Characterization of quasi-crystal structure by optical frequency doubling

Volume 87. numbcr 3

CHCMICAL

CHARACTERIZATION

OF QUASI-CRYSTAL

Gerald R. MEREDITH,

Valeri KRONCAUZ

Wcbrrcr Research Cmrcr, .t’ero.t Corpormorr,

III fml

Rccclrcd 28 Nobember 1981:

* and David J. WILLIAMS USA

iorm 6 January 1981

Solurlonsoi sp~ropyransin Aphmc as photoproduct

1982

STRUCTURE BY OPTICAL FREQUENCY DOUBLING

Websrer, XCW York lljS0.

solwnts undergo J untquc sequcncc of rcxtions

spccrs, submtnott SIZC globules. iollo\\tng undistion obtwtcd

26 hrch

PHYSICS LCTTCRS

wr~h ultranolet

ts tncorporJtcd tnto both cryst&nr

Iudrng to ag$rc’@c’d colloidal

Itght The lughly poLr mrroc~anmc

molecul.~ spcccs

nuclct .md amorphous coatings OI the globule.

Thcsc glob-

ules possess lqc pcrmancnl dtpole motnunts .md conscqucntly dcr~lop a It~ghly ordtircd IttrcJd-likcr slruclurc wl~cn iortttcd m the pracncc of a SMIC elcclnc ticld. CJUSIII~ ~hcscmcdta IO c\hibn secondordcr non-ltnca opuc.d cticctb Sccondharmomc-gcneration studlcs are rcportcd.

I. Introduction For many sptropyran openmg we rsport

photochromtc

molecules reaction

reaclion

of the surprismgly

which takes ~13~2 when tlus pho-

tolysts occurs in aliphattc presence of electric

medta. parttcularly

tn th2

fields. The basic photochromic

of a spuopyran

(A) in solution

reverstble oprning

of the pynn

ocyanine

may be wrttten

form(B)

ring

occurs. In thts paper

some characterizations

htgh level ordsring

a reverstble

involvtng

complc.\es

porated

tnto the globules

studies

rtng to form the mer-

[?,31

of globules revealed

superimposed Intensity

on a diffuse

pattern

of A,B

1s corr2latsd EI2ctron

If irradtation

m.ttertal

that the core IS crystalline

matertaf and the coatmg stattc electrtc

wuh mtcros-

dre m fact composed

cores covered by amorphous

[-I]. It was concluded

but

[3]. The relattvc

present.

copy revealed that the globules

occurs

X-ray diffractton

sharp reflccttons

of tltess sharp reflecttons

the relative amount oicrystalhnc

the

(AB and ALB) WIIICII arc incor-

colored

is amorphous

IS performed

m the presence aid

field, a very interestmg

Tl12 globules

AaB

r\B m.tt2rtaI. phenomenon

becotne drrartged in strings or

threads along the field hnes [I -5 J_ keral

obscrva-

ttons and arguments

have been mJde to support

td2a that the globule

in these threads are dtpo1.u .md

are lughly

oriented.

Thermodynamic

the “stnng

of beads” structure

the globule

dipole

moment

thr

constderattonsoi

lead to a lower luntt oi

of 10000

D [aI_ Thcsc

threads have been called quan-crystals

Another interesting feature of these threads ISthat Upon irradiatton solvents,

aggregatton

even under very dilute

sultmg in the formation

occurs in aliphatic

each contains

conditions

globule

of spherical

[I ,?I, re-

particles

which

MI in diameter [3]. Detailed studies have shown that irradiation produces two types of are 100-400

l

Pa~~~anent address: Department oiStructur4

Chemutry,

Wemmann Instttute of Science. Rehovot. Israel.

only globules of one stze and tl1.u tire

[-I I. A model has been suggested whereby the globule cores sizes increase m discrete stepwts2 farluon

are actually

formed

from a sing12 type of crystalhnc

particle

whtch has a diameter

Kinettc

considerations

of AB and A,B

matewl

of ~40 nm (table

I).

based on the relattve qumtittes available as a functton

of 7-89

$-. Experimental Clubules

and quJs1-crysrals

were prepared

from

I4 ~-1iic’Il1J~rylo~y~Il1~l)~~.~-du112Il1yl-6’-niIrosp1ro(111dol1nc-7,7-(111-1 = -C2. I l;OCO ~~SIJIIIIIC

Jbenzopyran).

