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n o ~ t i a oomenirmoe, the *cctnr . is DQ% ~ h a a cxpUcSt)J), nad
L::
af raOBocrrZeoar oaimte#l la tho 4iLmcrceiarzrr f 1 , 2 ...
and
wwra E+ u a e jm v i i x ~ i i ~ aosgffctunt. m a i s the 4 mxm of p i s i ~ w i a i ~ ; ~ % f l ' t ; ~ & ~ L i a ~ ~ %kr@ fcrfrrfa rru@f2&cfsn$a low
b w3&ff,an & a@- a$ 'elm a&&Ycltf f wu. QBUQ
uu' u~t * * '"1~' s a$%(- uiJ ) - I
ua*' i s gatentiril entrrgy betweat aolcculao i sod 28
j Prttlch haw oziatlLaf ions A a and fi a, 3.~~3poc%Pv&y.
w12we r 1 t&0: ~& fua an4 qyZPmirJtca2
helgh* o f a ~phorw;b'Xmdez, ro 2- Voluclo, (n 3 A@
%ha bta?mmn fke 2- d? n~2rlli**c)08 ca:feWjlq
in #aa 4Axwa.t;Saw n rud n! r e q p ~ ~ a v d L y ~ Eq. ( 5 2) ifa
rnba;lWtd 233 eq* ( 3 1 1 L70~
fwm?ilm $?(A) *f& ~ ~ m s m a emrm Sa
G B M by saXwPng the m z 4 1 E t C S ~ equai%Sca
%&&a &ves s;r s& at' ne3Unam 1;?3aapaX @eat&- bop
Q < n 2 !PUB d i ~ t r j b ~ t i ~ ~ f l m t ~ % f ~ ~ f ~ l f ~;;leh
eq. (11) for the E&lB?xalt+ $'see enarm can ba uusd to
@ ~l;r.tgp@**ie~ 131s %ti0 814p&-*
~asrqpg~ (j%@) an q s p l a ~ f , t ~ trmfatf atuL
ualutian to ep. (43). Por large vdurrs o f laieih tc -L + t), the rdntlrs! om,^ in row@ D-4th XU-U r(- a
av/V ran@ -pw-~r53;:
<P2) of th. ~gnuitlar pntllt =#% I
a,&# =&WQUV~~$ (BW t k m ~ , 8';?74). me P ~ B O U S ~
~&ct im d(l+,p ) ai ox%Wra& (4,) and biaarSera4 (tiA)
3-oe lu?e 4.5/t and 3.v~ re~pwtl.ew. %effkmla (1954)
&so gat B ; B I ~ ~ Z * C t r i d . ~ for 4 ( N 4 ) f o r bat& aph~zcids
W d r&&t t;cutlcdw azUZkb4&ZB I S ~ @ ' p f s t : B 0% C~bsai;@r
Ie$.bar~a cmflelwad a* %o reracorrrd vSfrl& ctaef.fiaf en% bxs
5M v a a l i~~glz&tm%it31 a& hmma %he results ~b%;~Amd a m
m f r i c r Z T j egJia&U t h demiP;3r i s vsrg
6.4186 6*70 asdm parv-m <pZ) t he
#kt ~ ~ 8 i 0 3 l p~X33% fa2 X 6-4166 L mPL3M3, ta b a
0*%7g.
m&e3k, cXavlt9rZopilt t e s ~ t i d A y a %a Zs-citsi~ aa' Jt3U#xy% appza%L-
mmtiiruli. f;h2s tacnBe2. apam 4s aotmidwad au a &*la
ouhio QE ~ 6 4 . l ~ ~ A Jcait at? 2txqgGb x is ira ttrarAem of
x fdU a&Jmo. mz~&Ang a3.w o m rz$" -a t2aw.1~~ Q&&C ~ U S ~ ~ ~ W H B ~
ngu taa aonaista of :$ m ~ s ' enit M o a ~ a . ma ireo energp
tha sydt3reazs o m be wr%2;f;%n An &@-xixi of the number af
~ n r ai a~~rmg%r@ the nulac&s, %otn f OF a )gAwo%t vPrlu8.
