Influence of the potential on the intensity of depolarized light scattering ; in dense liquid argon

Volume 85 number 1

1 January 198,

CHEMICAL PHYSICS LE’l-l-ERS

INFLUENCE OF THE POTENTIAL ON THE INTENSITY OF DEPOLARlZED IN DENSE LlQUlD ARGON J

LIGHT SCAlTERlNG

1

VERhlESSE

Lnbora~orre- des Inreracrrons

93430

Vdlermeuse.

dloler&rres

er dcs Haures Prcssrcns

C IV R S

Centre Umwrsrlarrc

de Pans Nerd.

Frame

and D. LEVESQUE

and J J WEIS

Laborarorre de Physrque Thiorrque

Rrcewed 11 July 1981. m tinal

er Haufes Euergres

iorm

l

U-nrernrd de Pans Sud

91405 Orsay Ccdex. Frmce

16 November 1981

The depolarlzcd hght snllermg IIIMISI~) 01 argon 31 the rrlplc pomt IS calculaicd b) molcculx d) namvzs usmg rhc ISOpotcntcd The rcsrllt driicrs from ihx obwncd wrh a Lcnnard-Jones poicnr~~l by no more rhan 159

body Bobcuc-Bxker

Depolarized hght scattermg (DLS) measurements m mert gases are susceptible to gwe mformation on the colhslon-induced polanzabdlty anisotropy provlded an accurate knowledge of tie mteraction potential IS avadable Most theoretical DLS mtenslty calculatlons for dense hqutd argon [I-S] are based on the Lennard-Jones (Ll) potentlal When further a dlpolemduced-dtpole (DID) model for the colhsion-induced polarlzabthty anisotropy IS assumed the theoretical intensity calculations are approvlmately a factor l-5-1 8 larger than the experimental results [4,6]. Before ascribmg ths discrepancy to the fadure of the DID model and remptmg to refine the amsotropy model it IS desirable first to assess the influence of rhe interaction potentlti. Indeed, the effective U pair potential doss not give an overall accurate descriptIon of both the thermodynarmc and transport properties of mert gases [7] and far better agreement wtth evpertment IS obtamed by usmg a multlparameter pau potentlal as e g. developed by Barker and coworkers [7] together wtth an Axdrod-Teller threebody (triple dipole) potential. Its effect on the colhnon-tnduced light scattertng tntensttk of argon is IIIvestigated here. In fact, we shall neglect the rhreel

bboretouc

body contribution to the potential Although essential to predict a correct equalon of state [SJ its mfluence on other properties hhe the dielectric constant has been shown to be qune small [9 ] _As I&t scattenng mvolves quantttles simdar to those encountered m the calculation oi the dtelectnc constant we can expect that the effect of the trtple-dipole potentml will be small in this case too. The DLS mtensity IS proportIonal to mean-square fluctuations of the polanmbdlty anlsotropy Usmg the notation of Varslmeya et al. [4], we introduce the quantity GA(o) = &-yx

= $ p&=,

s=B =N-t([CjV~,~~<,,gQO(il)]‘)

(a,fl=x,_v,z)(2)

p 1s the density

and a,-, the polarlzablhty of the Isolated atom In expression (3) the polanzablhty amsotropy has been assumed to be Parr-wise addlttve and acting as a point polartzabdtty

xsoc~e zw Cenuc National de 13 Rccherchc where e, is the component

120

(1)

where

0 009.2614/82/0000-0000/S

along the (YMIS of the vec02.75 0 1982 North-Holland

Volume

85. number

CHLFNCAL

1

partlcfe i to partlcfel.

torjouung

the hgbt scattermg double scattering

mtenslty [IO]

Eqs (I)

