cavity measurements, which are influenced by both the conductive

and dielectric properties of the measured medium. By keeping the frequency

of the applied field low enough (< 1 GHz) so that the real part of the di-

electric constant is constant, the imaginary part is very small and the con-

ductivity high enough so that the capacitive (i.e., dielectric) character is

shorted out; then measurement can readily he made. The main problem

remaining is minimizing the stray capacitance and residual inductance.

Section 2 describes the impedance experiment designed to measure

the conductivity relaxation time of seawater and related electrolytes. Section

3 reviews the present model used for describing the electrical properties of

"seawater and discusses the effect of conducthrity relaxation and other mecha-

nisms on this model.

"2. ELECTRICAL IMPEDANCE MEASUREMENTS

"The major thrust of this project is to measure the electrical Imped-

,nce of seawater-related electrolytes. A special conductivity cell was de-

signed and constructed for this purpose. The following describes the experi-

mental apparatus used and presents the results of the experiment.

4

21 - I

-. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ -7 - Qwy.~wWWrrr ~ ~ K !¶''2~

STD-R-1071The Johme HOPIth UnkwlitV

APPLIED PHYSICS LABORATORYLuei. MWW,,

2.1 Experimental Apparatus

Figure 1 illustrates the experimental apparatus. The impedance

measurements were made with a Hewlett-Packard (HP) multifrequency LCR

meter model number 4275A, which operates at ten different frequencies be-

tween 10 kHz and 10 MHz. The LCR meter was computer controlled by an HP

9845A computer. A conductivity test cell was connected to the LCR meter in

such a way that the shields of the 4-terminal network were connected to the

shield enclosing the test cell. As shown in Figure 1, the current passing

through the cell also was carried by the shield thus canceling the magnetic

field generated by the central conductor. This reduced the residual induc-

tance of the network.

Figure 2 shows the unique design of the modified Jones cell that

was used as the test cell. The cell can be filled and drained without discon-

necting it from the LCR meter. Also, the cell can be temperature controlled

by an external bath. The c:l constant is 17.2 (±0.15)cm- 1. The tempera-

* ture of the cell is monitored by placing a probe inside a well in contact with

the circulating bath.

The accuracy of the impedance measurements depends on the LCR

meter and background effects of the test cell. The LCR meter does open-

and short-circuit measurements of the test network and measures the stray

- capacitance and residual inductance. The values are stored and then sub-

tracted from the actual measurements. The open-circuit measurement is done

with the cell empty. The short-circuit measurement is done with the cell

filled with mercury. In this way, most of the strwy capacitance and residual

inductance are accounted for. Without this capability these measurements

would not be possible. The LCR meter reduces the stray capacitatnce and the

i'rasidual inductance to some nominal level. These levels are measured before

every experiment. Figure 3 shows the accuracy of the magnitude and phase

of the impedance.

-5-

i . . .. . . - - . -.-- • .. . . . ..- - .• - --.,- • . -*'.'

STD-R-1071

APPLIED PIIVSCS LAIONATORY

L0 MM

•.. Ow 0

E-4

E-'4

04OE4

o -I d ..4,. I

6i

STD-R-1071The Jab., Hmeb4.. u~bakqigAPPLIED P"HSIS LAMORAToRY

Lameal. Mw v mbd

12 MM I.D.PLATINUM WIRE THERMOMETER WELL

i i" PLATINUM

ELECTRODE

l ! TO TEMP. RATH

APPROX

"51 MM

GLASS TO 1 MODMETAL SEAL 7 MM I.D.

GLYPTOL 4 MM I.D."SEAL

SC• TEFLON PLUG• • STOPCOCK

Figure 2 Modified Jones Test Cell

-7-

FSTD-R- 1071Tim. J..m Hupkim OruIuve

APPLgUD PHYSICS LASONATOntY

IOMO Equations In table represent:

IWO ~ 1wedanca accuracyPhase angle accuracy

Iwo l/m: See Figure A Accuracy Coeffi-

La lo measuremet range: .-

log-180.0000 - 8.O0

Display counts for JZI and a (normal

to .WGSroRangesj IZI 8

*36 - 1999 0 -180001

0. - 199" 0 -18000I imm v~w 'w~lmw. Approxiftte value (unspecified).

TESTFREQENCYNiuber of significant digits displayedfor IZI and 0 depend on test signal lev-al. range and frequency (5 digits imax.).

Accuracies in Ilnd areas VM areunspecifiled.

ACCUPXY UIWFICIiII

__J Ift.100k. IM- IOMHZ(L.C)

N! I N --ri--M2(

%OI

Fiur hig LreseteuAccrac

-8-RIZ dipa A6hg eslitm --1-1Idslycut

Figure~~-4 3 C eerAcrc

STD-R-1071The John@ Hopkins Uni•,omilty

APPLIED PHYSICS LABORATORYLaurel, Maryland

The test cell changes between the open and short circuit measure-

ments and the actual measurement of electrolytic solutions. This is because

of the double-layer effect at each electrode and the difference in self-

inductance between a good conductor (mercury) and a fair conductor (the

helectrolytic solutions). These effects cannot be nulled out by the LCR meter

since they are not present during the open and short circuit tests. The

double layer effect is caused by the electronic-to-ionic conductor interface.

The result is the formation of a leaky capacitor at each electrode, as shown

in Figure 4. Also, the self-inductance of the test cell is much larger for the

electrolytic solutions than for mercury. Calculations for an infinitely long

conductor indicate the difference to be around 5 nH. However, end effects

will certainly increase this number.

2.2 Results

Measurements on carbon composition resistors were made to test the

system background. Since the resistors are electronic conductors, the effects

of conductivity relaxation will occur at frequencies much higher than ionic

conductors. Two resistors were used, one with a resistance of 228a and the

other with a resistance of 7570n. This range of values of resistance is close

to those of the electrolytic solutions studied. Tables 1 and 2 list the results

of the carbon composition resistors. The format is typical of all experimental

results. Background measurements are made after the open- and short-

circuit calibration measurements [a zero offset adjustment (ZOA)], separately.

Thus, the stray capacitance and residual inductance of the network are

recorded. The stray or parasitic background capacitance is measured at

40 kHz and the residual or parasitic background inductance is measured at

10 MHz. The measured background capacitance and inductance as listed are

typically the meter's limit of sensitivity. The device to be measured is then

connected to the test network and approximate values for the inductance and

capacitance are

-9-

................... -. 9.-..-....

STD-R-1071TOW Jeakto Mepkips Untviwid

APPLOID PHYSICS LAOCAi0.TORY

1- uE-

r4-.

r-44

c%4.