O f d@RB$'k~t ?I,&, *tit 6Z'!%4%Zlf;&%&Ci?%d. &fi'?k~Zt.bi~,'bi OIE fk3'3Ct;itSl
la sbWmd by &a!l~&x&n,g %he free &mrncy- ~Qbeaa c1dfwe-
$A?S,gg the Z- to me B - B B ~ ~ * P S ~ aojeLE;a~%ent, %he
of r s ~ e (P~) a ~).BIS.AV~'V I
0.525 ;& & 6 3*8j/.. fth- 4% t a d m y at g@tting
poasfbXa 4- ta r S1652+ SOJ! r 3*BSr ha lrflozl s t W d
az a% ;ItPUliYffaM ra*u*Ya* & w sand dYdPY *r 0. tz a* *s BE
ttWd2ed tram5tim prrrgimM~~xr fox! a mm B a t fXu$di.
'ENs again ;tlpia& t o lar&t, r a u o o i <P2> arul Dut
fn fsiltX %ema ZaW%ae ~ s b , i* Ea i # 8 r ; e i m Go rw%rS@%
Wxne r n J e W ~ ~ d to ar mt 02 3Ek4;Moe xt;?ttw im4l %hr
ax- aS ̂ aulwdbz bm~~~li t ; ~ *hSm db61~~ma;s
~ ~ t h w J l h b J 69Lxec$Ew* B w w x m a wt
Em& *m *t;3%@
&Gka~- rap%*= bat ma3;%ricWng Z9re s a a d m t o
crsctcz. appsix&aa;ion dews aaf dfmt She ah~r1~- 05: PSI
a d d gertia3at W m r y {BEE> i a a *hame w h r l l e
been apgUrit Bo a m $ s ta%Am%lt!a&
prapmiabo af mdmt9314$6 rdq;Ld o m $ & by a u m i 8 ~ ~ ?he
~cmt inusuas orllantn%Sogla2 d&~=buMma rsdkiafkta
denaril~;;~~~, &B we bm mmtiamd i a %3916 tntamBwMoa,
SPZlI -8 u r i g g a ~ U y &evaX3qwb by 3&Ams a t ot3 (1959) for
a WSLI- o;tr m r p k a t r ~ ~ Ther eqwaW0~1,af JsB,%&rnd I
From SP2 was eazrju.firy 5ctslrntid to a e mmdb5lji%y
eq~a t&a at stat* ob%aimrS by fma Ptmwa-Xeif uk (P-Y)
W Q X ~ 02 ha;rrll; ?@h=~ uFtUd;&#. COt?tSt' a (3970 a,B,a) 1ktxf;193~&labd %ar i@?% f o ~ z so mmtaa rlJ tristr?lt rm* W t w twg starK& t b ~ #- p3"oprrtxUee og
M. m r ula irrotrclplo phe . vitb <P2) o (Wtka.
m&d zikrl&mr t978olr) W S ospsyytlw =(283?& a?%&-
a# (P,) * I (Cottaw yld mrtlM 1 % ~ b). Later Oottu?
