6.1 Ing:robuottoo, - f3tEldiasr on blnarry alzturss of as@

aawoundt &re been 0A' oonsidso.&&a Ssltsmatr, For

e m p l e , t n Bhs idenfifiaa%lon or acsrsetreraa tlypes.

ulh.8 twsr wmto&war cara a x e d togsthrsc, usually $ha

&%*-a arPxrLbi) only $he nem%&o pkoraa, %Pgll, $he

ammuafio-IraroCmgia, trane1t;iiJn berarperertiwo aS audh M x w e r p

mrxiss linaarly w&th lrompebltlan ao sr &it& arppoxi~~slUa8, $43

2x11 au& sgatenrra, %ha dopan(2eneo o f tbs g~e1t;fnp: polat @ol

Qhs aolid oa %ha oorql;lor;tt)lon waa bo derriarihed bg the

&mAe+Van Z&w eguatlm. 9

fiow*ver, i n $ha rooenti gmt, n e w $;ygea of phsae

d l s r g l r ~ a h v e bean PouBcZ i t s bSnerrg m b & l ~ @ @ @f @@%I%

~ ~ ~ Z Q S F ~ M I . '*20 %t~bhea drtursas show me aaneetio A

@16~@e (a& B C U I Y ~ ~ ~ W B sr$?Par. l i~~)@~tSok~) i d , esofar rqrs o f oo~poriMonn (ras4lurs aonaenO~crf1 me) even r A a n naimer

Q E J - O O . ~ ~ 111 the p u n @tiate exhibit^) the eltu1aW0 A ghrse.

OenMalsag aus slrtteixtie11 to suah o*n 'inQuseb srnraolle A*

phma (or Andwad A g a h ~ * * ) ~ Oha MO 8raneai$iarr boutlory

ohiaxarste+ietla&lSr axWbfta a rou f o r or a e r ~ n

oomgoeibien wM6h 5, muol%y 50 slaaeP o f the aoaponents 6 .

S . S t i r now known M a t .hhs idlutred A phase is

oberal~ved i n o m 8 o o ~ o s t i f f cm ranee of the sll;xatrola wbw

one aP 4ho oari)onen0a hau, %ha stroagly polar @yam oa:

nlPlra and grwp wMZ+ We o t h r oaapownt bra no eu&

maup. 2hw Lntezaotlan* wtw@en ye-neat Bip~1. m w n t

o f jibe sts'm$Jy poY5s irrolealalts m a t h e XnBaocsdt dip&@

m w n 0 oC the we&Zy paJw raoXcsauZc ssgpem lsu be $war-b

far the aaswgeaae of &e SRduccadl .& pU#a. We nraootbae,

bowever, mntiilan %her% Daaron and 13;~~lard" a d ~ursnrh~"

have Sound $he Anduead A i r r . amat mp0dltt~~ Oran wfx@n

nei *er ooml;rwio~a$ ha# bhe wane o r nttro P*

Pmk 90 OX'' sw@aQad tbti Lseu~ed A phase is

i omrd by virtu, of nx a W & e trmofer intexaacrtion of tho

omponc)ntls o f o b J ~ w y ~ S x t u r e aontaiatng rsWawly ipoXar

a& wmrrkQ p a Z a ~ soZ~c~ul6s. f a szrgih *1x$wes, ahar,$e

em%^ oomrplex t~~mull i~a W o @ pboa between Che

me;ls@ulea of Oh* Bwo kintl6, the hd&lg p o u r a~mt3omat

~ o t f n $ a@ Bbe rPeo*lrt;sr while the o t b r ~mponemt mtl~

fLka ca donor. BvlBow* f a r @%oh an iatararabim ha@ been

XQ@ by riltebrw 4% 81'' who 64t(liaBbd 81f addltioml.

absorption bond nLth negrrfiva dZoh~oic4~1 i n tb@ ~ l @ i b b / ~ ~

Q , 6 . 1 ~ : Phase diagram of the binar systemr 4-n-pentyl- ttenyl-4 *ahe~>tyloxybenzoet~? (7.0. SY) 3 rl.-n-pt~ntyloxy- 4'-ayenobiphenyl ( 5 (IBP). (Reproduced from re f . 16)

Molar percentage of 7 C B

PIG. 6. I b r Phase diagram of mixturen of (2-hydroxy)p-ethoxy- ben~ylidene-pl-butylaniline (OH-EBBA) with 4'-n-heptyl- 4-cyannbiphanyl (7CB). (Reproduced from zef. 17).

sm;rsotnur of aaru aix.tiuraa axhibltirrg, thr iaduo6d A

p&aes. 3EhlP ilajrrxaefion ~ e s ~ 3 t i s La o prw~ng Satanal

atSrsacr8Scm batwrcn blrs J;wl Qgpw of w3@ouhs, en& Ln

turn m n load t a @ha Esrratisn o f a layoxsb

-ti eh~~1?w*barfsU;rso a f Pimaadito pbareerp.

rUll 8iraeucaaral i n Ch6 araeli6r csh~tara (I, X X X

and XV), tihe P pbea %xBibi$Qd by h i & Q po2u: cswounQa

wiXl br d f 81 bll~lgttr vaxicty, hare Zag@%? aperoiayt: b a i w

oona281ar&bly gsbkltao **a a6 aoXsoukar: ~ew%.~* BhSm

alruc)nrr@ ~ X % S Q Y &we to the rWaw arnBip~lrall61 aorre

latiions MbraQen the nri&bawb% aolsoulse aiP fcrsasimf

galax 0 0 ~ ~ n d s r X* binany m ~ t u r e @ a f euch ooa~poundrz

tri* wra~arleX,y palas! eonpournder, it iu found %a *an OEB.8.

tha: Ww bbXatragss amcMo Zm AaJdsralbla u f t k inbus@&

A p&sr2' ( f 1 g . t ~ ) . t i ma bizamr aez,Fraapoatr tc~ nrox~j

twa molcsauhr rerrlrt$hD (La., % ghar), o m grEs ta phaw

b f a m i t t ~ n Ezlw (B bilarw I p b o r f a a raoaahger A phase

( A ~ @and (as dimaurama i o ohgp$a~ x j.27

cbuEsa o l -bhs goXas awp@nan.fr on om bawl, toad fhs @brae

jrmmta* aorpSrx folbrarrticus be Gvrrsn *he Owa tym@ o f

mcliteulee on %he o b b r brPB $a al&nUiorupf inkfura~ars on

thl phyeleal prope~tiarr o f Chr aisl$w*rp. Sar sxia~~ple,

Pwk eB a&'' have obewved s$rens panritiv~ drvhffom fn

pI0.6.2: Phase Eliagram o f mixtures 02 4-a-pelitylphenyl- 4 *-n-ootyloxybenaotlts (8.0.53 with N-p-eyanobetnaylidene- p I-n-octyloxyaniline (On0aA). (Reproduced from rmf .26).

the mJlw @Z dieleotrio arsi@ot*opy (he). A SOIW wwk

per #en$ of i l - ( p m s ~ a x p b a n s y l i ~ ~ n @ ) - p u n - b ~ ~ ~ ~ i U ~

(MBBA) an4 4-ayuuro-4*-7genty%bipMrqjS, {OFlI1] hsr ;Q a e

of 7.7 wbesaara icn ssllat;?le addiMVff raw fayglias or, value a i

9.8. 9Che i a temcb imr abbe aswe o b 8 @ @ ~ i n d@a~l&%iarrr

and *hatlLa 001~01ssllba Of thl O I X ~ \ ~ ~ U @ * "

ALB wa waw i n We pnarPouar ehaptur. mcaatic3-2iks

ahnrt raw* o&zrz t n the mbiw &nSlu.nclari, eon8uct%vity

aarootrapy $o a oonei8rrabLb3e 6tsbegs.t. Xicook &.ti arlE?' have

- w a n d thca el@rrPri@ralL. @ollSuo$ivitp erf %we 2k4atfB 6xy#Pml

#&ra$wea, @xhSbiWw iolXd%ed A p W s s . 2hda resulOar

ahow Waf as)n iua t lv i ty a 8 a ' f ; r e p j the &tw%~3, wnioh

i@ n a w t l v ~ aO Xa*rex aorra@nZretiom o f the po3.ar o ~ o a r l r r t ,

Sraoraaneks end p ~ s i t i v e with inor-iw QonedarpOrw

$ion aP gofax uerapsmmrb. S a g hav@ a%S&bu$e& bhSpr

t o %ha wawfw biilaycsr rlkru~ttture fhe pal&.r ooaponcnt,

the3 & Q V ~ dilt;ow#i~n i f i: alem tihat op@atf&a

raokwlar int~rssotiom ixrPTusnaa the pWs5aar3 p?opr$ieb

of Dhe a5*funsr omroide~ably. #. have a Wdied sevee8X

bt-g agltxtw@s wMkfoh ulxibi t the induced a ph@aro oz 81

w a a o gap betwwn A@ aond induaed phsse,.

avo omponemtie of B e mixZure ware ulri&tie&

aoourataly (ueiw spa ru%~hlaurea Perkin Ebmr )bodel A&&)

fnao en gZarwr dug prmid86 w i t h a ~ ~ u n d @US)@ i?utOpper.

me a x t w e VBB AeaO~4 t@ ?it143 tlraerap5a pbea a& Bzix84

thorowSailg by a~nrmioa2 %tit "~h.rn i t w a a ktapt in

Oh@ &~8rop lo ghaao fcrs a Sew bwm. @ w ; l e wm

%ha $ranraferar& on to a slide wM&e It waa la

lootrapfa gfiaillie. %tr tPhm&ntrioa t@ap@x~hxc~tdl w a r s date*

s&ned bg u a i w aa Hetr0hr bat-@tare8 (FP-92) fa eanjumtion

wiOh r whrlm- aiamercepe. !EM ras$e@ of hear@%* and

oooZing used for Chis p'ixlrp@&o w e ~.Z'/alaulrb. Flaisai.

txaxurltlam wore alrro ceof1rolard wlw di t l i i f e ~ s n t X ~ r

~lsdannbg caelo&lllsl%sr (Be~Um-r D&Eb;?). Ew* o i

QFsnaJ1 tian* p ~ l r varSow &&%%re# wars &SO detomfaald

4sw th. DBQ otubfea.