C( Cti3)=Cl12.

Illreads

J 111orr consenrrared tlic l~ruJu~I1011 ul’ IliwJcls

in 11iiicltic

III IIllS 5lllcl~ WC IIJW UIlil/hl sc~uiiti-hJri11u11rc gciicrJIior1

lllc ~lll?llOlllCIWII ul

I.51 IG) Jb &scribed

II1r’ I’olloain_c sc~I1011s 10 lurllicr iiu~cl 1nJIeriJls

51 IL rcsulls climlr.ak

k11o~n

wn-Imar \(”

Ikulx

ii&l

SLIS~~~II~IIII~

Jnd 1s a mc3surc

J5> nlwetr>

I0 llic 161 AS IS

ino-

order non-hwrlly

tl12 111olesulJr %3xXld(7 1. I[ n2s 3iiIl13pdlixi 11131 prexncc

01 lhc intmcy~niw

Spf3XS D aullld ~~ldblC.I ihmirerol’1113icr1~1I

I IS

I _PI1o:ogrJPh of

grxwraI1o11 Jnd

I ) WIIICII 1n

iibcrs. The rels-

obhned

than Ih~t previously -0,~ q p- of 1hJds Ihrd

iron

conrained

70’; co11Iancd

IO:t contamed

2St1-

WJS sub. glob-

second

generation.

Tl12

rlcctron u11crograplI oi fig. 3 sl~o\ts 1112globules preziplrJred on glass in rhc .Ibsr11ce oi an elecrric lield For 51 IG obscr\a1ons tao Iilul LOvCr slips.

IIIC qu~~~-~~ys~alhncll1rcJds iormcd 1n a 1icld of I 5 kV/mm

IUKL’ bcr\%scn clcL1rodcs rlic 101nl pJnllcl cxrcnr oirlic

7-90

grater

(fig

(1;g. 1) wcrc sliowrl

s2Lcral microgrJplis,

IlircJds. LS1 mm

samples

tt thin

Irolrui11 ~clly (Vxehnr)

III 1112~2@obulcs

umplrs

rrcl11sior-

n1JIcriJl

of rl12 l11ghcr generJt1ons.

ulcs ol rlw KirsI grnrraI1on,

ol 351 mr11cIry

of urganiration

s~~nt~all)

from

co111pk12

oi smglc globuhr

oiglobths

roughly

(1 5 X 10m3

dnd 1llu1111n~t10n

ess2nI1Jlly

1n 1110x dense

11~2 contrn~ mdted

solurlon

aas uj2d

1111croscope c\J1nin3t1011

glJlS

tor 1111swork

into qu3jI-kx>stJll1nC

more dilute soluI10ns

In noii-ienlro-

Ir) cnl1Jnc~

i~dI1011 0i II12 J~yniiiIrlry

to 2fr2cr solute

IO co11s1SI of strands

\Vlllcll IS

1112rocyJ111n2 dyes c~IIIl_xt It12 JppropriJIs

oiIl12

2kcIron

Jppro~r111JIion

_ $2)

1n31nmm2d

iiidtioii

Tl1is wsult2d

in IllcX

.md proporIIoi1Jl

1s 1W~H~3fl1SllII~~ollly

51 iii1UcIric mcJ1J She

dlpuk

I‘roni .1 r1~11141ii2dr poI.lr1rJI1on

m llic Jpplwl

wL~1ndarL[2r wll

In 1112 2kcIrIc

cl1Jrxtcrl72

splropyrdn

Xl) 111nirth~lLpclolle\~n~

ws

“grl11c’rJIiuilj”

WI a th111 cow

deposited

JS dcscnbcd earlier [A ] I lowever

plait IIIIIC cJn e\l’lJm

1n Gelds oi I 5 hV/

were produced

IIIIII Jnd subscqwntly

1.2. RI

R, = I I Tl12 quxI-

layrr

wr2

plsced bei- mm

OidodecJne

\v,tj InJected bcrween

or p21112

and preap1~X~~I on a glass cowr shp The da

\‘0lu111c Y7. numbL!r 3

Clll UK-

\L

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26 \I 1rJ1 I%32

lwh/aIwn

output LOU~IIII~ IQLI.NIICI l’hal

IJSCr WJS 7-5

Up2rJtCd

micro11 SpOl

~2

IIIC IJSCr pO!JrlZJIlOll dOubk

qUJrICr

filrcrcd from

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rtlolllb

will

rOI3It)r ~lld SlgllJl ptl\Jr-

~lii ILII

tlirougll 3 30

pJt?d

ckc1rO111c

IS d2scnlhkl

Jpp3r3tUS

SIIC

TIIC

1125 Jnd aerc

rlweby

Iltcn

ckslrodcs

IIIIhr

TII? &xlrodL’j

hr

ing

95%).

