Effective molecular quadrupole moments and orientational correlation parameters of liquid benzene, hexafluorobenzene, mesitylene and carbon disulphide

Volume

94. number

1

CHEMXCAL PHYSICS LFZI-PERS

EFFECTIVE MOLECULAR QUADRUPOLE AND ORIENTATIONAL

CORRELATION

1983

MOMENTS PARAMETERS

OF LIQUID BENZENE, HEXAFLUOROBENZENE,

MESITYLENE AND CARBON DlSULPHlDE

Julian VRBANCICH * and Geoffrey L.D. RlTCHlE Sclrool of Chmistry. The Universitv of Sydnqv. Sydney. N-S_ IV_ 2006, Recerved 3 October

7 January

1981; in final form 14 October

Australfa

1982

Effective molecular quadrupole moments determined from electric ficld%radtent induced bircfrin~ence drc reported

for benzene. he\afluorobenzene.

mesitylene

and carbon disulphide as pure liquids. Conrbinrtion of these values with the

correspondmg free-molecule quadrupole moments yields the orientational on the tield-g.tdicnt birefrmgencc constant is anal) sed.

I_ Ineroduction A direct method for obtaining molecular quadrupole moments from measurements of the birefringence induced in a flurd by an electric field-gradrent was developed by Buckingham [l] and applied to gases [23]_ Using classical statistical-mechanical theories to describe the field-gradient birefringence in dense media ]1,4,5]. the infinite-dilution quadrupole moments of benzene and other non-dipolar aromatic molecules [6 1, and of carbon disulphide [71.

were recently

determined_

in view of subsequent

studies of benzene, hexafluorobenzene [8] and carbon disulphide [9] in the vapour phase, and evaluations jlO,l l] of the effective polarizability anisotropies of these molecules as pure liquids, it is of interest to compare the field-gradient birefringences of the liquids with those of the dilute solutions and vdpours in order to estimate the orientational correlation parameters, g2 [lo-131 _Although g2 is related to several observable properties of liquids, values have not previously been derived from studies of field-gradient birefrmgence. in addition, a statisticalmechanical treatment [ 141 of the solvent effect on the Kerr and Cotton-Mouton constants of non* Present address

Chemistry Department.

The University,

Glasgow G12 SQQ, UK. 0 009~2614/83/0000-0000/S

03.00

0 1983 North-Holland

correlation

parameters. ga_ The solvent effect

dipolar solutes is extended to the field-gradient birefringence constant. The analysis shows that reliable values of the molecular quadrupole moment can be obtained using polarizability anisotropies derived from analogous measurements of the Kerr effect.

2. Theory The molar field-gradient 1,1Q, is defined ]6J as 6n(3er •f-2) ,Q=

5e,(d

lim

-I-

2)2 “xx-0

= (3~~,/45e,)[f&,, =: (2iVA/45eoX-T)AocffO,

birefringence

constant,

[‘z~~~zy] V,, + (W)-‘o$%&]

(la)

(lb) UC)

in which (rzX - nY)/Em is the ratio of the induced birefringence to the applied electric field-gradient: II, er and V,n are the refractive index, relative permittivity and molar volume of the medium;B,p,,p is a tensor describing the distortion of the molecule by the field-gradient; asp cff is the effective optical-frequency polarizability, which differs from the freemolecule value because of local internal fields within the dielectric; and oup is the mean quadrupole moment of a small macroscopic sphere of the dielectric 63

volulnc

94. nt!!~!bcr 1

cen:red

on a fixed

CHE\lICAL

molecule

with quadrupole

moment

Gas IS related to the mean total quadrupole moment of d macroscopic spherical sample of the dielectric by extension of Kirkwood’s st3tts1t~~l-t~1e~ha11tca1tre.tttnettt of dtelectrtc polarization [ I _A] Eq ( 1c 1Applies if the molecule possesses J three-fold or hlgller-order rotation ~1x1s(the z axis) .tnd rllc tetttper~ture-tndependent contrtbution is neglected Aa(= a__ - a, \ ) 1sthe pol3rizabtlity anisotrap> .md U IS til,-ttntqttt ntolecular quadrupole moIIWII The products cx$t~~~a dnd CQ@,~. the frrem~~lc~ttle equtvAent dtffer bec.tuse of contrtbutions from sltort-r.tttge .tttgul.tr correkions between the molecule 31td tts tteigltbours. Jrld aiso because of tl!c qtwlrupule moment mduccd in d uioleculc by its oxi II re3cttott-field gr.tdteiit. dtt effect which cdti itiLre.tw tlte qu3drupole tnoment by = 15”; I-l.5 ] _ lncorporatmp these contrtbutiotts [I .4.6] QOP_ The qustitity

