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PLACE IN RETURN Box to remove this checkout from your record.
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MAY BE RECALLED with earlier due date if requested.

 

THE COTTONéMOUTON EFFECT IN
LIQUID CRYSTAL AT MICROWAVE FREQUESCIES

by

Glen Alan Mann

A Thesis
Submitted to the School of Graduate Studies of
Michigan State College of Agriculture and
Applied Science in partial fulfillment
of the requirements for the
degree of

MASTER OF SCIENCE

Department of Physics

1953

ACKNOWLEDGEMENT

I wish to express my sincere thanks to Dr. R. D. Spence
for suggesting the problem and for his interest and help in

solving the many difficulties encountered.

308682

TABLE OF CON TENTS

INTRODUCTION . . . . .
THEORY . . . . . . .
EXPERIMENTAL APPARATUS . .
EXPEREMTAL PROCEDURE . .
RESULTS . . . . . . .

CONCLUSION . . . . . .

ML}. WTCES o o o o o 0

2'7

28

INTRODUCTION

On the basis of previous experiments1 it has been sug-
gested that the effect of a magnetic field on the complex
dielectric constant of liquid crystalsa at microwave frequen-
cies should produce a rotation of the plane of polarization
of the electric vector in a circular waveguide. This thesis
reports measurements of this rotation and suggests an approxi-
mate quantitative theory for predicting the magnitude of the
rotation which can be eXpected under a given set of condi-

tions.

' THEORY

The earlier experiments showed that the substance
para-azoxyanisole, which is a liquid crystal between 120°C
and 135°C is anisotropic in the presence of the magnetic
field. When the magnetic field is applied parallel to
the electric vector, the attenuation is markedly decreased,
therefore decreasing the imaginary part of the complex
dielectric constant. However, when the magnetic field is
applied transverse to the electric field, the imaginary
part of the dielectric constant is increased, causing an
increase in the attenuation. Along with the change in loss
there is also a change in the velocity of propagation through
the liquid crystal when a magnetic field is applied.

If one uses the above facts to formulate a simple
working picture of what will happen to the electric vector
as it passes through the sample at some angle besides paral-
lel to the magnetic field, or perpendicular to the field,
the electric vector should rotate because of a differential
absorption and phase shift of the components parallel and
perpendicular to the magnetic field. Using this differential
absorption idea to explain the rotation, we can develop the
following expression for the angle through which the electric

vector will rotate:

 

[I’llfl

 

Find an approximate solution for waves in a circular wave-
guide. Consider two TEll fields El and E2 which satisfy
vector wave equations

V” E‘, + ALE, = 0

v’EL-I- kaz=a

and whose polarizations are

Y Y
Q Jros ‘
E. g; x a “a h
<7M¢me k. }X\/

For El (5-13 )4y. <<(E‘*)14K

 

X

 

 

 

 

MdJu/m é;

 

 

F” E.2 (5,1)” << (5.23)”

La; = IE, + B’EL

Then
72—5, +11%ij +535” =6
V? +11L4E [L E 3
and (7 [a + L g L? O

7?, 442’; 3/1343) E2, = 56015,,

V1463 74:53 z flair) 133 .~. -/[fl)‘,3
for small (5“) Eli and sz 2

V74 +1fgxzo
Vlfa-fl’zfa 2,0

The above are approximate solutions since they satisfy
the boundary conditions but do not exactly satisfy Maxwell's

Equations for this problem. In polar coordinates they become
I .—

5, =2r4(777 J/Kr) cm¢¢712)+,28(27 J(kr) ax—gflaZ‘E)

- _, _ 718

gram %$J,(kr).—~—¢«U+23' 'IJJ‘MVWWW )

éf; 3 éfrckw§fl “Gin +4-?9
{ ;£,,__-.¢+5¢w°¢

T. d......... of the Bessel Function 1. given by
f}- me = 32-376)“ {(57
t. ,zfl/Cj 1(1,)X’:§¥/M{filar)— \ZKMX’I—‘f—ZIO/é 288
+2 3%}; MW ‘31? — (5, m r) -- J: (k 0% 5319” )ch 7‘3
E= mfg 1(«r)){‘~jf) )‘(ATJW J:(x<r))[—3f”/]e— ”3
a'fifififé WI“ ‘sz {a "M- 3‘ (4 /){’*:°’”)] ”“2
J15) ,5 aw Io Jenna its) 1/

310") = 53%) um

806x andéy become
:x- .4[J;(«r/+J“ (“kW-Wk" 7,2 +Bj(/<r)p.;2¢e
fly (m @0er (map Iz."%+,4J;</<r)os—2—cfla

whYch shows that in the central portion of the waveguide we

”2.

