X.F.AY :Dl?PRIH1~IOH ~tfU'n!t~B Oli !ili!f~O~J!!flO 

fJU.Bfl'lANURBI Tli'HO'R~q!! fJ!L lt!(J)ttlaOWfUS 

AND EXP®RllmHrtAL f~lif-flQlJlifm. 

-, 



23 

G~aeni.:fication o! liquid eryrrta.le n.'nd their structures: 

In eoction 1.1', we mentioned that thermotropic liquid 

cryeta..l.s were broadl.y divided into throe groups, ·vi~ .. , nematics, 

cho.l.esteri c.s end a!llectics. To date· olat::mificrr.;.tion or different 

l.iquid cryE:1te~ phases ros·tn ws..inl.y on thu work of Ba.ckma.nn and 

hie. co-t>/orka.rs1 whioh was based on the mi.ecibi.li ty etu.£ly. The 

mi.saibili ty. ruJ.e ::rta.tee thet if two ~1quicl crjrf!tnlv :::Lre minai-

onticn.l anir:otr>nuv) were 
•. 'I "'-"-- • 

a~so taken into considerat.ion in this cl.o~-8fdfic~J·tj.ot1, system. 

A. de 'V"riee2 , after\iara.s, modj.fJfJd t~de cJ.e,st~ific::tt.iou ayetem 

on the baeia of mieoibil.ity relf:.tion, n:icroncopic te:r.t~.lrfls 

and X-ray diffraction pat~c:rns .. Det[1.il.s of ·thf3ne clancifiaa­

tion. r;ysteaH3 and structures can be had .from the· revievJ arti-

A-, r.!Oh ,,..{:) dt:~.. 'if;r•l c.~ '3.. ~,.. ~? .,, TI t,...-i 4 i n t5 .,. M• ''" , .bf6 
........ IV u.J. ...., II -"· .... , ~ • .~J . .I:}e . .r·e ...... e ' (j. L'OUCC ·,) J.J.,.'\! •11.71aro.J. 

and G.ray ut .. 7,8 
:it.L. • 

of controversies are sti.t~ going on about the structure~ of 

!!ema~:ic pha.&e,s (1'0 

We have mentioned earlier that in nematic phat'lf!Us:.:,, 

the lone axes of the consti tu.en t moleculEH3• do have a pre-
~ 

:ferred C:ireo,tion of orien·tation ca:l~ad the direator ( -n ) 

but the molecuJ.a.r oentree of' mans are randomly di~tr·ibu.ted 



order about 

~ 

direction of VI 

24 

• The 

nematic pbeaes ooeur on~y. \vi th materi!UB which do:not di.s­

tinguish between r:l.ght antl·l.eft; either eaeli conet:itu.ent 

woleeu.le must be identical. to it$ mirror i~na.ge or; :if it is 

:not, the eyatem muet. be a racemic mix·ture of the right and 

~ett handed speoi oe. l'1l'OID a ''ryetallographie point of view 

the s:ymmetry in nomnt1(:r? ce11 be iY13'!$C:t'"i 'bed. bY:; 'Do<.. h in 

the nohon:fliet:l nota t:i.on 10,~ (1e 'llrier;,9 _ howev:er, ob~erved 

another typo o:f lH.naat1e ph~:t.tDe caller.:l skewed cybotm.ctie 

nomstic (Ns;c;), where the mo~eeulen a):>e ar:r~lP$~d i.n a.mal.l 

groups in tn.1ob a '""S.Y that they are pn,:callel to «$Sch other 

I 
mA<Ss o) ·· · ·. . . 

Wi t'h the cemtren o:t? the mo~e~u.les in a fe.Lt··~.r. well defined 

plene~ and norroP..l to thE; pletle makes certain' ccmpi(1ereble 

- l:ter. c'b..ole~tari~.s- ~ire nothing bU.~ 'twisted' or 'chirt:•l • 
~ . . 

ncmm.ti c~,. de Vries''"" aloo :propof.red two typfJ~ o:r chole~terie 

phn.pes - ordinary n em a ·ti a eholes·teri c (SH:tr,;)'r~md lay~red. or 
. . . ~ ~.- . 

!lmeatia. choleErteric{Chr;;). 
"•"" ;..;;.: 

Smeatio phatses 
. . l t. 

r.rhe r.igid-.rQd-lik..e molee\.UtH'3• believed to be the 

bui~cting b~ocke of all ~iqnid c~y~t~~s, oan array them­

se.lv<~s in paralle<J~' ~&y-arn to form a smaotia mesophase~ 



2S 

The molnc~ea may be norro~ to ~he p2~ee of the layera or 

ti~ted within thew. 1~hey m~~.y be rnndoml.y O.intributfiJ.d withln 

the ~eyera or pEtrtly ordered or, in ~orne Cf.H':lee, they form a 

two ~.imenr?iona.l J.a tt1 ce w;t thi.n the ~a.s e:r!\. :;:•hC'r~ can eY.ist 

correlationB betw"en "t.hc ~ayere but, a:rc.ept in. more ordered 

onEH:;r, there a.re none. These lend to th~ potmi biJ .. i ty ot s 

J.t?~rga num bar o:f smectic polymorphism a::~. d. elr~ady a.s many. 

e.a e~even ~mecti c phat:;es bave been i.:!t!!rd;i "f:i.e<1 end de signa ted 

fJ.,.. ' Srt 
..!..> v 

Mt!l'1:5~ -· 

In most em (HJt:J. a ,pna~en~ the Jnole~ul~H} e:re mo bi~e in 

tv.ro directione: and. r;e;n rotnte e.bou.t nne m.xi~h ·Thn in·t~r 

,.,,,., ""n-1~-i. C I' "" }]·"" .,...... { Q: ) ._,.L.,, 'J '....,;~ w.-. -1. }:! ... t~ t:~;";.,. '-4 ~ __________________ _.;~. 

pha~H~&. l'ii thin tbe layers of 3;:\ the long ·a:r.ee of the 

awJ,.ecuJ.ea lie :pt~ .. ral.l~l. to one ta?:v~ther. their dir(!at:i.on 

being normal ·to thn plan$ o.f the layer. The. &11).lemAle>a 

a:re free to ~otuta about tbni.l' lone ~:ret) e.hfi the dir!tri-

bution of centre of mam.1 of thP.J rno~eculec wi thi:n the 



28 
./ 

layers is r~d.otn 11- 1 '. Thus the .l.aye:~s have a low degree of 

. order, et'd'h J.ayer being ;; n two dirueneional l.iquid. The 

l.eye:r th:ickneoa is, in most· oases, elo se to ·thf.l tuJ.l mole-

oul.tU" le:ugth. The ldole~~ular!.~ t.:~,.rl:1lin~uru~n t is ~hown in ~"ig.2 ,.1. 

d:e Vrie~114 , '15 h¢w seems to beLieve t~m:t 'the mo.le·\jule{';! a.re 

·til. ·ted in f.J.1~ pht:.r.:JO · fi!ince the orientational. order pnrar£tter 

clso be ment!oued h,ertll th~t new· 11 ref.':<ul. ts have e!llerc;ed in 

the l~u;ft few ytiarf5 concerning the e~K1st~nc~ of re-ant:r~nt 
0 

nemai•:te and nm€H.rt1c plu~.ses. bi~sye:ro-c:r~ot~nyer trann1 tions. 

t.mdu.l!-ltifln ~tru.ctUl:"~s €illd ooexieten't tlotu;li t:f waves of 

k n CO"'V•.~1 ""'. n~"''·"""""".f.·•a •-:..::~~·.,.~.7 • .., .. -~t.i><;o 16-27 '.L. .L Q.,~ c. J<.;~t.4r--t:..:h- ii·V r .. t;.;11,:'~ ~ .. ~7•~5 t..:.4;4p • 

:!~he etructure of s0 phe.f!e 1~ ai~ilm..r to that. of the 

f:!fb ph8,~e ~·~:e~.JJlt iaH:tt the long a:xeA of the m.o~eculef.l rJ.:rc 

·til11€:?cel w;!.th re~peot to the plane~ of th.e lE".yerf;J {li11.g.2.1) 

that in 

bo temper~ture dep('n·dent bu.t. for ruo~t ea~H,u~. i. t .is t.em­

per.aturo :in.t!!ependemt, Depending mai.nJ.y up~ln. ·,the terol)e:rature 

dep~n.d:enca of tilt tangle a.ttam]~t~ heve been: t1a.d.e to di·vid$ 

s:-r pha$e in t .. uree eub-g.t?Ot'!Pe28 • -· 1.~ 



.·'27 

11111111111111111 I II I 1111 
1\ n 

1 I i IIIII\ IIIII I 11111111111 

I I I 111
1

1 II I I I 

(a) 

II 1/ I I /I I A 
n 

I I II #II II I I II I /Ill I /Ill I 
I I II I II II I I 
$11/11111 

(b) 

Fig.2-1'Schematic representation of two types of smcetir ordct·: (a) smedic 
A order; (b) smectic C order. 

rG 
u 
~ 
0. 

u 
Gl .. 

-~ 

c' 
' 

& , I (;; 

·'. 
001 

1 

0 

200 

1 110 
I 

1 

W77 o· if.. bu;·' .-i:. I •-\:fifT ib 
. ~t 

c' 
Q 

~ 
I 

I 

001 

.
1 

no 

1 o2o 

•
1 

110 

Fig.2 .2: representation of real and reciprocal 
lattice for SF anrl SI phases and the resul-tant 
diffraction pattern as sho,·m in Fig.2 .10 and 
2.11. The molecules are Darallel to c and the 
pseudo-hexagonal packing~of t~e molecules in 
the plane perpenr"licular to c is sho'i\rn, Hi th 
arrows indicating the direction of tilt. The 
hexagonal hko net is shovm together \ITi th a 
perspective view depicting the tilt geometDr 
apa the diffuse bars of scattering parallel to 
c*. A schematic represent:ation is given of the 
X-ray'diffraction pattern with the beam parallel 
to the layers for a sample with disorder about c*. 



28 

SD t:lecopba.f1£1 po:;:r.et.:;eae a cubic arrt:~ngeaumt of sphe­

r:!. cal. mi cellee and vmuld a.ppear to be an exception to the 

rule tt:P..t ~ll f.l!wectia etructures ha,re well d_cfined ntra.ti-

The structt.U"e·s of tLP., nnd s1 phnses ha::re been 

dete!'r~ined VE:ry recently b~:r l•er:10better crnt1P31 ( ~Ji') 
s.ud Sc.ckm~nn group'32 ( ~:11 ) and the reJ.:?,tion hetw.een the 

', ' 'X~ 

two im elvo. eota:blinhed by Let::;.tibe'tt$r nna hi.o' .co-'laorkere.,.,;. 

po r;:i tiona:l. no.rreln.tiorw ( almut )0 moleeuJ.Jtr t3.iameter.n) 

within ~rryer.a. }3oth of them hmra ~th!'(~O ditnor.t'n.iorH-:l.l loug 

r~mge 'bond o:rien tation~.l orfler' ) 4 ot tbo- G-,cef\ tr~i.i mono-

al.i.nio lnttioer~. 

s.... the tilt is 
t' 

directed towai~th'l an edge of 'tho he,:P.1gon. wh;Lte in f'JJ: it 

is direct!)tl townrda an a:pax nB .Hhot<l-1 in J.<':i.g. 2.2. 



.. _ 

.,. 

Th~: mo~eculeB i;:J t~i phe.ee are a.l8o arranged in · 

lo.yera with the lonf~ ~!Xes normal. to the ~e.-y¢t: p.lnnes. Within 

the l~y~r11h the mol~eul.ar ee~tres of.' me.~v. are· f.l.rranged in 

!:lexng!.')n!."',l [;ymreetrsr ( 'f'~ig~ 2. 3) .. :rn general the lo ca~ ~true-
,... -

ture is & ;b-er;ring bnn.e PElwOking and t~-~ ::tv~_ra:ge he:tag:onaJ. ..... 
:']ymmetry if! ?btained lly ~upaeyo~itio~ o-f three· different 

• ot. t' f th , ·1 t' h bi -ll :;:; rnh - " t·· • OI'l en ~a ~onB o · _e .,.eyen,. o:r nor .,.om. o ce a · • .r- e ~ .... ua-

tion. ir;: dynamic nn,d. indj~v:i.(.h.tal tJO~tH!t.U.es rQi;-@.tc'35 •36 ~mong 

~1~ equi·.,t?.le:nt $1 t~~ <>n a 't:i.me Bce.le cf' 10:.. 1tr;;·. Tb.e he:r.a-

( 2n/J, b/)) f'o.r B whtn·e a and h are 'b£-tBi c he~s..go::u~l la. tti oe 

'"ecto_re37. 'i·ril~yer A.:BcA_ ••••• , rt-l..:::Ldc:nn. AEG •• _ •• •, highly 

air:.o.:r:dered ruono~r~.rer J1.A ••••• paeh.ing or no irl':terlr:tJr$r 

corre~ntion£1 m.:r6 e.lBo reJJor.ted36 • b ~o-G.\-\""'-·.~ ~ o-.. ~r<L2.. ~-\'~...~ 
h.A.~ ltr~A.C~ ~ e. ~~&. ay-J..v.. , ot ll\J\..VI...S e. , ..,j, \1A..-- Ctr'\-\rn~ I.e. err\ -e..N-..:b0-\ ~ ol.-V:l ~ · 

..e. rt..e.. lM---~ ~-V) • 

~l A ~· ~ ~ • (~ ) . 0mwcu10 ~ p~aB- ~ • 
• ~,..1' 

.,.__.. • ... • ~ !iOL ...... ~-.... 

·Tho- 8~ ~1odi.!.'i cation i H n laye!'co. r~trtiCture v·r.i.th a 
~ .. ~ 

J.eVt.Jl of o.r·dez• ~'lOl:"t.~ cilo De-J.y appron obing to, thnt of th~t 

rY"•·u~.;,~1.l·•~l(~ ll:'f:A .. C~29.-. )B,J9 +.}--.nn tt-,o.t. "'-b---•e'P"':;,d· ·1~0..,• -..,,.,.,,.,... Q v-1-r;; ..._) vw. ........... , ~j·. • _, . 'W' J.f.Aio _.. , £..o.(~\. ~ V !:'"J ,,.... V~_, ...1.:.~ ~:itiUJit. ~~13 • 

enlee .:1.tl n:E !?hnce ft:re nol"r.'Hl~ to the layers. l t wa:::1 oon-

c.luded -i;kmt wi.thir: tb.e lc::;ye:r.e tl~f! mo~(Hm.leri. 'i1B-'IH~ H: chevron 



30 

(r1_) 

Fig. 2. 3 a) ::3che!<Htic rc>l")r,:;sentation of -~mectic_: 
structure. b) iiexagona.l he.n:·in·:J>)one packin·2 as 
seen alon,_;- the lon·; axes of -the molecules. The .linL~s 
inni ca te -t~~ 1 e 0.1:: i r~n t .l ti on of i.:)1,:: no L~c1..1.l ar pl-J.n c> s 
an ,-1 ci rcJ. e s rn0.rk t __ ;h:; no;,; i t...i, ;n ::; o :- t: l'': W\0.1 •" c·u l . 1.r ·"'-: ':-:;; 
thc-:: <'ircle.c:: f0rn1 :1 ;,,.,:.::~<~;on:-1.1_ ~~::,_--"l:,r. 



