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opal bg Ca%tw (ft3ne.b) &YO&

g good 4l~wapt;iogl a&' the maat;Pc p"w,e 02 P&-U&B

nalttcdsa. Pn =a &qp%dr, we extam% Mra tac&a~td parti eXa

tLEaa~y 30 %ha iUmb%io

uu;~e e n t ~

~ ~ c ~ u l a s hawe a aphaxrr#yXWrlrPe& aMprs. PR OF&@% $9

br &Ze t r r .crampard tgra samill!d3 CIPI c9fes-like )~dfa@w&m wg%h

%%we on rs&-X;ltb I Z ISQX~~XWB, w axtenti t h W y 'ka eb

B 3 @ $ 8 ~ sf 3?&3;b% 4 3 M G & E G Y ~ S ~ ~ ~ W B * X f 3!' fa ~ & A w

QZ C J X M Q Z ' 5 2 % ~ hB2&21%~ 6b4tbj-f w'~;W

;M = srr, 1 i e > 3.5 dtcur: i i i b ~ 4 i k a ~ B F ~ ~ J ~ u X W (4.5 Pax

rad-Ukcs ag?taso&etp. Ma ?&LAX Il;a #s mw% ~aa%&a?a, ~-9,se

erm ~ X W C L ~ B ~MGWJF ~ a - t w (15na) M 1flsr~t6Mkd

%o euah s qeQm. papartbrta~r a.f r&-U& &%ti ~APEUIP-

3 . x ~ ~ pa32lLicsrm b** o

;h2aj;cd gar%f,~Ies and a ayotieu r~3e,irrrrd w l % h an

aWmtst%v@ s,akibXJt&aZe

of rruflire or and hkt&t 32. ~z%em&.d iR the (UmmWtmfii

-re gJ 1 ,%I, n tha m m ~ ~ ~ r arientrt$oas awad 3 im: thc ntdlacula. f) * B[Vp vA4 taxakddd $0

%ha t3mWa CXE 149 rtggu3.u~ c~~~ wPth 0 d m t d l i t S a j by the

2~ large *;ilaas of a and L , ill(cr. 7, ) mast approach the

9 % ~ gropar.2Sas a% #mmmbh am#

b e t ~ ~ a f ~ d by the @hap$ P~uLo3rl~ %he paaWlaa *;llff~So# 4

4 th. Sf t~Ul@iU@Xj t ~ q ~ a t l ~ . . k* XP ~~IULULUI. (7) .

isin el. l o w a\ and ~ ( 8 ) bnls beam an to2~a of

BVOPPP Sllo&mdr~ p@)Qa-ab. Xe i ~ j ~ ~ u w z ~ ~ f 9 p f o W w a & a the

edor49e in axdor tm m&es c&c&a$icsm. hate pXa$t& ?he

t ) r ~ ~ e m ~ t i * ~ M 8 by mt tm $0 %ha ~WtCXt3d~

fourth aad xcixt;h srdrer bgwrtr ptlXglnWaLs &a ffg)uz*@8 l e l o .

FIG. la: ( I q a F f s r n between 1 coo 8 1 and the values obtained by retaining; terms ul, t o d i f f e r e n t even Itisgadre golynosPials in the expanrrion of \COB E)\.

B I G . 1M: C q a r i o on be tween ( s in @\and tho vcSuca obtaimd by retaining terms up to different even Legendre polynomialn i n the expansion of lrin el.

FIG. l c : Comparison between E(8) and the values obtained by retaining terns up t o Oifferent even Gegendre polynamials in the expamion of E ( 0 ) .

Pt %a dllc.wr fLgums %hiat the wm radmd

ur%r *Q

~ ~ [ c o a 43) rmLy. t b .rmr &a krE(8) l a putts arnail o v a the

en%W o f oa1,wa o f Q lca), w W 3 s the! @xmr &E

\@as t3 \ stul raad.n. sa4ilcesble far ~ J a o (Fig. la).