X42

have approximately two perpendicularly polarized plane waves

with propagation constants l} and 7;,

28”? K‘-U—-— (mew K W‘s/«c
1’ 2. 7... 1.

I.” = me =— («we/5i) = /< "‘0 6W

1

‘l (I
From earlier data values for 6’; 6,16; and 6L are
:’= 2m é.’ = 3%“6,
~‘460 6b”: I560

other known values are

A3532 CM
4—“— [675m
net
7 (2.7; W
A ={3X7732m—4c‘} =44 4577/?
A,” =(i—i’) (3343».275) ):/J.3-3.o7¢

Therefore

7.—

[l :- -/],4 + £59ch

261‘ ‘/Z./ +3a74‘

And q andfl become

ow ,2» am w
I :: 3.48 (61' —‘-' 3:577

I

From consideration of plane waves we can determine the
of the angle of rotation to b(e
1- )IE
Jarv¢o¢w % (n 6
”2% “4):" ( -1)“ )éj
/- fee—64w )

where LII/0 is the angle the incident wave makes with the

 

magnetic field and z? is the length of sample.

Using the computed values

Wig; pug? gag-6076173)

/_(é;,¢ 6H3?)
For ¢DS¥JW m%;/

and 72.2% = W}

M [232

M j
0

6.540'”
13.5
20.4
27.03;-
32.4
36.9
40°820°F

59-94.

I

N

\‘IOIOIPCRNI-‘O

’0' .-

 

EXPERIMENTAL APPARATUS

In order to produce incident waves other than paral-
lel and perpendicular to the magnetic field, circular wave-
guide was used. One inch tubing was used for the waveguide.
This will propagate the dominant TE11 mode at a frequency of
9,375 megacycles. The TE11.mode was used because it is the
only mode in circular waveguide which has the electric vec-
tor in any degree of linear polarization. .All of the other
modes in circular waveguide have electric field configura-
tions which are so complicated as to render them unsuitable
for polarization rotation study.3

To provide a magnetic field, a small electromagnet was
constructed. The pole pieces of the magnet were.made 2 3/4
inches in diameter to allow for a sample length of 7 mm.

Eight coils were wound with 2,200 turns on each coil. This
was obtained with 1 Amp. Max. The wire that was used to wind
the coils was flat, ribbon-like copper wire with a Form.x
coating. Because it was so thin, a current of 1 Amp. through
each coil was the maximum for this wire. Between each field
coil was placed a water cooling coil. The theoretical field
for the magnet is 3,000 gauss.

Since the sample is a liquid crystal between 120°C and

135°C, a temperature bath had to be made. This was a copper

tank 7 inches long, 3 inches wide and 7 inches high. This
tank.was inserted between the pole pieces of the magnet.

With a pole piece separation of 3 inches, the field
obtained was 1,400 genes as shown in Fig. 1. To study the
rotation of the plane of polarization, two rotatable Joints
were made for the waveguide. One was placed so that the
klystron could be rotated to change the incident angle of the
electric vector. The other joint was placed on the detector
so that it could measure the rotation for a constant incident
angle but at different field strengths. A large circular
protractor was mounted beneath the rotating detector. To
operate the klystron, a power supply and square wave genera-
tor was built from the circuit diagram of a Browning TVNV.