PH\ SICS LE-I-I’ERS rametcrsr,

and (2) for

muftrple

scattcr-

c p(r) = Gni/r3

GA(O) ftas been evaluated by molecular dynamics

fcrence results froin tfic slightly

ustrtg a system of 256 partrcles with periodic boundary condttions for a thermodynamic state having denst-

witfl a U potenztaf

tn connectton witfi

fiigftcr tcmpcrdturc

the BBpotcntiaf,

ence tn G,(O) tscsscnttally due to tfte dtfferencc mr,,, as can besccn by compartng the rcduccd qu,mtttics S*iZ =r6,SZZ (cf table I) TIIC prcssurc obtdtncd u1t11 the BB potcnridl IS -4 14 aim and rhc intcrii.if

were set equal

mof-1

larger

arc -

It has been shown recently [3,4j that, near tfte triple point, tfte value of .S@ has an osctflatory dcpendence upon the cut-off however, a constant radtaf dtstribution utg a cut-off

most fthcfy to be

untty vafuc

farizabifity Baroccfu and Zoppr [ 13,1_1j + propose a pair pofartzabiftty modcf for argon wttft tfte cmptrtcaf form

IS

rn the

’ The cocfficicntsd and B of rhc psu pokiriubdrty anisotropy gnen m rcf [ l-11wcredcrrvcd b) rncans ofa moment analysts usmg 3 won& xduc ior the polarlzabdq of the ~&on aton1

vancd and for all

(BB)

potcnttaf

In rills pqx!r WCUSC the corrercedrThcs of rcf f t 31 WCarc grateful to Professor r Bsrocchl for pomtmg thrsout to us

[I 21 wttft pa-

Table 1 Depolzrlzcd hght scaiiermg vtiulous polarrzabtht) xnsotropy models Tlic pokzabdltrc, firk”d v.hercas the pol.ulzsbdrt~ models detcrmrnod for the Lcnnard-Jones and b ewen m table 3 of ref 141 tcs~ectrrcl~

experiment

IISS

approktmatefy

IS

considered we were carcfuf to cftoosc idcn-

LennardJones

I)

with tfus asymptotic

g(r,)

ticaf boundary conditions Ustng the Bobettc-Barhcr

Bobcitt-B.&x

table

ascribed IO tflc mtdequdcy of the DID model for the po-

In any case, we are here mainly intcrcstcd

Potcntl;ll

results (cf

CIIOOS-

approaches unity

change of .S*fl when tf~e potential potentials

152 atm and -I A37 caf mol-l

experimental

value for distances at WIIICII the

r, sucft that

c.if po-

(as already noted earlier b) Afdcr et al [I 1) so that the dtscrepancy between tfte mofccular dynaiiitcs and

distance rc approaching,

function

leads to results conststent

cncrgl -1-155

of the three-body i\uilrod-Teller

Tfie light scattering mtcnsity in dense fiqutd argon Is thus fatrly tnscnsittve to the intersction potenttaf

IS unity

functlong(r)

Inciusion

tcntttl would r.ttsc the prcssttrc to .t sftghtly postttve v.tfuc [S] For the !_f potential the prcssurc .md mtcrnal energy

than rc = 2.9 rm (r, IS tfte dtstance of tftc potentraf mmrmum) For the patr potenttats considered here this distance corresponds to a value of r for wflich the radial dtstubutlon

tiscd

tfte remainrngdtffer-

ty p = 0 03533 mof cms3 (792 amagat) and temperature T= 92 K (close to the rrtpfe point of argon). The averaging in (2) was done over 43 000 time steps of IO-‘” s The patr potcntiaf and pair pofonzabdity for partzcfe separations

(~0

(‘IIl = 3 821 &elk = I20 K) (cf. tdbfc I ) wf~tcfi IS stinilar to what IS observed at low density ( Is]_ Part of tfiis diT-

IIf1

to zero

model

IOn5 A3 Th~sv.duc

1s =f 5% ftagfter tflan tftc one obtained

negftgtbfc for argon

mg f~as been shown to be entirely

1981

= 3 763 A e/k = I40 23 K and tfic DID

for tflc pofarrr3blflty anrsotropy. I = 1.68 A3).wefind G,,(O)=> 55X

retam only doubfe-

Higfler-order

1 January

Polwwbdny smsotropy model

~niol cmm3)

ior IIIL BobLUc-Uarhrr .md Lcnnsd-JunLs potcn~rals and JBB corrw ond to cxes (I) and (2) of t~btc 3 of rcf 1131 IO rhc pxnm.tcr wt\ a potentul. P !J .md @_ corrtspond