snd HartSre (1Cr70a) -9 WouZsrtLaaco b;p mwlx$et&ng MQ
no%rsltol;rLRr axoar te threbp p % q m m U r r r ~ &Jma.t;Ji~~~bar. ma mder p a r m * a r <z2> QI the n a pbamse w a s Po3,tzxl t o
daorsnar gs r deor.aoad. Ilowc*ar *he wix3.w~ o f ( P ~ )
( r~ (3.66 fbr x - 3) was moPI Xazfgar than the expexiraan$al
i t Irs aleax? th&* *f A P ~ 0
432 rraw tic &O a mi- the rnrfntlon QZ (2?$ atL *ha mU,mb 3-eb-
mmWXy WCaU W b (1972) f ~ u n B Waf 7 a 4 et the f.1T
% ~ " 8 ~ ~ i % c r n pa%$%% foe -slrry-ole (Pa) . ths
o a r bnd dLT #a rail &prCS& L&m .r Qb* ?t%w
pww33 hariO m 3 1sbBi31W 6s na% @we a mod deseripWa3s. at'
zlffxlsat&e l i @ d tala*
&Zt%F4B r% f a %ha k %W= ~ x ~ a t m &UL%b
seoodl ordw kg-- p o l ~ n e o l 12(0m 8) ( I Q ~ ~ X
sat$ &up*, 195"f, 19238* 19554, 19QjC)). Xa all fherrcs tf.iao;r?&w,
m e mt a c p u @ f a y rrrha;d, O h eaozeafiw Ih1#v8: mamk
tiaT?L.y a aaphr~~:iW ahips am4 %ha rczrcPudsrlr va3wm eiimfw
m nu$ Wilma P%%~Eu maaun2. %Q gat y = I f ~ o a
*eatrise, i t a m p u t r d that A(P)~ fl (eao ~ e m e h a j r
an8 --st, ww)* BU* - C Q W ~ ( ~ g r n )
&a aami@f
?he C O ~ P ~ $ ~ % O & ~ W 21g & m h a poelrsm;&igz;P, r5~., ~ ( l ) ahmild Be
prcrport~ami~ t a P' a ~ a a **IS. t~a*kroe t o = 1.
mw *be*& 1Imd .Q)P1 at*wwv&3 i%X?Wi@ ~ # L " S C Z a -~ t
ba raaUatlct m m r n W U - iaQ t2a X9grrfd ax~jf.s%-dh*
f3t-ar jre am a ~JWUBF~ ;o;P boa.3 &ost zwage
e m % 2 n a &a9hr h+ ~ i ~ a r a i d d & trPjkZrCf rod
(~gtmr~ EPO~@&), (u)
the gaolat t u i * h , q c r m W &t& Sum Plis aa&u\llnt.d
Wfx et ra3 (1976) have uat3ii %he fmiZfar O (Born-
Gmggtl-Wc#3-T~)~> &*@&&& 0 E J W % & O ~ f 02 8 C ~ W B & O & ~
IOQ%CQ~TSO uC&U%d ~~lXl&%%&t&& & &;piwrihl.A &i~Pe~+id.t&@ SUpesL.
iBi
m m s * B vnxt &me w w tWw$* ar81 mrmrikc&re
t o hawe a isphm@yWrIi(r09, B~XW. %a ha?4 ra3
omtztbutim as srPtb2aca2e%abbt &q aaal~glb pePrut;2cXs
W e-6, B-VB wws to ba d&atmcte
d eat md oi tbs iwm gt- in eq. ('17). The E l r 4 f ~ O O t ~
sea ewrgy iof Ss alb%a%t?rd aa EI fanatiow of d ,
maZecliLw elutpa. llra rrau3.ta obtsimd Znr %I, d-,
m h eq@rA-S9+
b a the ralurrs ai < p a ) nmlk: =-a war$ ~ ~ ~ 4 t h large=
eestd to *Q exfaas
fjl~ltd WAS ate~gm w to *EB Q W X W A ~ *@a b a &ah& o v d by
tho potantial &van An agp. (18) bur not b j &at i;iva
in 433, (47)*
~pbroagU/Merut w f t h x 3. de have wrfe cufouh~'Ef