Aa we ha% eeaa &a 1-t Glwa chezptaxm, tM izurZunivxtr of

af 42q$dPlnd*~, we,

aha3.X saa that M e ~ ~ ( o o e 43) tara &a 86\smt;idL t o got

a ~ u ~ . I & % & ~ v ~ X Y ar~~aa1S S~D, W W . -Ma have

W o c%iikear3;i~'t;;;t up to P2(coa B) . P ~ ( C O B e) ma ~ ~ ( c o e 9) resgeotivd21. In tho apa=ion. ( 7 )

gar a 3wtjEa3.6 ssya

f a also inaAubob, Ws W W a ~ S l l t n e r a m by ~@*r.ffafw

term ap t o ~~ '2(caa B) ad I ? ~ ( ~ w @) a tho qamaion;d (7).

(a) BafiulW ior cs f~grrtta 9t" hirmf c$Ugdt%m -r

the pum~j aoxwtaa qyatea (Qd Oa Q, 0). we

=die the craliMt.raf%aawr faUhowrs. SUP sr @van W&UQ r t i XI,

S,p&%iokl, ( t i ) rrtm ba wsB a&kmala%e %Q Q f k ~ ~

gote&ieriLilil o f %ha i~ new &$wt9rf by

instanos, ad^ ~ b . fircli t in oq. (7) ma o i i r ~ ~

'16,11%a 0 . ,i(P2) * % a&% 90 the gI f~Prdf1ai y-

a8 -Q~&I)= oi' f j l a m rraoPrjr &!a i&g* a* 'tiiks Esm *&&ti am

F10.2: Variation of (P2), dnem and llf'/~ aa functions of B obtained by retaining terms up to P2(cos (3) in the expansions of angle dependent terns.

9,42B for W < 0,4 ;tin figasa J. S&we& h-Je ot)p?~a~and

to oaloulaYono aaO. bp rstPlniw tccrou up %a ~ ~ i a w G ) ,

P (eus 49) aPd ~ ~ ( o a 8 O) ~leq~@o2;5,7fQ rcr; daucr:bad atrow. 4 The entropy a l l &&%)r (aq. 23). k P i e o -

the- c q n a s ~ l b A U t y p (aye 24) of the liio+ca#;tio @mns

a t the Ex Urn p-t A n i i w W 4ii-OQI*

Iw3uCSIME: high* Wdar f61:m, w;e3 gat; t3e a&~otmpII~ pawe

for tho eslZircb r-8 of wa2uet~ at R, 'IPh-:h (d) = O 9w 6.

P 0.5, ~ ~ ( 4 ) a d ~ ~ ( 4 ) stilX crontributs to +he s t & l X A *

OF the no%cntlc pblSe, 3%- b&, Ta, it 3s *sea dh&t m Ti-

0,s fzm either @%&a, at *&e EEI trwf %Am ins1c"c:ms

systan o f r&.ight c i ~ a e ag~ndaza i s r 0.91. ~a b v o

not sh~wn the msPPr2- iw $he XWB til.31 <ii<0*6 Ssa, fk. B,

alnoe tjr ~ ~ l l o u l & t e Q W u e US 4U, caxca~a G.41 In W r w e .

%is ungEy.altool 3cmrr2E &@ ~ w r w e d Qy Ue3,uBiw the @*fpm

oxder ternr iio la eeen in f&oree 3b and 3c, and dam at &I

gs&.nt i8 a aaisa$oatl?o Pax flfc2O.4.t. It mum Qt9f Pba~i~ EBPILSEIQ- -

. FIG. 3a: Variation of (P2) , dnen and obtained

by retaining terms up t o p2 (COB 0 ) in the expaneions of angle dependent term and p lo t t ed ita functions of 2R (for ~ > 0 . 5 ) and 1 1 2 ~ (for ~ ( 0 . 5 ) .

. PIO.3b: Variation of <p2) , (P~) , dnem and A?/F obtained by rstdnizqg terns up t o ~ ~ ( c o s 0 ) in the expandons of w e dependant t e r m .

mO.30: Var iu t iom of (P~) , (p4) . (B6) , dnam and AP/p obtained by r c t t a i n l ~ ~ g terms up to

' 6 ( coo 8 ) I n the expanaimla uf mgle dependent terns.

FIG.4a: &/Ilk, ~ v / k l and $ obtained by retaining terms up to p2(coe €3) in tho expansions of aslg3.e dep enden3 terzlis.

FIG.4b: k PV@T and $ obtetned by retaiaiw term up t o P ~ ( C O S 0 ) Zn the expansions of angle

dependent t erns .