31 

lay ere., the arranget!H:1n t be:i.ng monola-yer or bi~ayer for 

d.iffflren-; substances. t~o the structure is eongiderably. 

three-d:i.menli::i1onal40 • 41 : Howe·ver, there is al£30 conaida:rabJ.e 

dieorder- because of vibre.tion ol'" libration, if not complete 

rotation
7 

f>f the rnol.e~uJ.ee around ·the moJ.ecul.ar axe a 42 • 

-··--·-·.-

All theve ameotic phae:ee. 'b.e.ve long range three­

dimensional order33 in the form of monolayer arrangement 

i ; h · 1 ..,., d t-t.i d-; ,4 r lilh ~~,.. • '"' h vt ,. aoncJ..c erau.&.e_ ynl:iu.'l c . _aor ..... e ..... e ._;.G pna .. ,e· as a 

<1-aentred monoclinic aell with p·eeudo-hexa~onal packing 

of the rooJ.eculea within the layero an.rl ·the roqJ.ecules are 

til te<'l tow~.r<1a un edge of the he-,ra.gon ae sho\''.'ll ·in ?ig.2 .2. 

In sH phat1Je the hexagon become more dif'.torted and tile 

eel~ ia no ~onger a-·cel'ltred aB a result of a quenching 

of the 6-folrl rotational. di~o:rder of .the molecul.ea whioll 

e?t10t$in sG. The s0. pbase certa.in~y has rotational di&­

order.:in whioh the molaeuJ.eB reorientate36 about their 

l.ong s:1res on a time eo~e of 1o11 s while thir~ is pa.r­

tia~ly quenched in sn phaaE'H~43, 44 • 

The s• G ph~se waa -fi:t-st dest.zribed by Doucet et u. 
olP t:'t')""-'""B45 . d ~· 'b.. "' ·it' •'!• "'~""r.r -l<'o~~"'"'!. -P-o .... J..()r d.lvl'_..n.v c . an .... H .Puase a.LOng 'IN n ·~ G h .... ..,. ..l. ~u - • 

aos:.·'1 • l">.A.n. Gene et a~~~-·-; first showed that s• G and 

f!'n di.ffer from SG and SH phases only in the tilt direc­

tion ot the molecules. In these oasea the mol:eoulen are 

til ted towards an apex of the pseudo-heXi'J.gone.~ mol.ecuJ.ar 

packing. Thus the mo~ecule.r ti~ t in SG and n11 phaees 



32 

correspond to· the ti~t in G.~ :phase while that of Qf . 
~~- G and 

. ~· . 
Q H phases correspond to c. 

~"'I phase. 

Though the smectic phaf::'les E,. G, H, G' and rr• . ~ have 

long range three-dimentional order like the solid phase 
~~e.. 

still they · i. . identified as liquid crystals because of 

the following reasons: 

1 • :··:n.;.~~ ~· : ~ . · 0nil~~.~ .. ~;jrr~~~·~.J. ·::~ ~:~ or": ,;~ 
i~~· 

2. Posseao fluidity 

3. These phase transitions exhibit no supercooling 

effect ,..,hereas phase transition invoJ.ving solid 

phases aJ.most always show considerable. supercool-

in g. 

. . ..,., 
··~ -- ~ -

The mosaic texturesof these phase~ strongly 

resemble• those of SB phase. 

Mosebauer study46 shoV!red. the F.:~olid pha.e:~e to be 

'decidedly more rigid' than the supercooled SG 

Jlhase at the same temperature. 

b• .A crystal structure of an optically Etctive compound. 

hae a ~ong range '3-d ~attica juat like any other 

crystal. structure, but the ~attioe of a :- · '3-d 

smectio phase becomes twisted if the molec~ea are 

optical~y aatiye. 

The a.snignment of the sy~bo~s to the different 

pha~e types. was simply done in the Ol."der in. which those 

phase types were di ooovered. We ha.:ve. hotvevcr, desor1 bed 



' 
accordance with the 3..:ncr~~~~ng ordernesa of the_ molecul.ea 

in the phases. The sequanee of the liquid. o.rystell.ine ~tate 

a.s indi oa ted by obn~rved. '"ISX:itrtn te .i~ as f\)llows: 

drJr8te..l _SH SG S:r.; SB Sp s1 s0 -, · . .- S13 SA . -
(}h 

. ' 
~:-~.::.~et Broectie :B and G modifications ·h:ave nO't been 

observed in one compo:und end so their res'ptiiut'ive ordei .. is 
. . ' 

not verified. 13U.t sinoe orthogonal pbatioc are .lsss -ordered -

· the.~ the til ted onen, we bavo wri.tte:n s15 b-et_ore s0 • A~l • 

other sequ.enaea have baen verified. 

· phe.aee and the correeponding transi t:i.¢n _temp&l:"a turae can 

be matte from rniooibUity etu~y,. mi.xroacopic tex·tu:re and 

optical. anieotropy study under e. polarising microscope 

erH1 f:ro111 X-ray diffraction study. Hut ·transition tempera­

tures can be maaflur&d m.ost accurately by -l2i.f:ferential. 

, neanning 04lorimetry t~;~tA~ ( :VSO) or_ Dif:f'ere:ntial th~mal. 

liln$,lyJ\'jia ( n~A) rd.ri<)e by the~e metho", ev~n e'tnal'l oh§tngea 

in ther~odynamic quantities (e.g. 1'1nthalpy r.tr :t;ntropy)at 



34 

tre.nsi:tlon ;poi:n tc can be detected vrhi nh eome.times may go 

undetected47 by optiea1. study ~.-nd the temperature range . 

or e ;particul!u.• !'hR.~e may be SO ~l!Hl.l~ the.t X-re.y r!iff'rnc-

tit."H'l Btu!ly ornud not b~ m~-de •• ~{~a.j_n f).9om mis_e~.bi~i t;t an·d 

optica~ mi cro~cop:i a studie~ a pre~iminary iden-tification 

o.f the ph:rz.fles ·cen be made. But to know the atruciural . 

features of mesomorphic phases X-re;y d.iff:t•aation studt 

ia the moat powerful tool nt hand. 

X-ray pattern of an unal.ignetl .tiqu.id ,c:r.:late~.~~ 

conf!ists of one or more inner • .ringtJ an<! one o:r mor~ 

outer rings. The inner rings correr.;q;:HJlH1 ~.o the molecml.ar 

length (in oa~e of nemG":o..tioe) or ~m.yer f.':lpao~ng$ {in car:;,e 

of smecticn) and the outer :ringe are the chareot~:ristics 

ot: the ~a.terel. distribution o£ pa.:rw.J.lel mol_~cul£w9 • ~. 
In aligned a;am:p~tH'h we get m(lr:idio~aJ. nnd e.quQ.tcr!al 

dii'fr~otion nu1x1mn = ae pointe or cret:!cGnts. Gl~aro.G-
-· 

terie'ties _of X-r~yy diffraction photogra.pha WHl texian."ee 

of different phnBea which we .have u~ed. whil{) ident;tdy:1.ng 

them are.given in Tnble 2.1. 



!fbl.! .. lal '. •' 

-~------------------------------~-~~~------------.. f· op•tt:cal. · . :·• . . • :x;..-·· ':'Mil ....... ~:·· • .. ;.,....;. 
¥011 ~1cati t • · · re-t.u• • • 9

., ..--• ... ~·~·· .~;..,.,...-. 
· ·· ...... · · 0 'lie·. p~pertlee ¢ · 4<'1• · • •• - - - .- - - - - - - - - .:...: ~ .l..i - ....... - - - .... - - - - -

•· · · · · · · . ' tmalitt;nea .-pLea •: ··· · · al.tga.eil .-;p.Lee 
• . t ·. ·' ; : "' . . . . . . . .. . ... 0 •• • 

( 1 > (~> · <~) f·t) · · · <s·~ 
...,. .. ..,., .... ~ .......... ~ ~.' ~' .......... ~ ....... ·•'...: ......... .....,_ ........ _.. ..._ IIAit' ...... .:t ........ ...._;'. ·~ .... # ~.' ~ ;.a, ...,_. ~- ,r!ll., ... ~· ~ ,... ~ .W. ,_. ·-

or<ttna:ll"'J 
N'$!!at1G: · 

08'botac1lio 
Ufl~a.tic 

~ eat~Jt:1·e oho-
1 Rll3't•ri o 

tm2.ax1:~r:: · 
paaititif: :i . 

:· :, 

'mlob:k.iertn··· "~~e. ,fJ!Jlgle .fitfune intHtr !i·.·~l~~e~ ,.;;b'is o:t' ortfecent 
4e4,. ~~~Dl•d• rille ua ~J!~I'.l• §.~:tune •;jt~:~L:oater areeoen'ts ar 
hotur~:s:•neoue .. outer rill£. (:F1&•2:.4) : ·.·:'tti..~t~e ring ·wf.th two· 
or p;ae,tit:ol eo- · .( ~~~~-< ¥1«• ·2. 5 ) •. 

. . . \Mpl·a. ;. : ·• .:' .Jf<tf::.·:~~:.:: •' 
~iaxiat:: .. ,:. :: . •tic• · -do- : ;~ --~~p~: ·.evmm:&tri. cd.. ianer 

;t, :,t 

. =~ 

Only :tnttm.$1 ty of ·· ·· · · is)p~t'a ftl.o~ with oilt•r 
1nne~ t"i.tg tn fu · :· ;~Jieenta <ir1~.2.7) 

., ·,' 
:~ 

•·::· 

r.rea'te:l"' thu that ot ; ... ;· :. :· ·· ·, ,., 
. ' " . . ~! !. i, '~. ;· '.::. j ~ J • !. .· 

the l)u;\er r1ntfFig.-2.6·~)i: (:: >:<: .. · 
.. 

-;: ·.1· 
.•/· 

· ~m:d$.t:4\J;l ;r: : · Po:~~ oonie, g8a4<- · 
n:e~tive: :o.~ Jeu ·ottS:PB·t 
irn:i~pi.'c:,, · · bOt!l:oge:n.eoue or 
opt!~)' teo~:ropi.o 
&o't.l:~e:.·.::, .;; .· 

.. 

88!ll.e· •ae ortiury: . 
Dft!lla.tia 

·· :. :. ·;fi~•: :. :~rdiDar-,r neeELtle. 
. : :'; ;; ( i. .· 

• ' ' ,': "., > •• •' 

·' 
'. ·. 

.,, ... 
-~! .:·. J· 

'· :.··t.·' 

!Jl():n,ct •.•••• 

. · . 

VJ 
~ 



'rable 2.1. (CO~l"l••••) 

-------~--------~------------------~------------~-.{... f~l i:ft, f-4\ . . {C) 
...... -- .... - ·--- &'*--- --- ·• :;.;. -·- .... ---- ...... .I..~- ...... --·------ ..... ,_··~:-;...._.·.....,- ...... ---- ..... -- "'il' 

-ac-.. ,'. ·. . 
~~"ti o 'Ob()l.eB- B1Utal · · :: ·• Po.~ :Oo-r.t:Le o~ 
t&ric. · .. <· · · c-.dl3e-~a .~tepa •. 

.·: ': __ .. ·:: .... : 
-do-

~ectic .l Llft!.as:tall¥.: ···.lf41>·~· ~l!lt.o. t• . ·mae.., inn&~!' ~g(e.) '~~~~ itttl.$~ :t.-!titl.«(:el: ~r 

s.•ct1o IJ 

faa ea'ti.o· :P· . 

f:ft~tee.:ti. e I 

1'0811!~:•¥;:;:•> .. O,~~~a~ PO~,._. Ma' ·e~re <t1t't~M o:~~Jf 
.;; ... ;:;,,:;;. ,. ~~~ •. $'bQ}.\-eil' .~ff· ' ' ' ' 

·i:. .. ~~~:( •! an~ ot~:'hr :~~ec­
.\ .;~tt~tt •o~ ttiffil:aee l'iag~ 

. ' ' : $ . . 

..... _ · · · ...... ~p~,. .ho•o-
·-·· · · ·. ·;:;: gGfiO&~e ring. 

··. ;- .: pseudo .... · 
: .: ,i$Otl"O:P1<h· 

1 ,;: • 

. Biax£¢Jt · · :Brok'mt to cal. 
POf.'it1~:~:~/: ·· CJ~>~1.~.lfl acbl.ie­

"' . · ·:~ /.: ·, : .: . r~n\ O%"· bOlJOt'!eJl.e-

;' .' ..• : -)·.;-ju;r ,:._ . o~~. . . . 

~:a~~~+:L:::r:. t :.. OheQ.;~.t•rbQard• 
· · pCi~~·~ ~;: · .. , bl'Olusn tan. or 

; ~- : ~aali,eren, •.. 
. ·~ ' 

'· ,.·,,.I 

fl: '!"' ·:: '• ..-

-d~: .: •do-
.'~:' 

' ' 

::·.;.: 

; 

·V&~me· ~e 5,.· 
,,.~; 

I 

: I •I I 

· ·W.:ttb. .. 'iu'l!'-n m~-x::l. tta • L:br:e ~· 
-~:-.. t. -~!: ::··r;; .· .-: .. · .... ·~ ~ ";, ",1 • • • 

(_.l\if:i:ir-~if!til i?!lner nne 3ttter 
:.~- ~: ~: ':':'W .'; .· .- .·· . . . -· ,.: ·=•~•e.: p"1n1ie a:r• . r··:!· i•' ;·~ r. ·' · 1 

. . · : •~:thr>~~~-~~1. C ?is.. 2 .a ) .• 
:. ; -~ ~--S- t ~--~ ~ ; . 
.· .· ·:~~'.& .•• fl,~·· fml.y lin•a:F 

. :t:hi-tii).\lOl: the lntHU" :$p'l)te. al! 

·· ·11n.r1' _:tniter u~..xiea. ~ila ta •=• 
·_. '~:: N.on-o%-·~bogon&l.( Pte.! •9 ) 

I ; , ~~• 'L~ \I~- 1 

0

' : 

$e.t~• se a:tJ •. Onl.y• ou1;e:r ·.· :: )1;a,~~:· ~~~:. ?.ntt .. o:zw~.eJ- in!ter 
r:tag is Ct)l!lpare't~vel.y . • : .~e'p~t$ er.1 o~• ttha.r.P 
.ltt8ft tiff"r.~:e. : . ·;'k~t~r riP,e ~i tb fo,~ 

· • · :a~tQ.etri:c:U-. i.llpote 

•do-

· ;. '(F:t:~•: . ~-•2 ~~-1. 2 .1o> • 
: ) . . ,. : .. · .;·, ~- il, -~: ·~: ... \ .. _;:~ .j: .... : . 

· ':it:~t:· or_ :2n•!·. or~er inner 
: :.c,'o\ts ~d; t.lu::~;,e .,.~e-tft- ~ 
. 'oe.l: o'uter ~»0'8 (¥i.~·2·2 Q) 

' ' -1.1.~ ;2.1~). 