an nttvord prnparkkcs at !EBX for d l 2 2 e r ~ ~ t t v&wu of r bs
el?,@ B@'fl&L@p€A by CO%"$W, Bk& 33&+&%8 G3X?@
&u~o~s;lud~4& w&%h uyl a=~tUm pownu& ~g ela;a E4&e;le*ip@
p . have a o~euEs i " td %hest prrapear-ea by
a imprat& av&uat;i.cras e ? ) i #a PWXQ dep~nrrda~t 02
tile ercluded volmu [eq. 12). &1c%hor the on*uuXutia
lmve Pram ai9Wmdd t o rrsl;uLfg %&we yhwa tmmubt4.on prsperk%~a
ioP; W&or prefwttJ:me
4
r, +&%a ttm << >> aenotsa the am-
5 &(r*j2(1*a ) + (3-~3 + p . l ' ( ~ ~ ) a l * t a B ~ \
an other bend, w h a a a rrnd A arvt rer;r i=c;e, tUI(or.A)
-3 apprm& mv~p:#ibHb TV w&: af ~ T P Q ~ ~ L % & J % a ~~ #mqp.Zo aph.wc#pgUW&~a Q)PT%*;~ A& ?&m f L ~ 3 . d ~
la t& abmr sprfion t o br amtlrf2rd both f r (PZ) a 63
arl (P~) # O, a Pb. sprd to 1. m mdbulst. f(n)t
4.a ey. (36) tu o rdativdly amde one. l o &s i t
urn (raxmt, m haw wn;md& (ID* t) SJ I) up t a the
f i r a t two tsnmr in q * i
AZl, ma c a l o u l a t i cazs were made on an IBM-360
omqpubx & rZpplbla3 g ~ a ~ P o t m . %bar h t t t r ~ i n 3 , ~ w e edL~ah4ait
b~ w% 32"p-* f&la&Err EM*ssd*
ILr
Foe a pard$ herd syatesa ( % r O2 92 QO). .tl..r
W@trb%icr~txep &t a & v a ~ & * ~ j b @ of 1El MILP 1PmUW#.
Ammilin& P nmd1o-bXa tr&w fir ( ina tm)amiuau (451 ars
&aU~$Ats& 'k0 &#% @@XfmcWla.f;atC V&AW@ 0: ZClw r*-6
2 ) tbr p m ~ l r r o 02 fha esn*io plume i s 42433aU~d;ecZ b2 ~lasiag %he rrqwtiea ( 2 3 ) . fqpuafia&
f;hfrrc f s *%a p%aemra rtrdf 6he &@a%rapi~ pfaaa, dioo 80 oa3-
ahat ;&. QIBbir exmzgf feg* JO) Is c&a&U*d far
bow ~ a t L @ m b isio.krw&rt
o ~ L ~ C ~ W R ; ~ by the %bC6 B X ~ ~ S ; . ~ W OX \ ~ Z B 63 ' (ail. 5 6 ) . Rm order p w a t e r (%), A?/? . AS/%& ivld
d~/d+l? incrsasw d t h r and enare PV& draorrurse as
x Xrrsj[lrwsw* rt frnrnW@ P * . ~ @ w ~ Y
d h.ar tho tro ts3.n iq2-i on & 1 oiu faAj j , Wo
fM that t b P w min!g& anI03~ a t s r (p2) Lnorunese
bq ~ 3 ~ s is r 1 3 w ZBLlf f ~ r x 11.5. Indeed C D t t a r
b&~mI9 nuItaa8 %a% r~s;oXud% M&ea? order %o= in
b. *%w==xs8d ..*..--- w i t h on sttri-13tM- - -..-- InalWi&$ +he ot4imdcWm potaatinl ~s &ven in ap. (1 - -
w h ~ n , fw ad j~stattlo PS~EV~RTO 29 and 02- me Q
eriWrion adapted ibr o d a a t w tho vdlrrcv, of da a134 d2 was t o .d$uet %I oad tha patPing frn~timr of tho ncli~ri&c
(L) ct t o 409.8 uld 0.62 reopectively, wkdcth
&XW &X~@Z?hXHlta%k 'PX1- $ 0 ~ P ~ b t .