00lzz

E-.4

CL)

-10-

STD-R-1071The Jhm Hgetim Unkiwesy

APPLIED PWISIC LAWOMATONY-. t~and. Mlrv•MS

'-4

v-s Table 1

2280 CARBON COMPOSITION RESISTOR RESULTS

S0'.'0$:4 t11:1:30 CARBON COMP F.ESISTORP..EY S ETTINGS AR.E A1PSC2Dt'F20HI IOMZRSISOTI

++" ++;+i" . ......... f,',- +.+.+...*+++.. . .. ++++..++.........+FE, E,'l C'Y PARASITIC SgbKGR.UND CAPACITHJCE AND CONDUCTANCE

FF, L:'.CJEJ C''Y PARASITIC ,ACKCGROLIID INDUCTRNCEIONI 5.OZEeoOOOOE-10

P E RE$ IC:TuP,S, ' ÷~t41 ÷÷* ... + ++-+."-+4+4+44+4÷÷+÷,-++f-r4+-,*44-+4+÷++++++++++++-.÷++4+++++ +÷,+4++

A"FPR',Ir.RTE INDUCTANCE-. 000000011056

CELL CAPAC I TRUCE2. 030000000OOE- 14

+ ++ + +÷++++ ++ +++++÷+÷++ +++÷ +++4++++÷++÷++++÷+++÷+++ + + + + +4 ++÷+44+ ++÷4+ + +++

MEASURED IMPEDANCE CORRECTED IMPEDANCEF R:.QUEI4C VOLTAGE CURRENT MAGNITUDE PHASE MAGNITUDE PHASEI .OE*04 2.40E-01 1.00E-03 2.2828E+02 +0.00 2.282•.E42 +0.002. 0E'04 2.30E-01 1.OOE-03 2.2830E+02 +0.01 2.2836E+02 +0.01S4.0E+.4 2.30E-01 1.OOE-03 2.2029E+02 +0.00 2.2829E+02 +0.001.0E-05 2.$OE-01 1.0OE-03 2.2930E+02 -0.00 2.2830E+02 -0.002.OE+07 2.30E-01 1.OOE-03 2.2829E+02 +0.00 2.282.E+0. +0.00

4.0OE÷r0., 2.30E-01 1.30E-03 2.2825E+02 +0.01 2.2825E+02 +0.01I. OE÷O06 2.30E-01 1.•OE-03 2.2825E+02 -0.01 2.2825E+02 -0.012. Q FQ06 2.30E-01 1.00E-03 2.2820E+02 +0.02 2.2820E+02 +0.0t34. VE+0•0 6 2.30E-01 I.O0E-03 2.2S12E+.t2 +0.03 2.2S12E+02 +0.031.OE+o7 2..OE-01 9.OOE-04 2.3046,E+0Z -0.1$ 2.3046E402 -0.16

CHf•tGE V ./LTAGE 16:35++*' ........ +4 ...........+++...+.+.+... ++.+.++.++++++...++.-.+.. ++. .

APFPOr11•AIRTE INDUCTANCE-. 000000Pl15710

CELL CAPACITANCE1. 40000000000E-13

MEASURED IMPEIEJIlCE COPFECTED I!. FEI•lC EF;-E EI, VOLTAGE CUF r:'ENT MiAGN I TUDE PHASE MI A CH I T 'U'.E FHAS;E

Z.0,04 2. ":'E-02 I.O0E-04 2.2e19E+02 '+0.01 2.2 9E+:. +0.vi2. NE "04 2. :'E-02 1. 00E-.04 2.2823E+02 +0.01 2. 2':22.+0 I0.14. Oe.04 2. 305-02 1. 0OE-0• 2.'232E+02 +0.01 .2•. .2+•+•E +'- 2 +C0.0I

1. OE ..CI 2.E0E-02 n1.0OE-04 2.2024E.07 +0.00 2."2524E+02 +tO. 002.OE+-;-,5 2.30E-32 1 .00E-¢C!4 2.. 2'82 3. E _+80E20 +0.01 2.2-,':'.2:3E+0: +0.014.05E-.5 2.30E-02 1 .eE-04 2.2-8 19E+0" +0.02 2.:--S1? E+O."- +0.0.:I. 1E.1E 2. 30E-02 1. OOE-04 2.2-21E+02 -0.00 2.- 221E+0" +0.01

02-.cE.c 2. 305E-0 1. 00E-04 2. 2':15E+02 +0. 01 2. 2e15E+02 +0.0:

4. CI+E 2.j20 9 0..E-02 ,.0-5 Z.20E+02 +A0 -00 2. 2.S09E'•T " 0I.OE+ir- 2.OOE-02 3.0 OE-05 2. 3056E+02 -0.26 2."056.5.0' -0.15

- 71 -

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STD-R-1071

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4 + + + + .- ... . .. . . . .+4 + ++ 4 w W • • . . w+a 4@ + + + 4+ I- N N 0ý o , t- V N

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+r +O 4W 4 - -oo -o- - zQIX) ~ .) +4 + 4 . . . .......

C) ~~~ +.. 4. +'4 ~ 0 0 0 0C~~ ~ C C, 4C *

C. aZ C M ~ +-. 4- .. .- .. .-.--.

+l E.i l i ! I I

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STD-R-1071Tih jiwum "e"Wm UeRJNW

APPLIID PHYSICS .AORATORYLeu. Mwvyimnd

obtained. Then the computer directs the LCR meter to take impedance mea-

surements at the ten available frequencies between 10 kHz and 10 MHz. In

*; addition to the frequency and the magnitude and phase of the impedance, the

computer lists the approximate applied voltage and current, and a corrected

magnitude and phase impedance. The measured cell capacitance is removed

from the measured impedance to give the corrected impedance. The cell

capacitance in the case of the carbon composition resistors is the capacitance

between the two metal contacts at opposite ends of the resistor. In the case

of the modified Jones cell, it is typically the capacitance between the two

spherical ends of the capillary tube. For the carbon composition resistors,

the cell capacitance is very small (0.4 to 0.1 pF or less). The impedance of

the carbon composition resistors is largely resistive with a small capacitive

influence at the higher frequencies. Notice that the listed approximate induc-

tance is negative. This means the impedance was actually capacitive and not

Inductive. Thus the LCR meter could not properly interpret the result.