Co~at~••••• 



'• 

·~&l.bl• 2.1. ( Oont«t •• :.J :' :; : : ; 

-~-- -~--~~~~--~·-----------------~--~-~-------~-111 (!J ) : ·' ' :. f ~'\ ' ' ' ' . ; •' ' ' 14, } ' .(5 ': ; 
.~ ................... ~ .. .J;.. ......... -- ... ~ .......... ..., ~- ........... ~: ~ '.!.. ~ ~ ~ .. .,.,.. ~ ..................... llile.il!l-..,_. .... ~- .... -~ QlliMo ............ -~ ...,...... ...... 

S.eot:le p 

s. e:ct:i 4 3 

r~.•·otio B 

; :· . 1_:- . :·:. ~< ·.;. • - ' 

: ii~·~; '':t:~ner rtng -epJ.tt• Intropl:c · : .!~J.G'tiropi.c •osue 

·:. 

'.· · ...... :-

- -;· 

'• 
·.'• ~ ,..,_ 

... -

~: i 
·: ...... '·' ·.-~:- :-': :<. .(: 

·,: 

1 • ; ; ' . :. . I; ' ~ i 

I 

· e,; m.cu~uc. 

f:fp1~~~+~·y: ·• l!io:Mte.. st•p~ea 

p~~it:t~,e .•... , . drops·• h.of.l:(tfE:~ 
- . ' . . 

neot1·e~. ·. pt~elltf:a-

', ., ' i ,ao.:t'ropl,~ .• ;: .. : . . ·. -·' - ,. ·, .. '· 

) --~· L 

', .. ~@li.eren. 

. -,. .; ,_;. :~: '• 

Un.i&xi~¥ · Moeeic or poeu-
.: '! • 

P.~:B11;1:~itt. 
- : 1~ ~:; 

_-;. :; ·:: .; 
,; 

'\1 ';· 
. ;;· 

: .. 
, ;,_. 

. \ 

~t'ao"tro:P:t~~ ,, 
;. !-~: . . '. ' 

( Pla••l.*") 

..-:~--- ~, . M.-ltlii:IL.il. ,,~v <:vJJ ~·o;;.lllji!Q'JilOJ,.Q• 

ono ~t;.rp inner r!ftg 

l!lltft: one sharp onte:r 

.·nag. 

~ o~ wore aha:rp: k 

ifmer rings e.n.d 

::;up' ... ~~~ ~~ epota in 

; -~!- ·~~~p~xtmat•¥ b~xa-
.- ;~·"\;:·:·:. ;:_: l\. :::· _;. :··:!_ ._:, ;' .... 

. . : :'!gq~~r~, :~~.~uae•~nir 
' ; :':; '~ ;: ' : ;: :· ~; ... ' : .. . . •;: . . . . . 

: t:~1~~~~~ :~412}. 
;_ .T ·~:> ;t; .-;;:. ~~:~~-·;_ · .· 

.: ,~h~~ inner r:i:ng or epote. 
. . ' ' . . . . 

,. e:h~l."P' .o1tt~r l!'ing \'9i. th td:s 
"'•,: .' . . . 

· :: •bxl.ma: JOitt ~a or ·twQ ~1~•--
.!i :i \. > l: . : !'A .· (• o.t ""' 1• ) ;; :"~:~ ~~:~ ...... s;.... :; • 

:~.·· ; 

· 2nd: •. or· mare- order tnn•r 
; . '.'· 

. ··; . . r :: 

"P.o;'t~: ;tm d l!leooacl .o-rder 
.- ·i .··! ::. :. ;, : . 

tb:re• o~ ~ore 1~ha~ io~;t.~r;; :~ote 

ou~er ~~ngB(Fia.2.14). ' ·.~~~tl-t• 
ia h~~e:::n1al 

··,·:;··.\:·-1 . 
·'i' .. ' .· 

:i· 'l' .;;:. 
: :: · .· cont~ ... ·•·• 
,• . 

. , 

,,. _;' ~. 

' ... 

,• ; !.: -~~ ~-:. 

' .. 

~ 
.....j 



'·; ::·. 

: '~ 

~~·tae 2.1; (Conttt: ••• } ;: '.· 
_________ .... __ .. :~ _ ;_· ..::·:w:_t; .. ...; ;;... J.. ___ - - - ~ _ -· __ - _ - _ -i-:i!J.:. '::1,:.:- - - - _. ____ -
(1.) r2> · .... <1> ... · ,.· <4> <=>.l·r·, ... :: 

..., ......................................... -- ... ·~.; ... : .... ·~!- ...... -- illlllfl. .... 1 ................... flllllti• ~ .... ...,. ~ .............. ...., .... ....-, .. ..-·:·•· ... ~ ......... ~ ...................... .. 

S.ect1c G 

e.eot:lo u 

S.eotie o;• 

&~eetio. H• 

P.o~i tlY:e· · · ··· '·' :· '!i!i~i·:t·1t ·'toxturo. 
bi&~~---·:>:,.<: • ,: .. : 

'... . ;',1' 
·.·:: :'',-

'• 

~: :·,::~ ., :> 
'' 

·.,.·;;· 

·:. • ; 'f ~ .. : 

-de-. ···:·:· 
·.~ 

-a~·: -.· ~; 
·I. 

·: '· 

.. 
.. - I 

•do-

' ' ' 

... 

-(~i)~ 

..._do~· 

-do""' 

·~ -· 

~o, or mora .uo.eel,f 

~~4 o~tell!' ~n••• 

(Fig. 2.15), •. 

-ao--

if-ette t\a "tlG 

•-'!o .. 

g~~nt :(Pr Ja-o:re ···:or4•r ....... ;: . ' . 

't~:i~rc '~~a . o·~tel" 
. :-_ .. ;· ::;: ]/,.:.; ... !~·. ::::· . ·::' · .. 

rlne; 

. ·-..::ll)ll,"I•:•~Jot~,.< til.t .ut.e 

; _s~;;~~~:.-, ; : .. 
. . ( '~f~ ae ·~ "~ ~":re 

. -~ _:~.$:\or.1Mt.l ou.tar spota. 
. :.::, ;.· .:~· :;_~ -{- .. :.~ . ,. ~ : 
:·. 'Sttoo:ntt· tnli eQre l!irder· . . . . . ' . -

-i; .·;:'. ·: :::·-) ·;: .. : 

:it6.t:~ei- ·~:n.•di cuter apo'ttt 
,J- ~; ;: :: .t-; ·~ .. ; 

' ....... . 

: .:: ;{ ~1~' ~ike SI ) • 

' -~.c:l......... ., ""' !f.!! I 0¥~l'' •· 
';IO·'~'"':~i { .... .j.;O•. u, G. ":.00 .,. 

QO:l\"G; ·di ~:to-r~6Jl cyUitGr 
;" ~: . I ; 

·:~-t~. 

,'. ............................................. 
-~~-------~--------- ~~ ~-~-~ --~·~ ~·~ ·~ ~ -~ ............. ~ __... .... . 

,.· ~ 
O'J 



~) l~) 

·.,2.41.~ apb of ordinary neaLU,c( 0l 
\Q)tlho{os-ro...~h o~ L~oh-op\c. Uq_.u..id r-ho.~e."l.: 

~ ( ) 



40 

Of aaect:J.e C 



41 

. . 



42 

"1>3 
P!.g. 2 . 13 AlJig:ned photograph of Smectie B phase. 

Fiq. 
"l. 

photograt:'b of Smeetic E pha.s 

Fiig. 2 . 15 Powder IbotograPl of Smectic G t:'ba e"L; 



---· '; 

" ... -,,-·- 4·3 

. ·..,_ ' 
.• J , ~, -· . r • 

It :b!HJ el.rea.dy :beEUJ" stated that thtt:, 'nematic ~iquid 

cry;. tala diff~r 'fro~ ·;e;tro~it'o ·l:i'qui(l 1>y:' 'at~.ortg range • 
• ': f 

orientational. order of tbe.J.orig _ec"xl.~e of th~l rod- l.ike_ 

mo~eci~es. ~be nema.~1t.f pha~e -~~e $. "l;I)Vter symfu~tl"y than· 
. .: ; . 

the high temperz~tu.re teotrop:l.o 'l.iquid. :we e~~~eas thi~·· 
.. ·. ~ .•·, . 

quali t&tively by sa;i11g 't~at--the nematic· pbhse'· is taor.e 
. - ~. . . . 

. ·, ··. 

define· e,n order nal"arn~ter \'r,bi eh is non- £,ero in· the nemat;.,c-
.... • . ·! • • 

tioriu pptentieJ. ener\~Y ot .a:·mol.ecule in. i>h~ nematio 
'• . --- ; '".. . -

.·. _liquid. can be i\ltp':r~rised: ·:i.ti torms of thie. ·o!"·d~r parameter. 
. . - ' -- ~ 

Such en expre~sion is given:. in ·the mean f'f~ld :tilJ~eory of 
... 

. - ·~· ~ 

e~16ne for the .orien:tn~ions{ 1noleeu.1a.r dfr;:'t'fi.bu~ion funo-

tio[i :are der:tved and' the_ the1't.'nodynemia tun·c_t_~pns simply 

oaloUlated~ 'Jhs- ohar~cter o:t '-the traru:~:foma:tion froui. . ~ . . . ' . ' . ' . . ' ' 

~·'. 

. . 

2.2.2.: order parameter: 

In :nemat:i.os_ tlle ~eng ipte!l of 'the mol.'eetuen . i,!o nave 
a pref'ert•ed.·, cltlrectio.n · oi" :o-rien tat.ion ceiled the t1irootQ,t- · 

' • • • 0 r'• ' • ' . :-

· n • Assuming .the· mol.ec~~~ ~s rigi<l l"O<l~', the or!en-
. . ' . . 

'ta,tion of a pe.rt16u.lar mol~ouJ.e. -rd. th ree:pect to the .diree-
' . -4 .tor · n 

.·,··-

,.-.,. 



''. "· 

... ,' :· 

. - . . 
·::: ·, 

. •.:" 

.~~ .... 
~. ~~ -- _, :, . ; . { 

~: __ •:: ·.-;._;,~~- 44 
~-· -:-;:.:-: .. ' 

,_ ~-

.' .. ' -· i/~:-:·.:-·~:_}~_::~-:-.·_,::.;_,_. ·_ _;~~-~_:" .-. <~.. -
; ~ .' 
i' . ~- . 

' ·' -...:~~- -- -~_:.f~- .. 

defined by·- three·_J.~uJ.erian •hr.J;e~::"·;e~-:. , · cp; ·_ ·$n:cf _·'l-·_ (F,tg.2_.-1~). · .: 
. ·,-_- ._"' . 

Due. to th~~mu ~nergy ,tb;,.::in~ivi~tmal.' m()l.~.fltile:~ ·or: ~mnll .. • 
ewo~p ·-~t-_ m"l.e-~u.les·:~fl.udt~;~ ~,liut. tb~: ~ir~~to~--may ~e ta~o~ .. 

' . - ' -- -__ :" ~ . .. - - '. ' -. - .. - . 

ns ·the rJost · '!'>r~bable' 'direction. lt: "is- men~ti'oh~d earlier · :---_. ·: 
.- . • .. : - . ·~ .. · - , · .. -~ ._: :.· :: " .. < __ < ...J, :<. . ·. :._ ,: ::·> ·• . •· " . . .... 
that tb.e dir&<::rtor , '·-n . ·. · __ a~d ,_:-_ ~ · are eqtti::V~ent an~·: the.·· . 

moJ.eoW.:e.m. are· _cy;l.indr.iqei~,y· aymm.etric •. Jl~t; tn: :praetioe·: nan~ 
of .. the: ~\bo'~c' ·;c.mnwpti.oz:_~:.:a.~~-r~:~;iotly_· v~;J}ilt;~; •. ~_._ the -~oJ.~·-··." 

.. ~- ·:· ; 

· cule~ t!re f'l.exib~e. t•~ nQw~·.,·~~-t~ntl '''there ~r$~ _e~ti'eis vih~r&-

the bee.d(.A erit? tail~ ar,~ ~14'~ti_t~tfUis~~lble48'_ atid the mol~. 
C~tlt:J. a;re. more ~~th lik~~:·th~~~· oyiii.Jld~i OB~~S'.; nowever·, . 'th~ ._, 

de~if:,tio~;-~~.;- f~~W _:the_ .. idea.li~~d· -~~St} in ~mall a.~ld the .mo~e~ . 

-< {J ~) .. ~~: Jj'L .:t>-i.-;::_· f~d.~'l~-- >,~;·\)' 
.. 

·•.· -::-

,;:,. »- ••• 

•.• ·~ (2.f) 
·" ·' ~ . . -. . . . 

Th.e r:ivera.g&~ ·i~:~ tnken:~ .'ove~<a:t:l•:,t)le_·~ moieculo~~:· Th(t ezpresn:io'n 
' :: 

WtJ ·nave obo~en f_or orde'r p'.uraht_eter j_fji S€H!CJlHl order Legendre 

·. polyn~mial~ F;r 9. pe~f~/~tiJ/'-:~-rdere(t_,·~ampl~·: al~ ~ = o and 
- . . . . . -~ . . ' . . -. , 



~- . ' 

:. ,,_ 

~-- . . . ' 

~:- _: . .•." ' 

. . . .. . 

~- c.6 ~'l-e--> :a_ 1 oo that· = 1" ; .\-Jt;~u."ean when all. 

·the 
' ., •':':. •,.· 

moleeul.ee .e.re .rs.ndoml.y orien-:te~. ( 14.-e;-._,._isotro-pio _iiquidl· 

<c.os'--s '> ·=:'/:!>·and· _<(P'l- >- _ =- o .• :In the,-#:ein:atiQ phil.~~ it 
- --. ~. . . . ~ .: ·: .. -~-· ,~._ .. ~--~'- . 

· baa e.n. intermcdia.t~ v.W.u.e wh~cb dt!creaeee w~th' tampet·stui•e 
':· ~. . . ·' ".. . .: .. .. 

'. ' • ·- ":t' ., .. . 

. and. drop abruptly. to ~~ro· a.t t_hf# _nema.ti.e te<)tropfo poitit _ 

.Mol.~oUlar mean· Field tneil.r.Y ··of J{et:.l~~i9 ():r~t$te.la: 
: .¥'." 

. :.. . . 
. ' . . 

· · An appron:Gh :th~.t h:.ts ;Pl:'OV~tl to ~e. ;~;tl'"emely u~e-
. , . ·. . .. I , . . . ·. . .,, •: ', . . . . 

tul. :1.11 deve.lc-pin_g a. th~~orsr., o:f' fl:,Pol.1't.:"lll$_ou.s<·~~!lg ·rang_a Qrien ... · 

ta t.ion~..l orde.r end ther · re.lated __ . :proper:tieo -o;£ . 'the n.emf! t1 o 

bou:r!!!. Th~ firr:rt moleQ~n.r ;fieJ.:a theo~y. c;t:_:tl;t~e ne;t\tic· 

state was propoeed irL_:1916--J~y:•_ll~-~-50~, ~:h~j:)'g:~,~t~d_ t~o 
' ... .. 

',·;.-··, .. 