(2, (-ZIP = -

+ 2)(‘C7 + 3) =--_ $,O _

5(3C, + ‘Cl 1

a$

=fk,@ag -

(2)

it hcrc @a;1 is the free-molecule quddrupole 1110ti~~tiI. E, .md E, .tre the relattve pertnittivtttes of the bol\ent .mcl nou-d~po1.u S0lule. iespiXtiVCly_ Jrd

I or 0bSc‘rvdttotts on &lute soluttuti~ 111.t ttoti-quJdrupol~r. tsotropic.tlly-polxt~~ble solwttt. extr.tpoLied to tttfitttte dtlution. correl.tttoti effects 3re 3s wined ttegltgtblc .ttid ~p1~1tcA101iof eq (1). together n1t11

~.hcs

01

rl!e

ctfecti\e

pol.mr~biln~

huiotl

1983

elude the fieldgradient birefringence constant_ Followmg ref. [ 141. a spherical sample of fluid containing a single non-dipolar solute tnolecule of polarizability rzZaS surrounded by NA - 1 isotropic solvent molecules with polarizability a1 is considered. Subscripts 1 and 2 denote the solvent and solute, respectively, and the solute is identified 3s the first molecule. Both solute and solvent are taken to be linearly pOldriZdble and additive contributions to the molar Kerr, ,uK. Cotton-hlouton, ,,,C. and fteldgradient birefringence. .,(.I. constants are assutned for a given tnole fraction_ In the analysis, only the dominant contrrbutions are considered and the temperature-independent terms in the theoretical expressions for ,,,K, m C, and ,,,Q are neglected. Thus the dominant contribution to ifie molar field-gradtent birefrinsence constant is l,,Q = (7/15E&T)(+

Ij

(ap~)/aED)G$$,

(3)

of molecule i in the presettce of 311extent31 electric field. EC. whose frequency is well removed from absorptton frequencies of the sample, i e. pt) = c@(EY + Ft)); FF) is the field 3t molecule i due to 3ll other molecules in the simple. 022 IS _ the quadrupole tnoment of species i .tnd. by deftnitton. 6,,0,, = 0. The angular bmckets ( > denote canonical-ensemble 3veraging in the absence of external fields. Invoking the point&pole approwmation [14]. -‘\‘* in which

[I:’

is the dipole

moment

frmi!

L’OllStJllt IS JllJ~ysed

in conjullction

with

the

~‘lfe~t!ve

p&rrL_tbtlrt> rtmsotropy deduced from Kerr-effect studies. -1 theoreticdl Justtftcdtion of this o!wr\.ttioti c~tt be dr.twtl from the results of 3 statisII~J~-I!I~!J!!Ic~

t!eatnle!lt

Mouton Cotton dtpulx sohttes [l-l].

the

7 January

misotropy

the ttifmtte-dilution niolJr Kerr cotigrant t>t tilt sviutc‘ 111the same solxcnr. yields values 01‘ 11112!noksul.w quJdrupolr nioiiient (6.71. Such d proc&te 1ltcrefore p.tr&ls tltr eaxmn of the ttiolecul~r m.tgttettc .tttisotropy frotn the tnfmttedt1uttu11 tttol.tr Cotlott -Mot.ttotl cottskmt. 111tltts Lttter ~.tse II 1~s been est.tblislted experttnent.tlly 1I5 .I 6 j that for mmy molecules a rehable value of the m.tgttcttc .misotrop> is obtained when the Cottondmrcd

PHYSICS LETTERS

of tl!e solvent

effect

(4) where the correlation (y-U)) = (r”A -J#l -0 =

&I$

tensors are defined as

y4’iI)

($J))--5

afl

[jr;li)$i)

_ (r”i))~gap]

j,

(~~1 (5b)

on

and Kerr cotisfdtits of non3nd thts is now extended to in-

attd r(v) is the vector connecting the centre of molecule i toj. The solvent effect, defined as the difference

;

Volume 94. number 1

CHEMICAL

PHYSICS

between the molar field-gradient birefringence constants of the solute in the solution and gaseous states follows from eqs. (1 b) and (3), and eq. (6) of ref. [6]

c.&QZh’f

- ,Qr@s)

LETTERS

7 January

1983

-0-4 + O-2. Incorporating the solvent correction, the molecular quadrupole moment derived from concurrent determinations of O(mQ,) and -(&z) is given