si11h?artiix1s blwhmg

Illr2C-dunCrlslollJl

simple m die

plJnc

due lo Ii&l

~olifi~ur~lion

Wlhp~?

wcrc

Sd3+/l’tIG

k.2r

conl'lgursd

JS

bJnd oTcrysIJllmc

ttjrd

I‘win 532

bv

ObSerWJ

pJ\C

riw

writid

IO SlgllJlS

3 Rtdtj \! IIt'll

Tllc r2SollJIOr

w11l1

dl~IribilIl~lli0~1llr~ddS

umlorm. Tlwrcior?

IWI

Ill2 lllJ\llllJUf silt To

J\OIII

posj1bk

111gor dlssoh 1112

SIIC

WCrC

iiiJIcri.ils

111r‘SJIII~ISS

globuk

Lluc 11) sndl-

JS rdpldl~

lo IrcqIwncy double

&Zld

due

10

Ulll CJUs?

311 Jr11l;ld

wuld

irilli our e~pcrmicnts. tlc~lris-Ii~ld-iii~iiL~~ ge11craIlon I LFISI

globules iormcd IIIthe Jb-

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\Vedg2

frulgCSJlld

0112 0i

rlic

the

.iblc

wrC

IO pCrIurb

versus ophxi

pJth

LFISI

hglli

wmdow InPxirrakcs,

1112

rlO1 pdrdllel WC IO ln23SulC

iil3\111l3IIIIIS2ll1l111lJ1l11g JIIY

11lag1l11ude olti12

@IJSS

3rrJll~2nlClll \VJS ub-

it 1112 Il1gll2stii2ldsuscd

~ecaus2

mtcrlc’rc’ J2SJIId-

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cOll13lll2d in Ill2 glJSd2kLIrd2 serwd

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rlie geii~r.d 110ii-

susccpr1b1llIws 191 WC

Illlrd-order

WJIIICJ 10 JcI~riI1111~ 1i such hrnon~c

ll1CdlJ.

dS posSlbh!

Or ~~scliilc

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altlllll tllJl ot~~lllOrp~lOus

p.1111 bc1wce11 1~

IO allo\r.c11 tllc Ic~s~.r~~~blc

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the ldjCr bull1 a

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wcrc 11i0uWXl in 3 tellon

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IO

the tFlSll

JI

uiiLcrI.unIy

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wI1cwIILc Icngh

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ewn WI~II

IS Slgllllisady

\‘olumc 87. nu1ubcr 3

CHCMICAL

more nttense than m most materials

26 March 1981

PHYSICS LETTERS

of the field after this treatment

tion of the magnttude

[!I]. Therefore

smce SHC signals from the rrradtated sptropyran Samples \ccre signtficantly lugher than the nttrobenzene

c3used 3 corresponding

IIFISH

mm which was apparently

~natima,

the n2glect of EFISH by glass and

uiin12rston Itqurds In our int2rpr2trrtion.

winch 3ttrL

but2s the SHG only to the thr23ds and globules,

is

vat~on dependent beam polarrzrd (Er)

~3s seen to be strongly

The srgnal generated with the laser

p3mhel to thr qu3si-crystal

was usu3lly one order of magnttude

when the beam MS pohntzcd

thr2ads do-

rccrion (r;,W). Tlis harmonic light wits obszrxd to be equally

ncll

p&r~zed

(.St”

WICII 3 st3trc electric

plied p3r3lkl

kV/mm

was ap-

sample (Ei>

SlgllJl incr2Jsed oker 3 period of IO-60

01, the

s, r23ching 3

trmes greater than the ortginal zero-field

VJhJC q _---I

(Er , Sf”)

SHC

of “perpendicular”

field for 10 to 30 min SHG (E,W,

Szw) dou-

wasobserved. Evrn 3fter this the induced zero-field

SHC remained approximately

tl12 s3m2 level. Smce therr SHC signals might

*STU).