: domoristra.ted the pott~1-b1l;l. ty<ot a. t'rlfrm~d.ti'ob: t~ro~ an . _ 
- j - • . • • • • • ' • - ·' ··.-:. :~- -~ '.· ··;: • -

. . " . ~·~~ 

i~otrop~c pha_ae ·to .~isotrop.i.o. $l'le .-aa. the -~:eblp~rltt_u:e~ is 
·.· . ··: ::_,.. ·.~ . .'" . 

lowered. 2hon~sh thtn -~es\ll,t ia ·1mpor~.nt. q;u~itatively 

'- -

now< W'ell .eot~blif)h-ed that- parra.an~.nt -,dipole m!)_menta. -arc not 
. " . - .. ~ ~ . 

phase. £·10rl14_ovtir, _ 'th$. theory predi ete t!te.t ·th~ ._aligned 

phase ~houi.d: be ferroelect;M:o, ·which_ doe~ ]l~~t. ~ppear to be 
. ,_- .:: .. _·: .. '-; 

.. 



·the caee ·even when ·th~ moleollles are Dolar· •... !he most \"iidely -- . : ... ~ ·. . 
: ..:- '( 

·_ . . ·:: "·;~ ~- ' .. 

( 1) the moleoul.es: it1teract through· an· attra:r!t:ive orients-

tion dependent van tlor Waals iJ:!to~otion ti:t} .. the orien-· 
.'.: -~ : . ~ 

tation dependent int_eraot;ion d.oeo t1ot e.ff_eO:'t :the ~onf'j_glh­

. rntiQb of the· CtlUtrt.l ·cff me8.Ea ot' the mo.}.Gt)'~~~-~ :~nd. : 
. . . . 

(iii) tht:J· molectues ~!'re i-1~13-Umed. 'to be ~.n an' annrOYif!.ltQ;te . . .. -.-· ....... -- . 

. . . 

3~:ntFJrmolecula.):" ·short .re.ngfi ordt-lr and. ~tluot;(~.e.tion er'fects 

.~.;;;-.,,;:r~ ~ 

che!l.l to~~~\;!_ the 

J""ttLe. f,:\ .. h ·~ ~f'!.' .. ·h~.:~·~ct· . .,..2 .: '"'l'n. <R+o•t 
~ '""!io<...,. r:; "-n ~. .ut .. ....-c, .· :~:"'·}~;- . • '"., o .,e>;"'" 

.·._ j. ::.~-.-: ·:· :' 

·. · . with ~:t comp~eteJ.y g:ft~te:r~ pa;tn•ise int~erin~.l.e:euta.r i~te--

.:-. :·· 

·. ·:.; .· . 
. ';'! ,.,. •' ,. 

l"<lt}tion potentia~ •• ~ .. fter expand:!.tl(t in fi B}~~;t~}~! .of a .. !'})rO"!" 

. priat.e .oph:erical. hnrtn~mion· we w:Lll .rt;ffit.ema~t1.';ea;tly nverage 
... ,.· .:: : < . 

·the· pz;dr-inter~oti.on poteniliu to obtain· .~·· . .g:eneraliaed 
:_ .-.:; .·. ;~,-;';. -:. 

vo~el.en of ·the s~n{~e· moJ.eo~a !>ottm'tiel ~fu .. 'lcti~r.t in the 
. •;; ... ; ;: : 

._: ~: ... ,:. ... :: .. 

. ' .. . ~ 

genera~i f}ecJ poten·ti~. Uany:··coordtn~tes a:re requirr::d .to 
~ . ' . . . . . 

devori be the orientat_i.on ce:pende:n1:: i:tttcraoti?)n· be:tw~en a 
rn· ... , ,:, ''"' •,'_ .. 

_l}eir lli aeymetrio molecu~ee .. 'Fi.e. ?..;.1.7(e,) (tepi:cte the 
. . /\; 



- .. : 

·- .,_ .'·.· 

- :, ~ .: . 
' . . . . ' 

ei "tun.tion• · S;lnce· there_ appearo- to· be· no o~~~~ng ~t- the 
-. ~ .. 

tnol.eoul.eo about their: long axes the .. :bl~e~o.}.e~olJ).m.r pai~ 
is. a riulc~ton bf · f:lv~. coo·~·dthhtee5 ;:. 

'\/l'l. -:::. "l'l- ("6'1 1 e \ ; 'cp ·,· 1: ·~ 'L·I ¢ '1-) 
··. ' 

- . ... . 
,-. ·,· 

pair potentia~ as . 
'.•,- ·• 

- 4TI I u~~\--~-~ l"<'),_:;'1L,~ L~_l ,~i) '/:2~<~~,~~r 
· • L 1 L~ \'A 

.-_ ,'_ 

,; f 
.·I ·' . : .. -

where 'IL.W\ (;e ,.Ct>) are the -~~:nuil.-.barmor.d" en. Th·e: :Y-pre~~ion 

. - ' .'~ --~ . \ 

rlintm1ee oud orien-tn:tibn. dejiemdehi.:m :nt tho:. :po:.t£ln_t:tal 

- . ,.....-{;"" .. , 

.e.re' fauru.l'::> to deere::-t£.~e rap.itl~y w;tth :t.nc:tea·n~.ll€t L 1 ~o. L1. .. 
.. . ' - : . :.-- . . 

.Pu,r·ther, term a onJ.y. with even-0111 aiid L?. a_r~. ~~Q.t1i rei!" 
. .. . . . ----) . ~ . . ..... .. 

ai.uce n · .. and - n · ara .equ_ivucnt. . .. 
... . . - . -· -~ 

· ln or(:\ er to .(ler:i. ve ~ m een: t:t e~ d approxima. tiot-,. to 

the paton titi.l.. v12· haa. to be ex;pl"ees~d in· :t,irf~e. of a 
' . -4 

po~a.r · eoor(Unato ·sy$tem · barH:~d oh tbe. di:i:•ecrto·r; n ·. aa 

· . the pol.ar axis • :l1he coordinate· axes·· of the ~blecul.ee 

ttJust .be rotated: fr~rn th~t' ::~_i1o\•m. i~ Pig. 2·' •. '11{:aJ to that. 

sho\\'n ·in Fig. 2.1'"/ (o). The: primed:e-ngl.es tl~~~- ~eser:fbeC 
·.'= 

. -~ :-

I ._•, • 



-, ~-

48 

n z 

y 

FIG. 2.·1((; 

I 

..\ Q..O:. eM. 'o e.. tl,..t.. etY\ R.M. 'r ()...\-\, CI"'\A. t1- 1),. w...e.L.a.. ll..M. \e. 

\N. \'\.~ IM.o.J..;. c. lA. ot_IA.\ cl • 

I 

( a ) 

' s~ 
/(~ 

't',~ 
I I 

r 

( b ) 

/ I 
921 
~, 'f/ 

\ \.!;:j 2 

\ I 

\ 

FIG. '2· IT-

o\el)eM,.IoQ. ~ ~tiA..~IMA. ~.U"-. ~ M~w..-..e...mc:.. 

-.......o~t..AA..\IU\ •• ~) 'rW- ~~4Nt...t>\.a.~o..l\.... "tfl..~ ~ t\...c-

\M.o"" \-~ \ ~" \ IV\.. c,.,.,o\ s ~ l ~ ) ~ cU,....,..Q...cko'T ,.;t 
. 
"' 



·, .:_: 

- - '· ~- · .. -: . 

. . ' . 

. ;,nto·--the _-ff.):mn ·_ .· -

.. -,. 

-· .. 

'· .-

- '-. :.\'_, 

. :.~ ' : . 

'.49 

(- . 
,2.4) 

~t'l " 411 I. uL, ~vvi l'<' ): Y L; \' (a'.,~·,) 'f 4;~ ( &~ '<\>~ ) . 
l, \..~ \"(\ ' . . -~ ' . . . .. • ' . : k. ' ·--~(- .>. : .... 

Ci,.pw{'~:·)~_l-·:~<t~-- _) ·:_:;-
... 

. .. -

'· 

~.rom. t!Ji s pa:i:rw:tee . ~~jterruo_i$~Ui~r pa.telf.tfai ·:the poeudopo- . 
. • - , .... 

tential. can 1la obtf11ned :or ·:tS:kin6 :t}}re.~ ·nnc_c~eB.i.ve f!l.V.e~ 
~ _. '· 

_---~ages _~f--. "V12: _·. (-1_)_ av·ar~~e ~ver -~:J.•. Orl.On~~~:_~ipnn· o't .the 

1ntez-moleeu.l.ar vectoi- . :'fl ___ ~-(ii) av:~rage_,:o\1-,~~ NJ..l.- qrien.: 
<:: - •' ·_. :;,. .::_· .. - -- '-. :..· '-;.:~- .. ·(.~ .... . -.. _. 

tnti;ont,-· of tee moleetile 2j_ ·(iii)~averalto_(}ve;r.al.J. values 

. -· .· 

. - .· ... \ ~-.: , . 

(<.<",~))) .,. t (Uwl..""t")) ~Lc~~s~)(rL> .. 
: . ·,: .·. · ", _· · L.M .·· .. -· ;:'· ·- ·. '· .:· . >t:: .:· • ·-. {2.6) 

: ',,: ': 

0 

.> 

0 
0 

'- A 0 ': •', 

0 

O • : 0 A o,' <,'· 
0

, 0 
0 

-

· v!ne:re ·. ~ ~; $ -: are -the :Ltlt. : o_~~~r- L~ge~d:('e_ · p,()l;~oruiaJ.~ •. 
' -

. . . ·. • -~ l - . - . - ' - -: . . . . . -- . .. . . . . 

· Thi_s ie the .. d~E:trad ·~ingle...,~o~acuJ.e. _pote-n:ti~l' in- tlltlf.m · 
.,.. . ... -

.. •'!.. --~ . )'.....__·; 

. ·:ei~lcl hppt.>_oxim~ iii on·~--- we w,:i-ti) -_it:~~ > --~ 
--,.:-. - ' . ~: 
.. 

. ~ .-
~ . '" : ·-
_.' . ~-

. ~"' · t-t.o ~· s j = 'L · u~ ·_< p-~-~7 · \'~-- ~~_s_e,~f· .... : . 
. . : . . . . '- .. ·- ·--~- •. _· >:·· ;> .. ·. , .. · .-~ .· .. · 

· •.: - U L: ~.:;-L :'-~ (-~.:L. ~ \M\~j("\1;>;_ - .. , 
.. ~ .. ,:\''<·- -

•• ~- • J 



,·· ·' .. 
- -· ,. 

- ........ - :_--, . :<. 

-:· ___ :;<_ ~-' 
.... 

.. . ~· .. 

.. :, .. -

'' 

Now i't :La mentione•f earJ.;ier ·::that ]~• s ·:-~noti&.t:l he.ve Q~ly e'\fen . 
. --. . -' >-· .. . ~ ,. ' .. 

. . , 'val:u.ti and ~ina~ L =·(~ i~···mei$ly an ~t!:,\i tl~:e; :0bn.£Jtnnt' 

eqn.. (2.7) o~xi ·be writte~ ~:~-·:{~· 
:.; .· 

,~ . 

. <.:. 
' •' ' -~~ 

·:· i·:·.,".: .. ·. 

" 

" •(Mll' ~\ 
-.. t:. •v 1 

sym~ftr\lry· o:f' 'the d~~trilnxt!on: 1:unc'tian for the' o:rie~ta-' ·. . - . .· ' .. ' . - ' . . . . . 

... ; :··_:. . ·. --~· :-·· 

wotil.d alno ~in~ear :t,n the-:_.a5o~1g.le mol~eule Z@Q~t.e.ttti~ · v1• If · 

·onl.y 'the firet ·term i~ 'eqrl•:-Y2;e Lis re~~~~l.~d .. \o/e .. Qbtain 

the mean · f5.e~d theol?Y ·at ·r;;I~~r l?.ttH\ f1aupe,· _Rin-o~ the .Qrigi-. . . . - . - •:. . . . ~ 

:.· •• ' ,:, -j 

nal ~xpansion. on wb1 r>h v 1 1a:· ·b~sed (~qn;. if~:))· o;;mve~ge~ 
' ' . •' - . . . . .. ,.. . ' . 

• .... rapidly. r~t~nti~n: of onl.y the . .' ti~gt term in V1 tihO~d . 

pro-vide n good approxi~atiofi·.--t(). tita theory.~ !'lotfipa:ri~Qn 
4 • ' ' r ,'. • - ,· • • '< _, ' • ,' -:·, >, ", -' <" • -. ·. . .. -~· ::: .. r .. ;~~ 

wit~~ exlH:ri:mnnt sho.w~ thcc:tt ttil.e .'ig l.ndead. the; ~a.ee., a{l.di• - ,· ' ,." ' 

:tio.n ·of the hilsher ~r<ler teras ~Will. <9:t_;· co\ir~e ~~sul t in a 

.·.bette~ Etgreemt¥i1t57•53 • t!ut·n~~ti;;~ .:~~~).'ue:fj: .Pi. .< P 4- ). 

.·.ft.J~ld .. in. ·some· ~n·ses5~t~~9 ,· ehn~•o':t~-~~:p~ed:t.d.t'e;d: e.ven ,if . 

. the. high~r. order term is ·inci.ltt(lEtd'':i.ri'·'.the mearl ti'e~d 
. . . . ~ -~--<·-. ·~-. ·, :. _-. ~--_·_ .. · .:- . ~ _ .. ~ ·;: -T~.:~_ .. -

p{)tan tial •. · .__ .. 
. ... 

'.· ... 

·, 



51 

di.~tri but.ion function which _if.! the probnbili ty of finding 
~ 
VI . then 

it onn expreesetl in t.erm a 6'£ 

-I - ·~ 

I 

il' 
1 

o.Mcl 7..,- _ ~ 1::__xf' \.::_-~'1 1 Leos{-)) J c\ (lOS.C7) 

0 

{ 2.10) 

Binoo both v 1 and are even tu:nctionso:f cose 

the in te~~r~.tion i.a limj. ted w~ thin 0 and. 1 • Bq, ¥'!·( 2.10) 

i e not yet useful. 1~1 comptrt:l.ng average val.'l.~f.l!f.l since V 1 
con tnin~ unknovm averages ( 'P 1-- > 

1\row rdnce <. P\_ > io the avarag@. value of Lth. 

order Legendre Po~yr1,omial. we can write* 

P ~ (.COS 0 ) ~ 1 ( C.D S 0 )' ct ( C.O S 0 ) _ 

(2.11) 



52 

which is a f!l€1~~-con~iatent equati~n ·for the determin$,tion 

of the tempe;rt:2. ture depentl.ence of t:__ P ~...) • The t1limul tan eo us 

Golu.tion of aquntio!HJ (2.8) end (2.11 ), by ut~ing a eor.2putt:~r, 

y,ie~cls tbe tempert'{.tur~ dep~nd.enoe ot all the z f'~_ >' s 

originel~y :tnol.uded in the potential v1 • !n parti cul~r. 

c1ence of the order para.metel:, of the tlf;wa~ie D.ha.£e. 

Of all tho pom:ei bJ.~. so~u.tiona the on.e which. 

f'!atit?f'.ies tho theraH)dyna:mio c-ond:i.tion o:( minim1;,m. free 

energy \Vill gj.ve the ;phyeicm.lly o-btilerve<t $tab~e ph~;u:;e. 