Tables 3, 4, and 5 list the main results of the experiment. For

sodium chloride and seawater solutions (concentrations are listed in parts per

thousand of solute over solution by weight), the impedance is purely resistive

within the accuracy of the LCR meter. The inductive effect at the higher

frequencies is less than 0.1 percent. In Table 3, the cell capacitance domi-

"nates at all frequencies and only the corrected Impedance shows an Inductive

character because of the high resistance. This result is different from

previous less-precise observations that showed a 1- to 2-percent inductive

effect at the high frequency end (Reference 4). It is Interesting to note that

the electrodes in the present experiment have approximately the same surface

area and separation as the electrodes in the previous experiment. Because of

the capillary tube in the modified Jones cell, however, the cell constant is

approximately an order of magnitude larger. If the observed inductance In

the previous experiments was caused by some electrode process, it would

explain the order of magnitude smaller Inductive effect in the present

- 13-

4'. .• .q., ,q,.• b• • .• .•, . .• ",. .. •• ,. • . • •., . ,' • . .- . •'- .*. ' , ' ."•" .' - " l" '".• . . '' "•'• '. '.:• •,•.,-•, .; ; .•: • \• ,'•' '..',..•°.,: " \o• -. •.•".l•.',."•',r,...-,..,...;,.,••..•,.•/, •.•.4...•

STD-R-1071

The is Niuk -wAMPI.D0 PHYSIW LASOATOKY

Lm"S. tm 0Is

Table 3

NaCI SOLUTION IMPEDANCE

0 .l 1>64 14:57 IIRCL ':,-13.4PPT T:23.50FI s"" 'E rT ).iGS FIR A 1 E.1. FI•'C rF 2'H11 1-1:;.'P 3 1 IF T1I

,-+4+4++4+++-r'+44++ +- • !"4+4"444+44-++4++++ 4+r++44-++4+++44 ',-,4+44444+++-l '--4+ i-

F9E'P.IE,::'I PA ; >1T C iCKLG- 0i.tltI ,::P I T-R! ;.,N:E FitlDl i:,,I icr ,'4t"F -3. 0:O'OOCO,;OO.OE- - r -. 0 00CQ,0 c!C+4..p-", t+44++4.r444*4+ ... +4.+++.4.+t44.++444++$+ .$ .'-4-4, I. .+ .. +.+ .i. . .4

FREQJE.'riCY PARFiITIC: IC.BACKGO:::.D IHIDUCTA:_iE101 e. • 3'9@D00Z'-}03O0E-1O

15:01 T=2-.".• 4

4+4.•-.+ f.t+ +++++++ ... + . ..- .++ ++ +++++ +4 4+4+ + .. .+4 44. .. ++ + -.... .- 4++ . . ÷ . . ....

APPPCI,:*K inTE I i1tL'C:'FNCE-, 00 ', 'C')3 31- "•-"

CELL C*P, T TI:JA CES. .-.oa.>T0•L1 3 0.0 E- 13

+4*+++ + + + + .....+' ........++.+..........++ +....4++ 4+ + + ++++ ++

MEASURED IP1PF'iDX'ICE COFRECTED iMIEIuiatý.EF R..EC, LuENHC'T VOLT'I:GE CURPR&T MA.IH TUBE PHASE FI',F1G, N I TUDE PH.E'; E

(HZ>) VOLTS) (HIPS) (OHMS) (DEG:, (OHMS) D jE S.)I.OE+04 9.,OOE-01 1.10E-03 7.7227E+02 -0.04 7.7227E+02, -0.042.01+04 - t..0E-0I1 1 .IO-03 7.7229E+02 -0.01 7.7 7292E +30," -0.014.oE+0 , 8.90E-,3! 1.10E-03 7.7215E+02 -0.01 7.7215E..- +.. 0.00

1.0E+O5 S ..0 -1,11 .10E-0:3 7.r196E+02 -0.00 7.719aE+0. +0.012. 0CIE.-A" S.'E-01 .I 10E-03 7.716--+02 -0.00 7.1 7. :9E+02 -'.134.0E+05 8.90E-01 .10E-03 7.71311>+02 +0.01 7.71'1E02 '0.0$0I.OE+O. 8.90E -01 1.10E-03 7.7i12E+02 -0.04 7.7112E•-.2 +0.142.OE-.06 3.:-VE-1 1 10--03 7.7063E+02 -0.03 7. 7 C'P-5.2.E +" 2 +C0.-'4.CE+;g-F . 7QE-0 I .10E-C3 7.6952E+.0 -0.09 7.60347E+0--" + Q.3I.0E+T 7.. DE-.j1 ? Z'E- 1-!4 7. 7022E+0-2 -0.15 7."6994E+202 +1.65

++ ++ + + +4+++ 4+++ +44+ + ++..+4..+. .+....4+4-...... ++4+.....-t..+ + + +-

APPRPV,,, 1ATE INDUCTANCE-. Q30i. Oh-i3:'

CELL CAPACITAI!CE

*4+1+ ;-+4+++.r4+44+4+. ,.44444., ~a+÷+,++++++++~~44+44444,++4++44I+4+.++ ++,.

,1EA"'I.FED I HPET.A•IW:E C~r:F;P C. TEYr I I'tFEr.,ri:EFP E ::. ,'" '.fLT A.; CIPREINT M1IA HI ITI.D E PFHATSE IIH'"'± TUl12. F Ph.i'E

.L:: rs) VO AD ( MPS:> (OHMS> (DEG ..) :OHMS. ,: t-,E .* 2+04 S. 0E.-01 1. 102-0' 7. 70:1E.02 -0.04 A 713 E + 0- -0.

Z. CE'+O S'. I.-r 1.10E-0. 7- 7031E402 -0. 01 ... ý' I,.0 -3. C14.0E+-)4 3. '.S-Cr 1. 10E-03 7..7022E+02 -0.01 7.70-2E+0Z +0. 001.02E*0 : 0- .IOE-0:3 .7.7C14E+02 -0 .01 7-E0 +0•.oE0

2.,"+¢" ... SuT-='l 1-•.. 102-03 7. 70..".E4( . -Q.C1 7.7Tr,'.'LE-02 +rO. 0.:.." I,.-, .I CE-01 7. 6?•Q,.CE+C +;. O0 -. ' -: +'.