(5 ) p'-aitroplxanyl-pawaaOf 1.~ltg$ennwbe (81EJW)B) w i t h

t 2-~a~%y)-pl.tho~Ben~yJ,ide~~~-p~~brit ylr~nilfsu, (O&BIIBA)

a d (&A) p ' r s i - @ ~ Q & @ ~ p p c ) y ~ n O b i p b ~ y & ( 8 WB) with

p-bu~ojypha~l-(p~~porttyr6ry)be1~10*td, (4Q.09). 8 008

ww bzmgh* &am PQIIPgSBa-a &@he -6 u5.d ulthoul,

iur$hor purif io&bi~o. 4D.03 aM3 OIIImBA ware nynbh-

riasd ig our ehamlrrbrj SaboxaSwy rMia the %haOB elurrp3.e

woe )ainBXy @at to oar by Bxel. ~c f ;r .@lf fh ,

%he ahntakrral i'orxiube o f a l l %be aa.qparad@ are 4 h e a 1n f16.6.3.

pbuarars &&&warn of t h e ~ . aixhbufes fa rhoPm i n ti$, 6.4.

lgPOCtf'l ham aha a.trrow3.y pol= nfwo ow8 $COW rad rxhlbits

r pa~~%iaSly bilicml* A phatee w i * layes @wow 2', +iS2L, whem R ~s tha ra%eauler. ~ e w t h . 0 8 - ~ B A Bn~m

er&y a t;f@ phma~iar sye kai (~*RiBlt@ a pranourred

&srimrra la We &4t bapmdaxy, indll~nilllvs o f apn ln$uoed A

gh&a*+ B e malr i i a Pbe il.4 boundary i s obaraevad $OF

wdiw aonoentlra.fricau (d SUP PEP t h ~ ~ B f a r aamp~aan~.).

%!his with naerorat, rdlrlier obla*sratlons re@ ~ t g * ~ , la,&). 8-x O ~ C B ~ ~ A ~ A ~ R OUPV~ i~r a180 m x ~ & t l ~ l ~ a by tRa b-ES borndarn ada be men fzw t fw Murgara.

Plore ixlt/e~@rxtdw;lg, 'th# b,B ' b W s c y e s A i b i t ~ ta w a E

Mole percent of NPOOB

FIG. 6.4: Phase diagram o f mixtures of NPOOB with OH-EBBA (sys tern I ) . K stands f o r the crys ta l l ine phase.

briiaea mimimum for a aornyoaition rieh i a $hs B - 1 ~

p a @ aoaponant (~',?49 Q.C IOW0B)r $ha% the

fbp0~rrrrt;urs rangee s f oeslcllo%w% b a t m a 6h6 A and E,

B rnnd T phase@ are Perlsly narsew. PPw N g h s ~

proentrrges of 0SmBA (>74&)), $he ialrfwm arsrlzibier

~ n l y ttba lu p W e .

( i i ) 19ixburrrrs a$ 8 OOZI and 4Q.M --- m a 1 *- me

@we Qiawraar of $hh i%riil~~%oaia @hwa Sn iQ.Q.$$. B am hta $la@ sffowl31 poXac oyana, em3 (group while ncr euch

s$zoa@ly gobr esoup~l m e prraent; in 40.05. 8 QciB a&$-

bier, a pw$iorlXy b i l a y c ~ ~ & wk%h hyer sgaatn((t

cJ,O .4 k . !&A@ ag~lPl~ra cPZeo axMb50s a well 4aZineB rmxi-

mm ae weU a& a adaAxnu1~ An $hr A 4 treun~$tlea bounaery.

Em@% il~ i# ucrkhprhil. soapwinas aha g b r n &$amam o f

ily~tem BIB a& r f (Pligw,B.4 aria fi.S)* ~vaura the two dlagraroa

i% Am &em sht i n egtateaa i t , ths tsnilenoy $0 farm tlho

iaQu~tc& 4 pRwe i e meh aWoxig.1c dhdan &a @*Sera Z. Xn

the formr, bha d Naaa wit#$@ up? 50 o o q hi& tap~pratukux?ca@

and naw %he peak, i f t~bhnaiozai, diccletlZy tro eke ia ; ia~oyia

yhrislar. Qpl t h e o%er hw&, $he p e a i a r .t_haa Swluoed A-ti

bow&dlry ef: ~yalialn S i d auah lea@ ya?onwnosd and l ie@

wU. belw the &-I *~rtwttia& b ~ ~ n d a u r g r fhilp asam %he%

the ind;erwtiom respons ib le ' f i r act &&d?ao$&~#r cf .Wd A

phace asr.6 meir rstronger i n @x@%ul IX Wan &A a r y ~ t a ~ X.

Mole percent of 806R

BIG.6.5: Phase diagram of mixtures o f 8 OCB with 40.05 (system 11). K stands f o r the crystalline phase.

m a L probalg. a oomepurmoe of th. LPterar hydmrgl

group is C)&SB&. A8 B meaurB o f thir ozit3~rfiif~m4, We

arcrsmm ~~rucahian batwaeh Q*Nli,A ULQ IlrP06B oolcalrleo

i 8 Xfk@Zj f o be la*rqer th&arh %ha$ bofwron 4Q.05 an8 8 0GB

aolecaulee. "EBur $be a@u& a;l,nten*a.tilon ex$^ s%~ryomfb3e

for the lrndoorrd A phase fm aye war f t a 611P1021.~~ qhdifl i n

eycsdsm i f . Xn aystrra XI, bha m&aX~lua in $ko A43 bodurry

w o w @ $or a airture aoNirlniag d B ! $ $ o f EP O(W &&Zg me B Q ~ X S ~ I I 5a obtsimd Zw dl OQ~~QISISIOII SLBtir&$ cJ5tlC1Y;k 83 OCab.

POT 96TY high piBfQ@Xx6@((S.. @f IC)rOfS, th attxtu~et~ ahcw

an& t b s I@ pliraae.

b.mg*saturcl an4 a q o e l C i on ara lirtad i n W Gli. I .

we Piad that i n eyetern X1 the obseswd rand oabaabrd

w%l,uer of euteaESu tewer&$urare we suuaX while ti2

@-%em P I , the obb&@m@Q WTW @ff %hebie euttaaClrv fiemar- xabu~h i n r Lower SFia %ha ea30uhLsotertP rducs bg Bbolnt "PO. En bo&h the ~*uyar$war, fho ckrrPemed faallwa Qf wte@lrlc

aclnoeaCrotianro cf the polar ooullpmnrle (am23 a d 8 O@l

ase Xessl $&&a Oha rsorreaponopiq ca2au2utM ohuluba.

fPclnrllw 4evic;8tlom Leva bean feu?& i n rorlidlr i%%u&frre

on @pt.k,w rxhibLfiin(t iMuocrb A phaare. r7 m e wag arr?iee

ua h v q oae2ouli;atisd @M efttrswip o f W(B A 4 t w a f -

t i ~ a fmm J389 ewvaa. %'he rrrsuL%~fr wuee pr@asnW for

apvcsra X in flly.6.6. Zd &a SxcbemsUq G L ~ nete $hat, t h e

&&ape of Shi r owvr ira wary aSlPlibt ta tXlllC OX TAR, Q X k b

bieiag lo laruhrn for a oo~pprnirlo~ whfeh a&@@ exblblfe

tw wim An %ha firrive ~ O U M ~ Q . ihw~;tlrrr, the 4-48

0.rauaXtien f a olmoal aa~c\o& wc8er i n o h m c tfeir for hba

@oapori%tun aldzibitin@ tka aiaLrow~ i n ah@ glerrtle bcunaarry*

x very @i&ZSBr bxe& S1ZE IOU& D c ~ 8ysyatew IZ, Cnca @atropy

ot: A-SL brmtipiiaa xurew: W a mxhm hSng very eauelr larglox than the h i ~ f m a t Y&UQ 5P GYP tea P. XS i b X n t e l ~ ( b a U ~

to note that i n haw .tho r r y ~ tala, campeaai tionas e(~rr.- spending ~4 rn ol;entals in Gks 444 bouMnracss irtrvg

Mole percent of PJPOOB

PI@. 6.6: The entropy of the A-N t rans i t i on of crystem I as a function of compositicm.

gmhaz e 0.91. mi@ WCSQ iiii hi~hffar tbaan mt rayortrrsd by bhrs, PIQkafZaLan ~hewy,'' r;la*, 6 0,837 for

aeolpnd oflev H trarmitioars, %Irb oncae sagatn ol@u~J.y

shows that %ha int6~aationa rcraapunaibjre bar a 4 iwu~rad

saeatfc phase i t n r'Z a n swh %h~-h0~1(1

$a sjetsnli X I X t &@ anppropsS,ate %to stexlli~n Zbt

BuLlr eO &%I3' haare a.Ou82eb 2he M $=ml%iorn %n%h&lpy

or ia iunatisa ef ompwgtion in m d + % w c s a t EBBA md 14 0ts.