~lor this we C.Ol'H?i der. the Heljtnho~ t0 free energy ~ :::1 :E - ?S 

where E ia the internu eners:,v ntid fi the entropy ttough 

the Uib'rjo free OJ.lertrs ahou.ld be C<lrH~ideretl in. Btrict s~nse 

as ~oat of tlH~ e)tpr.lrimen.tal ment1-ureta€,:n ts on ~rde:l" p~~ama-' . . 

t~rs are done untl-er oondi·t.:ton of aon~tant preGt:ure :rat~1er 

than at con~d.tant volume. For a sy~t~m of N r.~:o~00\.tlee: we 
~., 

. h&ve ~xpr~:;:r;ione:; 

. ~ - . 

-,::- H/T /_UL(.PL)+N\~:l"".1-
L 

(2.14). 
\_ 

The eondi tion of r~i}'linu.m free fmer~y i.e. (or/'{) ( rL >)T) f,_.,. o 

regains tbe requi:r..eo r;se:L~ conBi.etenoy equation ( 2.11 ) . 



-
·'t 

53 

Purtharmore_ testing_ aqna. (2.12) and (2.14) we nee that 
! 

univeraal. function of T/T:ru• But experiroente~ yti.lues aro 

. found to differ_ rrlight~y60 • 61 f'rom the predict~d v~luer:. 

It nmy be noted hel."e tha_t tTL whi oh dster~;inen the 

~trength of in.telouto~ecular poten·tia~ defJC'..nd.t'i :on the molar 

vo~ume V via intermoJ..ecula.r aepttra.t:ion and this mu.at 

ahange with tem:pe~a.ture. 

Whil.e elucidating the neture of in·termo.leoula.r 

:iora(ts in nem~tica Ma.if:"r an,d sa.upe Eu~;:;;umed .~het't this wan 
. . 

mainly due to Lond.on di.mpertJion forces (i!t~. induced 

t:1ipolefihduced dipole) whiQi';r ¥!$.&:1 depand.ent on: tho intor­

moleotU.ar' eepara:tiott as "0- t • So V 1 should dep~nd 

on V*- 2 • Cotter62 he.~ :?Jhm•m 'tha:t for the t.'l:eory to h~t.ve 
ntat:tatical ttH!ohanioal OOf.!f~ietenoy. i~he J.>otentia.l.. ~'f.tu:d; 

theory. Ho we shall be e.b~e to test the !Jr<ed:tetiono o! 
r 

:as theol"Y wi.th the experimental valuea of . t__ P'L) at 

oonstant preeeure. 

being an ~djuatable perameia:~:r. · :?orce .fi ttj.ng the ~xperi­

r.Jental param~tero, howe,r·el .. , yie~ded :val.u.e:tJ o_f "'( ac 10 

in oome cane66 :3 whieh are t'H~ither themocyn.amicnl.ly eal.:f 

consistent (v-1 depend.ence) rtor con£nl.etent to di.spe:raion 



I ' ~ " ' 51 

nen t dipoJ..e ... permanent dipole force~ •. indu,t;J_ed_ dipole­

inrlu.eed quadrupo~e part of the tli~~IHl~roion f'orcetF. In vi.ew 

ot these ambiguj_ ti~e regarding a knowledge o:t· vo~u.tne depen­

denca. it i:!, however_. pref~rab~e to treat the eo off! e:i. ~n ta 

of V1 in. cqn. (;,~.8) a.~ ilHlepe:!.'H1en.t of Vo~-um-e' and to rest­

ri.at the fitting Qf the theory to Gxper1mf1i'rt to a narrow 

r~.ng~ o:f taG-:tperature. Finally tlif:t'e:rent forms of vo~uma 

dependence mny be lnol.uded. 

""4 However, according to Luclrhur~t0 th.Q ~ong WQ.Ve-

~ength orientations~ ·f~uctu~tion~ :i.n the rn-ec1l.uoo diminish 

effective ord.~r parameter. IJ.1he a.~::mmption that the mole­

cul.e ia a. rigid .rod is e.l-so an overairuplifioa:tion and a 

rettliatic calculation haa been made by Ma_ro~lja65 taking 

the eontr:i.bution of ;f.lexi bJ.e f'..nd chain pnrt in the order­

ing prooEu~e which accotm'tG f<H' the al tarnation in the 

transition tempe:re.t.ureth the order !>a.rameter ~nd other 

re~ated properties of the 4\!UeOf.H!H;li ve members of a homo­

~Og(')us series. Recent theorcti cal wo::t:<k ·by Luakhurat66 , 

however, ~hows the. effect of' the flexi bilj, ty of' mol.e­

eules on order p~ram~ter is on~y «FK~ marginal. 

Order pa.rame'tera of flifforent met;ophaees ( .$pe­

cial~y for nema.ti cs) have be-en detf&l'minc by tnany workers 

etn!JJ.Oying VE.U"ioua e](p<a'irim.emtol 't$Obl'~it1U®:9 V;:L~ • die.~ngneti a 

t:J.n:1t~otropy67, · optiaa~ anifiiot;opy67 ,Ga, magnetic res!)nanoe 

apeetroeco1>Y69 , Ramen sa~l. ttering70 • 71 • inf~(~r~d a:pectroe-



55 

71 . . 70 .. . 7? 
copy , UY ~.nd vini bJ.e SlH~ctroeoopy ", Motmb~uer ep()otroecopy t;;., 

l'!leutron ocattaring72 , positron anhila.tion.72,, d:i.el.eotr.i.o ~xm: 

emieo.tro.py72 , Guest-host irit~raction 7;>. 74, X-ra.y d:U!fracti~ri 
-. - -: 

etc. Comparison e.i _these resul tl! wi tb Maier-:Gfl.upe- ,theory has 

b ' .c-l b .<l• · :~ 'k 0 ith7'5 m• .~:~ t .:1 . f ..,."1:'1 th rl.CJ. y ~en !.UGOUf!~.!tet .. vy oJoiD ·. .· ., rne .,.,e, e .. l..s 0 . e.....r.. • · e 

experit'3on·taJ. teabniquee a1 .. e reviewed by tliff:erent t-mr1c;ere72., 

ln this dj,,m'3erta.tion we aha.ll. d.l.scusf~ in su:'bsE::ftuent r~eotion 

only the X-ra.y diffraction technique. 

tlle discovery of X-ray (liffre.ction. Lota of 'aiu,~.ies mad.e 
. . 7~ P1 

in thia area hn.ve been reviewed in references '-·-·~ and the 

detail th(~or~tica.l conniderations 11tre given .by Vo.inshtein82 
Q. . . 

t:tnd Luckbu~Bt"" ;J. General:Ly, nema ti o liq<.li d cry ntal :;'ample a 

,, but 

there is no pre:t'erred dirEH~t~.on for the SJHH~imen as a 
v1hole. So tn~ X-ray diffraction pattern haB a. ·eyr:m;otl":'y of 

revolution around the dire·ation of the X-ray beam an -ie 

evitlent. from the. :?t ·unif'orm haLo just like, that or an i.so-

the opec;tmen 

oriented by some menno eret there·fore, needefl to spec:tf'y the 

state of orrlering. 1"or r:mm:ples oriented :per.pa;mflict.Ut:l:r to the. 



56 

ineident J:;..zoay the d:tfitu~e main ring (ha~o}: :sp~i t~ into two 

cre~Soents symmetr:tea~ a·be1ut tho. origin. The a:~ he:Lo or the 

ertH~eenta appemr d.ne to inte:rmoleoulttr scattering. !h~ . . 
intenei ty maxime of the ere,f.n:.'!tmts lie iu ·thfl. e_quator1al 

meotion ·i.e • perpendicular tO' the opti G e.ii:$- fdireotor) • 

8ome oth$:r ring$ e.rt';' al~o ebEerved .. i.n the: m~ridiotl~l 

~ee:tion (parallelS}_) to· the director) which a:re due t~ int.ra­

molecular aoa:tte~ing. :¥-'rom the (li ~tri butio~t- :o_:f' in teni:!!i ty 

in the equatox-ial p:te.ne o'f tne dift'ra.otion pat-tern (of 

orijf'J~l ted eampie) J one e~n obtain tb$ a toJJi.c cyJ.indri cal 
', - ~ 

di~tl"ibution ft.mctio:t:h giving the probeb_:ili';t,r of finding 

two mtom~ at e. part:i. eul.~u:~ di,~tanca, the atQms: may, however, 

belong to ~eitme or di:f:f'erufit ~ol.eeu:Lee. M'or_~over~. a. C¢ord1ng 

tQ C.~h:tBtyeJ!;o·v60 ,. ti:\.t} metho.d involv6~ an integrttti.ii>n over 
. . . . .. 

the sca.t:t;ering veotor from ser-o to i:o;fini t.r: which oon never 

- - / 

ca.t!'l era. • the plate bein~-s _no:rwu to the .X-~Y beam. Oaleu.-

l&tion of eylindri~..l dii¥Jiribution functi.o~:r: ·and order 

p~ra.mete:rs from x-ray. di:f.':Crm.ction works hll\e l.~t.er b$tin 

done by de Vriee84 ·•.rhil~J .oriente.tione.l. di·t~t~i:bU.tion 
· · b~e-n · · . . . '. · . 

function and Qrd~r p~rtu·n_eters lu.~~:ve ~celculate(1. by varioUfl 

workere85-9o. 
' . ' I ' 



57 

Orienta tional dietri butiQn :functions and. 

oyl~.ndriffllt....lly f:!Ymt.'let:r.l o molellu.leff ~~~t\ be stttJ~i eientl.y 

n£H~eri f)f..Hl by e. d:!. r1tri bution ·.f'u.n (di;i.on f ( ~) ·.· . 'depending 

only on th(! firngla b~tween tbe mol.eeul.sn:• symt}rt'?!try a~ifj 

'!. ;lj • .... . t -88 ~~ . ..:2 • • • "l' ~ and t,j {~ ~"'·rae or a.~ men t>:!,on(:h,,r. l.!'l ~eot:ton 2 .?. .. . 1• .. .. ,..ray 

<1:i.!frect1on phoi;~is:ra.phn .reu:t1I"dC' intenai ties· n.:verP.ge~l Qver 

a rel..atively lone ·M.me nnd over ~ t:n:r,i.c:t•ot5c.:op;t'o. ~teltUlH~, ~o 

rodf.!i j_n e uninXif-'"l pha5e ar~ therefore~ t.1'1i!fined atilt 

r liJ'L H~) · 
j '?~,.. (_t<)S~}" S\"f\~ c\ ~~ 

0 

oricmta.tionul· ilintz•ibu·t.:tbn function ~ l(!>) , LeHdhetter 
....... , 

nn·d ~iorri:i::1 ae.numed thnt the" rit!.itJ r~r.1 like roo~eoul.~e 

r.rwJ.~ou:t.es ( .f:, · 10 ) ant:l o·rrt~ined 

Tl/'2._ 

It+) - e. I 1J (~) sif* [J~~­
. ~~-: '\\( 

(2.16) 



5.3 

/ 

Fig.. 2'o.L8 Schematic. represer:i:a t_ inn ·' :-'" the 

)~ray diffraction photograph oF ,=,r C:)J_-ter,::,~c1 

Iiqu.ir'l Cr'.[St.al. 



59 

ra the:r than the true siZ-1(~1 at tU. s·&ri 1:)u.tion f<in.ot::!.on ~ ( ~) • 

~i'baj" haV6 a~~o o.rH1UiiHH:l 'l:;;~w.t for ~ perf e.o·tl.;y ~~ign€'iHi 

aample t. fo.( \.) ) -= b ( (?) · J 'the .1:;ea ttnring i a iOero e:toe.pt. 

for the direotiora~ of~ the scattering vec·to:r pe:rpen(1icul.o.r. 

·to .. r.:lu.eter a:r-ia. 'lh(fJY'' nave however, ca.J.mi.l.~.d;ed ·the effeets 

and f'wund ·that ·the (l~via.ticyn in ~tnal.l excfJpt for hj.gf>~y 

ordered ph~1see. l <:_ p ')_ ) ~ o · 1S ) • Ji~areovcel'" • ()Ofl'HH~tl"i~g 

the VEU.uea oi Jc,t ~~) with t ( (J) t;>£ the e&.me t:ample 

obtained by oth<tr meth.od~ they ~howed tha~ Lt ( ~) 

ra:ation plto·toe~rP..pb£i Wi.l~ 'Qe def&arj.'bed il'l se¢t:ions ::?.;4.1 

and 2.4.~. :Po:r:· ~;.,a:tua.t!~fl th~ ir.tegrt~~n in e'lr;~l2.15J and 

2.16 sngul.ar aoanning :for one quad.:rant ( '\".~ o. \-o 't-~ fiJ')_) 

i.a su:t£ic1ent. w~ have. however, or:J.ou.la·t.ed 5 ( f=>) and . 

order pl;l!.ratnf~·ters val.tl~s f;:>? aeu::h of'. the. que.d.ran tn ~epa­

rat~J..y and ·then tool! "tht: av~rege. At the .snm~ i;ime Willi 

< ~ 2 ) and 



60 
. . ~ .: . 

~nrl intensity <tiBtrtbation ftmotio.n ean be expf:lndt'Hl at:! tt 

poW~:t* $~r1e~ 011.ly Wi tb GVert t~~~l~7.,9'0 • :i'\hetr~:f~:l'$1 W~ 
write :. :· ·: ; .. 

"'(> 

ll'\') - 'L' 0.. 'l"n 
'"l."h 

'\" l.CS. 
')'\: 0 

. ,· . 
':(2.11) 

...,. 
·- l.'r\ 

\ t~) - t ·bl~· cos. r3t;' 
. '. '·, 

'h "I) <2~1a) 

Bqn. ,.A2.16 }- ifl roodi:f~ .. er.l;·by~ at{~st1 t.ut;ing . s\Y\ o< -- c.o~\-> J~ t , 

'iih-

ll'\') " t ~ *· (_o() sw." ,!. ~. 
' ,. 

. . · .. ~~ ' : . 

' : : ' 0 

From eqne. (2.17),C2.18)aru1(2~19~ ,tnexoefor·e.-, he:~e 
- - . -- f. ·--- . ' 

. .~ . 

' \if ').. ' 

J ~~ ~Y\·1 t< cl ~ 
0 

(~~20) 

Sinoe '\' iu a.~'b:L trst-y, th13 ooc·fficiAn:tu of':' con 1-_'rl.. t must 

if.fxtf~~· 

' . ' . ' : 



61 

\IJ'L 

~ <;i-nL'MI <f c(.( 

0 

yr, '\..-

')_ (Y'>~J 

l 2.. n ·1- I ) '· 

'"\'(\ ' ., 
)_.- l '10 \ ) -

The t5er:ief' in iqnth (2.17) ~nd (2,.16) C<HJ.'Vtu•ge r~:pidl.y. 

Ret~.it;ing ~ight ter~:H1 in the trtmelf?_tod tu.-:r:!:.ee~, e. le~st 

atpJ,aTE;H.'l fi ttin~ 'ffa-e. me.t'hr to obtW.n ·the e(,e.£:1":!.. cir.mts from 

fiqn. ( 2 "17) with eol"rected r):'l\]H.n·i~en ·ta:t i-ti t~~::l ~:i ty V$luee. 

~.... ,.,.,l4"''''' ,_ .•. : . .-,: "<4,1...... ,..,...,.,..{J ..... i -l:t"'r v<e~ ,...,lf;......,_tt:.& v,... · r,lfj....::;; Y.~ QJ.,. l,.. · ..., - . . 