field of 1-l

to the tlireads 0i3

aIlsI”

to the zero-field

these threads to

whde a slight decreas2 in tlte “p3r-

increase tn “comphnnce”

higher than

in the perpendrcular

“perpendicular”

bled in magnitude

polar-

level of 2750 V/

correlated

stand n-r 3 large perpendtcular tl1e inducsd

iron1 thrr3ds

of SHG, but only

restduel stgnal level. On allowing

Justiti2d. SIIC

wriation

for applied fields abov2 3 threshold

observed

during

be an indication

value at

had been largr trnnsisnt these esp+rimcnrs which

of freely

rotatmg

or migrating

threads, optic31 and electron

microscopy of stmilarly treated samples was undertaken. We found the thread

n1orphology

of such samplss to be indtstingutsh3ble

irom virgin samples and consequently

we do not con-

SI~IKII. After the field ~3s turned ofi, the sgrul de-

stder the beltavtor just descrtbed to be due to extensive

cr23s2d to appro.timately

external restructuring of threads.

Apphcatron field Mtli

opposite

thread formatron. However origitntl

the orrgmal zero-firld

of an 3ntrp3r3llel

value.

field (15: < 0). th3t IS 3

polarity

to that used tn the mitral

resulted tn reduction

OT the

SI~IKII.

removal oi this tield restored 3lmost the signal wtrhin

the s13t1c ftrld bdlJVIOr

3s well 3s tl1e rekatron

When the procsdure Jntlparallel

oiapplic~tton

of 3 sample

of tlte pxallel

and

fields was repeated sevsr3l times, the signal

Induced by the anttpxallel

in m2thylcyclolte~3n2

tn 1112Jbsence of tl12 electric

orrented (fig. 3). Applr3tton

or restoratron

on prshtstory

solutton

from s3n1ples prepared by

of the spiropyran

mstance globules werr randomly

.I few minutes. Tl12 eifect of

depended strongly

No SHG ~3s detrcted nr3dt.ttion

tield reached approti-

thrs2 sllllpl2S

fisld. In tl1ts

posittoned

and un-

of tl12 st3tic field to

reduced significant

SHG within

3 f2w

nnnut2s. but the stgnal w.ts lower than the signal from the threads under the same condttrons.

We place httlz

srgnificanc2

in this sines the harmomc

i3r lield radra-

tton psttern

depends on the d2t3tls of placemsnt

mutely rhe same value as a signal tn the parallel field

the tndtvidual

\~lnle the srgn3ls renianung

This IS clearly dtfferent for globules In tIneads or

of ctthcr pol3rrty of

Appliwtion

aftrr

approached

removal of the tislds

zero.

a I 5 kV/nim

stntic

mndomly

ilcld to virgin

s~~nplrs in the pl3ne of the shde but perpendrcular thr thredds (Ey)

tnduceJ3

new SHC capacity:

coherently

prectpitated.

to

gener-

v3lur. Rr-applicatron

Tl12 signal fell wtthin

pendtcular

ftcant SHC on spplping

Tins component

of

notse level and wtthin

s2vemf mmutes achieved 3 value ==I/6 of the SHG when all light polartzrrtions

(Er , S,f“). reduction

were pJrall21 to the threads

Remov.d of the field caused an tmmedrate

of tlus new signal, but there WJS 3150 3

second slower rekrxatton

which

led within a few

minutes to nearly stable SHG levels ==:1/3-l/:!

of the field-on value. Simihu behavtor was observed if 3 reversed polarity static field was then applied. Varta-

of the previous fieldon

produced

spiropyran

to the threads(E,U).

in benzene solution

by irradiation dtsplayed

the same electrtc field. Tins

m SHC since benzene is known tion of globules. concetvably

of the

no signr-

was to b2 a test of the rol2 of non-globular

the immersion

10 s lower

of the field resulted in the im-

medtats re-estabbshment signal. A prectpttate

of

partsles.