%he ;afix$aiure e%h4bite inBms& A plaareeb fax Q00pWitl~)XW

rangin& tmao nr %e# t a 60 & of B &)QIt. "Ehs heat cE t rm~lil-

$lw reanoh% a ranarir#raa valua for tb oomyroi:f t i o n arhioki

we have nuwurrd tlrcs %lraqcara%urca vwiuUerm@ o f

the ZIiryer rlpocaingrs i n the A i t @ r irnd o f tho @ m o t i o 34ke

ahwe s oraib~ i n Oha B pbt le @%@@a .Fie %@, IOI? vwSwue

a m m i t & ~ g i ? l a$ ay8tm6 X em3 XI. %he rbi:ulrx~ are @ham

i n Eiw, 6."Ptt 6.8, BePoTr dlscruiladw We rchznlra a f

our clxy@rlmn%s, w bxibflp teoiaU %he #&rXller werk by

BtnaeZarm, s t alZ6 i s h ~ M2wrvtt rrrllwwed t ;E lO ~ a x e z slpea62n& iarra or

fousrttSbn i?rP u~e~~wi&iatn Sn Y P ~ ~ A A ~ % G T @I 4-a-pexi :~pZph@w1-

4"mn.-o,2tyJoxybon-ti(4 (8.0.51 aru! %-pcy&na'5ernwI::d~)rw-

p~- lm~oeZylnxye~~st l la~ (m0aj~ ). The ILay~3r ~"~u@Anhf ySotOEOd

WePna* @soarpa;~ihien i n t&;hla aycXidtzu i@ ahwn i n f*,6*9.

FIG.6.7: Layer spacings of mixtures o f NPOOB with OH-EBBA as functicms of (TAN - T). Phe numbers against different symbola indicate the mole percentage of NPO (IB .

r-. ---.-.-.7...-.-..- - L D Q

o o a , o - = t - ' c ; c u . i & , 4- 5 c o r - w

I I I I 0 - CQ @ ; x u 4

0 0 cT)

X

><

x

x 0

0 X

e X

a 0

0, - X S -

0 @ X a

0 a @ X

0, cg X 4 e s" 0 X .~.. Q) -

0 B X

1. I 1 L - . A CJ Ln

0 o a l

PI

; 8 4 (U

; 5 3 al

4.4 9 (d

ol el 0 id4

- ~ 1 ' 5 1 0 .i

0 a * P I

0

$3 4 '2 k

- $ I - $33 a'

+k, 9"; id

a PO P) (d

!l rn CI R

0 if* CV C ; : a o

(U w g f ! a .rl 0 .al

rn &Z +r 2 R ' t!

Q il's 3z (dn a, 14- 6% .. co . \O

cs' m c.4

y UI 6 u ! m d s r

0

AB $lie, paraenwm P ~ X O&WA 2n $he nix lwe , $8 lmwaaed,

Bk.@ Jayi~lex t i h i a h are3 deamarsea olmorra l in.at~%y up Co

a'bou.t $a# ~ o U A . Whrn B h i a l S a ~ i 6 a ex&rapolmOad CO

11e t o %;ke maLeauZorr

Ienlgth a% GWQA L obtakmd. B\r$ &arlnrra]l

%ha% a n l;he moirtbure &a laom SO: (bi( BoQA %he

rgaoinlg l a b r ~ w a a *$Etita ~ k ~ ~ p l g r ~ p p ~ ~ ) @ ~ h i a ( $ B b PlSlOyar

vurlw of 611001 m 6h8 8.0.5 oawmbroltiarr, f a Qlronipxsed %o

seize. It Pa i n t w e ~ t t n l ~ , tro notlo@ &at the inklluarb

rnmuli~-acissaatfo * ~ & m i Z l o a allicw PIOX P c48polrStion

w i t l a 5O. l CLGQA. ZYroiadW atlrtlSlar trmdls am be a@50& era $ti@ $$a haas% a fuddr4 Lrg ua, %%pa vaxlatf urn oE layer

srp&aisgo with ctow+oaftf us are &how& Psi fi&,u,C. 811; (81128 6 , l l

als BX 0-011 x~bat lve tarq98mWre TAR - f r 2.5% fcr the

@yo teas I a& Xf re@@e@$Avdl>y. Bhd aOoJ~cular iea~%;karrr o f

bhar f e w ~owmlada~ saPaulra%etrcab unlw ::@fanif: madcl3ar arsr

24*0 ( I m B ) , 281.2 (@&=&A), 22*9 1 (@ OGS1) mrJ *

24.6 A (40.09). U$l .ng thesw &at;&, wa sw Chat t b layer

I

Z

-- I J-LL-LLL- 8.0.5 CBOOA

Mole fraction

pIG.6.9: Layer spacing p lot ted against compositf on for mixtures o f 8.0.5 and QBOOA. The spacings corre- spond t o the temperatures represented by a dashed l i n e i n f i g . 6 . 2 (Reproduced from reE.26).

FXG.6.10: Layer spacing (ti) and the r a t i o o f the layer spacing t o the molecular length ( d / l ) Plotted against composition f o r mixtures o f system I.

F10.6.11: Layer spacing (d) and the ratio af the 1.ayer

spacing t o the molecular length (d/k) plot ted aga ins t cornposiiion L o r inixtures of system I1

QoaPpaasnOi h m b o a snonoxwagrrr dm& P l t l ~ ~ s f ~peOL603

I x l mmmen% wAm marulba an lat;hrrx: bynbem. j6 Ckr%w-

baortiona a% ga-T 1 ;"?*5*cmhov B M b (di.4.) rra.tio vlxrjlee

nrmoa*Xy firom a wine namim2Xy Iaatns Wcus ona for -%#

waEd.y pobr a e R $ w n t %O d Ire3 i n *bhr oarm ab pure

RPOm in mgertsam I and Oo ~ 1 . 4 2 An %W @me o f s Oills i n

cryrsbsn 5%. 4M P raa;luft& oS grCIQ19 @bnB 8 OQB @ear. wZ%h

atrrXpt2isr msrrswaraenZle, 32,114

PPSnima Jln the ph;plll~o d h m a ;ta&io;sr%e t b t Aa ma A,

(5.a.. imhoad arrsarnf;i@) N a e m y urot: 'be atruaaraXky

Bm1%2ilblla ( i n solare owe@ 14 i c r iounb ahat tliha A* pnsue 26 arnd the 5nBua.d A ghnm ox% iar;liarrkblrr 1. Hwevepr, t;hr

aoaxiotenoo o f botrh We b&sohod@r m d ismrorroX%@uXar?

&peelea far cm@aal.trlw& nhMs -Qa dbe dntma, srj tradf-

oat& by a aarrkinuou8 v@x4ation i n PaQbioe @xms~PltP.

BW*F@ OU% aw PO@@ &bZbl* A4 I d l t ~ ~ g l k t $ t 4 X I .

wib &pgmfrttln er oolFm~~o&rion c;%,waJpoP18$n$ $14 tho ml.rn2mm

isr $he A 4 b s w u r y gr%koa a.$ Auhas f ~ i d a s . B3.a 44.x b:rour$h% out

crlsarslgr S n ffg.c",,l&!,. m t h . ~ ~ , %he aqtna.$.on trclsP%claan$

gnemmeio w 1 f A Srincsseaear (PE % w p ~ r . a h r ( ~ . far 4nx &v0n

Mole percent of NPOOB

PI0.6.12: The thermal. tlxpanslon ooeffiolent o f the layer spaclnga of mfxturea o f D1900B with OH-EE3EBBA at Ir,, - T 5 2.5".

oclmpw19toa ia tMla s%gim. On obbex hnrnd, swrh

a tmm4 16 ruaO very BQIB~&UOW l a 8y0Ci.m rZ * W

rt9xlbube P U S dl5iwraae i n 'lrghaviow batwwn ithe tun

ap t - t a the large dlifocsaoa fa m e o$l?eas#lr o f tho

In%moSeoulnr iatu#toofttoa* betwwa Qhe oaapoarrnbr ttl

t M 4wa orno&, Ae 4ilaour66d ear l ier , ah% i n b O ~ t 4 0 n

h d w ~ ( ~ ! n Q&8 b * ~ ~ l l & y paU8 6\ld wa&Q polar

moSaa;uIe.*a ii aekat iveu we& i n isga9aa X, w&n2r boauaao

of fhe larttertcl hydror~tJ. g m g ,1'8-=BA aa;L@@uks, wrd

psrhapa bPljt @Ugh%J;Y higbrr am istrraa95on mw%y

wlriah &ve@ r l a e $0 onbJipralaJ, c)arr*latiiam botneoa fwo

m l s a u h r , Oerreeqwntly, She

t q e r r a t u ~ r i m solsod, Ifirob2~ tit10 b$eraal s x ~ l a ~ r

ooeS5lcSe& US b y e x a p ~ ~ ~ l i f @ osn be (~amibex&Ze a6 w6

dl@rmas.d i n uhptex ZEX i n ihe @%so @i 00aylsudla j&&

bulky l*tcrrorl t%$uenle, m4 &wthrt $he a6roolg5y

goleer-m&U g a k r wirs o m craatlg b~eal t up aXlow&ng

SWOB noJeo~Xes dre ~ Q X D a w e aatigaraU@l p S r s axid Otnsa

the Zhamal erpanerion omocriPPaSenO @&a Be vc*?p la;sr&%. XC

o m &&so be acbdl t h a t f o r aanpoarStlonar m a r PSalmw,

fhrsro oxr Wixw BIWm raQILeouX@a ;ror irswazlg QE-mBg wlcroule.

