H __._:_~_:_:____35:;:_E_:__::___:_. "‘ 32;”?s3ai A? o O :15 W i‘. v t 15.1..“ \ E 3 .3? E Then 8. x m '6 .s‘dFJ. IA pv-wu. 3?. u... 9. ... L. «V 1 A».U Ed 3,. ("a um um \\\\\‘\\\‘\\‘u§\2\\\1\.\;fi[fi\i§l§\1¥§\fi\|\\ ‘ 3 1293 entitle d MM mngj": ant”! <3"? ”5““ Cyan/.1 eeeee ktedbg 7MM‘L has been accepted towards fulfillment of the requirements for iii—degree in _@ \ l LIBRARY Michigan State University PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 11/00 c/CIRC/DateDmpGS-p.“ THE MAGNETIC FIELD DEPENDENCE OF THE MICROWAVE DIELECTRIC CONSTANT OF A LIQUID CRYSTAL AT 3 KMC. by Robert W. Lee 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 19Sh m m 3 (3.; ACKNOWLEDGEMENTS My sincere thanks to Professor H. D. Spence for his supervision and guidance in the work of this thesis. My thanks also to Mr. C. L. Kingston for his machine work on the experimental apparatus used in the experiment. {MM/{u 344514 THE MAGNETIC FIELD DEPENDERCE CF THE MICROWAVE DIELECTRIC CCNSTAHT CF A LIQUID CRYSTAL AT 3 EEC. by Robert W; Lee N ABSTRACT 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 CF SCIENCE Department of Physics Year l9§h Approved EZ>HZ7- s;;u»~¢4_ v This work discusses the determination of the real and imaginary parts of the microwave dielectric constant of the liquid crystal,para-azoxyanisclo, by transmission methods. A ten—centimeter wave guide apparatus was employed to yield results at a frequency of three kilo-megacycles. The magnetic field dependence of the dielectric constant is discussed, supplemented by a graph indicating the order of variation in power absorption with and without an externally applied magnetic field. Experimentally, transmitted power was plotted against sample column height with and without an applied magnetic field. Theoretical curves were then fitted to the experimental curves thus yielding values of the propagation constant of which the dielectric constant is a function. A derivation of the theoretical curves is made as is a comparison between the dielectric constant values thus found and values obtained from various other experiments at higher and lower frequencies. Photographs and schematic drawings of the wave guide apparatus are included along with a detailed discussion of procedures used. INTRODUCTION. PROCEDURE. TABLE OF CCNTENTS THEORETICAL CURVE . EXPERIMENTAL CURVE. EXPERIMENTAL RESULTS DISCUSSION Page 12 22 214 INDEX CF FIGURES AND TAB I"S Figure Page 1. Relative Power Transmitted Through Sample Column Height X. . 6 2. Graph of Experimental and Theoretical Power versus Sample COlumn HBight o o o o o o e o o o o o o c c o 13 3. Block Diagram of Experimental Set-up. . . . . . . . . 1h h. Photograph of Experimental Set-up. . . . . . . . . . 15 5-6. Sample Holder Section and Magnet . . . . . . . . . . 16 7. Photograph of Matching Set-up . . . . . . . . . . . 18 8. Block Diagram.of Matching Set-up . . . . . . . . . . 19 I. Table of Typical Experimental Data . . . . . . ‘. . . 22 II. Table of Experimental Results . . . . . . . . . . . 2h INTRODUCTION Liquid crystals, as first observed by F. Reinitzer in 1888, are substances that act much like liquids but exhibit prOperties generally associated with anisotropic crystals.1 These liquid crystals have no crystalline lattice as we ordinarily think of associated with crystals. They do, however, give interference patterns in polarized light, and often exhibit mobile thread-like structures when observed between Nicol prisms. Para-azoxyanisole is one compound exhibiting these characteristics and falls in the nematic class of liquid crystals. This class is one of the three; smectic, nematic, and cholesteric, and is characterized by long, thin organic molecules. The smectic phase is characterized by a soap-like'layer which does not flow like a liquid but "glides". The rmmatic phase, however, does flow like a true liquid with the exception that it exhibits more than one viscosity when under the influence of a magnetic