T (fi)

5”:

GA(O) (IO-5 A3)

Rci

DID

0 03533

92

0 57

155

tt11c worA

P

0

03533

91

047

2 09

rtil:,

pBB _

0

035 33

92

0 39

I 75

thus uorh

DID DID

0 03333 0 0349-l

90 89

054 057

120 Z IO

1111 111

PtJ

0 03494

89

Of2

I 70

141

P2u

0 03393

89

0 36

1 45

VI

0 03-135 0 035

90 8 86

worh

17,1=017 I19 $0 IS

121

Votume 85, number

I

CHICMICAL PIIYSICS

LETTERS

1 January

1982

usmg the same empmcaf form (4) for /3(r) but a ~~nil~rd-Jones potenttal The results arc surnnia~7~d tn tab!e 1 Ftg 1 shows both poianzabthty models together wtth the pure DID model and the radtal datnbutton function

I

1

2

r/f_

i-rr! 1 Bchwmur of the par pohrtzabthty anaotrop) ior argon as a functton oi dtstancc for the dtpolc-tnduccddtpolc (DID) modes, BP” (solrd Ime) and ,FB (dashed Ime) Also sho\\n IS the radral distrtbutton ftmctton near the tnpk pornt for the Bobcttc-Barker potentt.d

f$() =

6143r-~+ Ar-6 - Be-‘lrO)

(4

Usmg the Bob~ttc-Barhcr potcntlaf they d~t~crntn~ two sets of paramrters whxft fit equafly well the first three (even) moments of the low-dsnslty two-body spectrum of argon It room tcmpcrature Both sets (tdcnuficd as (I) .111d(1) m table 3 or ref 1131 .md denoted fly* and 0:’ m table I of tfns artrcte) lower the scattermg mtcnstty (with rcspcct to DID) at the trlpfe pomt of argon and brmg II m closer a~r~cl;l~nt wtth expcrmrcnr Sttntl.~r tindmgs Ir+~vc‘ been obtamed by Varshneyz et 41 I-!] who fitted lo\\-densny specrrnt moments

[ 11 BJ Alder. JJ Wets zmd H L Stnuss, Ph> 5. Rev AI7 (1973) Z&i. [2] B J Aider, J C Beers II, H L Strauss and JJ Wets. J Chem Ph>s 70 (1979) JO9 1 131 AJ C Ladd, T A LGowz. J H R Clarhc and L V Woodcoclr .I Chem Phys 72fl980) 1759 [4] D Vaishneyl S F Shtrron. T A Lttovtrz. hl Zoppl snd F Baroccht. Phys Rev A13 (198 I) 77 (51 J H R Ckuhe and L V Woodcock, Chem Phys Letters 78 (1981) 121 iS] J H R Cfarhc and J Brummg. Chum Phys Letters 80 (1981) 42 171 J A Barker, tn Rxcgassolrdr. Vol 1, eds bl L Klcm and 3 A Venablos (Andemtc Press, New Yorb, 1976) IS] J A Barher, R A ~rshcr and R 0 Watts, bfol Phys 21 (1971) 657 191 J Vermcsse. D Levesquc mtd J.J Wcrs, Chem Phys Lcttcrs 80 (1981) 283 [IO] T Rcyrs. 3 Chcm Phys 70 (1979) 5438 [ 1 I] J.J \Vus and BJ Alder. Chcm Phys Letters 8 I (1981) 113 ii?1 Bf V Bobctrc and J A Barker. Phys Rev 67 (1970) 1169 1131 r B;uocchi and Ll Zoppt, fntcrmolecuku Spcctroscopy and Dynsmtnl Properties of Dense Systems 75 (1980) 237 [ 141 r Bzuoccht M Nerl and hf. Zopps, Chem Phys Letters 59 (1978) 537