Z w a arsm vdue 951 x , tm @WEB uith some v d w
a~ 9/v4k. ~d oatLm t)le oann5ateao~ ~ a - t i u a e (mp.43)
t o get .elX-colregntont vi~uoo oi (PA lie p r s e a c r s
~f taa nt5~f&ict ghm~ i l :du%ht~d o ~ a a % l a m (22 8#d f 3 )
fia aqpgt.& "t;o %ha a.t;mrzfierf lcr ;r@smre 542 t.?~%~:~,i.;ba tlw
at %I 4Zramitiar paint are &tUd by uo- ?he ralrrtfano
85 9azamltf.aa.. H-~E %ha l?wafo wltk Ww
.xpeximmtol dn- on Prll (see tabla I), &t i o sssn thrO
~ a & a ? a a for r r 5. ond lgo sld g2 -2-
Po gat y * 49 I-rr mm€i, mia
fa t b a a u ! i p i & r A w % a &*
aa P M (am &?add, #%5
& *p@* I%)*
t o the %(om B i j ) tQI. P %haulir_fm
[see WbU X l ) * b~.Qq&% outi
at QIt *+a hf*a ~deyz1 3.D *B
W- ~r oalczlxs0l4sb v a ~ o , o~ (P~). AC(T
AZT- ulS,th @qmjlBBg;~gt;lla3, tfe* Qxs BAAr a ' t ree Ojr X
1I1pAw kWWBX& tr2 a d S* fZ y 8 U d etpp-
the oal&r;:od vdaeu of beth (p2\
sadJt a 3f/&%l? wmXd sUUI ba e m f d-e-iZ,Xy M&ia~ *I- eeir
U P 6 2 W e k Y 3 ~ $ 2 ~ %a 0 * ~ 4 3 ~ 4 % & ~
o w up f o r2 (coo efj 1 in the
%OW s e e Q&N! t ~ ~ a (spa 4 3 ) ag-itii3i9ctl 3 % ~
3. $exa%Av~ p r d w %a %lac pr.eslasurQ oqu& to b m ,
lTttd p m s ~ u ~ o aZ' the isamp&@ pkasa a : ~ ~ a t d by sot%ln&
.r 8 i n (224 ('3'1 ) in &a u w t & t o
33 "ara snd diao f a ajpr-ksd, 3%- %as lifbb 'a frw
~ a e ~ & e a af baa tM
%? i n b$ i 8 d ~ 2 t A ~ a ~ I P ~ X ~ @ ~ ~ , U Z : Q to a r i a =
b~slr@w x ~ w $ & $ 8 ~ 3 8 m w M 1 4 ; ~
gmmreasl a&r*&*& a& $ r n P ; S ~ ~ f b l pwu*
.~ammhmW ra~uP,* given W E m m u a* *aZ t197@)
!i!b%#me;f,W a3.W atsP various
a, 1065
0.1m
0. i a 3
rclm18c915;
0.1 343
o,r t ts
dl, 1 $23
0*3 335
a. t $43
0.1 la3
4% t 483
03.32Q"t
0*32m
0.3-
0.3 257
GI* 1274
43,1294
Ig>,l33a
P. ~zPP, V ! aad
A { A = - ) A I ibgorlcm*nl data
on p U for the wdation of V, and ~ ~ ~ ' i l ~ with P
gZcatt@d fao: the ofdm of iwqjariaan, Aa ua o m
8ee dtrvolln $i&m t , U1B. @&G%&&W vaua a2 4% @d w$r:/kw
up t a O kbwr:, tkre q o x - n w value @*47 far
PM (aaa ~ b ' a X 3 , , 3972~
u4i air 59761 &~ka&#ak%X s% eo3, 49mp b = w W ~ and
-h%ctfiar, t 99). ructuo &&'a= dea~lt~wca i;s; 2 &~msases
w.kt@E;I f a in pwSj,%aUvar iagmxmrnt w i & the\ wcp@r%@euW
bar- atl P a r 3 t E ~ g ~ r o g ~ d h a r ~ ' I r ~ ~ s ~ l f 4-p ' -b~ty&&line (lm)
( 5 s )
(flora, t 978) ant.9 D-p-es~ox?;9rb~rzaty%ddmey ?-'bul;y3aWUna