• Then 

Ti) '2. . . 

1 1 (~ J 1·\Y\ ~ J ~ 7 K ( sO-. 1) , 
lJ 

and th~n divining all, the. h1..'n Va:J. ue~ by .K v.r~ ~ ptained 

the no!'mtU.i~eo. val.ue~;; of -tl:u-~ o~ientat1onal dintri hutj.on 



. :. . ~. . ' ' 

:· ... 

62 

I. 

(f~). 

.· ( { b-.." lo> 'i"- (!> ol. ( t.,; (!>) 
...b "1\<. 1,) ', .: 

'.{ 

(~1.\) .. 
' '/ 

: ~ . 

optic®J. denoi ti·e.a and ·oorreaponding 1nten~i;.ty valuem the 
. : ' . . . 

er~ra in /... P'2 '> ~d ( f 4. >. · V~{tea wel:~e efttitlH:tt.ed by 

drawing (\i:fferent .illten~i ty_ tli~tr:ib'U:tion ,:curves within the 

re,n~e Of. u,n-oertt;tinty. P.or all tl'HH'RO curves : ··z r02 > Q,nd (f 4 > 
' :· ', 

' ' 

~ .. ,. '· 

however; i;l~a.t unce:i""'tla:in ty ·in the 'tetii'per~tp.Ji~i~ baokt:tr(Jund 
... ~ 

~ . . 

conuation and .irregu.ln:ri. ty in the :til.tn e.o.~:ting (if' any) 

OQu.;t.d no:t hav~. b~eu . t?.Jten into Qcao·unt in :t~1.e er:ror t-?~nti• 

. ·:'· ': 



63 

···,!, . . · 

·The n:orcuu:i~et\ d1et:ribution function can be witten as 

( ~~eetion 2.2) 

. · .. '· 

'.'1,' '., •· 

where z i~ th.e. o~i~n~tion~l _pa,rti tion 'fune,tion which a.t a : · ·. • 

partioul(il.r te~1H3ratu.r~S~ w~s treated as .oonetan~ f't.JHl · 'I ( ~) 
. . .. .' ' 

1's the (J.ngul.ar. pe.:rt Qf the in termol.ettuJ..a:r potential. Yi'(T he:we 
·' ;". 

:f'i tted o.tii t \ ~) VEll.uo~~ to t:ile tom · 

or 

f t ) ~ ·t.. (b 

. ~ . :: 

. ( -.: 

-\ 

A J..ea21·t eq,uare fitting of' ; ~u. (2.25) vr!tif ~el.9ula.ted 1\~). 

va1u0s tor dif.ferent .· ~ at a pttrt1e~ar temp~Z'f.\'tlll:•e givee 

cL. In ·thie f.i tting· ai:t term a are ret$ined i:n the e.tPrie~ 'Go 

obtain a. good id.,a. a.br..u't th~ ptteu.dopott.)~t:;LtU. 1:\hf.ltteoh~:rj.e$. · 

et tt.l.91 in Q\.!1' J.al:Jorai;ory ea:ri1ex- anuy~~d.- :the erro:r$ :i..n 

Ot\~~W-e.ting it'he :coei';f1Qie.nte oL (~ o0 ~ - -\'Yi Z) and found 

. t tu~ f'i :t~1j·t fa,; (np to L = 4) <» eff'i ()! en.to 'to be well lh!f'ined 

:. , .. 

... 

) .... ' 

.. ' ; . 

:' : .' . 



.,-· 
\ 64 

A gen0ra.~ aniB() tropio pair po.ten tia~ may be conat­

~ueted (eeo. ~.2) as 

"l~) = L olL ( ~ L > PL (LoS~) 
L.e.Ne-v. 

-J.,. where the coefficients dl. oan novl· ba obtained. comparing 

~qns. ( 2.24) and. ( 2.26) as 

'elL :: 

We have calculated 

Since the eoe:f.fieim:tts d 1. d~term).ne$ the at1.,,ength Qf the 
~ 

in:terrao~ecula.r foreen., the-y ahould. depend on the 1:n ter-

mo.leoula~ separation and .ao Oti tempe:rattu-t.t. Initially vte 

dent of temperatura a:nd con~truated the peeudopoten·t1e~ 

tald.ng the m:verag;~ valuna of ita and d4 thor different 

tempe:rE':tures and ·then inalud~d dent:11i ty depen~,enoe. With 

th3.~ pa~ud~poten tial t.tnx~ oon~tru.o'ted the norr:Hllised #. 

, di~tr-ibution function }(~) valuetJ were 13a~~u.lat~d 

bo tb retai.ning ( P2. ') and ( P .!\ > 



( 

Aoe!or£ling to Vainsnt6in6 2. a :f~trJ.y good ~:pprl):xima.ti_on , 

for order pa:ra.metBrf71 e~..n be obtained bg re:pl~-.oing f((') 

values with l ( 't-) val.uee (4t a o~nstant Bragg ane;~e). 

We have al.Bo cal.ou~atQd order pnramotere tU~ing thi.n e.p!:):ro-

and 

Fz·om the d.iff'ractj,on ring di~.tne·ter one. ~btaitu~ the 

oorre~ponding di.:ffra~tion angle 2 e • The spacing X. bet­

ween two ~uccEH.H.dve :r"aflecting points or p:lanea is related 

to the eorreE.Vpon.di.ng diffrao·tion angle by a fortr.rule. of the 

typa92,. 

where :>-. ia tbe we:vel~ngth ·Of the Y..-ra.y and K is a con~-

ta.:nt depB1nding on ·t;h.m ehep~ and arnngemtnrt o.£ the mo~ecnl.~e~Jj • 

raetion ma1:ima JHH11 tiona at wide~)" d.it:terent ang~ee. That 

the outermom;t til.ppea:r.e due to in teraetion of n('J:i.ghbau.r:tng 
'i'." 

ptJ.rallel. molecu.lee while 'the !.:nner ring i~ in aom.() way 

related to tbe :u~n&th of the molenlul.e, wa.e eetabl.iehe·d 

by cle 1Tries9 ' 94 • They a~r;~o t1ieoust;'?!ed in tlcetn.i~ the ohoi~e 
of K in eqn. (2.28) ~lep~nrlint~ on partioulal" spaeing r.ve are 

concerned. with at! well a.s tb.e ahe,p$ a."'!.d orie.nte.tion of the 

molecules. \'j~ used K u 1 for inner maximn i.e. 13ra.~g law. 



66 

'· 
or:i.erited ana u."!lori.ented ~a~)Jlea. Tbi5 i.t;~ b~,.H!tnu3e if we 

consider the f.H1Btteri.ng from m. pair of molecules. {!).t a 

diatt~.noe n apa.rt and if tb$ <!hains are all.GWfH.l to 

rotate :is freely~ around .each other, the po~i tions o:f' the 

~a.x:i.ma :.;U.Qng the ef;in&. tor· are rletermiru~d by the funotion9 
. 'U\ 

;r,; t"') = 1 c..os l 'll c.os o( ) clo( 
0 

where ?L :s4.CI:().' ct. E:GS\'T\ a, ancl thif.ll ~r,ivea for i"it't4t 

maxima X = 1.117. 

tlendo:t~f:£ et a192 aalau.ls:ted K V<"~ues from ·the 

pho tog:reph of aomJJ cbolerrte:r.ol. ~n~t&:t"e by taking X va.J.ue» 

in eqn. ( 2 .2lf3) from <lorup~etely a:~tended form of the 

UH)l.~cu.le an(1 found ·tna t K:. lies ile·tween 1 for ;p~r!'~;Hrtly 

ordar&d moleculea and ·1 .229 ~:·or completely :rL'i.ndoro orien-

tation of the .roo~eoules. 

1\ll the x-ray d.i f:t"~t.ation. photo graphs \•tere taken 

in fJ.nt p:la·te oamert'\ with Radon Hou~:;e (!ncU.a) X-ralf gene .. 

ratoxo. An X•'l:f~.y tube Yli th (h4-ta.rget 1Naa tlsed, Tlie fl.et 

pl.a.te C8.mera. used t'or ta.kcing ·x-ray photogrephe wa8 B 

equippet\ with high temP~'u.:•attXf.FEl arranf~emen.t fabric.ated by 

Jha and Pa~95 in our J.abor~tory. Tbia ee"t up a.J.z;o he.e 

provi11ions :!:"or in tercr.uuJ.ga.bl.e ool.limf.t.tor, in terohanga.bl.e 

apnaar to vtu•y the ~ample to ·f'il.m i'l:i.star::tae atld interehmt- · 

g&b~e pol.e pieoon gap of the e~ectroroagnet. Fig. 2.19 ~hows 

tbe SI!'!Ctional dim.gra.m of the Wh0~19 a:rra!lf:;ement. 



~----1 I 
I I 

I I r---, 
1"'1 I I I,, 
·~-, U: I 

1.----.J 
I 
I 
I 
I 
I 
I 
I 

17 

:----, 
I I 

,.1----', 
I I,.., ______ J r~l 

__ .., ___ , -11 
I I rJ 
I I 

'r- --J 

17 
16----+, 

I I 

~---..!.1 18 ~----· 
I I 

I I 1 I 
I I I 

I 1-+--15 -+I 
I I I 
~----.< L __ ...J 

I I · j : 
I I I 1 

f---...1, . lO 11 L--~ 

1 I ~ ~ j 

1 r._. I I I ,-, 
~ ~I 
~I I rA -:- t/1: r11 

~----,t_--[j,/J/lllllllll!ll I Ill 111/Jillllllll 17/lfk=~ ___ j ~ 
I I I I 

: : ~12 : : 

VrJ[!)r!II!JIL;RI!zmzzzzLmZml!oomai!OII!l 177 )IZ,ZTIA 
I' I 

" " 13 ::-'-'-J ci.J_J.......-
' zz?fit/1111 I I I I I I /Ill II 111-=f--14- ----41=/tl 7 7 II I I I I 7 If J I II j)£ /Ill 

Fig.2.·1~ .Sectional diagram of the camera: 
11) X-Ray; (2) Collimator; (3) Bra:.s Ring; (4) Ring of Syndanio 
Board; \SlBrassRincn (6) Cylindrical Brass Chamber;(?) Asbestos 
Insulation and 1:-lear~r Winding; ( Sl Specimen Holder and Thermocouple; 

. (9) Specimen; (10) Film Cassette; (11J Film Cassette Holder; 
era> ease ?late; C13)Levelling screw; (14) Brass Plates over the 
Coils of Electromagnet; ( 15) Removable Spacer; (16) Supporting 
Brass stands; (17) Polepieces; (18) Asbestos insulation. 



i~~l the mat(~rials; ut~ed are non-magnetic. A v.e.rtfc!l.l 

Y~ray beam inoidente on the specimen (9) tbrough ·tb~ ~olli­

ma.to:r (2) wh:io~ ia push fit into the aampl.e bol5.er. t.rh~ 

cylindrical hre..so oh.a,nJbo:r { 6) hao heating aoils itt: ~thi.oh 

are insulated by eal:uu.dios f'ibre (7). ~he sampl.e h~l<ler H1) 

' '!r.. t - d • t/ . {A) its .wel.l intmlt.\.ted PY t:u.avf::'$ oD fjhee.t& an ~·.tlndanyo p'oa.r~~$\ ~ 

:f":t•om the pot'lts (16) vupJ;o:rt1rag the 2a.mp~e holder (8), the 

aam~l$ being taken in e. thin WE:'.lled ~ gl.a6fl cap:Lll.nry of 

<lifitnf:iter 1.0. mm ." approxim&~eJ.y. :rhn $ample hol.(h~r inelut:1-

ing the infB.ul.ation. o~ b~ redueed to 1.0 to 1.5 em. thick• 

net:u:: at the position of the tllftmpl.e eo ·tbat n strong magne­

tic :t'ie~d o~n be a:pp~1e;i·. ~b.e fou:r> $Ul)po:rting pot!,!tS are 

rigi.d.ly atta.ched to a heavy bras~ :plr-.tte ( 12). The ·ei.l.\'11 

oaesette ie mounted Qn ~ ~e.t:1sette bol.tler (11} l!i'hich ~-s 

also ~UJ>J;J~u"ted by the pomt~. Spao._~_y: ( 15) ann be intl"'o­

du~ed along the pof;ts batw<ilen the cla.pe o:t the ea.s~et.te 

ho~der e.nd the bea.vy bras!\~ pl~::1.. te ~<:> "that rep:t"odneil:'Jle 

g0ometry enn be ob·teined. Level.~:tng screws (1)) can be 

Uf:ifJd for adjustment end better ooll·ima tion. The ;!.~ole 

pie~ea ( 17) of the aleetrome.gn-et oan be brouga·t· vary 

close to the eatrll;ll.e hol.de:t"'• t.hf) pole J,Ji~~oEH:: ·-=-~\:Ve--6'-i~-

proper.ly abaped fer thif! pul'1H:>~e < _ -~ fQ~ production of 

etrcmgest fj.e~(l at the ep.,o1men po~j.tion. 

The X-ray tube ie enclosed in ~n iron container 

in oro.er to provide wa.gnet:l. e ahei~ding to bigh ,peed 

electrons and in o:rde.r "to a-void the ~,_ t·tra<~tion o·f' the 



tuba by the magnet it is supporte<'i by a wooden :Plock p~aced· 

over th.e pole p.ieces.:rhe temperature wa.s regul~ted within 

!. .5°0 by supp+y:lng variable vol tagee to. the heating ooi~e 

from a stabilized pot-ter supply and. was t11easured with· the 

he~p of a aensitive galvanometer and lamp-scale arrangement. 

and calibrated, copper-conr;·tanta.n thermocoup~e. The sEWJp~e 

holder was calibrated upto 250°C with a number of ~amples 

ot known melting points. 

The strength of the magnetic field at a fixed 

distance (2.0 em.) ,.i&f:l measured for different. currents by 

a sensitive galvanometer ( BCI1 model Gli867,}. T!'or all photo-

gr~phe Ouk r1... radiation ·monochrome.. ted by a Hi-filter of 

thickness .oo9 mm. w~s used •. the beam was baing collimated 

by a collimator of aperturo 0 .s rnw• Whi~e ·tuld.ng unaJ.igned 

photographs by thir~ set up ·the _pole pi()cee were removed~ To 

heo~ve better renoluted low angle di.ffractio11 pa.ttel"n from 

:t'RAZl BlONmJtGH/iJTIK, GDR) with h:tgh tar.npere.tu.re a tta.cbem€'nt 
I 

For each observa:tiotl met, the exact distance 

between tne sample and ·the film ·wae deterroined by taking 

Al-powder photograph,. Einae f.or Al the unl. t eel.~ dimen­

sion :is knm:·m, the Bregg angle for '-"' K, ~ re.f.looting pl::'"ne 

can be determined from96 

( 2.29) 

... , ' 

\; ~- -~~ .· 



I• 

' 

'l:hutl knowing :Sx-agg ang,les ef)rreepon.~S:tn~~ to 111 and 200 

lfib.s~FJ:rved. oiffl-a<ddo:n ringa97 end U'HN:\Qt.tring :thoir diameter· 

:fro~ the photo~~.rr.q:;h ·the e::a:ao:E ,3attple to :fi.l~n dJ.eta.nce aa1:1 

be o 'btained trot¥1 the :ri~J.e. tion 

Radius of the l"ing 
tan· (tQ. s-----------

Dam:ple ·to film uietai:toe 

In crrt!J.er to d.ti!termine various PF.L!"idneters, the X-ray 

diffraction photograph~ were 8canned both linear~y and 

whieh has ·po'iHim tj.&metr1 G reoordiug ( ~r 200) f'a.aili ty fer 

.linear f:lCBllr'l.1ng. Tbe eiroular neenning W1JJHJ. ~a<1e nuu:1ual~y, 

th€1 rotation (ltege W~:ie rnod.ified by un for this purpo~e. 