1. . : *:. := iE- 1. 1-E t -0 7 S. E +CoE+.0 + -c;. 04 0 . 02+-"0 Z t. C17- - .'E-:1i. 1 .I0E-0. 7. .24E-0 -0. C4: . " -0- +0,0

.¢.. " 2-01 1. 1OE-02 7. 3'.- 02 -0.0? -. 7"+-...0.$T

1.>E-Or 7"t5c'-:1 0.00.2E-04 7.6C'v379E+02 -0. V! 7.ý- ;"2E+O* +1.50

-14-

%'" .. '

STD-R-1071

APPUID PHYggas LAUCRATORY *

Table 4

NaCi SOLUTION IMPEDANCE

0> 13-84 15:21 NACL '-:5,PPT T=23.7Cf E' E:;TT I ti'. ARE A 4 P:M, -':0 D0 I 1H I C'SF P3 1 :::OT I

r-F E,'> Ei. PAP, STTIC PI.K,.OII. C FiF. IBT-.,irE ,!' i- . .-*. :1iOC ICj0A , 00:'iOE - 17 ::0.;'c, C 0 c, 0 -

+ + w""+I-' i€ + + .- . . .. . . .- . . . . . . :. -.• . . .- I .t .-. .t . . + + ++ + + ÷ .-- + + + . . . . . . . . + + ý

F .P.'E' .2wEUiC'.' PARF"R IT IC: BA.:• 'CPCUND I -DLICTAHElC41 ,:H ,.00L0C0006O52

'15:20 T=23. 81:++++ ".+++++.1.. . .+ +"+ +.+ ++++++...... +....+ + + . . . . . . . . .+ . . .+ .+ ..+ +.+ .+.

APFPK::;I MtATE I HDUCTtHICEL . O0000.2014152

CEt'L CAPACITAUCE0 S000C'0E- 1 4.

• I -t4*r..-.+ .,+++ ,.*++.+-+,l- ++-+-+-+-+- +++ + ÷ I' ++++++++++ +++-+++++++++÷,-..÷ ÷÷lk + .p++•÷ .- ,+++.

MEASURED IMPED.'tCE CORRECTEL I;1PZFL'--';CEFKEcQ.IEtI!:Y VOLTAG'E CUI.RENT MAGNITUDE P HA.E r, IHG;A TrUE P H. t--',E

'A) (VOLTS ) (AiMPS) (OHMS) (DC) (OHNS) (D'EG'-1.,E-04 7.00E-01 3.00E-003 2.3014E+0^ -0.11 2.3012E+02 -0.11L.O&0£4 7.0OE-01 :3. 00-03 2.3m02E+02 -0.05 2.30.2=-+02 -0.054.uE-'4 7.OE-01 3.00E-03 2.29953E+02 -0.03 2.-995=.: 02 -0.02I...+.. 7.OOE-01 3.O0E-03 2. 29952+02 -0.02 2.29'5S+02 +0.002.0-i+05 7.00E-01 3.00E-03 2. 2992E+0.2 -0.01 2.-299"E+0. +0.034.,YE-.'5 6..0E-01 3.0OE-03 2.2985E+C2 +0.01 2.2"?9,4z+ +0.081.E.',-r 0 7.00E-01 3.00E-03 2.2971E-,02 +0.00 2.029,12+02 10.17Z. 71r$E,-71 7.02OE-01 3.0OE-03 2.2"53E+0 2 ÷0.05 2.29,53E+02 +0.394.2 Q< h 6.90E-01 3. 002E-03 2.2918E+02 +0.07 2. 29!. E+02 -0.'41.&-.07 6.t0E-31 2.60E-03 Z.2930E+02 +0.22 2.291,-."02 +1.j*9

F'PP~:-i- MRiA F. IN14DUCTANCE01. 0 00 .. 0 2-14 11

CELL ;APRACITANCE1.•92000000000•E- 12

++.+.+. t 44+++.++++ f+- ++. +.+++++++ . i ÷÷÷ ÷+÷÷+++++++++.-'- +, .+ +++ +•y++- +- ..i.++++

rMEASURED If1PEDA.IE cCPr.RE,:TED IPPELA:::F E C. EO6;,CY" VOL' 7 'GW' CURPRPErNT r1H"J I TU.E PHI E MAIF• 1TLE PHAs E

H, ., .';,/:L Pj. ) , ANPS ) kOHH ,tiE: ' : , TE":1.0E- ¶ 7.00E-01 3..00E- 2'.2 -2." -0.1 ".2.57E,02 -0.102.. E z 7 ..- a1 3. -0 .. - - .. 2..5 . - e 1E- +:!2.. . -n.4. O+04 7. '03E-C.' 3. 00L-03 2.294-.7C-"2 -0.-0Z 2.2.472-OZ -c. 0,.

L.01,5 7.00TE-C1 3.00 -,0!": 2.945E+02, -0 2.2'452-C: -C..,02.OE+-•5 7.130E-01 sI 00E-0:3 2.. 2-94 •0"- -0.01 2 . -94' ':;." +0.0?4.2Q.TE + .Q0E -01 3.) 0- 0 T 2. 2'?,37.2E 7 +0Q. 01 Z.2M7E-' +

6. 6. . -0VE1. S. 3. 0 E-03 2. 29 :E v.: +0. 1.7 7 2-. " " Ci :.2.0S..U 7. .oOE-:;1 3.002-0 Z. 2.•.2E+0- '0. ..4. 02:E Qo0 . '02E-01 3. 02E-03 2. "::94e-"2 .0.O- 2. Z E +0 Q . 711. C.E 07 6.1tOE-01 2. ;0E-03 2. 2909+.2 0."E 2. Z:-':"'E+CL +I.:::I

-15-

...................

S. j.

STD-R-1071

AMtiUD PRY&=c LASOATCAY"Lamd.

Table 5

SIMULATED SEAWATER SOLUTION IMPEDANCE

"1-;.>4 12:59 INSTANT SEA 35 PPT T-23,.4

.E :.:ETTiG$S ARE 4A4B3.Ir2DOFIIH1IOIM.3F31'.:.CTI

P-F N•£C.N. PFAS )TIC RAC::.G7OIND CAP''i:I TANCE AND CONDUCTFANCE4•:: 6. 2C2OO00~0C,0OE- i17 -. 0,00•00000022

+.... +.++.+++ +++.+..++++.....++.++++++++++++++++++++++++++++-.. .++++F PE '0.SCY PkR•SITIC BACKGROUND INDUCTANCE

6. 32600000000E-10

T =2'. 5C

......................................... lATE.....C...C

CELL. .-CAFPARCTANCE1. :40c•o.>jo000E-12

+ +-++ +" 4.- a'+ i+ . ... .. a ... ... ... ... ... ... ... 4+P .+•+++ .+ . .+++•9'+ .÷. . . . . .