The para-azoxyanisole was prepared in the following
manner. Para-nitro-anisole was mixed with nine normal sodium
hydroxide. This solution was placed in a flask and heated to
80°C, while constantly being stirred. Then glucose was added
to the solution. This is an exothermic reaction. The tem-
perature of 80°C had to be maintained while adding the glucose
to get the.maximum yield of para-azoxyanisole. The result-
ing mixture was dilluted to 2 liters with water and suction
filtered. About 200 ml. of water was added to the precipitate
and steam bubbled through the mixture for three or four hours
until the unreacted para-nitro-anisole was removed. The re-

sulting product was filtered again and the precipitate was

dissolved in hot benzene and ethyl alcohol and filtered
once.more. The last process or re-crystallizing from the
hot benzene and ethyl alcohol was repeated three or four
times until the precipitate was a light yellow and the fil-
trate was also a light yellow. Fifty gm. of the para-

azoxyanisole was made.

Three pictures are included of the apparatus. The
first shows the set up that was used for obtaining the results.
The second is a picture showing the face of the magnet and
the meter that was used to find the maximum and.minimum
points. The third is a picture of the waveguide and tempera-
ture bath tank.

lO

 

 

Fig. 2a - Apparatus Set Up

ll

 

 

 

Fig. 2b - Magnet and Meter

12

Detector

Temperature Bath

Klystron

 

Fig. 2c

13

EXPERIMENTAL PROCEDURE

To determine the direction of the incident wave, the
apparatus was put together with the sample in the cell
and a point was found for which the plane of polarization
did not rotate when the field was turned on. If the sim-
ple picture we have is correct, then when the electric
field is parallel to the magnetic field there are no comp
ponents perpendicular to the field. Therefore, the electric
vector will not rotate. When this point was found, the
protractor was fixed so that the indicator on the detector
read 0° for a maximum output.

To determine the angle of the incident wave, the
detector was set at the angle desired and the klystron was
rotated until a maximum output was obtained. The incident
wave was taken for 0°, 30°, 45° and 60° to the magnetic
field for one given length of sample. The two maxima and
the two minima were observed for no field, 500 gauss and
1,300 gauss. The length of the column was then changed
and the readings at the various angles were again taken

with no field, 500 gauss and 1,300 gauss.

Mal.

lviin o

IVIaX 0

Min.

N181 0

Min 0

Max 0

Min.

14

 

Cell Empty
66 at 6° 67 at 187°
0 No field
2.6 at 89° 2.5 at 269
64 at 185° 64 at 6°
. 0 1,100 gauss
2.5 at 270° 2.6 at 89

Cell with 7.87 cm. Crystal
Temp. Below Liquid Phase

 

97 at 213° 96 at 30°
No field
.2 at 113° .2 at 292°
94 at 211° 92 at 31°
0 1,100 gauss
.2 at 111° .2 at 293

15

 

 

 

2? = 2.29 cm.
Max. Min.
240° - 76.0 150° - 0.1
NO field 60° - 80.0 330° - 0.1
228° - 96.0 139° - 0.1 E 60° H
500 85°93 47° - 96.0 3190 — 0.1 Temp - 127°C
1,300 217° - 100.0 136° - 0.1
gauss 41° - 112.0 315° - 0.1
225° - 64.0 135° - 0.1
No field 45° - 66.0 315° - 0.1
500 211° - 102.0 124° - 0.1 E 45° H
88°53 34° - 104.0 3050 - 0.1 Temp ' 127°C
1,300 27° - 120.0 122° - 0.1
gauss 211° - 110.0 302° - 0.1
210° - 60.0 120° - 0.1
NO field 30° - 64.0 300° - 0.1
5 18° - 140. 110° - 0.1 E 30° H
00 gauss 1990 _ 136. 2900 _ 0.1 Temp 3 127°C
1,300 197° - 176. 109° - 0.1
gauss 17° - 180. 289° - 0.1
180° - 86.0 90° - 0.1
No field 00 - 88.0 270° - 0.1
5 0 0° - 200.0 271° - 0.1 E 0° H
0 55°35 181° - 200.0 89° - 0.1 Temp - 127°C
1,300 179° - 220.0 91° - 0,1
gauss 0° - 240.0 270° - 0,1

l6

2% = 3.60 Cm.