~he optical den~iti.ea obtained from tietk~it:ometr1c octmn-

irlg were then conve~ted to re~e. t.i.va in tentJj.. t;tes ·by c. methot:l 

,. t .ll b 'tQ. J ·~ I> 'I . i.! 96 P. • ·t . ' ,;. ""'l auo·p eu y !.\ u:1tg rmc~ ... ~..t.e~E>.n6.er ,. ,..,n l.n e:tHiil. Q~· ac~e wa.e 

prepared by expoaing diffe1"6nt j,)ort.ion of a fi~ID to :X.~raya 

coming through a amal.l rectmlgu.l(l;\r n;pen:i.ng with e~onur& 

ti~ea ;, 10, 15, 20 ••••••••rt.eeflll. Mu . .lti:pi.e fi.lm tec:hn:ique 

wss u.oed. Optioo~ f10nni1;ief.l. ot thel$e apotf'1 were then men-

eured wi.th the n·.d.cl~odenB.i tomQt~r and Zl. gr~.ph wa.e. c1rawn by 

p.lotting opti c~...l. dentl:t ty ve:r~us t:t.me in aeoa. (i.e. X-rar 



the optic:r~l de.tadti<.':l$ o:f X-r~~3 di.!'t'rf!.ction pheytni;r~tph t:m~ 

{.;tradia tim'l a-trip,.· 'tbe den ei t.iomete'r $eroing wa,~ llm~.e o~ 

unexpot!ad X•ruy .fi~ms, no tn.1hCra,et:i(.)l1 for unexpo~e-d. film 

op.tieu (lE.m t?i ty w~e, therefor~. nooel"bear.y. Howe'Y'er1 the 

bt'fmd~ nnd type of the fi~m. the developin~ 'time, compo­

~1tion end temperatlll:'e of' the d.e\.,.elol'H~~ ha.ve pronoun¢!Jd 

effect u.pon btl)t.b the op·tieal denui ty :IMHl "fil\1'! feetor of 

the. response cut"ve. So theBe fltu.mti.ties were tried to 

keep to th~ $~~e values as applied to prepare g~~d~ation 

et;ri.P. 

We men tione<l earJ..ier tha$ in order to e~lcu.ke'to tht~t 

average intarmo~eoul.ar ~i5tenoe· (n), thti di~taeter o:t. the 

outer d:i.ffraetion m~xima (l:'ing, h~lo or cl~~acents) :ttl to 

be datarmi:ned. !!'rom the ~inear ~eanni . .t:le~ of the outer m~J..%ima 

thrQugll. tl:H~ central ~pot uBill5 the potantiom£.;trio recortter 

a g:ra.ph relating op1;ict~l \1ent-~:tt~t V~h linear f;int~..tHlf:t ~;s 

peale poj.nta of the outer rJra~irua {;';i v~n 1 ta di.~rJeter. Ther~ 
. i~9 

a:re ~;lif:fe:t•E:m~t matho(!s~~ for locating thE! };leak :poai t~.o;n 

from ~in~ar t!l.w,~d::an;;:e vs. o. n. curve ~u; shown in ?i~t·2 .. 22. 

tb~ ll~ d~nwba.c}{ that etati~rtioal. tU'H)ertn.ini ty in the opti­

cal dene1 ty vaJ.u~s ttt and in the inu:nediate vlcitli t::r oi~ the 

· ma:.rimttl1 mak.C.£1 1ttJ precia~ location uncerteith In G:J.W(iel" to 



2.0~------------------~--~------------~----------~ 

1.6 

>-:-
(/) 1.2 
z 
Li.J 
0 

_J 

<I: 
0 -
1- 0.8-0.. 
0 

0.4 

o~--~~--_J ____ _J ____ _J ____ ~----~----_J ____ _J ____ _J 

0 20 40 60 80 

X- RAY INTENSITY (ARBITRARY UNIT) 
-x-"t'tvt 

Fig.,. 2:o.2:0 Optical densit.y vs .. intens.i"ty cvxve. . ,.... 



avoid this problem e commonly en1p~oyed metht7d is to locate 

tha peak at Px' tbe point of interaeetion of tvro t!!trtd .. ght 

lines projeeted from t!Hi mont linear portion~ of the slop.. 

ing $idea of the proi"il.e. Another m.~·th(lc1 im -~o -sef:i.ign ~he 

pe~C~~k posi tio:n to the mi.d point Qf a ohord draw pa.ra:~J..el to · 

the background· and located. at one haLf of the maximum peak 

optical denai ty ?y~.- or be:tter at higher ~evele $t~toh e~a 

~1\.f~ or ?r;14 • 'i~he differ~&nt m€:7tho8tJ give oOttH!t 

what i.ti ffaretl t va.lu.a~ 'for ·~the p.e~k pG~i ti.on daepi to the 

relative ts,harpne~H''! of th~ liw1tt pro!':tlat~. ~J;hen tile poak 

is we~~ defined ~: we J.lbowever, fPii'L(9ly· ·tr:.:,ke the F ~ posi1;ion. · 

in otber C&:HHHI "'f~ uaed ~'1.1;, p¢eitto~. Know:t~g the <~iamete~. 

the Era,g~ ~ngle (j c~r.t~espoDd.in£\ to th7. n ~i:C:I:'rtt()t1~4')n ring 

is dotermined using ~qn. { 2. 'o) wbe:n the actual rtafZ}pl~ to 

fi~ru di$ttan<J~ i,f1 known,, and tl:um 'the ~ver~s;e inte.rmole~ular 

di r:1tatJ.oe CD} if~ Cf'~~cula:t~d tl.~ing f#qn-. ~ .28 ~.,·r.ne BBJ!lt) pr<>­

cedttx~e l. v ~u=topt•tH.l to determine tb~ Jj,i;:tmeter df thf:t- inner 

tnal unguler por:i·t:tons. Oo:n:1:?1 t1~r1n,g 'r ~ o e:t the me.xi~am 

i:utene:tty p,ofl!itioD, the linear scam.nil'\g if:l don0 for '+' = o, 
!:,. !{)0 

.. j'bo meti.,\.l'J. of the di~u~(rtero \lbtained \'i!'nf! ta'l:.en as the 

a-.atua.l diEtta¢-tel'. 



.. 

. --~------- .. ~---. ~--. -:---- -- ·---------- -~-------

I f , r I f ~ ' 

--'-- '-- Fig. 'Vi. I Densitometric linear scan. , 
Scanned through outer maxima points._j 

0 

A Px = 50.145 
·f 

P0 = 50.145° 

> 
.... 0 

U) 
p3/4 = 50.138 

z P2f3 = 50.136° 
UJ .... 

0 z P1j2 = 50.134 .... 

BACK GROUND· - - - - - -
49.9° 50.1° 50.3° 

,~- ~~{ 
28 

--~~--

FIG. '2..-li. jVARIOUS METHODS OF LOCATING THE 
PEAK POSITION OF A LINE PROFILE. 



In order to ~J.atermi~u~ the ol"ientet1onel. distribution 

!unction 1-l~) • ordel .. pere.nu!'ter~ <P'l) and ~P4.)eircular 

~c~ning of the outer difi:.raotion ring a.~ shown in Pig. 2 .1a, 
iP.I requ1re(1.. 'l'ha vF.Lluea of optical. den$i ti.ee obtained !rom the 

denai tometric ci.rculo.r ecsnv..ing are converted to Y..-.ray in tan­

eli ties l-71 th .the hel.p of' om~lib:retion curve. The converted 

inteni!d ties are then pl.otted again~t differmit azimuthal 

l:ie.okground intenei ty vaLues arising du.e to air ne~ttering. 

sity vaJ.u.es. 'l'he peak inten!Jit;y l'H'lt1tition ~·thi~h wou.ld oorre~ 

pond to 't = 0· was detft?r.min~d. at the POflli 'tion where th~ height 

of the ~ngl.e vs. intenai ty curve ehove the br.ekgrountl lin~ 

~pet~ or even ~, eli girt' f.lonm:d.:t'ormi ty in fi~rn eoet:i.ng raised 

eome problei!Js• fie a. Emooth curve was d.rmvn through a l~.!'ge 

!Hi.ta.ber of points mnd in deterrming the peak por:-i t:i.ottB care was 

taken, where l3nch ambigutteu nro::1e, to ~~Q thnt :r ( '+' ) wac 

more or .. ~eaa e.r--mmetrio around 'f" s o .. We hr:nre used tho ~ean 

I { '-Y} values, of the fot.tr q,tu~.d;rtll;nta to o uta,in t(~) • ( f' t. ) 

~Pd C.. P 4) values. 

!-• .,;, • • +-....... I ( ,\., ) ·~P·• "' . .a. ... f'r· .... -. ..v = 0° -iro·· .J.. :::s "io· 0 
i:=i~~tng l"'l.ne u.::;:~r.t l vo~"""""11<' """ V'-'1 I ... -~ ;I 

at five degreee interval :f'rol'!l! { 't) vv. i' curve tl~): -~(J}ci,(~L> 

were ce.J.cul.ated using Lea.flbet"tq,;r' a ap:pl~ox±rrm .. tion. ~rncn f((?) 

VEh ~ · curve waf:l. drawn. A co&npute:r pt>ogl'"l:trr;!l'HJ.. Ytf:.r: deveJ.ope4 for 
l.1fl 

this e~~culntion to u.IDejWipro Ge.rir!D ®600 com:puter oyr.tefll. 



.. ,·.·' 

1. H.Saokt~.~ ·attd ~-n~u.,, ltolear;rs't.lilq.C~e'\-.,.-

11•. ,,.1-._.( 191.'3). - '. 

a. . . 

., •• - A. de V'ri•:•·• Uquid. Oryat-eltlt ~he l?t;tUth nta;te o~ 
.. ! .. '. 

p.f ( 19_?2):•. -

h. lu __ _ .4• Y;ri_oa, itol.;Cr,y.a'b.litq•Grl'e"•• £2• 215 ('Its;·)~ 

4. S.l!b:a,-,. P:~~~r3,.e,. Ra:f.1at P• 16'.-

5 • J. none:•~·:. ,~e l~olfJ-cul.a.r peys. of L1q\\td 6.tey'at&l.s. 

Ede_._ (f:.:R.X,-ln.tP.at tu1·d G.w.Gray• Aoa~•ic he•a• 

1rr. »•- ~?5 _( 1979 l .- · 
6. - L.V.Aaa.~f,~, Mot•or,-et.LS.q.orym't.,. A!• 1' (19ao). 

7. D.il$m.ua;:: .. J_.w .• Goodb1f, . G.w •. Gray nnd lU_· r§acl~ann. JAQl.. 
·. i 

· o:ey~_t .. L~q.arrat.·,--a, '11 {19So). 

ea. G.W.Gr.ay.t :!'bid, 6,:.:· ' ( 1981) • \' 

'b. -- z.~_.o.~ttlJ,._Nttt. G.'tf.o~.:- Ibid, Jl• 't4S:\ (19UJ •. 
. ; . .· . . '.I 

t. A. ••· Yne•• Mol.fll\'l/S't•Li:t•rtr,.e"t. l!• ~1 ~ a1t (1910)~-
- . ) 

10. - P.G-._ an .~011not2• ~e Ph.J-1''- of liiq\114 e~:rJtaae, Ol.JJ.rendon 
. ~ ; 

PMse, .. o:~crd., p •7 ( 197 4). : 1
\ 

! \ 

G.tJ.Y~bar!h .E.Gol.er.1n.ter an« n.:&.Pie~~~~ f!-ol..Cryat. 
•, 

Ltq.rJ~y~r~ •• 1.i• '9 ·(1[f72). ': 1 

12. Set:I1~;L.t,~.: ::P• llnttd ana lt.Sackmann• I~4. -~) 105 (1972) 
.- . .------. . ' .. \ 

1'5• G.~.~~c~bur•-t aa«· .~_\.~ti.Mn:, lhidt li• 179 ~-1972) • 
. . . . ~ ; . . 

14. i,., tl~ Vrioe.- M<tl.crr,-~"·Liq.cr,rct. Jl -(Let'bj~ 14'5 (1979)-. 

1$. · A •. ~· V.r~e~• A• ~a:chi: end If .• S,i.el.ber~ l.'bi~~, t'-2• 
! \ 

- i 
! 

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I 

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\16. l'{.R.Hah• P.Jou.che:L"• 0• n.a'tftd•, .A.H.LeY-.l..u' 

atl.lt J.Milltheto1 MOl. •. Or;~t-.ld.q.Oryrt'*•JJ J1;t. 

277 (1904). 

117;• S.Mele, G •. .Pel.Bl., l.J.4t11' ant! DeDftue1 Ibidst 

!a• 2?· { 1~8,). 

', 

It .A .• :r·. Va~ •• Ze!f'\niv and J .w.nof!.ru:. !bitt. ~. 

21· 7i ,(198,). 

:P.~.tJtlalie1 Phya. R~tv.Lett••, J!• 48 ( 1917) 

P.,.tD.aclie; R.x.·:sosa~ue, w.n.nant•J..r; and 

· U.R.4:fa)?lcr.Ib1t!; 2.• 120 (1·9'11)• 

10~ P.U~r«outn. A.M.Levelut, J.~a'ttar en~! G.stga.r:u1, 

\ Boltd.S"at•.C.oaan., ~· .,., (1t80). . . 

I ' 

21. \.r.mar~our.r ~na A.M.·Lu~ut, ..r.l?hye.(hrie)~c 

!1,.41. (1980). 

22. \ f! .•. etpnd, N.A. tinht P.Ka:rdoutn and li •. Oaapa:r.o=• 

· M~i1{.c~:et.Ltq.orre~ •• i!•· 81 (1981). . 
• \ I 

2'3• n.;~'•!ttMU.nw~(t$.dt B.K.Ss:datdva mu!. X.P.L.!tooM..thTa• 
I 

~11.1Jol•Jir ,,,, '(1f'ft ). 

24. l'.lt~r.dcn.t1n. &.s1san~'t u.~.A.Ohara u6 tt.Gs.~panur, 
Phr~ •. I~•tt •• , l1!v ,., ( 19?9). 

I ' 
' I 

25• e·.~·~:rowne•Y,. bd A.J.Lead'be~"e:r, l?hyfl.~CYaLett., 

.... ' .1600 ( .1980 ). -· -'······. 

26· A.J.~~dbott•~• J.O.Ft'!OJJt.J.P.Gousb.an• G.·w.Gny 

&:ncl. A.~oN.e.r• J•Pht&h(PM"ie), !2• ,S ( 1919 ) •. 