MEASURED IMPEDANCE CORRECTED IMPEDANCEFRE PEENCV' VOLTAGE CURRENT MAGN4ITUDE PHASE MAGNITUDE PHRSE

,DH' (VOLTS) CAMPS) (OHMS) (DEG) (OHMS> (DEG)1.os,04 7.80E-01 2.20E-03 3.4419E+02 -0.O9 3.4419E+02 -0.092.oE+0O4 7.30E-01 2.20E-03 3.4417E+02 -0.05 3.4417E+02 -0.044.0•.1+0- 7.80E-01 2.20E-03 3.4415E+02 -0.03 3.41415E+02 -0.021.0IE+03 7.30E-01 2.20E-03 3.4415E+02 -0.02 3.4415E+02 -0.002.':+,C5 7.80E-01 2.20E-03D 3.4415E+O2 -9.01 0.4413E+02 +0.024.0E+O3 7.70E-01 2.20E-03 3.4408E+02 +0.01 3.4407E+02 ÷0.071.35-+Oi. 7.70E-01 2.20L-03 3.4405E+02 -0.01 3.4404E+02 +0.152.0ES0r 7.70E-01 2.20E-03 3.4392E+02 +0.0,% 3.4391E+02 +0.!:44.(-S06 7.60E-01 2.20E-03 3.4351E+02 +*1-.04 3.4349E+e2 +O.V51.0-E+-7 6.70E-01 1.902E03 3.4398E+02 +0.13 3.4:385E+02 +1.67

23'. 7"1t2--.--2+ 4-.•. +÷++ +.+++++++++++++++÷+-+++-+++÷.+++++++++÷+++'€+++++++++++ €'' .+

APF'rC,., INATE I;DUCTANCEui)• , C-,) 12,5 4

CELL CAP.CITANCE1. 0 1•c. -.1 ":O0f0E- 12

++..-r+ ...........++4-++++÷+.++.+++ +-++++÷+÷++++++++++÷++*++++++÷r-'.t+ 71"

MEASURED I MPEDA;CE CORPECTCV I nr-'E11nCE"FPS-*½.iE,-.Y',' OL 7" AG CUFPENT MAP.i•I I TUDE PFH Al.=E NAGHITI.E P -sE

.< V,'$,LTST (AMPS) (OHMS: , PEG) (OHM IE1.0,.04 ? ;.='0E-"OI 2.20E-03 3. 441,E•.02 -0.09 3. 441"E+02 -0.092.c-E+o4 7.20E-01 2.20E-03 3. 4411E+02 -0.04 3.44"1E+02 -0.044. Q--3A4 7 .:QE --.11 2.:0E-Q! 3.4405E+0-2 -0.03 S.440r!E÷02 -0.021 . ct+C5 7. :CE-13 2. 20-0 3. 4402E+02 -0. 02 440,E+02 -0.302.. .I ; ".E--91 2. 0-0: 3. 4397E 02 -0.0, 3.4S'27E:-*'2 C .4,ý:E ,¢ T7."7 E-01 2.20E-03 3 . 4".: E + C!Z 4 ! . ?E-')Z C17

E"O 702E-.1 2.L0"E-03' 3 . 4 1P4E÷+O -0. 1 :4S,02 *"J 1"7., " . 705-v1 2. Z02-03 3-; . 4 P6.E+ Q +0.04 : 4 •.4 :,' : -0

4 C. 'O- 7 .f---7 I 2.1 0E-0Z3 3. 4?27E2'0' +0 04 .0 .4 .,:.E+0.1,...7. 6.70 -01 1.ý0E-03 ^.4T72E+02 +0.1:.: ,4-6E.0 ÷1.4

-16-

4-. --...... ..... .-.

STD-R-1071The Johns HoOpl&I Unkwdmy

• APPLIED PHYIICS LABORATORYp ~LaursI Mwlawl

experiment. That is, the electrode process remained unchanged while the cell

impedance was increased by an order of magnitude. Further, the relative

changes in the impedance are essentially the same in the previous and present

experiments.

Another set of measurements attempted to observe the Debye-

Falkenhagen effect (Reference 3) that is observable within the frequency

band of the LCR meter but at very low concentrations (around 1000 times less

than seawater concentrations). Tables 6 and 7 show the results for 0.01-

Molarity (M) solutions. The Debye-Falkenhagen effect is much stronger for

MgSO than for KC1; thus, a comparison can be made between the two tables.4

* Within the accuracy of the measurements, no differences are observed and the

corrected impedance is purely resistive. The concentration is too high to

observe this effect.

Finally, much of the initial motivation to carry out these

experiments was to measure the conductivity relaxation time. This number is-13at least 10 sec, which is based on the initial assumptions of Debye and

Falkenhagen (Reference 3). Based on the experimental results of Table 5,

the maximum seawater conductivity relaxation time, T cr is 5 x 10-10 sec.

Therefore,

1 X 10- 13 < c<5 x 0-10 sec or

3.2 x 1 c< f )< 1.6 x 10 12Hz

3. PRESENT UNDERSTANDING OF THE ELECTRICAL PROPERTIES OF

SEAWATER

The problem of understanding the electrical properties of seawater

- is a very complex one. This is because the detailed physics of electrolytic

solutions is not completelv understood and seawater is a heterogeneous solu-

-17 -

4LA

STD-R-1071

A!ll•tEED PHVU LAbfldY

A, Lir. Mv~mS

9,•'

+ + 4 4+ +w

+ + + + OL00

+4 4+ + + + +

+ + +cc4+ + + + z0 0 0' C n

+ m .T. 4+ +4. ÷ ++ ..... +"4. +. +. P- 4 0 -0a' lt ' ".

o + +. W = or- O 0 0% .7. IZ COrJ L4J2 + +. + 4 . em el 0o 00 I 000'1 , ,ic ^

+•41- 4.1- "4. 4. 0 " 4 4 4. . . . .

0 1 2 + •,+ +* Lu =' N N• N• %N N, N CA kN N. M,,•..

+ a_ "Z++* ,e

*--..1 44. 4. I-I- .7' -0 .7 IC '' ") 'N

4. w 4 +4. J . . .

lk +00 4. V

- ~ 1 +4 4 . f 0 0 -Q) N~ +0 +~ +

S+ .= - + + + M + + + + + +w + + W I = *C 0% Z0 0O'n0 M 0

A4 +0A 4. G.'4. %N1NN 1N 11=M+2 4. 0 .....W

-. - t4 0. .+. 4. "Z I+ r- ---

* 4*C

r; ' -"- .=

IQ.. + .-. .'......:-.----:- .- . - : ."..-* 4 -rM 94- +*z ~ LO ~ zn~ o

4. o to, +. 4. x=00a-ZZ0z0.0I

+ + ~ +. CZ .. .w.o . .O .O.O .

+~a. +0 4. + J)44r-.