M t h e r , for t h e e oompoobtiaaa % and A* a t r w W a r

ooexdst arng tho A 4 4rcml0ioxl has a sr@en& or?der oharaeter.

&@ a ro@uZt, %hs %hemX emawioa QwQIIIQIJB~~ rirtairnd

l t ~ ~ p o . -Xu6 fsr g m o s &$ion aBom t~ tho .Ila;Enimm in the

phase PlounBwyr

(a) 9iW~io d i e f 6 ~ t r i 0 -- ~ t ~ n a P ~ b @

%he bewex~rrhwe ~NistA~n* OS $he grlWlpsaX

&ierfso*tslo romtents (a,, utdL ad) in Oh6 A oad I

phsrarea and sic i n tlPa im9ropic gfesrar ww8 waat%wed

Zoac +onrime @ye tern and am @hwn i n fim.Q.13 - 6.22.

Xa tM oasee cS puxe Pt , both e,, ma c,

ahow a daere~cae as OM rample $8 oacXsd aemsca Tm

I Wr t a w & a re ;in braad a(glec*n@at w i t h

slarlbicas maasulPs~(ent* era this o o ~ ? p o u a d , ~ ~ * ~ ' IWOB h a

PI mkXg flrdll order A 4 tzeura2'tion (Pig.bi.6) a d the

inarrsarre of &, , olad br@rascn, olt cA caa the aueqpla f a

5ooleL.d i a tha I ph.8. prob&&y rnaann that thgl w*i-

par&2e2 oocmh;slliw So no0 WaEy sucl* w i t h %mperrature

i n %ha A glPOilo aMj, $he v&~Iatiw a re ementt2a11y itetw-

ariaod by that o f tihe os%ent&tioml cxdox. 'Ehe ." t,, * 21, c *aSw iacrrmaer, vh$b tlsageratux@ Pn ma

PB phace, Pnsioslrtint~ boxr*mr@nai% demaa~a OP anti-

pwaU6L 6oerelation;o (u ascuawd in abpturrrr fXI an4

SV), & phs foqer~t;lPm 101 nrire6 i n the i~lotropfa

pkuasre, E ~ , , exhibtOa a bmad arariaaur, w i n Ctue $a a

deoreaiae in mtigarsr1le;E. ao8seLar;ionr, sti highar s w p e

=*we@. Xn Wo nrlxture ccn%ainiw 9rJ.ap BPWB, as tho

~)mgile ds aoobd, t,, doareasale lhiaighfZy aomsr Znaa

(.25&.6,14), atitam a broad iniaiaunr ma4 then inamauaea

aZigM1y l a the Zoc*rx barnpeatwe zmga QIP $he A pha#or

lpI0.6.13: Sow frequency dielectric constants (measured a t 1592 HZ) of NPOOB as functions of relative temperature. m e vertical arrow on the temperature axis indicate8 im.

BIG. 6.14 : Low irequency dielectric constants (measure8 a t 1592 H5) of a mixture o f 90.2 .inole per cent of RPOOB with 9.8 mole per cent of a-EBBA as functions of re lat ive temperature. The vertical arrow indicates Pa.

€ 1 1

22

20

-

-

90.2 -‘---T 9.8 % '10 OCiEBBA NPOOD

18 0

10

I!,

-

--

- E

G IS

s-- v - - -- - -+-- CL -*--- v--

e* rolaatm pxaaticafiy aoaraerpnti i n tlls A pha*ct.

2 a(laln laareewer with fi

whiah i r &as t t a a deotwrr i n anDfpw~tlr1, m~ra la$ iom.

91rmi9ar .tixea&a a re obrsarvrd in t;&Q ~ ~ 6 r s r k x z l . vari*#cn

of 6+, Jn the s%x$wre oantialxping 76.88 #Par38 (fa.&. 19).

?4& B M B (oorm@~;~ondlw $0 %tibe ~ i n f e u a i n .the A-IBt

bouMharrg)Cffg.B116), 7 2 k r m (fis.8.17) a d 67$1POo]i

(il i&.Q,S&). &a% it flnc imQ.*rerstltag t o note tha t fos

D%uarrr mtrtkre* e+ inarernaw wi%h deoraaao of trartpcrraaurr in

-hhs A pbaarr. %?Mipi o m ba eass31gr undurautcob i n terff5 sf

the tmllslssr I n tb swrbe~ (1S atsong2y pobr?lwe&ly g o h r

P I O ~ ( P O E ~ ~ l i l i ~ ~ ~ a t $he gxpenoe 09 Use antSpa~knl2el

**<XI&%JP P Q ~ X BLQ36QUbE PIE@ * d$;dtU&w Cb8

Qharge-Drensfar oamplexca iil w e for&*, A t i s @Pear tbt

Bhe trMef9*"r% poSwla&iilty and bsnar re, erkruulOD inoreaae.

Aa ean br sewn lhroae 4hh d 9 ~ 0 ~ 1 l e . &a ds&rra oS @&ancb

m n t f n eI WZW) itte)rw#bs wZCb Xnomooiw %onoeatr@tiara.

o f Of2-SBg. Lehira waka i~rh~wrr ahob a w e auarbss o f

eOatpl@larr~ as* re-d Wk* ia@mslSs OE--A

maldaull*#. Pox &ear aawsliitf om 5 va2tae inwewear

ali@tXy as ths Qi@m~riatwa U1 l o w r a l in Che Bi aa8 d

p h o l r ~ , daasewss v%;eg 62&helg as the ts@oratura

is r a i e d I n We itrotropla itbllPIar "Eh8 aurrplllka peak.

olaeu'vadl i n #war TM w&aw i%m the start?% tmdeoy

of like dkrro.lot t o o~icsn* hamofrgyisrallg i n ZSrr A p b a e

BI0.6.15t Low freyuenoy dielectric constants (mauured at 1592 He) c f a niixtwrr of 76.8 mole 5 of NM)OB with 23.2 mole $ o f OH-EBBA as functions o f relat ive tempe- rature. The vertbal .arrow indiaatee Tm.

74 O/. N PO0 M -I-

26 "10 OHEBBA

FIG. 6 . I 6: L w frequency a i e l e c t r i c constants(mea~ured a t 1592 H Z ) of a mixture of 74 mole per c e n t of MPOOB w i t h 26 mole percent of OH-BBA as funct ions of r e l a t i v e tempe- ra ture . , The v e r t l c a l arrow i n d i c a t e s TAN.

72"Io NPOOB + 28 "10 OHEBBA

FIG. 6.17: Low frequency Bielectric constants (measured at 1592 IIZ) of a mixture o f 72 mole 7; of NPOOB with 28 mole % of OH-EBBA as functions of relat ive temperature. The vert ical arrow indicates Tm.

FIG.6.18: Low frequency diel.ectric oonslantt: (measured a t 1592 Ha) of a mixture of 67 mole b o f MFOOB wl-th 33 mole % of OH-EBBA as functio:le of re lat ive tempe:rature. 'Phe ver t i ca l arrow ia;~i.oates TAN .

r ~ r t w e e aowoaiuma)) i n the nemboipho& of

Zn aiatures biaouslaed sa far k ehwa a p o z i ~ v o

*mp a* %x. ~fowevcrx, w e ~ a t a u d e ~i the jurpp

beareaem with 1aQrrsxor of @%m;BA ooa@omst. Swh

j w a b v e beon abseplved tn uevwa2 earlier si$udrtar f6.97

wUeh are naw well Wemtood (as dieowa.d i n ahepter XV)

aa srisial3; i r a r a a dearerne An tihe mnber af arntiparallal

gta&s, Wi6b tihe r e s u l t tbt the sIf%clDlvta aontribu%ion

a t Ch, Qipolax w w p a 6 1 Me paJw aaolrraules t o tho

d io l aa t r i c EIonatanli i e enherwed.

Ere remulta far a BLIx%Ure 00nt$r;b&w 54,5$ WPOOB

ur)nicrh i r a crmp@s$S;2oa aePw %he IP&X~F$U@ i n %he ~'4.d barulbarr~r

&fa shown i n Pi&.6.19. %he %eaycrlral4ust3 $8 dcrcsreiured, a

vary smaS;e d$sreass@ Sn c,, orralue l a bbmnlbfved mar ta.

But r , show5 a lager jhung new !Em I'~stl% 8,. on8 e*

lnamaea with Bmra&as of %csmpcaratuco i n %Pas A p b e .

%64se rasa&t;e are nore prast~urcsaad An ra enixiSurlra c o n t @ U n g

44.6$ NPOWI9 wlaoh Pa even ~Zetsrrar %o %he -1- (fLg.6,20).