field. That is, the viscosity when observed upon a plate which has been dipped into a nematic liquid crystal perpendicular to the magnetic field is different from that observed when the plate is dipped parallel. The cholesteric phase is less clear out, having characteristics of both of the former classes. The swarm theory suggests these long, nematic molecules are arranged ji‘lxarallel bundles called "swarms". The swarms themselves, however, haVe:]30 order. It is thought also that the application of an external magnetic field will align the swarms such that each swarm lies with its molecniles.parallel.not only to each other but to the lines of force of the applied field. Furthermore, there is associated with this class of liquid crystals not only an induced electric moment parallel to each molecule but a separate electric moment either perpendicular or parallel to the molecule. In para-azoxyanisole this electric moment is perpen- dicular due to the ionic bond between the central nitrogen and oxygen atoms as shown in the molecular formula below. Thus, the aligning of the molecules as brought about by the application of a.magnetic field causes the addition of these electric moments. The above phenomena supports the difference in the dielectric constant of the liquid crystal as measured in and out of magnetic fields.2 The compound used in this experiment was para-azoxyanisole whose molecular formula is : CH;O-O—I;I= N-Op- CH3 0 and whose liquid crystal range is (118°C.-135.8°C.). PROCEDURE It is the purpose of this experiment to investigate the temperature and magnetic field dependence of the dielectric constant of para-azoxy- anisole by microwave transmission methods at a frequency of’3 ch. This particular frequency was chosen to bridge the gap between dielectric constant measurements that have been made at higher and lower frequencies. Low frequency, long wave length (of the order of meters) determina- tions of the real part of the dielectric constant ( 64 ) for para-azoxyanisole were made by Abegg and Seitz3 in 189h, yielding (h.0-h.3 c.g.s.). In further low frequency work by Eichwald in 190111‘ an 6 ' of approximately -3- 6 was found. BuhmerS repeated Eichwald's experiment and found an value of h.9. In l92h Jezewski6 made dielectric constant measurements at 0.1;? No ( A - 720 meters) and found a value of 6.9 for 6’ . In the same year Kast7 independently made measurements at a wave length of 200 meters and found a comparable 6 ' value. Further support was given to Kast's work by Ornstein8 when the latter developed his crystal aggregation theory of liquid crystals. His theoretical results compared favorably to Rest. At the other end of the frequency scale, E. F. Carr9 in 1951; determined both the real and imaginary parts .of the dielectric constant of para-azoxyarrisole at frequencies of the order of 15 line. He used both reflection and transmission techniques with a 2 centimeter wave guide apparatus and found values of approximately 3.8 and 0.145 for the real and imaginary parts respectively. Carr's method requires a column height of sample several wave lengths long and an electromagnet of sufficient size to maintain the entire sample in a magnetic field. This enabled him to experimentally determine the wave length in the sample, and, subsequently, the variables of which the dielectric constant is a function. However, with a 10 centimeter wave guide apparatus as used in this experiment, the Carr technique is impractical due to the comparatively long wave length ( Ag * 1h. 56 centimeters). The wave length in the dielectric is of the order of one-half the guide wave length, Ag ; hence, several wave lengths would require a approximately 20 centimeter column height of Sample. And since the wave guide cross-sectional dimensions are 7.2 X 3.1: centimeters, this would require approximately 2000 grams of para- azoxyanisole. Also since a magnetic-field dependence of dielectric 4,- constant is one objective