-? +.0 *ý+.C +- A: Q Lo+ V.w Zj w 7'? Liw

+ +4J + .-- -f;, . .)..

+r I.* .N'Z .1 4 .S

?"'.. 4'Z U" .0" N.4

-A * t C . ..

Q =: .:: w*. uA wZUw' w J

Iz LL ~ + WN. - C+

%a4.4L4 . N t~4

STD-R-1071

is Jonm Hekhg Ushdmmt

afturn. wwvga a.*no"my

+ +4+w

+ + q.+. +4. . +++

+. + + +~: o 0 0 0 04

W 4.+ + =

+ 4 4. + Q =t .- . . . . . .6

4+- 4 =. N W 1*- v0 00

+- + +" + : U J -n •r •D • Nnt. 4 4- "4"UJ -"+ +4+ I4"4" 4-

.++"4

+ + +W ++" + + + X "

•,t "• •,J+ + + ••" "' '" D • : - s .

+ n tj +4.

+-', 'r + + + L;,• ;,,,+ -- ÷ ,"+ +"

i~~ ~~~ w" cl ,+ - r" -+.•- -" + + @0 + L.•M +0 4 + + Q•w0 a-- N C;O, , .• P,'

•~~+ • . -:,+,'•+ + L+J +•W'Ju •U LJL ~'4 . Oi* 4. •,4 • ,• . . . . .

-4.I 4. ,-,., 4. 4-• . -"4 :J "-', = D ''''', • ' '

-,'+ + " -- -+- + I"- -. '- ' '• '' 'D

-- + •, +" "+ qr- -r -r"- "P Irv• '÷

+ 4. 4

1=1 4. C6. I. -I- +~~7 +~ I= if) Cd- Utt L w+ 0r-W+ +. + w = fliJ'-"Ch r- N tD 0 7 O

I-4.WC'4+ c + +..===QW........................k14 cE sl N 0d 0 00 0 -CA r- U

"". + +- - . x. ,. . ,. .. . .

'~ ~ ~ ~ ~ ~ A U'J ;-P =" '• + + + D f÷• * U UA " " •••

= + r 4-+ +- ~ ~~~~~ 04C. I4 00OU WW W~J

rn -0 +-4Z t +4.jowuiu . 1w uuWL

0~~ ~ ~ ~~~ k .4 4 .4 dC!NC ) 0))1

O ~ ~ ~ L 4-~.0' L9 4. WM -= - --.

+ ++ 4. +0 0 00

+ 'rC +, ++CW WUW Wh+?. +4 0 + Wa 0 0 0 0 0

LY +. +. W% 4 (.) .0.0.0.0.~ 4 -#4.- 4.Z Q4. -WU U jL uWU

+ +. +. G j =)a00 Mz

+W.C 4 .0. WI +. 0'&)4.r4.4..C 17. In I

+ ++.N +04 -. j-.:. .00.0 ..0 .

tr+j 4..

C41 w4.WO.- .

+ IN L 4

-~S +- Ci.ZCQ *S04

-, , . -,k-n< . . . ... .... =, .. .:., -. • . . .. , , . . ". .

STD-R-1071mk 40T M MoeekIM UfWmitW

APPLIEO PHYSICS LAORMATORYLamweI. m yla,

tion of many electrolytes. The importance of the electrical properties (i.e.,

dielectric and conductive) at radar frequencies has required some form of

tabulation as a function of temperature, salinity, and frequency. This is

currently done in a semi-empirical way using the formulas of Debye, and Cole

and Cole (References 5 and 6) fitted to experimental data (Reference 7).

The result is a reasonable representation of the true dielectric and conductive

values of seawater as a function of temperature and salinity below 5 GHz.

However, precision microwave radiometry requires equal precision of the

known electrical properties of seawater. To improve the present semi-

empirical formulas requires a greater understanding of the theory, including

observed anomalous electrical properties. A brief review of the present

understanding of the electrical properties of seawater and seawater-related

electrolytes is presented in the following section.

3.1 Microwave Electrical Properties

Microwave data of the complex relative permittivity for electrolytic

solutions is typically fitted to an equation of the form (Reference 7)

"I

•Q s (TTS = )

r( ,TS) =r+ e (T,-S) -e -(TS) (8)-+ 1 J + D (T,I) SII 0

where

T = temperature

S = salinity

= the relative dielectric constant at w>)•/•D

= the static relative dielectric constant

* : permittivity of free space (Farads/m]""2f, f = frequency in hertz

= conductivity S/rm]r = Debye relaxation time

1 = empirical spreading parameter of relexation times

- 20 -

a

|k"I i-:"." .'' "' '.. . . . . ."•'.... . h..- ". . ..'' "" ' ' '."" -"" - "- '.'' ' ""-I-" "" " " -''" > " •" -" "": ""

STD-R-1071The Julum Mkki U"min

APPLINO PHYSCS LABORATONY

The conductivity relaxation process is not represented by Equation (8) and

neither are higher frequency resonances which impact o . However, since

this model only claims agreement below 5 GHz, the details of the Debye and

conductivity relaxations are not required. For example, for a = 0 Equation

(8) can be expanded to the form

e(= el., + (cs - e..) (1 - (J - (TD)2 -a*o (9)

a - (s - (WTD) 2 es - e0) (wrD) + -'

Because wYD (( 1 below 5 GHz, this expansion will work very well. The

expansion of any proper function would produce the same first-order struc-

ture. Thus, curve fitting data to Equation (8) at frequencies below 5 GHz

,. will not definitively determine the true structure of the dielectric properties

beyond 5 GHz. This fact is recognized by Klein and Swift (Reference 7).

In principle, -,. and a, are functions of temperature, salinity, and

Sfrequency, and eS and VD are functions of temperature and salinity. A more

general form of Equation (9) is given by

8 (T.S) - ,,(w.T.S)(.,TS) = ,o(,,T,S) + -(0)

1 + (JorD(TS)]

J 1 aDC(TS)

0

21

,,... . . . .,. ... " .-.. * * . .-. '., .*_ "., ,,,

r . • . .' ." - +. .- , • + •+,+ ." . .. . . . . . . ..... L.J.. I,+ ? %

STD-R-1071APPLIED P14Y .LAWMATORY

where

UDC = DC conductivity

c= conductivity relaxation timeT61

The Debye relaxation process accounts for the damped rotation of the water

molecule in the liquid state. The conductivity relaxation process accounts for

the damped translational motion of the ionic charge carrier. Debye in 1913

(Reference 8) approximately determined the Debye relaxation time, rD' by

considering Stoke's law converted for a rotating sphere and Brownian motion.

The following formula was obtained.