Par tM@ aorn@ocaiflan we we %a$.%% a ntrmg rduQt1an i n

a h , an& t, an ata asrrgrrce $.@ aoolad di4oacrci~l5 ktnro. "hb

m y bee atat.tffibuEeCt t o the dlat~% th% Ma haat csf A 4 Qmml- %%en l i a r qu i t e X w ~ e far Chi@ aoa2aai%Lcsn ( f . i g .b*b ) clad

eke rcaaar.i@n%atioa& iar&csfr pwmeb@s o m btr expsacEwd OB juplp

$a a higher value in the A ." IIhQ ~ ~ O ~ U W I C I in E,,

5 4 . 5 % NPOOB

4 5 . 5 '10 0HE;BWA

F30.6.1'3t Low freyucancy d i d . % C t r i 6 eonatants (mmeured at 1592 He) of a mixture of 54.5 mole 16 of NPOOB wiW 45.5 nole psrcent of OH-El3M a B

iuno tiona of relative temperature. !the,

vsrtioal arrow Pndlcatars TIUJ .

fIG.6.20: Low frequency d i e l e c t r i c cons t an t s (measured a t 1592 H1;) of a mixture of 44.6 mole 8 of NPOOB w i t h

55.4 mole $ of OH-EBBA as func t ions of r e l a t i v e tempe- r a t u r e . The v e r t i c a l arrow i n d i c a t e s TAN.

partirly aua, t o aca, imndeoay of tb 4iireotw t o prefer

hono?$*aarotr@ oligmraenb la thia oempwitioa Ewe . Wowetaat,

th6 @%rangy pour-wee-3 pelar rlwlsoulsx pa&@ atlouP4

Be very Xw(l* fax: theas oa~yoalt ioar , rhiek we aloee

50 the acaxikw i n the p1l)maare bouldarg, and %he g e m w n t

bIpaXe lnoawrnte o f the ir&it$$ural mleculae BeZon&ng t o

auczb paertrn fu l ly eanbribute te a ,, w n U k i n th. #me of

pulp#' oQ" an%Zliprnca1142 HPWB wliaioube Sn whiobr mwe Is

a : :4rtiaX wmarna~crtien of the dipel4 m m n t . ESUrtlbr,

Ihs ohrge lclrsa~nsf@r cowlex &sir@ illnomare with d e ( ~ r % a ~ e

cP tempomturn. Ikhucl to fld(Pma6~ crubstisaUa2ly as the

ciratt~m 'la! Zweead Sn ths A phmae. a& atao imxcrmrs w i t & jhglearaebr?@ o f t(~~1plauutwe rs aSready Qi trousrsed f o r

&he :?rp~cscl%loaa having & higher aonaen%r&*&oss. of BPOOB.

Fur %ll%at% oawesi0iaaa, (aXa@e ilo tkdo ~ X I M ~ I P i n the A 4

buundsry), na jurqg, is obsurvrrd ia ralw af THX. 2hLs

i n r t o tho r~l la t l teXy BI)B~U stunber of onatrprallbl

palre An tach CmpasaiUennr.

%%Oh itlltme~ 4e0zewe BP BtYOQka concen%t&f2ua

(30% BPOOB, .tig.b.24), the 4frm$otr; ob&&rner& Em %ha 44.611

I,PFQOB rir-re (pet T e ~ a pronrricmoed ~d w&@m Wdarblg tho

inrarsaae a l 6, W A ~ B l~ ru l r i ng o f aesapeZ&&tur@ beomem ~ 6 a k r

FI'I0.6.21: Low frequency die lectr ic cronatanta (masure8 a t 1592 ~ z ) of a mixture of 30 mole 6 of NPOOB with 70 mole yb of OH-EBBA a s functions o f re lat ive tempe- rature. The vert ical arrow indicates .

%!tie grXmipS dicllsa%rio constarm%@ o f OE-EBBA are

@hewn i n fig.B.22, Am o m bo men f r m the Eimplsrr

OR-mBA fbao l f hoe o eem2;ra9tva diealers%rfo maalrerstmpy,

as tb$ ne t dip@%@ isomnt o f %i% m ~ l c s t d a art&ea a lasgi?

&wm$ka wit ih t h e X0mr8[ mi&. rl iracrc9aa~os and a,, & e ~ ~ e a a @ e I,

wibh dtncrraae el: tsnpwatwxre. t sew4 ria deoraaars

almost linawlly wiiih i i ac raaa r~f tcbm~?~lra@~.. AX1

OhracPr fxendo @on be Wass tood i n tarmss 05 Bhe Wrsr

and Hoi@s's thwzy ((POI)@ e h a p t e ~ fY) ahl app2.fed .to a

a a ~ e u n d with n@&atiVQ A@.

2he 8iaXmt;xle enlrsa%roplbarc nf a U %be @ A % ~ ~ c ( B B ~

thtiit we have &a;udia@ nra osXJ.sates& fn 13L&:.6,2!9. TB b

quf te a l s a ~ t h a t t h e BrsrqjiarraLurc~ vns&% t ian BZ Aa;, i n

tho n phase i r s qui,t@ &ilbZsvcsrr2: Eor corapa8ltSnn~ o l m e

.he cthe c a i r n i m ~ ~ a , dn %ha 4% h~indbap:~ camp=@& t o t+aacf@

@Y.@eai¶ $8 %he mxtmw.

In sarngor;SCfom e l w e f e t ho rPinima, WL8 A-kl

O~waf tSon is war~k euaB hema the ameoflo ordor laareme61c

( ~ b the t e m ~ x a t u r e 26 Zowena la %ha A phase with a

corsa~gcn$fngb inorease i n Ula dipolerr aorrala%%an fraabor

i n the laycrrsd s t ruc tu re wh&h tend8 t o to . mrs WWM oaqaneaae fax xry lnwc~raaae i s t ,, dun t o

r.frram&or ahawe BrmrZer int%rr\ati 0x18 end henoa 6 ,, does

not PnerePurs weh a2 Zower C ~ W ~ I F U ~ U F ~ B . iS#no. AL

BIG.6.22: Low frequency dielectric oonetants (measured a t 1592 Hz) of OH-EBBA as functions of re lat ive tempe- rature.

TN I ----T

6.23: Dielectric imisotropies of mixtures of NPOOB with OH-EBBA as functions of relat ive temperature. The numbers against different symbols indicate mole peroentages of NPOOB and the arrows indicate TAN.

8eareascbar at lower Bsmp%rraturoe.

Sear the whtatuar % x i Dhe pbed boundmg (W.9&

8wet8 arr M.B$ PO^), tihe A 4 $rannai*iaxa h a a*roag

fisrrb order @naraelrax&~Ue@, m d &nosrras* tn tihe

ua$ipara%Zel d&alor assrelation oierabors would P e a %a

a wxw w l t r h r jump of e,, (iiip.6.1'3 dr ~ i g . 6 . Z O ) aart

$&a A-I3 $ra&xaartlass. The j u q la the arictntlatiar&

a&er pormta~r r~uld 2erad t o 8 de(~r(b~r$i(l l a EL aldro

at %hi@ ;,ufLnd, 3u+, ,a@ the ~ m e a c ardw f s afseaiay

i . Z TdavrS i'ku %i@~ar3 )rat t r u y rauali w&L% a &Ether

1av4a~ii?, 3: tim~@xnt;um. %Q i m m s a f n %he number o f

@ h u r @ ~ Urwaf@r paire: wrjulJ la&& %o 6413 Lnaran8Qt 09 a,,

due t e t N amra ~ f f e a t 4 v r canrrfbueisno o f RC9, d i y o b e C

ira mch , ~ l r r , sffeut q p a w s . t o be 8trongger than

tk.,,%: Pnarcsc s o f E, Q u ~ $0 %ha inosaaee i n tb $mn@vw~e

golurSet4bi2lt,y o f the @ohargcs tranr~fsx g d r s m d Aa

aebcqmlly $ns@$l~_&@ wi%h 4(IsaMcosiae af f;6niyb~abm. We

& l a d ;:@it$% auk fwa comlsuu~!X Setatweat (I) %he arfxture

u i t k 74," h,m n lawsr vallir o f Ab %an *a$ fioi

th6 iaf-cfusc w l t h 72% BPEIO'b in the 1 phacrcc @load t o 'Pat

(19) fC01001u~~e C F the 0pp081be variation o f ~ c r r ~ t h $ a p e -

roxt~ara in %la@ A p%nse of %ha mkxtures viOh 54.5 $ IPWB

oolaprrd %a ~dxturas, with higher x?.srcm$agea of lilPOOB,

ah aoffieleolaly low teaapom%~%~erli, $ha 4o-r M e

~e m h e s bhm aany r r l r b r e s c i the Ipi$Pex typcr.

Z t i r a l s o intecalartlw t o oo*paaa thr arrlasumd

m1ueB a t ac ond 5 of the ezix.ture0 wiPh the aozlx!e-

~ p p o n w nmbem ~a1~u;La tad en We barris o t lrrn a&&itive

l a w of fhla tgpe AS* * PI ncbl 4 P2 AS^, where Pl 1,

s o l e fratrtion o f tba fwret c~oaponont, e ta . gbi*

results sara d o r m i n fable 6.2.

Xb i r elear tht a~m~aa/48~ Ja - x f b n

unitj. ( I n a p e e m a t witti ~clonr, erer~ierr cbsclr*lntima1'~

anat lslorsatam with inexeaafw pereclmtagtr af CXH-BDBA.

!&As i s rpcinly be~murre ths pmbablllity sf brreaklng up

of aatf psrrs le 2 cacjaoiatdanr M0wiaan gtm)OB moleaulabl

inezvsure~r with inareomfalp peracrntaoes o f C)H-mBA rmolsoultass.