cf this study, the pole faces of the electro- magnet must have the dimensions: 7.2 centimeters X the maximum column height. Furthermore, since the magnet must be immersed in an oil bath, its size must be kept to a minimum to keep the oil tank size reasonable. These two factors, the limited supply of sample and the magnet size, forced the use of methods other than those employed by Carr. The method selected consisted of measuring the power transmitted through the sample as a function of column height. The real and imaginary parts of the dielectric constant were then obtained by fitting the experimental curve with the theoretical curve for this quantity. THEORETICAL CURVE The real and imaginary parts of the microwave dielectric constant I of para-azoxyardsole are 6' and 6‘ respectively and are written: 6 = 612.6” (1) where 5’ is represented by the ratio: 1 (.2 €— " 7r (2) 3 being the velocity of light and g the velocity of the electromagnetic wave in the sample. The imaginary part 6" is a measure of the power absorption. Carr's method9 uses the relationships: ,,_ )3 n e - ”Ad 8 (3) where X is the wave length in free space which is related to the measurable wave length in the wave guide, A? (done by measuring the distance along the guide between successive maxima as indicated on the tuned amplifier with infinite standing wave ratio) by the expression: ll’ Kl '- A91 +(Z_Q)2 (5) g is the larger cross-sectional dimension of the rectangular guide and u A d is the wave length in the sample dielectric. B is the imaginary part of the propagation constant: 5: g I... ’Lfi II (6) which is also expressed as: to 3‘7;— (7) where _4:J_ is the usual angular frequency and _L[_ is the wave velocity in the sample. The unknowns of these relationships are not all obtainable frcm curves with so few maxima and minima as those obtained frcm this emeriment; hence, the necessity of determining a theoretical curve. This curve must be a function of variables from which the dielectric Constant can be derived. As shown by equations (3) and (1.) along with -6- the relationship, £2 2-”. **-' 8 Ad () the [3’ and. [3” are these variables. The derivation of the theoretical expression for power as a function of sample column height and of the propagation constant [3 is as follows: Consider a sample column height g and an incident wave of unit magnitude. This we can do since we are dealing with relative power. Fig. 1 shows the transmitted and reflected waves. a t-r' E u~né“”‘ r -pr <,__. . , (I-r‘)e ”(t-He'd” £ +r(I-P)€‘P‘_ r‘h-Méfifl ,_ v‘(:-r)e"""" r‘(t-P‘)e"3‘” 3 _ amps _ -.L3PX H‘U r')e £ ”‘1‘: r)e , r4(:-r)é““" > Pit-05359 P‘( p)é35p TAU-P") e.“ 59x ‘u- I I 'c— X gal FIG. 1: Relative Power Transmitted Through Sample Column Height X.- Key: I" = reflection coefficient £3 = propagation constant The reflection portion is of no interest, since it was matched out as explained earlier. The transmitted waves, on the other hand, are what we want so we add the successive terms to yield T, the total transnitted energy. This sum yields: -pr °° —£BK 2 n T2 (I—r") 6 genre )3 (9) . . ' . ( ~pr)2_ g as): t " To simplify this expressmn let ['8 " O. . Then EC rQ ) J ’1‘!) becomes: N z u 20."=I+a+o.+- ------ +0- (10) "=0 N n NOW, if 0.2:» is subtracted from 09) the following results: “a N SOP- GLEN a" = l- an" (11) Mo "=0 01', £0.“ CI-d): l-QN” h=o (12) And, since Q‘l , it follows that in the limit as N approaches infinity: [Ear (I-a)= I (13) 080 Or, god": Th (1’4) -8- Now substitution for _a_ yields: °° $.pr 2 n _ _______L.__ i (15) ZCCFE ) J “' )—-U‘e‘*"*”‘fl2 hlo Substitution of this eXpression into equation (9) gives: 2. -,.;,gx l T: (I‘P)e '_r-,zeeczp>T (16) Furthermore, since power is proportional to [T‘z 2* [t-r‘l‘ é”; x _. 2- : .— P“ [Tl ‘TT ’l—Pte'j’szfz (17) 1 And since “‘4‘" is a constant, i.e., it merely causes a shift up or down of the p values, we can divide it out. Therefore, if we 011]. 