8? 17 a' D = - -- (11)

wheren = viscosity of water

a = radius of water molecule

k = Boltzmann's constant

Surprisingly, this formula predicts reasonably well the observed relaxation

time of water, which is on the order of 1 x 10-11 sec. Intuitively, the

relaxation time of the translational motion of the ionic charge carriers in water

should be similar to the rotational relaxation of the water molecule. Following

a similar approach as Debye, the conductivity relaxation time can be approxi-

mately found by examining the charge density in light of Stoke's law and

Brownian motion. The result is

6w1 bXo (12)1C -k-T--

-22-

-%

STD-R-1071The Johnsg bHoki. UnIvardty

APPLIED PIHYICS LAIORATORYLaurua, MuyIWd

where

b = radius of charge carrier

x = 1/e point of Maxwell-Boltzmann distribution

of charge density

Since

b-aXO. > a

then

"Tc > D

This result crudely verifies our intuition. It is interesting to note that the

Debye-Falkenhagen computation of the conductivity relaxation time is based on

the velocity cr mobility part of the conductivity and does not include the

random motion of the ion.

The real and imaginary parts of the general complex permittivity

[Equation (10)] are for a = 0, thus

S= - 16 (13)

coo -*%) DC Cle (14)

(6" - e°°)urD UDC "C/'o' (15)

oo Y

1 + (D) 1 + ( O

l. -

- 23 -

'. ,' •, • , , ) ,I • ' % % k ,,•• v ,• • • '-' - ". , , L , ••,. • P - L • " "3 "• •J• "N " "•r • • : "• "•. _ . .• : "•, . R '• -• • = , ,• a • • , .• "• • . ., . -', • ,= - -' , • •-- • -; • • • , • • '

_ •:• .. • .. ., , : , • . . . . . .. .. 7. . .W J W 7 U • W • . r •, .. . -• , . ... . , . . . . .

STD-R-1071he Johm NHolM UnknWty

,APLIID P1IY2ICS LAWiRATORYb" * "*Laurl. Mm,4land

Figures 5a and 5b are plots of e and r, respectively, for different values

of The cases for c= D or 0 are the same curves. Interestingly, with

= D the conductivity effects cannot be differentiated from the case ofc D

7= 0. However, for rc/ID = 0.5 and 2 there are observable differences. If

Irc - rD (it Is unlikely that they are exactly equal) then the conductivity

relaxation effect is an important term in the complex permittivity formula.

The efforts to model the permittivity beyond 5 GHz would then be helped by

including this effect.

Figures 6a and 6b illustrate the dielectric properties of pure water.

Figure 6a also shows typical skin depth attenuation of seawater (References 9

and 10). The pure water spectra show a fair amount of structure. The

hump at 20 GHz is the Debye relaxation phenomenon. The two peaks between12 and 3 x Hz are called the hindered translation, v and librattonal10"d . H0To

"band, v respectively. They are caused by H20 and H2 0 (i.e., dimmer-

"like) interactions (Reference 11). Most of the higher frequency peaks are

caused by the internal motion of the water molecule (i.e., rotation vibration

(Reference 11). Beyond the Debye relaxation, the complex permittivity is

represented by r., . It is dominated by these Infrared resonances. This

can be seen by examining the real part of W ,- j e•, );

4.9 > to > 1.69 > 1

Microwave Optical

C ., is determined by resonances and relaxations beyond the frequency of

Interest. Based on the above relationship, the microwave region Is heavily

- influerced by the infrared resonances.

• 4.

'4

-24-

, •X , % ,' ¢- -. ... .- -- -'• - " . . ." .. . .- • " . . " . ." . ." ." ." - .... - '" " • , - t. . ; e - ,

STD-R-1071-. ;.%

- ~~APLINDll PHYSIIN• L.ABORATORY

- - TC/TD - 2

dom 4.9

SD 4.8 /r

T'r D 9.1 x 10 1 2 sec F•~~~ -" 1 200C ,

S - 35 0/0.

f (Hz)

Flgure 5(a) Real Part of the Permittivity Versus Frequency

-::: . - .I•i

V., 0 1* D

C /D - 0.5•, TC/ TD - 2

_00= 4.9

30 V0DC -4. 8S/n 1""D - 9.1 x 10- 1 2 sec

T = 200 C

,"-S . 35 0ooiS=3S'

to

f (Hz)

Figure 5(b) Imaginary Part of the Permittivity Versus Frequency

25

%•,V.

..-. - 25 -

I:• • . . . . . .. .. . . . . . '* ...... ... " " ". ~ " °"2'•"

STD-R-1071The Jhm Mekwfl Unkwwty

APPLIEOD PlYICS LAIOMATORY

-- " r "---17. o e lmo 1 0o i.," l * * lop

IQ QP lt to o IOHIo in lp lw

to,- soo

t:ftj

I .I

I MW I IP

l it 0 0 I 0 Ian to

___ 1MWMg V 1M

Sto- o' i' is Io

U..,., (I•

Note: Also shown as abscissas are an energy scale (arrows) and a wave-length scale (vertical lines). The visible region of the frequencyspectrum is indicated by the vertical dashed lines. The absorptionof coefficient for seawater is indicated by the dashed diagonal lineat the left. Scales are logarithmic in both directions.

Figure 6(a) The Index of Refraction (top) and AbsorptionCoefficient (bottom) for Liquid Water as aFunction of Linear Frequency

-26-

1.. ~' J Is W

STD-R-1071The ijoiw Npkim Un1vwitw

APPLIED PHYSICS LABORATORYL@OWs. MuyVueW

f (GHz)P-_ 01 1 oo 10900

100 100

1' 11

DEBYE

RELAXATION

01 0101 1 10 100 1000

v (CM-) n-

Figure 6(b) Logarithmic Plot of e' (dashed line), ell (solid line)and alIwo (solid line) Against Frequency v (wave-number .') for 200C and ' 5 S/m

- 27 -

• • • • "'.-'.'.''... '.'.'.'.'.., ,.',, ." . .:'..',.": •".:. J ",•., . "•., • •, • ; •. ", ". _ . ". '." , .. . .; .. •" •,Z I, •.: " •.• f•'•." .:'•.,.• • .' -' .'.. •" p

STD-R-1071The Johns Hopkins Unkwsity

APPLIED PI4YUICS LAOORATORYLamnul. MWluWd

The presence of a solute does influence s,3 . This is demonstrated

by Figure 7, which shows experimental data of the "L and "T band of pure

D20 and D2 0 KC1 and NaCi solutions at 4 Molarity (M). The solutions are

highly concentrated compared to seawater but do show significant changes in

the spectrum. This will directly impact Io at microwave frequencies and make

-: it a function of salinity. It is also well know (Reference 11) thrt these bands

are sensitive to temperature. Thus e. is indeed a function of frequency,

salinity, and temperature.