(33333~) @wsr, t 9781 UafibnnaeMI st d, 1979). Vu~intitoa o f
fke mlar r a h m ai *he nst~afla phnaa Y,, n funotlcsr of
pmarsuxa (flguxm 2 ) i t a Sn ~ u u d agpawCw-t 1Ji'tXs. tho e q m ~ i -
mm%l rcrsulP;tt e v e n by OPT e* a1 (f'";"?5) a d WhA i
st ol (1379) an Pa. 'ilha thwrclticd. valuee a f OV,?*
(fAguxa 3 ) , A ~ h k 2 GSU~ A&*I ara moh 11v45er % h a the e~puTI)
mental values, but their vwi;i%Zw wAth F' mas 329 qu3aJSlatSve
*paWb~aW data $OX 1E"U at vari ous pre ssum s
4 ~ ~ 7 5 3 22% 04 01 72 S* "r2 348
4oa.a~ 9 a~i.a;r o, ?a so 173 t42
4ro.br 39 Z ? ~ # B Q 0.71 0. $73 3 F9 412*70 83 224.93 Om70 0,171 139
416.55 rho 224, w as9 u* 175 r 40
4mrm 249 ;?125*4f0 Om@ 0, 173 140
42T e 55 3% P%!,~O 0.65 a.3~0
435 25 %t$ 221.92 $*G6 "3, '171 1 4 0
435.23 S 4 WIe92 r)At 0,166 135
16W*21 S 2 Z;E(3*65 Q e B O o I @ 15s
452.66 Stis 22Q.29 3-37 O*lW 4%
( 1 0 ~ ~ 2 5 1 a ~ i ~ s s a, 54 G, $60 131 Clrrrr*r--rUIIILU -- -.-- .-.I.-
dP kbars
rIG.1: Theoret ical variation of P at TN1 and of ( d ~ / d ~ ) with the I1 t r ans i t i on teroparature Circles indicate experimental data on PAA.
PIG.23 lCllecmeticsl variation of the molar volume of the nernaticr phase with the NI transition tealperahre. 0 represents the experimental values of PAA by
Stishor e t a l (1976).
FIG.?: Theoret ical va r i a t ion o f t h e relative change i n volume with t h e HI t r a n s i t i o n temperature. Circles i nd ica te
experimental d a t a on PAA.
P b 'tmi3.m d 7 afs:kop u;lf
axogve abW.qpd by flew 338 2 In V, i s X W t o
b~ CJ 4 (a- X$m 4) flQT proa-;~pmms r i~zqg f i t a m 1 bar to
2 -mr AB 3c3w -0 fthp~aefi% 4% 8-
~ ~ t s i t a a * rtgli PA& ~ ~ W Q P ~ Z a@ E]FW@U~Q flt
&n@rairs& g a ~ r ta 6,s kb,wt %hdb %b~mt%a%X V&U% 02 y
uM3po;mezs t o 6.5 (14949 4 =prf~31~n*d mauum
bu'E: %ha 7fd.wra
"*o'&& by U f i ~ t mxy SZlm 2*ti t.0 5*3 (sea
Xionrr* Rae&* t9P3 a ~ 3 Eayw -4
FIG.4: Variation of in Vn with in 'EIX. y is the elope
of the curve.
o140r bm m 1- w w o a up k)
'aka-
* wtria BIFP %zwm.%uan &**** 5% * o m @ @ %he V'riLwl~
of P , A?/ 7 4V,#h%. tBY'42. ate. gar higher gmmme, wm t h a w &a aua e~ 1rtrpzo8uc~% QWU.EP~ZP~
b a * ~ G$ &as'& af fhg 4Cr8a~PthZ3 ~ P ~ ~ B X ~ ; ~ C S B I UklEt
AS. au, @/&I, AV,'~,, I,, @to,
as, A. *9w
iit&W , id*P!. ,I%, 19Tt 3 J ~ e a . 3 ~ . tic;, 2 ~ 7 .