IFIG.4c: da'bs, PP@ and $ obtained by retainio~( terms up to p6(coe 0 ) in the elgansiona of angle dependent terns.

f%m@tlt-, ma daw.t%y

d e ~ f * w m r%Eajrti~eZaf mapfii,3y im %Em -mtr~py 02 tlla

only up t o ~ ~ ( ~ 0 8 B)

in expanaton, A?& epgraaohaa -0. Inohiiing terms

to 8 ) ( f i g * 3b) and P ~ ( @ W B) (f~g.34~). A ~ P

~ W C 0. aeu,47. mmaw

ar War ~tkbpmr~o2; sqy f m x @ m ~ ~ $ale, *mLf-U4' r@Wf;*

Zhf a *and &a appcrerf "t;c3 l&s %@&ti fur ~wd-czph~zz~czq 8za

( o w cftrnptest~ XP rancf V), %ha ~ l W e e r ixild,%! f A @ & ~ b ' U a *

U r a * r ~ g i c a r the VEGW all < i'2) ut IiI tcdul f a

'bes g~%~axx%S&&y rj;fCf@patpnt a i d i ($&gfS3a), $~-EUW~YW* -PO rfa

our axfif'b 0$ *a ~?pst-e;st;$ns@t;f~n, &A %~ie:phg$m ak U&QSE

lQm3w t6xTm 1sPad m a dt

(IQUIPOEB jb ,, g ~ ) . (pa) imm~1~~eu W ths wriuotropy

dwarawra, &$aim a mxxtaun and has a ahaq dfp m WB

approach It 0 3 faking a eaiLP&w 'Pzk=iatsl, f c m ;ill!U*4ci'. Aa

asan in the same f&prae, (pa baa hi(;hnr v;sllreu O h a n

(Pa) in a a m U range oi vIk3w~ o f ZR w m t x 2W m 1. ds

28 rp~roaohsa the rii lus 5 1.0 I U2@) bee

d l e r . Hame to get the liI tr-m~ftion, <?& It;o

h??gw? and f e g @ r va-8 ara%m& 2s c! 1.6 ( d d e aq.i?;rZ)* *eta? &one u~(~)*o a% *a. 5. %ha F r u i u i t i o n is ma. tLy delli@zm$W

( ' /~")r*a-x~u harfng the asme rdua of &,, at the

at*&= a ##a%imm d w r ~ s a @haply a%ta&abg a ia&nA&mas

wiilue r~ 91% f crr li " 0.47 4b trnrli 40). ZxparAff3t9nf-d;Is

&~*ad.rs! orpf a& tl979) gumdl Wf AS;/~&PJ.~ -' CP, Ufi Par 1% (3 4

f sea eab2.e I)* Wse a&huZ.rstsQ ~'is3,u,e1 $0 f3J1 arihiw of*

tude larger. mJW.2 s - a appzoa&ob 3.3 SIC!-

lhm our tmJ.eat5- ~ # i a i a g ~ t w i)2 :!F$ r$gW

~criZ#NlaX t$y&irrb@~+@, A% drs @&ew a t E*%o ~&@-d@p@nd~s*

Itemu iOQ &so oW&uJlsdC wdt.~tur, %s bisl @xli;aoxwfd et t

40 f O W 9) f a :;L~&%Q~II~~V C O X ~ ? ~ C ~ 33#~t&'%@- 4 X~f.tit#,&= a 6&%=%&vct ~0d;413pU&kL~ U8 XfOIPD rtOEQfi%Z'e % ~ a

Ewers fZ9 a !3b ekzSBdt raf lgw i ti :sn

groputieu when tlte ex~)ru.&ion i a rcrttr$.icted :u .??;coo *C B)

and %w &a aaaunad t D Ba 0. G a'; 22j:rI. reca l l fFwk

f b ~ e is 3 ~ ~ ~ c ~ ~ ~ s P I A , $ % ~ f3ik t~&,%.*T;i@l'& ,az.cpaS?tAii.:: 92WU!