Qonasqueaf.ly, th. grw can azora egfeatLraly aonfri-

burbr t o t ,, . As oan he earrily area fropa tXra dfagrwr

6.13- 6.22, e,, of ntlxt;ursa ip muah hllmt an

addiDive l a w wcmld have given (Jusb1e 6.3)* 'Eh. a, m l u e

do@@ no$ al.we V Q E ~ muah beW\s.sn SPWB m d ON-=&& and

herrare does mot ~ofitribuit. such t o the Beda t ion o f Oh@

a b ~ ) ~ % zaf Lo &ma uait$fe ~rah @hew5 mjPUII wMah

are gxwcrtsr tha one by d 3 *2@ A

(Oomparleon af OralculrrrSFIa and observed vtnlwbs of e ,, cat lSgX - Ip = 5* for M ~ ~ O U S &%we8 61 Syu tw f

rc. 3

2084

a a ~ a

agd f6,SP 4O,OS of nysfea Xf wMah i s ololore to bhe

1Sirax&nw of Ghe bBI browi$ lm boundary. ILM xe@ulto

a l ~ ~ s h ~ a i m fit~ig.dr24 are b ~ i o a J y r a i a S h ~ t o

thosm fox tu olfkt3.a~ cpaapwftrlon o f lap4an X.

Pho dieleotsio disgerclti on wear meewed up t o

$9 . In fi@. 6,294.99, we have pls*lred the

dieZectrio lore rY, ar f ia~Pi ion of frwuenoy at d i f f r

and &%u drlrur+o w i t h

9.B& 26s am3 4i9.5P of EsH-mDI. llor dhr reZLxOuce aon-

talainglt 94.5$BPMB, ths m~~lkcwromnt8 i n 4th P atid A

pluarrsla are @how reparapte;lgr (figa.6*2& aura 6.29 rcrrrpeo-

tiue"ly),

BC al l *he aryatarrtrs @ k \ b k d i t h e ;pa& tsalur of

6 decnaaes w i * inaxe(OL10 @f %ewesotwo whtle t h r

m1axa-t;ien f;Fe.iurncg (iR) given by drhe aserxSDnra ral~, of

, inor@auear. The pw& m3w of kf', Booreaeeta relowly

with teaprraWm ta 4hr I ghrrse, rn8, mare segaitPly i n

We lt &wo, reaenfidlly r e f k c t i q g %he *orirflon of

aoLe-Qclcs pzot (t$, r e , a!, ) i n $he a w e of

HWOB Jw shwm i n i'ig.6.30 for a few teaopera%te@.

btXus Taw i r e i ~ u a w g p e r t of" the p h t Zie@ an a

BIG. 6.24; Tenperature variat ions of the low frequency d i e l e c t r i c constants of a mixture o f 63.5 mole 56 of 8 OCB with 36.5 mole 56 of 40.05 (measured at 1592 Hz). The arrow indicates TM.

I l3 I yk. 6 3 . 5 % 00CR- I -

'I 2

-. 3 6 . 5 ''0 11).05 ... '% . U, E,,

L. -+--. --..*,.-

11 - .

Frequency ( H z )

3'16.6.25: e;*, as a funct ion of frequency f o r NPOOB. The numbers against the eymbols indicate the temperatures i n O C .

Frequency ( Hz)

FIG.fi.26~ t?:; an a function o f freciuency for sr mixture o f 90.2 mole par canb of IPO[B and 9.8 mole per cent OK OW-EBBR.. The numbera against the bymbols; i n a i c a t e the temperatures i n .C.

. .. ~ ~~ ~ ~ ~~~~ ~~ -~~

NEMA1 IC .Sh fE(~ l ICA 74 "1, N P OOB

FIG.6.27: E:*, as a func t ion of frequency f o r a mixture of 74 mole $ of NPOOB with 26 mole % of OH-EBBA. The numbersagains t t h e symbols i n d i c a t e t h e tempe- r a t u r e s i n OC.

100 K 1000K 10,000 K Frequtzncy I Hz)

B16.6.28: Frequency dependence of c:; at; variow tesuperaturea (indicated aga ina t the symbols) i n the nematic phase of a mixture of 54.5 mole $ of NPWB with 4.5.5 mole yb of OH-EBBA.

Frequency i t-lz )

k'llD..6,29t Fxrrquency depenaence o f e# at variuus temp* ratciran (lmlfo ~&..ct;cd again8 t Blf far en% symbol@) In the nmectlc /i pha:ie, of a mlxaucts of' 54.5 mole % of N*GBR w1t.h 49.5 uols 6 oL' &i-mUA.

PIG.6,30: Cole-Cole p l o t for E,,- ela ax at ion in the oaae of NPOQB. The numbers shown against t h e various symbols i n d i c a t e the temperatures i n OC.

~ ~ J Q ~ C O ~ Q , O h r e are crbnoid.r&ble devfotZoB s1t

hi@az Irryubmies. P h i r r w u l t l ~ e i n yu J l t a M o e

agrrrwat with aa aarU%r ah5y on $&& appegotud by

Bafm cr* and tndfootera a hir&h%r fra~ueaap sslaxr

tioa. me latter ~ ' e m a t i o a p ~ d ~ i b l y br OW@

t o bh. hi* f l r e ~ u u r ~ ~ p rrhoulbw found I n W e e,,relrsrra%ion

af 7411 sad 7 Om by BuP:1 et iPl* ha@ b r a &WE&-

butiad by $!tea t~ @ p r s t i a l mwiea2aUm wiSRln ehor$

cazng:e ~urBar.8 glroups oulQ h t a r repcaauord i n a numerioal

oerlaulaeftsa oa the bsasia t3f ia aodel ~ 3 j : Brmfaan a63ti~11.~'

az~zrcthar gotarEbXe 0s3.gin fox? the rho\ll&ar Utt@ i n $he

l ibra t ica i i l &a4 reasllantrat;fsnal sotion o f the tsfutsr

vrraao digoXe aPamsnf oP the w%er g x ? ~ . This rr~lfaxatlan

fre.puenay lie@ ~BIQ ,-J 97 S%e aocrordinlif t o mlasamcl.e 3191.

'Phe h t t r r aontribulrtola cs~n be a%pected t o beeem more

il?por@nt whea the orieolatZansdZ or4dsr garaiea.ter ds@raasea,

an5 %Meed las oien be @@an i n E&,b.SO, the high ire~uttrrray

d@vlatiiane iran Ohe aualoXraullar p lo t a r e &me obvlcuar

st hf &her aaamperaWEurss.

ba de@@rdbrd in caEirjptcr IP, the re&arslt&on Clm

isi @$van bg the b$(rwtiot~ S~ m A %np(w/ltST) uhere

tM 1/2nfR, w m q + % i a %s t o t e1 ao%ivatlan ~~lergy

&ere a Zo We nttmaicr gatentilrl, e(l 1s 8br aotivr;rtim

rnex?r(jy due %kt ~ ~ B O O U ~ eifa'oata and A is er oom0ant.

gggvoa a Uvls Ska slope QE whish f e the arraSva8ian

encatg~r. A ploG 0f la SR vrr. far NPOOB irs given i n

fi#,B.31 and Wtu octiPaCion energJe6 l a A and I pkusces

The valugs braadly sllreo w i t h the@% oPtOak~Q by Batrr

ar t BLP* 34

Eke QoZff-CoPs plot Tmr @e aixetlre wlth 90.2%

BPOMt3 i a rahm Zn ifg.6.32. h a p a , +e~hua, i r ,

aaUg2gRtXg Zowrs B R m i n puPe PPmB ( S & B ~ . 6.'1K)jr IPh. Oola,tr-

Uole p l o t am be bettes fL.bted to asrsai@koXota at

hunpstraSures. But (110~iUwsbh beviotjlans are a m at

hl@;hcsr Cw.@erafwes ant4 at h&br irss&usaaiee. Tba

sotimtfctn eaexgg (Zig1.6.9?5) i n $he A ghaae doae not

elrango moh ooagaared to a t o f pus* (-beb.bla 6.4)

but; that; i n Ohe I @am ehawa e m Jn~~eklisl~,

&st OoXs-Cob pplaba, for Wa ~lfxture wilbh 74s

#POW arm @horn in fAg.6.34 and a m Broadly ~ r a a i p l i l l x !

f a tholire ol tile ~ ~ @ v i a u BBPflux81. Ilhu sa'tilvahtcja Prrurg

(fi&,,6,35) of the A phase A6 ~ I i g M l y M&%r $baa $hat

ef 90.2& a&%tu~rs, while *hat Par the H phaarc 16

oomidwabX~. In%a6idr tho #aktvalrion enar$y of the I

gaPuiaa -8 the &w,eLm&.we (SBJOle 6.4) ~ O P $hie ~ X ~ M X O

whjt& ctarxaagondil t o tb* aitti.mm la *e glns60 bs~nbart.

BIQ.6.31: Plot of in FR against 1/T! i n the uase of NPOOB where fR is t h e frequency corresponding t o st;, peak. The vertical arrow indicates (P@.

BI0.6.32: Gale-Cole plot for IS,, -relaxation i n the: case o f 90.2 mu1.e percent of HPOOB with 9.8 male 6 o f OH-BBA at three different t emperaturea i n 'C.

90.2" Io NPOOB 9.8 "lo 81dEBBA

3 i f ag:::altm:,:l f o r s aufx1;ura of ki

9b.2 ~ 0 1 0 ;it of ISPUOIl with %.& molr, ii, 02 ;II-BI3Ii.

The v e r t i c a l arrw indioatan PAN.