The relaxation time spreading parameter, a , is not zero and is

thought to be a function of temperature and salinity (References 12 and 13).

This is illustrated in Figure 8 for H2 0 solutions of NaC1. The precise nature

of a will not be understood until the conductivity relaxation effects are un-

derstood. The relaxation time spreading parameter influences the falloff of

,- the Debye relaxation. As illustrated by Figures 5a and 5b, the conductivity

"* relaxation process also influences the falloff of the curves. Thus, these two

different yet similar effects may be difficult to separate.

3.2 Anomalous Electrical Properties!I

In addition to well-understood physical mechanisms that Impact

seawater electrical properties, there are reported observations of anomalous

behavior of solutions of single electrolytics which compose seawater. These

are listed below (Reference 13).

(1) Anomalously high conductivity of electrolytic solutions at

concentrations close to seawater at 582 MHz (Reference 14).

(2) Additional relaxation phenomena at submillimeter wavelengths.

The dielectric constant is modelled as

I1'.*

- 28 -

A ...... ,......_... ,•`-•.'.:•v• -•.*••`•.• •-•`••:`-`- .*. . - *.• .:-:.• : -• . :`.. * .*-•.** .- . .•. -...*•. -':.-

STD-R-1071Trh Jhnw Hopkl Un1"nl ty

APPLIED PHYI!CS LAIORATONYLautd, MWVINWd

0.=100 /AM)

L T

D2 0 - NaCI

Increasing 2Values

0 f

- A A

600 400 200

v(cm

4-Molarity Solutions

Figure 7 Experimental Data of the v L and vT Band of Pure

D2 0 and D2 0 KCl and NaC1 Solutions at 4-Molarity

Concentration

- 29 -

B B'

L•'-'''-.. ' ,.: ,, :"I .,•" -..- -'-5-''•-"-' .4 ".• .. 'U•',.''• ".,;" :••\,• t"''.., 'N -i. ''''X \ -• •• -, "• -•,• "-,

STD-R-1071

'1 Thu .Mmmd MImUmhidl14U PY LMW4 k YOAYW

15

10

* 5

0 A A A A A A A A

0 1 2 3 4 5 6 7 8 C (Molarity)

0 5 10 10 20 25 30 35 40 T(0C)

Figure 8 Relaxation Time Spreading Parameter, a , as a Functionof Temperature (constant concentration c = 1 Molarity)and Concentration (constant temperature T = 25 0 C) fora WaL*er-NaCl Solution

- 30 -

4

STD-R-1071The John Hopkins Uniwult

APPLIED PHYSICS LASORATORYLawurel Mwyiawd

e n2 2 ew n 2

+ 2 + (j'2 1) +

where r 2 is the additional relaxation time.

4. CONCLUSIONS

The electrical pro- irties of seawater have been examined with

particular emphasis on the e~fects of relaxation of the charge carriers with

"the frec*uency of the applied field. Such effects have not been definitively

quantified either experimentally or theoretically. Experiments conducted were

not conclusive. It is possible that the conductivity relaxation time (the

characteristic time its takes a translating charge carrier to relax back to

equilibrium) is similar to the Debye relaxation time (the characteristic time it

takes a rotating molecule to relax back to equilibrium ir. a fluid or solid),

making direct observation of this effect difficult. The conductivity relaxation

time has been constrained to be within 5 x 10- 10> " > 1 x 10- 13se. It is

quite possible that c - T since the dampening mechanisms should be similar.

If this is true, the dielectric models will need to include the effects of

conductivity relaxation. Also, it is recognized that resonant far-infrared

(including submillimeter) bands can influence the dielectric proporties at and

-bove 40 GHz.

A more definitive impedance experiment attempting to measure the

conductirity relaxation time will require the following:

"" A test cell with a much larger cell constant

0 Impedance measurements at frequencies close to 1 G0Hz

, . A high degree of precision or a means of nulling the DCresistance of the electrolytic solution

£ Also, the development of a reasonable theory may aid in the selection of a

more optimal temper•ture and salinity of the samples.

-31-

%" ", . .""."•.,:.'.% , "'., + " + ". ,''. " " ',.' ' '•.,+ ." " '% .•. '." ".","-' ';." "" ." " .""" ,"",.""'.." "-.•

STD-R-1071The Johns Hopkin Unlmsiwy

APPLIED PHYSICS LASORATORY

Laurel, Morviond

REFERENCES

1. Condon, E. U. and Odishow, H. (Editors), Handbook of Physics,"2"nd Edition, McGraw-Hill Book Co. (1967) p. 4-77.

2. Jackson, J. D., Classical Electrodynamics, John Wiley & Sons, Inc.,1962, p. 225.

3. Debye, P. and Falkenhagen, H., Physik. Z., 29, 121, 401 (1928);;.F H. Falkenhagen, Electrolytes, Clare TPress,-T1934), p. 169.

4. Kolbeck, J. B., "Excitation Frequency Dependence of Conductivityof Electrolytic Solutions," M. S. Thesis, The Naval PostgraduateSchool, June 1983.

5. Debye, P., Polar Molecules, Dover Reprint, originally published byReinhold Pubsihng Corp., 1929.

6. Cole, K. S. and Cole, R. H., J. Chem. Phs., 9, pp. 341-351,1941.

7. Klein, L. A. and Swift, C. T., IEEE Trans. Antennas Propagat.,AP-25 No. 1, pp. 104-111, January-Mfl .

8. Debye, P. Berichte der Deutschen Physikalishchen Gesellshaft, Vol.15, No. 16,-pp-77 TW,(• 1T3

9. Jackson, J. D., Classical Electrodynamics, 2nd Edition, Wiley aSons, Inc., (1975)Fp-.7 .

10. Franks, F. Editor, Water A Comprehensive Treatise, Vol. 1, ThePhysics and Ph sica--'-e•istry of Water, Plenum Press, 1927-'.i• Chapter ,f - 95• -- -

11. Eisenberg, D. and Kauzmann, W., The Structure and Properties ofWater, Oxford University Press (196"3.

1i. Praegert, D. A. and Williams, D., J. Chem. Phys. 48, 401-407,January 1968.

13. Hasted, J. B., Aqueous Dielectrics, Chapman and Fall (1973).

"14. Hasted, J. B. and Roderick, G. W., J. Chem. Phys. 29 17 (1958)

R-1

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