2 relative power, we can write: ~10 x P= first—WP ‘1‘” Now to determine the reflection coefficient squared, use the following expression: Z -Z =: _l____’ 19 1"here 2‘ and Z. are the dielectric impedance and air impedance respet'stively given by: Z gal/0': UM- (20) 4 fl ' Z = 52M (21) Here 0:3 and): are the angular frequency and magnetic permeability res- pectively, but they cancel and therefore are of no interest. However, fl. does not cancel but is a constant: fl=fl=fl :3 0.452%“ (22) ° *9 I456 Substitution of eXpressions (20) and (21) into (19) gives: l I — r: Fag-em" " e = [3,-53A'A" (23) 34:7" 4- f6. fle+fi.“":.6u Hence , P_K5.-3')’+ a")? . __e;"_’_ (21.) Wmum‘: 6‘“ 0r. r‘-- (rt-159‘.- (w): . Ema-w (3:373 C 5'71 = ”1‘61"“ (25) ~1C=~ The angles ‘9' and q) are given by: (from 23) 9* Tan-'Bifli) 4’ = mfg/36m) Let “=69“ ¢) . Then the expression for power becomes: P e- as”): e-z flux [Mr/1e“. e"“"""‘lz R Re it R: . w e lI—lrt‘e.“‘“"-e"‘"‘“’"""5‘")lz 7.?» 2 I hm; e-zp'k. eaz (ex-6'10}; Let (-ll‘l"e"” 0:11 . Then Ebecomes: Rt: I1+Aeiz(aL-fi’x)‘2 The graphical representatidn of this is as follows: (26) (27) (28) (29) (30) asmad-Zfi’x) -11- From the above picture we see that R12 [1+ J1 COS(Zd-ZEIX)]Z+£45‘."(1°‘“15/X)Jz (31) Squaring and expanding this expression yields: R1: 1 +211 cos (za-z/e'x)+xz’~ (32) Substitution of 3'. into (32) and (32) into (28) gives: -zp”x P: 487 -4 u, (33) I—ZIPI‘ 8‘“; x C05 (is azp’x) ””4 e )3 mfide mmmt’" ”“1 d°nminat°r by e‘z’y‘x to obtain the final upmssion for power: I 2:- u 4 P ezflx-Z/F/‘COS (2a -zp’x)+ JL'L... (3h) ezp”x In this expression given a fl! and fl” all quantities are known except )5. Therefore 3, relative power, is given as a function of 3. after assuming ,3, and fl" . This is precisely what was done. Various combinations of (.3, and“ {5” Were chosen and some twenty-three curves were drawn until the best pos‘ible fit between the curves thus calculated and the experimental curves -12.. -was obtained. These curves and the associated 5:4 and B2 are shown in dotted lines in Fig. 2. The real and imaginary parts of the dielectric constant are a derived from these #4 by equations (3) and (h) respectively. EXPERDIENTAL CURVE The set-up used to determine the experimental curve is shown in Figs. 3 and h. The sample holder section of the apparatus as shown in Fig. 3 was attached to the bottom plate of the oil tank by a flange in which was sealed a thin sheet of mica. A small hole was drilled into the upper half of this flange to enclose a thermocouple (Fig. 5) so as to bring its tip as close as possible to the sample. This hole was then plugged and sealed as was the entire flange with clear glyptal to prevent oil leakage into the sample. Another view of this sample holder section with the magnet in Operating position is shown in Fig. 6. The magnet produces a maximum field strength of 1300 gauss and has pole faces of dimensions 6. S x 8 cm“timeters with a 3.5 centimeter separation. Peanut oil was found to be satisfactory in maintaining a uniform temperature bath. The oil was kept in circulation by a fin-disk type ‘tirrer whose motor was supported by a corner of the tank. The heating elefl‘ents used were two independent coils of nichrome wire wrapped bet‘Den layers of asbestos paper which in turn were wrapped around the 011 tank. In order to make even relative power measurements accurately, RelatiVe Power l'} 3.6 3.2 2‘ Li- ?“ " ‘ I.u- \ \ \ u , _ \ 0.9 / \\ \ e ‘5. \ .. \ 0.8 \ \ \ \ \\ {2 0.7r- \\ \ - \ \\ as- \s \ \p \ \ \ \ 0 0| I / / / 0.4 - 0.3 - 0.2 * VJ '- 0 n n 1 1 r 1 0.5 |.0 Lfé 2.0 2.5 3.0 Sample Column Height in cm. F's-2.EXPERIMENTAL and THEORETICAL POWER versus SAMPLE COLUMN HEIGHT Key: Upper solid curve- Experimental H360 Upper broken curve- Theoretical. associated with B=i.30,B=O.lO Lower solid curve- Experimental H = 0 Lower broken curve-Theoretical associated with B5l.3O,B'40.l4 Plunger -—i> Matching section—w A 'SWR iUNED AMPLIFIER l000~ Browning—TAA- l68 Uniform temper— ature bath / Sampie/ \‘