after remov31 of 1112field to a substanttally

.rtton of ItJrmontc polartzed perpzndicular to the threads (S:“T by 3 fundamentrd 3lso polarrred perSHG grew front the detection

drtven polartzed

material

to prevent the forma-

However dodecane,

which acted 3s

solvent for thw dried sample, cuuld

3ct as solvsnt for photochemrcal

tion of globules or of threads in an applied

produc-

firld. The

fadure to observe significant SHG from this sample under tdentical observations

circumshmces

to those of the prevrous

allows the concluston

to be drawn th3t

the laser did not cause s~gmficant photochemical productlon of allened globules during this or other caperiments. One can 31~0 conclude from this test that the mnially lbrmed globules w2re responsrble ior SHC m the methylcyclohCxane Case. The complex morphology, the mtcrmedi3te small (on the optical scale) globule and core crystallttc sizes and the lack of detailed knowl2dge ol rhelr optical charactsrlstics (and imually their general dynamIcal characterlstics~ made evaluation of the mhercnt nonlinear psramcters of these materrals very d~fiicult Since the harmoruc falls m hghly dlsperslve 3nd 3bsorbq

spccwal

WZ~NXIS of these ~STKIIS. the +iiort analysis ~3s 1101 conwdered to be

to complete such an

u~ortliwliile 3t this st3pz.

ocyaninc dyes [7]. we c.m also dismiss the posslbdlty of a signitkant cornrrbutlon to our signals from gcnenl tiurd-order effects involvmg st3trc fields. Coopsratire molecular alignment sucli ds agjgegatlon and cryst3llile formalion which incrc3ses net molecular ahgn3bdlty in the field (e g. aggreg3te dipole moment), as rnvoked earher to explain thread formation, must be responsible for the field-mduccd SIIC capibdlty of globules. The m3gnitude of slgn3ls obsCrv2d from SUCII small pJrtlclcs and thin s3mples require that the signals be due to electric dipole mtt’rxtrons. Smcc the second-order non-hne3r opt1531 elr’clrlc dipok suscrptibday

tensor.

(2) The latrd

1. Discussion Ewn rl~ougi~ he obswatlons

reported arc quAta-

tlve they allow some important conclusions to be drawn concernmg

the structur2 3nd properties oi These 3re summarized m the lbllowmg items. (I ) Globules cont3iu 3 non-cenrrosymmetrlc m3te. rl3l cap3ble of producing 3 macroscoplcally nonccntrosymmr’trlc mtern31 giobule structure. This conclusion IS supported by the followmg points One may sliow using the typic31 Ixge values of &(*5 X 10m4j esu) for merocyanmr dye molecules [7] 11131 mdep2ndent A9 and Al9 mokcular ahgnment under 3n applied iield t‘or mater131 m 3 I3yer the tluckness of our globules would produce less SHG than occurs 3t the m3.ylm3 of the EFISH frmges generated by nirrobenz2ne m the s3me fisld [9.10]. This layer thickness IS approprlare since 11 IS also Jpproxlmately the a-l absorption length oi 532 nm light in AB mar2rlA which hmirs total harmonic generalIon. These facts, the observation of greater SHG irom globules than from mtrobenzene, the obvious pseudo-rJndom and less thsn complete coverage of the slide by globule material, and the incomplete collectIon of 1112 cornpIe.\ harmomc radlatlon pattern m our quasicrystal ehperunenrs support thr conclusion rhat slmple field-mduced irldepazdcrlr molecule rotarlon by all molecules in globules is not responsible for our signals. Smce the rotational component IS by far the largest component of x(3)(-~~, w, w, 0) for merglobules and quasi-crysrals.

X(Z).

rvluch describes

tn_eonly in noli-ceittrosymtnctnl: the above stated co~~cl~~s~o~~ Iqcst

wr~ll tk

XC-) wnsor

static

SllC

IS non-vamsh-

structures. wc draw chanctcrm~c

dipole direstton

IS sorrc-

m ~IIC globules.