Pf* Wt-4, B.WarBaodn, 3B. bePOhnml and B Oaasparoux, J.&r FQ1. @, GJ+4Q (1979).

r f . $Won smB X. Jsnoarjr , in n8vanaaB i n Liquid QsyrfdU baaaroh and AJaplicraZbonc?a, EN. br $.a~~ar]E"ep.~pu~~on 0 X i 0 ~ d (JRBO) ~ 4 2 2 8 ,

ArJ *&e(pdbePDW, J.Ye&t~"s~e%, J *Pr&le-nt @.rS.&k?~~y and A,wosla;p, J, de Pm. a, f?b (19Tc31,

J 1 ~ l , a r a a ~ , msoi filer., a, &~o3 (*925).

100 80 60 4 0 20 Q Mole percent of N POOB

PI0.6.48: Composition-dependence of the re la t ive croe.8 over temperatures o f the conducti- v i t i e s o f mixtures of HPOOB w i t h aA-EBBA

boundimy, aatysoisarlly rzO lwsr tsmperatwes ( w e ZabZe

6.5). 99h iaaB fht the A-8 1I1Pawition i t s r a w vssk fir 'kb eompoaiM@a ~orr@*;golrdiw %o tb asliniaun% in the A-l4

Bclun&cnsy ronld blsao~ro ~kronger on eibhtx bAr12~ of thiia

a@aposAti~a l t a rmalJloctaS in the @ro@a aer te~twaturcrs

(ti!%) OEf the conduotirltgr adnaotrcjgr. Ae @sen tn

fia.6.2r%, - 2&a shows a rftr~aw p ~ a k fas Wa colagc

lpE t l o o e@1~msgondl~ q140g ( i h ~ aPntre\sr& irn the, A 4 bounctary,

&$me the crmobicr Ulsa rrhmh ~oitm&e wber ilucdt.uetians

eura vary straw 2n fbir, Baa. eve13 rjt ts*rpora0uuce@ fw

FIG. 6.478 The ratio8 o f the principal oonauctlvi t i e s

uR a,,/uA o f various mixture5 of NPOOB with OH-EBBA aa functions of! r e l a t i v e temperatuzc. The first number srgulnc t each ~yrnbol. ie the mole peraerit;+;s of NEOGU and the second number the moan s p e c i f i c conductivity

9 x 10 (oh. cat)-' at 76"U. The ~ P - C O W @ iNl ioate TM.

~rainly beoau*. of t he peuliarr m g s 0 f eha *..H boum3or~.

dlurtthcrr, r a mntloaed 113 ekrpter V, oR dsm&rs on fhe

arstuss and osncbur&.ser$lltan of 1411a oooadwting fmpuxl t teatr

th* velw ~f oEZ $ e ~ ~ ~ ) r a l l y @afw up S f %I& medi~1m h a

h&@ow o ~ ~ n b u r ~ ~ i v i f g ~ ~ ~ * ~ ~ BW erondiuatbg Smp~dhPaa

i n o w saraplea a re ~~nknorn, QM 221 f1&.6o47 wys W V ~

giosa tRo +&usa of %her meion apeoffie mn&uo%4fiiretty

rta4ist1, I! * (~*,/&)a" wwra L*/A 4blr rpfemtrke~l para-

maor of *he or32 urn b e ~ r a t a r d irm tkls moeurcob vn2ue

of the caqaoi$ame a%' $he mpty ask1 srnd l a OZ1$ aearourb&

aonduaCivi$y t P dha aadbua is i n t M Sarotrolplu gherar, o r .. a a (a,, + 2a,,)/rt tl SC i s fn $he Pd p h ~ e r X t is a h a r

thsrt BIQDB bat a anrah tnhi(sfier v d ~ e ei 5 a m OEt-mnA, tiho

sairtwera hating itam lnhrrme&S~ate ralurrcp.

Ma o m szranotliae, a fow fe&(bu~e*: (i) Undwebbarndly,

qR iaxlrr sore ahbsig3.y i n 8110 cssw where fhe A-H *ran*$-

t ian i a aZ $is@$ W o l r ahacbte$*r aolrmrad t n @he cmes

whcrrsa 1% b e a raoonB ordax ntPCura. (i l l) B O ~ a a d o range

of eclrrtlrooZtlw~ (baetwmn 76.rsP t o 44.6$ PPWE), aR verSlua

ahowe a broad ~lniaow st - T r? 32*cand @tart@ -*as- -. a@ hbe tharpca~ektux~ &a Zowe~*d f ur.thor, *I@ 28s probably

connaated wlth deox@e*s o f fa t o very lcw v~Pua@ fax?

7L O/o NPOOB + 26 '10 OWEBRA

FIG.6.45: 'fernperatore variations o f the prirmiperl conductivities of a ~ f x t u r e of 74 mole per cent of NROQB with 26 mole per cent of OX-EBBA. The vertical arrow indicates TAhi.

BIG. 6.44 r Temperature variations of We principal

conduct ivl t iee of NPOOB. The vertical ar8:row ind i- cates TM .

b~csonSag atir ire a few dspp~eeio &@ova a@ A@ t o

be expaabed 43b44 ( l o r an latrobuo4lan r n ~ 5dt~arnerlrion of

om1iatr m@mMlr oa ocnriluativtty asP;acples o s UauiQ

otgettallar, isee obg~tsa: V). A@ d5awatacsd Ln the psovioua

ahaptor, i n ir$e A pbrrae Iam~ 0an flow mom eorsfiy i n

$he plaraa 5 f the layer@ FIB- pw@fl(ti(t~Jar to tha

P ~ B ~ O I P . 1Eh.reiox6, the ooadurfAvlBy ga*gand$aulw te

$he Birwdor ( Q ~ ) f s @eaPttT thpa Oh* aanduotlvit&

w a l l e l $c CW d i r m t o r (a, ) An *he A p h w . a,, axh&b&ta, 'jump* a$ Q fox both 1S?OW (f&,B,44) at63

tihe Poi%&- wj;th M*QC 1A1P041) (15&.6*46), %his &@ 6 ~ ~ d

by the fa#$ tbt A-8 Braneibion hare a S i r r t order

@hwcahar fn both esasaos (f5~.6,&).. r3n the @$bas

W d , a*, lPorZlo slrerply up to In b.0 aaate ole fhe

mix$we with 74P 11$00B aanil -XI 181*10 off l n $he I 'Phase

(iig.B,45), ralaar the A 4 l i s m ~ i t i o n i r n Zhfs. o ~ a lr

ilraord of saoond mdar aWasateE, Ca OhQ o t b r ha%&,

a, ma?i a6 nrpoo%hly aoraelr gM far oXT the a ~ o @ i $ i o a

rs$urtied, Fkl@ dlfferencsa fa the vsrxSat1 oasr o f a,, ud

a, bar slremtg Wen disguardl i n ahap$ar Q i n t e m a of

Ohrr p e w a U o n proosealr due $Q .the iamrXa$ i n $ha A

p h @ e whioh aon%ributes tio e lowering o t o,, .

sat50 uR 6, , /'a, uu o h o ~ fo r a l l the rgtrtclaclri e a u a e q

a,, in t hc Y ~JIDM OQ@IQTO& %Q that in t he A p b n r

lea&# t o ta Lower reitlvartLan W I D P ~ i n Cha Sef$er

pk;r*rr.s a d (b) pearslue &af&usnlas a$! s a i ~ o l r o g l a

piaoLSnff @iZea.O6 h atre X $&@MI.

JCnt3e.d ia UpaGhs 2 , $he omnllsrQ &ifisranan

bntmea Ute aobivttbl~ln ener&gler of ths A a& N pha~sa

oemre Zor tihe nlxturn w l O h 74 mol. par om* bi IOh"801Fb

r~olLrrly brraelr rn Of ?ha &OW vdue 1'13 the IB &an@ s Ilru*ha% r

*a w e Rave ~ . * 8 earLi6r (I&& .G.X2), Wkbhin ainOzam k&a

$be asxilaw* %@emal ~Z~MIIW aotrff&ai.nQ QZ Zayar

apwroiq. Am we bbhiaeunrb i n ahspaor 1V, hi maah a

oarz *he axrlootXopin J J ~ ~ & L Q ~ BIB l e a s e i f e o t l r e kt

lmrrnix @he srafioRtXon anargg i n t he A plaaecr. This

ocu2.d a lno oon.trllpu%@ $a a reduoaiaa Sn tho diiiersnrsc

i m Ln*cltavrtSoa an*sgStt*a be$mr*n tZI. A snd W phssos of

thtra rix%wnr.