 

 

 

Max . Min .
180° - 72.0 90° - 0.1
NO field 0° 72.0 270° - 0 1
172° 360. 267° - 0 1 E 0° H
50° gauss 354° 360. 87° - 0 1 Temp - 128°C
1,300 1728 400. 267° - o 1
gauss 354 - 400. 88° - 0.1
210° - 96 120° - .1
No field 500 - 95 3000 - ,1
13° - 248 103° - 2.4 E 30° H
50° gauss 192° - 240 284° - 2.4 Temp = 128°C
1,300 190° - 240 281° - 2.4
gauss 11° - 254 102° - 2.4
. 225° - 36 135° - .1
N° f1°1d 45° -,36 315° - .1
24° - 132 114° - 2.4 E 45° H
500 88°33 213° - 128 294° - 2.4 Temp = 128°C
1,300 209° - 144 292° - 3.2
gauss 24° - 152 112° - 3.2
, 250° - 68 150° - .1
N0 field 60° - 68 330° - .1
231° - 72 1333 - 1.2 E 60° H
50° 83°33 44° - 80 313 - 1.6 Temp = 128°C
1,300 2273 - 80 1293 - 2.4
gauss 41 - 80 310 - 2.4

17

z? = 4.89 cm.

 

 

 

Max. Min.
0 O
240 310. 150 - 0.1
N0 field 60° 360. 330° - 0.2
210° 500. 308° - 9.8 E 60° H
50° 88°53 32° 590. 126° - 11.0 Temp = 130°C
1,300 26° 720. 118° - 17.0
gauss 212° 700. 300° - 18.0
0 O
. 225 3000 135 "' 001
N0 field 45° 320. 315° - 0.1
200° 1200. 109° - 14.0 E 45° H
50° gauss 19° 1360. 289° - 16.0 Temp = 129°<:
1,300 15° 1880. 107° - 18.4
gauss 195° 1700. 286° - 19.6
210° 480. 120° - 0.1
N0 field 30° 480. 300° - 0.1
10° 2320. 98° - 5.6 E 30° H
500 88°33 189° 2080. 278° - 5.6 Temp . 128°C
1,300 7° 2400. 279° - 6.4
gauss 188° 2400. 98° - 6.4
No field 180° 84.0 90° - 0.1
0° 88.0 270° - 0.1
178° 720.0 268° - 0.1 E 0° H
500 gauss 358° 720.0 88° - 0.1 Temp = 127°C
1,300 358° 800.0 87° - 0.1
gauss 178° 840.0 268° - 0.1

18

2'2 = 6.40 cm.

 

 

 

Max. Min.
180° - 12. 90° - .1
N° field 0° 12. 270° - .1
356° 110. 85° - .2 E 0° H
50° gauss 174° 120. 264° - .2 Temp = 129°C
1,300 171° 160. 83° - .2
gauss 353° 160. 264° - .2
o o _
280 E: 23 - :1
40° 71. 95° - .7 E 30° H
50° gauss 186° 73. 275° - .8 Temp . 129°C
1,300 177° 88. 92° - 1.0
gauss 1° 90. 271° - .9
, 225° 11. 135° - .1
N0 field 45° 12. 315° - .1
10° 38. 100° - 1.0 E 45° H
50° gauss 188° 44. 280° - 1.1 Temp - 129°C
1,300 184° 52. 97° - 1.4
gauss 0° 55. 277° - 1.4
240° 12. 150° - .1
N0 field 60° 13. 330° - .1
30° 16. 120° - 1.2 E 60° H
500 88°35 210° 17. 297° - 1.3 Temp - 129°C
1,300 198° 21. 291° - 1.8
gauss 21° 21. 1110 - 1.8

 

19

:3 = 7.87 cm.