gZ r̂ 0, S filr ar qyfat.cpm o f c ; r U , " ~ d ~ L ::;iP ~t3L.a rt.ili?s, ~ f f na0 7 the #xl,ootr~$io p8mE 02 %>ta ~ O % C F I % " , ~ : L J * f e s 3ci:a ,Pop 2. II. Q.5

u b @ ~ (9! 0 (OW $A&. 3iil. &L.%!xEI. $3 Uli.2 C330 i s H

& p p ~ ~ a ~ h & 3 3.5 I ? ~ F ~ Q eA";Pser s i d e , %I@ ;x~C'kis& 3ai%$~a21, t&@

t o e x ~ e c i the c3me~% ;~aak& & t 3 ~ ~ i 1 3 1 * 3 u t by L : + x ~ I , u & A ~

the et t raat ive potent id ( o2 # % 6 d ) aw bto

PI0.58: (P~) , 02/vOk end $dv0k obtained by includLng an attractive potentical an4 re tdning terms up t o p2(cos 8) in the erpsnsioas of angle dependent tcrma and fixing dnem = 0.6.

FIG. 5b. DPl F , Q U ~ ~ T and + o~ta ineci by includiw an attractive potential &nd re t u b i n g t e r m s up t o ~ ~ ( c o e 43) in the expansions of an@e dependent terms and fixing Sam = 0.6.

rnrr 1 0.0 OIO ~a~aulutionxs near Be 0.5 are a d pwmibla

similar.. UnWrr in the h.Fd y ~ ~ t i o l e aystsm, <I?&> ia

lees than <PI> rtLtah i(wU l a hpio than (P2> fox all

FIG.6a: (P~) , (P~) , {P~) , OdvOk and O 2 b 0 k obtained by including an attractive potential and retaining term up t o ~ ~ ( c o s 8 ) in athe expansf 0x18 of angle - dependent term an3 fixing 4, 10.6.

FI0.6b: AP/p , Au/&!E and f3 obtaned by inoludtng an attractive potentiel and ratainlag term up t o ~ ~ ( ~ 9 8 B) in the erpan- alone of a w e dependent tena. and fixing dnem = 0.6. -

t N- 2.4 f u r rad-Uk@ rndhenrlaa and at 2s N- 2.4 ~ G G ? disc-

FIG.7a: (P~) , (P~) , (P6) . $/v,k and %/v,k obtained by including an attractive poten t ia l and re tdn ing terms up to p6(coe 8 ) in t h e expansfa of a w e dependant term and fixing dnem = 0.6.

FIG.7b: bf'/u . A u / m t T and $ obtained by including an attractive potential and retaining temo up t o p6(co8 8) in the expand ons of angle dependent terns and fixing dnee 0.4.

FIG.8a: Chemical f omrmla of hexa-nlkayhen~oat ea of triphenylene

PIG.833 Structure of a d i s c o t i c nematic phase.

F I G . 8c : Chemical f onrmla of hexa-n-alkanoateie of truxene

~ e a X rplole~arr ham six Q M ~ ar paiptte-q? wi%h a

s.xw-m M a far p p z - & i - w

zrm f79+jQ t o "1*9 a* b4mz?ea#m

AP ~ m v e d by en ayyram\te arpmaafon Pzr vcxc2- Gala-

a vaXu.s dbas %Q 1. X t @%air* imr4fuil-y the d l t ~ L i e - ~

of x la dccreoctab fisther aad beki~ei t ~ ~ i i c t l y in

%kt@ sppmite r, qunlita%iocs hetrirvfour of fir,$

M'kd 32P) f~,ff0*&03'M d St Wk8IQ@3Q& 3U3: ~@tl&kWr

tho numb= of t- mW~18b in U;Q exqi,walon o f YlrjnXOE.

Efg ~ Z W X U L ~ S ~ & $J1 &.~;~TPO%,%- g * ~ f ~ t L k e J t %hay i rda ~ ~ 3 , ~ -

~atiotls for x 1 ~552 by rdwtiry; da Q;, to bwt

T 403% 4.O at BI~F o t i m r pro~ertiom; ot

are C w a t o b. (P2) 0.595. s,, 3; 3 G*478p fyJfF ;.i~.E64 sad Bhnr = o.97J. par eilnc widus of r by

fixLng $I * G O J T aOC = 0.6 nt '+t. WB iet IL

< 0.45. A?/F * Q.0024 turd &&klk 0.34. Le. , u