(r 1 dt&u&ivity Btudiasl *--*.. - _. . ...--_U

Tba priacrigrrl aondua%%vitlea (a,, and @a) W f

t t t ~ ~ s r~l9~0b~~:i'b;~ttve o ~ l i l p o ~ % t P m ~ B F ~ &awn i n fSlg.6.

b .44 1 lj .46. (~a l s haw naxawdrad, onn&cao.t;%wlx2t%ecoa i n 821

Phtr syabtaaarr aentioacsd earAisr, buS w1.y t b c e m p n -

rnatotitve diaft.scuaa err& presents4 haze.)

wotirsrtion ereaw in fb B phaes i a S o m ~ t t

Pop the nrlxrwe omm~yorobiw t o tb asrlatsnuar i n fbs A-8

houn8&ry. &is, A@ pxo'bobLy a aomeawnoac. of marby

errconr?l urctep A& .Itm~riai+~&on Pn *irr Oarr (f&g.is,b). me

lf ghcrsa w 5 1 1 have awongt ewtloede lib ahor* rawer @rder

in thLs eats* wbicsh l e refX@obQn &a tihs law aa82tatlon

oea~@g of th t4 phlahrrrsa. 14 wa have dJLactueeed in ahaptsr X V,

loyer'$nan(8 3arabs Zo a Zewurfnqt of e~lca &aUva.f;iaa emrar.

w i f n a-r byi~teulnr uiauwse8 la crPLar@%r IV. thr

tac+s,fu uktfci~ (9aagg:Ier LR O ~ B O team 02a0 am lwsr la

Xtia A A,;pa@ t k ~ a in tihe h @harP~r usApia 01 %hi@

&phenan@n,rtcan himrf~ lpcaalg diutauesrad i s ohaptu: XV Sa terns o f

(a) a r~lctanG WB)S)~F~ of MwarLt8 mef &%w¶danliE pnatarding t o

trhiah the l W g @ ~ % @ ~ . p l t r C L t ~ ~ @ Y b l f i ~ $ & @ Q ~f Qw ~ P ~ Y u @ = $

mo%@auPas

oontsibtbu0c alaao~$ enfflrely ta the obomed BSels~trl~

rehma3ior o f *he pplx(iUl~"~t~. %hw th81 ~bflwtlQa inOx@dtfJO

ln the sroltZveacS~~ enas?@ of "U1. ratxd\ors cPaaparzaQ t o

ShaD o i pwib BLBJ?ae?B #howl& b6 a,tPrZbuted Oc the for~p~~pFien

pafre. %hi@ &n%em~%tcwt l a slwo m~poasstibt

far $ha Zarge mbw0Soa of %he rehsatlan ira~uanoy

ttlilekE in Clzrs aiaWzus (oar *able 6.5). Zn order %o

perrtkcipa%e In t&@ r s l ~ ~ a e i o n procsars, aars % W m maofeau;lla

haa ta ettMr aarrry 9hfiha QE-mBh aaoI@aal@ lttlt?~ +waxdch i t

tnw famed a noJ,~auSl3ht omf12@1; sr brgl+k &wlly Er D ~ P thar

@&re &3lur$he??, );4@ QaZcs-Oole ~ 1 0 % ~ 8hww .t'h& w.l; Lower

$rrrpora-tura@ thr minturars &&a%@ awy ILCPP~J f~o la r o

Ikbga rsXsJcxaS-iaa (Eig.B.36). 2 k ~ c 13% @hior$ r a q e ocdrnr

efbt?@$e fll 5WPClaB-QmBlb gaatca do n ~ t la84 t s mg tatlifl

tn the h i & Smquea~y P Q I J S ~ . & %PA Sempaa;e&kdrsd &4

lnesreoscpd, B@M BIFO~-P~WIJB p&a arc ame el wrd Zurlsnalyr,

the orlsnap.atianar2 ord@r @lxr~)a@C;c.~r dalarpitarrte thus

~l~-mtsmien%aclrn9a motion lo%ter vfb(lbXa 3n %b I&,, r.oaursmn* ant? the high ,he kuatmy h X i i a rwln

ao%iaeorbZa.

FI4.6.43: Plot of In fR ye. l / f in the cam of a mixture of 63.5 mole per cent o f Ei Om with 36.5 mole For oent o f 40.05, where fR is the Smquenoy oorresponaing t o e:', peak.

PIG.6.42: Plo t of in fR ve. I/IP i n the case o f 8 OCB, where fR i s the frequency corresponding t o E:; peak.

The ver t i ca l arrow indicates Tm .

sas-tiexr B1SpoL6 ~;aancPnP; &&i to tha $otI&l dLp~?ols laa~~ont

et2 the latoXeerule and @vea r i o r %o a h&br peak value.

LPha acaavo.kion ansrgbs aala~XerOefl frsm i n JiR Wsr. 1/%

p&c;%e (Ylgas.B,4.r? and 9,411) oaso l l r te8 in table 6.4 &ow with the ds%a o f sgstea 1. %ho saaLrati on enmrgy ig

the a p m o is rrsnrcrllex than in I phonn in B OQrB

&#o. Xa the am9 o f She x&ftlPe of 8 Oegl w-l* 448.03

(i1&,6,41) the 1301s-0oZe plo* ina o aeaioXrr~116 with

tb obn$re 1gln$ ora tao e:, ax%# P i y a* %@war *UD~D-

xrait~ra~. AIC bigXle~ b i t r ~ c r a t u ~ ~ ~ the o$nICw r.E thra e i r m

b r # ? o tier ~ Q Z W tber $2, oxie wbkela ~ ~ S Q P P ~ Q S P re1axa-

Won Snvo?lvdng a i;listrlbutlon o f reXuaLion %Ams. 4 1

Ia$@e&, pplot of 38 SH v~a t/T (i$gyl.lS14J) &ma no*

f ield s straight Zins lae La @&es rtdilass, bltO a 3fae

cumnd auoh %h&t $ha ~a%hfoaiotl&tn @te@r@ whie r du r~ 0.43 eY

rat tlrrj, Mshekt tawrxaltlrrsr in the A ghnas cmSllnuoualy

SI"PO@B 69.5 350.0 63 .S %3% 36.6 2050 51.9 1600 47 .a 1250 41 cQ PK)O

- - - - * - L - - + " _ * * W - - U - L - * _ - - -

% c s , a $ a ~ w ~ * W P ~ f r . ~ n w ObI-BBO 64.4 3a5a

63.0 27430 Q1.B 2IlOis sac % 21,a 51.6 0 5W 4'1.1 1 aso 4s 920

FIG. 6.41 : Cole-Cole plot f o r 8 ,, -relaxation in the caee of a mixture o f 67.5 mole $ of 8 OCB and 36.5 mole S& of 40.05. Centre of the semicircle corresponding, t o 20.7'C l i e s on the E:, ax i s while t h a t corre- sponding t o 78.8'C l i e s below the E,', a x i s .

FIQ.6.40: Cole-Cole p l o t s for &,-relaxation i n the case of 8 OCB a t 44.5'C ( o ) , 65.1 'C ( 0 )

and 70.7OC (x).

Frequency ( biz)

FIQ.6.39: st*, aa, ti funotion of frequency for cn mixture of 63.5 mole % of 8 OCB and 36.5 mole $ of 40.05. Ike numbers against the symbols indicate temperatures i n 'C.

Frequency (Hz)

FIQ.6.38: Frequency degenderlce of he, at various tam2e- ratures (inaicated againnt tha symbol^) in the case of 8 OCB.

FI0.6.57~ Plot of i n fR va. 1/!C i n the case o f a mixture of 54.5 mole $ of HPOOB an8 45.5 mole $ of OH-mBA, where fR 1s the relaxation frequency. The arrow indicates Tub

PIG.6.36: Oole-Cole plots for e,,-relaxation i n the aase o f 54.5 mole 8 of NPOOB with 45.5 mole % of OH-EBnA drawn a t ilif fcarent temnperaturss ('C) Indioated a ~ a i n a t tho symbols.

%he Oole-Box@ plat: i s r s atxhb.ur* with 54.38-

Wmm whiah I* lotr re 6r& %be oowoaS4ion aosr#rt?ya3lt8iw

t o *ho mr&im t n We 6-31 bowdarry i o a9barn in fig.b.36.

"Sh. 116 with la amlolnt le 1.. mu very a~:ooB iaakc%Oiw

$bra% a eir@a rcshxafhoa ahlurxatarimse the tr?rblag%E@&nw

lPhe Pmquanr~y o f tiha e:, psiak at r*, Ma i. d 248 KlXs far

the 54.9 $ Prixtuce while A t ik% d 900 &Hr $o;c pure IJWOB1,

"XYhQ aativatf on smlpgy Sa the A p h r o he@ LracsocloeB

o~intsidambly for %hi@. arlrf\u"e (IrLg.6.W. &&%a 6.4)

00~0g(?~rd ta %a$ pure irlPW.

%$38 @la%:. ~f &@I~at%10 lan@ (e?, ',l W ~ ? R ~ R tmyuanoy

for 8 @ad btc Axtnrra wZ$h YI?i.l)d aaX 43.05 one whcwn

Ln f i g @ . 6. M 6.39. 3Chc 6% ',@Qs vtalsle geniazally

&@orease@ w l e k imseees of %crm~srstws, axerept i n the

xaixtuxr. the @t peak &I% lonerell a f th artuppercrboled temp*

ruat;ur* a l 17.!JbC. We oannart rule out Zhe pbeatfbility of

ia partial ~ f ~ s l u l l i ~ a b f o n &ul?ing %ha experrfrult; i n %hie

~~~~ &@ 1 ~ ~ l @ X % a i a 3 n &QQNBIM~(~S (by;) [ @ @ f i ( ~ ~ ~ n & i ~ , %to

*ha pa& values of gwe 1 arf, mrious tsarpex?er%mcss ar*

ZJo.E.eb Is3 t a b i e 6.9. Gola-GaZs plate Ew them tyy8hg~11

am tabam in i&@.6,4Q w& 6,4t. Xa 8 Om, the @ole-

OaXe plats ~@k~fQPPafe@~ F%ae peak F a u e of 4*, i f r

d 5 . B ab tha kiowsttt; demarku&tur@ whhh i@ wBb lower that in BPOQB (9ag.6.30). %he lattmr crnatpm lkhe

BIG.6.35: Plot of in fR agaimt t / ! t for a mixture of 74 mole $ of HPOOB with 26 mole 46 of OH-EBBA. IWe vert ica l arrow indicates TdlJ .

A1PeiFrarris-iicrw@81R E.Eegdir, F.Bandr%ks~; era& W, l X . 4s Jeu, Yeas ~ J B , s, GI-93 (1975).