 

 

 

'MaX- Tia;
240° 9.6 150° - .1
N0 field 60° 8.8 330° - .1
21° 27. 110: - .6 E 60° H
500 gauss 2020 50. 291 - .7 Temp 8 128°C
1,300 193° 52. 101° - 1.
gauss 14° 58. 283° - 1.
225° 9.6 135° - .1
No field 450 9.8 314° -,.1
7° 54. 99° - .3 E 45° H
500 gauss 186° 53. 278° - .3 Temp ' 129°C
1.300 183° 100. 273° - .5 '
gauss 3° 110. 93° - .5
110° 9.6 120° - .1
N0 field 30° 9.8 300° - .1
7° 77; 92° - .2 E 30° H
500 gauss 1890 '78. 2730 _ .2 Temp I 129°C
1,300 180° 120. 271° - .2
gauss 2° 130. 91° - .2
180° 9.2 90° - .1
No field 0° 9,0 270° - .1
176° 96. 267° - .1 E 0° H
500 gauss 358° 100. 87° - .1 Temp - 129°C
1,300 1788 200. 87° - .1
gauss 2 230. 266° - .2

20

RESULTS

The first page of data shows that when the cell is empty,
or if the cell is filled with sample below the temperature
for the liquid crystal phase, there is no rotation when the
field is applied. The rotation seen for O0 incidence gives

a measure of the reading error. These points show rotations
(F’ 620 of l0 to 50. The average is 30 which would

seem to indicate that the error in adjusting the angle of

the incident wave is of this order of magnitude.

Fig. 3 shows the rotation ¢ " $4, for an incident wave
of 300 to the magnetic field vs. the length of the sample
in the cell. The two curves shown are for different field
strengths as indicated.

Fig. 4 and Fig. 5 show the same thing as Fig. 3, except
that the angle of the incident wave is 45° and 600 respec-
tively.

Fig. 6 illustrates the way in which the rotation gpvtfl,
varies with the length of the sample with a maximum field
and at three different angles of incidence. It is interest-
ing to note that Fig. 6 shows the rate of rotation the
electric vector is decreasing, even though the sample length
is increasing and the magnetic field is strong enough to

saturate the sample. This is in accordance with the theory

21

of differential absorption as being the cause of the rota-

tion of the plane of polarization.

22

on

owwfiob e323 .3 $2862 .3 £323 332 - a .32
.23... mag 33...:

8 2 00 0' On OW O.

 

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23

eatfim hp con 6pm; phmefioeH 26% enacts hahetm .m> hospwpom . a .wflm

3:8 co... .
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NOLLVLOH

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24

eaofim on one ope; peoefiqu no“ nomeoq oaoaom .mp eofipopom . e .822

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26

modem 003.. pm moves
pnogqu .538an conga no.“ dawned oaqawm .mp doapcpom .. o .32.“

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.83 h o o c n u .
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__.L
8

27

CONCLUSION

The simple picture that we proposed for the rotation
of the plane of polarization due to differential absorp-
tion seems to agree fairly well with the experimental
results. There is some difference that does occur.

From the curve taken with electric vector parallel
to the.magnetic field, it is seen that the average error
in determining the position of the maximum or minimum is
3°. With an error of this amount, the rotation obtained
at a field of 1,300 gauss may not be greater than the
angle that the electric vector makes with the.magnetic
field as it impinges upon the sample. To answer this ques-
tion, the magnet should somehow be.made to give a field of
about 3,000 gauss. Even with our assumption that the
rotation is caused by a differential absorption, the field
picture of the TEll.mode shows that the electric vector is
not straight but is curved slightly so there is always a
small component of the electric field that is perpendicu-
lar to the magnetic field.

Another possible reason for the experimental curve
being different from our theoretical assumptions is that
the.molecules of the fluid tend to be oriented by a tempera-
ture gradient4 and also the molecules near the wall of the

cell tend to be aligned parallel to the wall.

28

fi ”1,
RP B -‘ 1
A .—JL

 

Carr, E. and Spence, R. D., Bull. Am. Phys. Soc.'§§, No. l,
10 (1953).

The Proceedings of the Faraday Soc., ”Liquid Crystals and
Anisotropic Melts", April,~l933.

Southworth, Principles and Applications of Waveguide
Transmission, D. Van Nostrand Co., Inc., (1950).

Stewart, G. W., Holland, D. O. and Reynolds, L. M5,
”Orientation of Liquid Crystals by Heat Conduction", Phys.
Rev. 2%, JUly 15', 1940, pp. 174-1760

Illll“NI|||IIIWI||||\|||||||||||\Illll\IHIHIIIHIWIIHI

31293017