27. !' • .a •. ~uneh• .R.~• ·sa•bt4han, G.Heppke ant! a.Hopt, 

Eol.~r.rnt.Liq.Oeyl!t~!!· 249 (198')• 

28• A. 4• Vri••• J.PhJ'•• (Pari'e),. CoUo~.,,§, 01-1{1975). 

Ito s.M.•l•• P..:Bran« an4 .H.aacklzaaa. MoJ..Or.rs~. Uq. 

er,. .... ll• 16, ( 1972). 



' '._· .. ·._ .: ~· "11 

"'• ·. 1.w.~ .. ~a ·f•Jr.Wiluto•.• l'bi«• ll• ~' ('1974.). 

' '. i.J.;r.•i\•--•••r•J•P:.oa ... , :s.x.u,., o.w..o~ •ut 
· -J~~~eito~J,' •. :, J•Ph7••: \hfto')• 42• 178 (ttft)· •.. · :. : .; 

. ~.· s ... *+~~'~i~u eata.s.ablaah. lfol..~.r.t••,, .. 
. . -···· a: (t.et:')$' 21?" (1980). 

:t • .\.c~~~~~- A•3•lln4lle~te7 ana P.o. · WJtlgld:on,. 

ato.t:_.c~~~i~,.~.,.,~ •• Ji~ 24? ( 1981-l; -. . 

,.. · · a.J-.· •. -~_. ••. •• .r-.1».: ·lat.'-•• I• ;php. ·· · 

,. 
. . . . . . 

thnal.> :r..$, •• 2-' .._,, ·C1tt•>· · · ·· 
.. ". . . . . .... lt~·-· ;&;-.:J•ltft4'Ntter aa4 , •••• "..... . ', 

ua.,hie'~:; 1.•~ 1ff·· :;(··ttta·) •. 

J6 . · A ;; ~-~d_~tles--: H•l:.H.aa ... Lll Utthdaaea · 
• . . .,;: .·: . .• .. :~'•5: (:..: .. :;-.- '· . . • /- . . . . . . • . : - • 

, Kt.tdl O»t.atale ·• ·att-.a.Ubai14ns~·-: u.,a. · 
· . - · ·-·. ·: .:_ r~>ii· <.~- .. . ." , . ·· • · · · • · •. _ ... . . 
· LOa••:· p·.6f ( 1tso-;)'•{ · ' \ · · 

\ . 
. _·:; ·~"· ·~- ,_._ ; .. -~ . . \ \ ... · .. -: ' 

J'l• -: A•I•L•4-tte.;lf.&~llat44t B•A..bUJ'•I•Vf•Gooclbr u4 
: .. · .~- : 'f.-::.:~·;:;i ... :r:~:;,·._ , ·.·-. ! 'r •• ·, · • . ·;··~ . -· ... ::· 

. •·•·•••
1

_; n,a.a•••t.•tt.. 4:!• '"' ( 1trrt;).-• , • ' ' 1 

"• . I•DDuo.i~: •.••• L~•tt' tt.LUhri,. L.%4'-" aa4 

· z..etn•••1·.· , •. Ph,a. :·(llut•>• c.u.,~-·&·1' 
.( 1fi7J ).~ ': ·::. :: :., :: ; ',.. . 

;t. · ·n.rio•t•tt•; G~·"·•lft.77·ea4 it.J.BaJiri.wa. Dl,o.,. ..... · 
Kct'a,OQ'·~-... : ·-·· · ·9t· (1t?Jl• · · \ . 

40. A. a.~-~-·~··' Ro1iCqn.u.q.er,rat. J.!•, '71 \(''''Y· ·. 
.. ·.. ::,!~;!:". -~: .. ::· ~- : . ' ' . : ' . : . - ' .. I ·\ . . ; . . 

41. A.. ~· Vl-1:••• en« n • .x..ft.ehel.• I'b.ta, Ji• '"' \ (~972) • 
. .. _,,_ .. :·-,,}· .. ;;\ '. . .. . .. \ .·:~··. 

42• t).B.OI)UCt·. Plt.:D·ni·8Hr-.:U;oa, Ke\ ~Dte ~··· 

·-·· ·~~:- ,.,,· (1974) •• . ::\: . 
. - J ••• ·' - • • \\ : :, •:' ; 

.• , •. · A.J.Jn4'*'"••·aa·· R•r&.uob&rt.a. ~h• Mo1·-·· ·or 
. ; - .. · .. :·: . . . . . . . . -. ·. .· .. \; .... 
K.~llit· Cf6:•ta&.•• B«a. &.B.kOlebu•t •« ··~·~~· 

·.. ....... ... ' .'' ... ,_.... .. . . . . . i •• , ••.• h••··· Lo•rtcm.. p •• , •. (1919). .J 
I :1 • 

i. 
\ ' 

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' ~~- ~ · .. 



78 
••• A.r.t.Ditmf)uX u..t F.Vo11no. J.Pbl'th {Pene). ~~~ 

·~ ·-.... -~ ·. . 

181 (191$J.: 
{t.-l,_::·r ·.•• 

45. J.noao•-t~ P.-tel.lu, A•l~.Le'lelut ana P.~rque-t. 

1.- PlJ7,;~;-·'iParte}. 2• 548 (191a) .. 
'• 

' : }.··:(· .··:·· '; .. \ 

46. R.:!.!>et;J•n• n.L.Uhri® eaa r1 .• P.Shelet• ~l'leah ·Le.'t;tf!~ · 
. ':' -~. . ... 

·.·.: __ .·:-· ,· :: 

47r.&.. J .R.F.'l.i~ •.. !-.,S.!ltlrtthsll ant! n.!.».Petrie, !4qui4 · 

er:re.t~·~- ~a Uderelt :Pl.uaas. 3de. J .• P.Job~aon antt 

R .• n.~~·~~~ J>l.·qllll hbl.i~heril,n, Vol.t,p.91 (1974). 

·. . . . . -:~ '· ,.,2.1 :( 1910}· : . 

o. tt.~.~~~ai. ttott.o:yeil.Liq.Cey•t·~· 405 (196?). 

4Sa. R.!1f11~;~·~~~~ l:.~em. Pbf:a.1G; 1 ,~4 ( 1969) • 

~. U.linr..~ritot~r. A·•t~uin;atm;~-and Jt.Wi.lliQ&J, J.Appl. • . _, ' . . 
.. : . . ··.: . 

Ph7D•, ,,~:. 'Gif {197!). 

49. tf.w.Jta.•ley,_ s.K.Khoo and G-.R.LuckhU%'1!t~ Mol..s ?h7•• 

$0. ll•'llOJm~ :o1-tsa. «•· Pbytt. i!ath., a1t 614 ititt ·(1916). 
-.-·. - .. · .. 

51. · W.~~!!~~r.:. t\CCl A.Snup<!Pit X.l1atul'forsch. ll~:tt 564 ( 1958 )J 

14a._ att!. (1959 ); :t.:ta• ~a? ( 1'60). 
. . ¢ 

, .. _; . . \ . 

52o R.~.H~pb~:le"• ?.G.Jame8 nnd .G.R.Lu~khnr~\• J.Oheru. 
; . ~ . . . 

SOc •. ~a;m.4.f1'~tUl1·,l'lt .fi!• 10,1 .(19?2) 
· .. 
' ... 
' 

54. J .A.~P(lp~ .. rt!:. Proo.Roy. so e. A2U,, 498 ( 1954)." 

ss. J_.R.swe~t and ~ • .a..steel.a• .J.Obetl.~-hYiht !li;:,022(19i7} 
. · .. '· ' . . \ 

56. fl •. u.~ • .t~ ?..118Uumtaey ~~eory of ADgul.ar liomc~~, 

J.Wil.lf!y tm! Sonttt NY { 19511• 
', ,. 

. ..... 



57. s.elut.tttUm.a8:ha• u4 v • .u .li~dhur:.tld_... Acta O:t:7st. 

A.llt 'G' ( 1911) 
$58. s.Jevt., _ w.A,.:Aa.R, P.tJ.re~shinl ~Wd :a~J.Fr1eeU•7• 

IPbJ'•-• itoY. iritt~. Jl• 1552 (191,) • 

.fiol..a~yet.I4q.o~r,-e"l.f.it ,.CJ7 ( '1931 ). 

Pb¥•• ,$0_<t.Japtub !!• -1140 ( 19t30 }. 

60. A. -fl~•••· ~" Cb.emle .• 1• 9? {1t6s). 

-61;. s.Oh~•''""-•*har end-li:•lf'•m&4btlt'Ju"'Nlt\t J.P:hftl•(J?ari.oljt 

2•-- o4 -_< 1f6,;>. -

j,· .';r, . ~ •. . . • 

.. . ' . 
Ids. u-.)l.:LuOl!:b•e:._. -a:d G.W.Gra,., A.~t!Gmlc P:roea• 

Oh.:. 1~ <(,_$,Sl). 
~ ,-,;. ·-.~- _-;_ :, . 

64.\ G .• R.L~okhl&9~· ~1f.rt~v." £!• 179 (1968)• 1:1ol.G:cyet. 

lilq.Qr:r~t •• u·~-125 ( 1915)· 

'!h 18.- lra~~tfl.~a,: I•Ohllb~Phl'e• ii• '3599 (1914) • 

66. D.J,.:L~Okhtn'at. HoJ.:•Ol'J'o,.Liq.cr,.st. • l1 (Lett) 

lte.f ( 1taOl~- - ---
.... ·· • ."r 

61. - A.ffau,•. ~4 W-•h.i•~• _ t-.ya-"d'Zo~ech, ''~" 816 {196t). 

68a. _ P •. tbat-.taa, _~Jul.J..ao-~ • .fl~ee,:uiner.Ol:'yat.J,!, 

•• 

262 ( 19-SS.) • .·· · , ;. 
. . . . : - .. .. . - . 

. . . . 

s.oh~l(l~aeldta.-.~;&··c~et.aq.Or,'e-t. J.i, 21 ( 19?2 > • 
P.J:..NO:~nt~o au« u.se~. fhe Mol..s Phge. ot Liqui4 

. ' . ·... --

O.J7_t!~flv lSt'la.·- G.B..Luokbva\ a;att ct •. w.{)ra,-. Acnd.etd.o 
_,. ; .. 

· Poae .(:191&) •. ·'' ·· 

P.t.Per~, ibid•;: P• '384(191-9) • 

. y.~: • ._;s·b:._·· k4Jdd •'twt•l-e·.m ~o Cfl\t-:et•Ei~ 
~ A"•'l':jf*:Jtaf' ~~ta•=~ &f':al;ldf ~ n••• 

. . ~ 

.\ .. : .. 

:_. 



s.m 

Edt!• G_~~-.G~ tm.d P.A.Winfjt)l-t J •W1.Ue, fUU.l S~IJt 

INc,. vo~_.it c 19?4) •' 

12. H.- Kelkar_. ana:_ R~ii•••• Htutdl»ok. of' Liqu14 Ol'fetal.e, 

9l (1968·):.· 

?4·. · J! .• J._ U~x~,_l.tol.Or,l't·.L1q.Ol:7JSt., .ii• 1 ( 1979 ). 
. \ . 
. ._ ... ' ~ ·· ... ~ -. . 

E_d •. G.F!.k )Bran.~•· 1 011ttea:lo Preee ( 1975) • 

16. J.~.v.n .• Liasen·_,· Ber.n._.oh•-·G•E~•• JJ,I 91' (1Sn3 ). 

11 • &el'ri~d-~l,. Atm1e.Pqs. J.!• 21, ( 1922.) •· 
. '·- - . . 

. -; __ :,-; -- ~ 

~a :Plastic Or:rstf!lll.e, ~de. G.w.Gray f:nlt! P.A.Wineor. 

El.l.lo Ht;~ocd, · Vol2t Oh., ( 1914) • 
. . . 

'19. ·· Ret. 12:-,· Oh.5 ('1~60). 

'l91t. (f. W•CIJr&J'• ~rDl.ecula:r o-t:ruot~ and th,e l)trop•~tiee 

ao. 
F.n. 
st. 

$,. 
Sf. 
s;. 

of Liquid Ot17•tal.s; .ft;oa~ie Preo~, Loitdon a: JY( 1962) 
t -·. 

- I.G~Ohtt!'lJakOV•' Sov.Pb;ra.UDP•• !• 551 (1961)• 
.. . ' 

L.V,._A'tJft'-roff, Mc.t·-.or,ret. Liq.er,ret., 60, _7, ( 19ao). 
'-- . 

- B.x.v~ituJnte-.n.- m'f'traotion of x-ra-r• o,. ri~un 
t:JO.l.•o~e~,-- m.eevt•""• Pub.ao. { 1966). \ 

·. ~ . ' . . ··.;. 

' 
A.de Yr1eo. J.Ohem. ?iqe • .2§• 4489 ( 1972 ) •. ~ 

P•U:e1.crf'l and J .Pn.l.gaeiret'ie~s, o ... ho'bd. 8eO..l\\C• 
-- . 

t.catl.u~.Pari•• Ji2• 2468, ( 1965 }. 
\ 

•, 

~ ' . ·; 



. . :· ;_ .. :· 

!!I• 1?1: (1t59).-. 

81 • A.J.:t..&flbe'ltell" ana· -J.}.X.Iiorrie, Hol.Ph)'••• 3,;, 
.. 

669 ( t~19') • . 
; : . ·. . . . . . . 

sa • tl.Zan•onit !htt lfol. .:Ph7•• o£ Liq_uii! O:ey-•t.U.th 

Bd.'s~ il:.i'~-L~ckhuret and G.-tf.o~. &Z):nx -Aead.to 

p~·····:: Ch•' (1919·)· 
·. ,; ··~· .. 

Ooll~.,-· 40·~ •. ' ·(1979). 
· ... · .. -.!, ' 

Jo. rc.et •.. 10, oh.a 
.. ,. ·;· .. 

91. ..B&attaob:Ujee• s.Paul. 8lu\ n.,_111,- ltol..Phya. 

!it 1.,9 1 :• ( 1961 )'.. . ' 

92. ct.Jt.we~do~il •a;, P·.P.Prioe, l!ol.Or;,at. Uq.017et. 

!!• 1at~·-{:1·9,.,,>. 

9'5• :r·.G.~n18trek:o-v,. R.I.1lohab1.ecb••• I-t·'!il.Jarenov aad 
. : ~ - ~ . .. ~ ' . . 

L_.A.JGu~-o•·a., Hol•-""·Ltq.nrgst•1• 219· < 1969). 

94. · -A. de v~•-B• Md~- ~eyn.l'A.q.Grye'*•·• ·.u •. "1 (19TO)c 

.1!• tit:- ~.(19?') ~r ·· · · 

95• :a.'!-tba. en.4 'R.P:;,~,,.- Pfto.lfucl.Phre. &:l.ld ~tate lpbue • 
... '• : . 

s,.p. ~nua, 'f9ch 49-1 (19?6). 

''• H~P.Elug end h.-~.U~4er, X.ray dl:tfrac't1tm 

.!f~t.--rtki~~ •. -Jotut· -~lil.I!IJ' Md. Sane, ft. Gh~:., ( 1974) • 

97. "•Ktttei_,' lat.~ 'Rol.i.fl eta'te ~e. W!l•~r kf!Jt.nl, 

Olh2: ( 1'76). 

- 9B. . Ref. ,,f,' paaee 114 and 47~. 
99. P.ef '}(•. p_&p ~B.