For SUCII sm3ll particlcs the efierts of light propJgJtioii tlirougli the nonhe3r medium on tlie Ii3rmomc mtenslty is rel3wel~ unimporkmr 3llowmg Illis sunplc statement lo be mdc. TIK sunplest mterpretstion IS th3t (fl),,,, (the mJ\imum component of the molecul3r hypcrpol3rlzablhty) and p(tl~C SI.IW mol2culJr drpole moment) 3s predlctcd by 3 simple ch3rge-transier two-level model [IO] 3re pJr3llcl In this mod21 the transition dipole (&,) is presumed pJrJkl to p and AC. the change oidlpole moment from lower to upper level W’e note th3t the thr2Jds 3r2 strong11 dichrolc in the AlB cryst3lhtc Jbsorptlon regums which would support this e\plJnation Alternxtvely a more comple\ picture could bC constructed whcrc the dlpol2 monxnt oi rl12 globulzs corr213t2s wnh some p3rtiJlly orlCntation3lly 3WrJgCd coniponenl 0i the susccptlbdtty tensor I(~‘. TIIIS could result iron1 the details of molecular p3ckmg III the crystrllitcs and/ or the complc\ morphology of higher-order globules TIIIS becomes log1c3lly necessJry to the cxtcnt th3t th2 simple ch3rg2-tmnsf2r rwo-1~121 model IS in3ccurate. (3) There IS an elcctnc-t”ield.mduccd rCoriCnt.ulon or rsorganizatlon of globules .md quasi-crystdls Tins IS the simplest mt2rpretJtlon oithe scver.d changes m SHG c3used by the appl1c311011 of ClCcInc fields to our samples. II IS conceivable that in the globules of the second and hlghcr gcnerJtlons. for WIIICII tllc

cores are thought to be compossd of several unit crystalhtes, some mutual motion and reorlentatlon

of the

crystalhtes can be Induced by these Gelds. 293

xc rcstortng

(4) Thcrc motions SllC

Tins

capabtltty

appltatton

ioroes WIIICII oppose thcsc

bc so smc2 tl12 thrcxls

nwst

long after titctr

of clrslric

formatton

oppositclg

dlpoktr

multiplc pul.irir2d

xc rcduccd

this IrCJttti2nt

dtfirr

and orictktltotts

rcspomblc

.~pphcd

globules.

by

1112rcstormg Possibly

clnwatted.

of the pxhmg

and ortcnta1~otts

i.2. rha net dipok

tl~c ficld

compli.mt

pxttculxly

witlUll

from

sccoltd

the smc

attd the second-order

for SHG 01’1112~2 globuleb

dt least p.trrly

durtng

oftltc

1112cqudibmtm

III tltc absence oi

~w~ncnt

that

0i tlte consti-

III tl~c cores orglobules

~ltot~ld bc attrtbuted

to

If ~IIIS IS th2 c.tse, tltis implt2s

and III_CJIC~ gcwr~twlls

sussrpttbtllty

of less

C3UWS 3 loosening

t~cnt cryswllilcs

immedutely.

amorphous coatulg

clectrtc iorces.

1112origiii~l pxkmg

iwld,

id

strcsscs.

or csscnthlly

the co111pl2\ cows.

p~chng

ap-

arc .tttrtbutcd

of rltc

ckttcity

IIIC rwJu4 (5) Aitcr

tows

but not

up011 tltclr removal. Tltesc

both 1112tntrrxtl md

~h~slt

in corrcI3tIo~~ wrtli the nisgnttudc of

pc3r to dcvclop

the 1i2ld and WIIICII .w quickly. rched

and smcc

fields c;luscs cltattgcs

the globule

IO 1112cii2ct furntallon

References

XI

retsln

OT

1I

I

VA. Krong.w and A A. Parshutkm. Photochcm Photobml. 15 (1971) 503. 12 1 A. \. Paal~utli~n .md V 4 Kronfauz, Mel Phokxhcm. 6 (1974) 437. [3l \‘.A Kirongaur and t S. Coldburt, Nature 271 (1978) 33. [-I I VA Krong~, S N. rtshmat and C S. Goldburt. J Phys Cbcm. 81(1978) 2469. [S I VA Krongaur and C S Goldburr, Chem. Phys Letters 60(1979) 251 161 II. Rabm .tnd C L Tang. cds . Quatrum rlcctromn J IIC~~W (AcJdcmlc Press. N~\v York. 1975) 17 1 A. DUILK .md C. rl) IKIIW.. Opt. Commun 25 (1978) 401: B I‘ Lwnc. C.C. Uctha, E. \\‘asscrman and L. Lerndcrs, J Chwn. Phys. 68 (1978) 5042: A. DUICIC. Chcm Phls. 37 (1979) 57 181 G.R Wxcdnh. Rev. Sn. Instr.. to bc pubhshcd 191 LI I’ Lcvlne and CC. tterhca. J. Chcm Phbs. 63 (1973) 1666 [ 101 J L Oudx 266-l.

and D S. Chcmla. J. Chem

P~Js. 66 (1977)