:

bY

= @n&/45kl?

where for an isotropically polarizable solvent OlaP = 0; the polarizability volume L@ is defined as (4z$-J)- [nap [ 14]_ By comparison with the analogous expressions for ,Cand ,K in ref. 1141 it foliows that for an axially-symmetric solute

and, analogously, the magnetic anisotropy, Ax, by

U,,,Q#--

,,Q,(ga91/,,Q2(tW = Lt,,,G) - ,,,C2(gas)l/,,C,(gas)

(Sb)

= SI,(,,$) - ,,“~(g”s)lI,,,Kltgas) = [ay/(c7’y! e-2 - a$_;,>][(z&-Z -I-“~~x)w;~)> + $n~)WJ + . .] = D/2 .

where in eqs. @a) and (Sb) we have used a binomial expansion for [ 1 + 02/4( 1 + D)] -Ij2_ The important conclusion to be drawn is that although the solvent effect may introduce a significant difference between

(7)

m(nlK~)V m(,,lC~), &Qd and &&4, ,,,C&PS)~ ,Qz(gas), respectively, neglect of the solvent interaction term does not seriously detract from the reliability of the derived quadrupole moment or magnetic anisotropy, since the correction, D”/S(l + D), is small (-4%). Molecular quadrupole moments obtained from recent vapour-state electric field-gradient birefringence measurements [S,9] on these molecules show good agreement with results from observations

Eq. (7) predicts that the solvent effect on the molar field-gradient birefringence constant is, to a first approximation, equal to that on the molar Cotton-Mouton constant and to half that on the molar Kerr constant_ From the analysis presented in table 1 it can be seen that this relationship is satisfied for benzene and to a lesser degree for carbon disulphide and hexafluorobenzene; the mean value of D is Table 1 $101.~ Kerr, Cotton-Mouton .md carbon disulphide a)

and field-gradient birefrinzence

const,mts at 298 K and 632 8 nm for benzene. he\ailuorobenzens

He\afluorobenLene

Benzene

IO*’ &mK2) (m’ V-’ mol-I) 1027mK2@as) (m5Vz mol-‘) 102’,C2&!:as) 102’,(,C2) (m’ (m’ A-’ A-’ mol-‘) mol-‘)

7.11 2 008 15.6 2 0.8 [I81 [15] 27.6 36.1 + * 0.7 1.6 1151 [20]

10z6_(,Q2) (m5 v-l mol-‘) lO*6 mQ2(gas) (m5 V-’ mot-‘)

118 133

f 3 [c&&z lm(mC2) l&,Q2)/f

*7 + Bd) 161

1.17

1 - n&z &s)ll&2

&as)

- mC2Q~~~l/*nC2(3~) - mQ2Bas)l/mQ2bas)

-0 27 2 0.10 -0.24 f 0.10 -0.24 + 0.10

13.6 2 0.4 19.6 b) 1161 24.4 24.1 f* 0.8 1.1 116) 1101 -153 -164

=7 [6] 2 9 d) 1.13

-0.16 -0.01 -0.18

32.6 57.5 -19.6 -13.7 100 93

* 1.4 * 2.6 [18] [lS] f2 01.08 c) ll5]

;:g’

1.20 2 0.10 f 0.10 * 0.10

‘) lntiniteddutlon values are for carbon tetrxhlorlde as solvent. b, mK2 = (NA14OSEnkT)AaAa + (N~/Blco)lK; Pa from ref. 1191,benzene V.&C of Pa/Pa =) M.G. Corfield Ph.D. Thesis d, mQ2 = (~_&%okT)Aa@;

Carbon disulphide

-0 19 2 0.10 -0.30 f 0.10 -0.10 -+0.10

and -yK 1181 assumed.

University of Bristol (1969). as quoted in table 1 of ref. [ 14J_ An. 0: C6H6, CbF, [B), CS2 [9]_

65

94. nu1nIhx

\‘olunlc

CHEMICAL

I

PHYSICS LJXI-ERS

solutions [6.7] (see table 2). Clearly, neglect l)r the solvent interaction term would be expected to Icad to over-estunation of the quadrupole moment. but dcfuute confiruMmn of this prediction is not yet p~‘s”lblr on &lute

!\ llr12 lwlk iilt

fkld-grJdicnt

InolJr

w~~gllt

Jeuslty

md

to

atr.lc1

lclmulcd I

6

frorll

cqs

Iron1 J combm~tion

high

Lonstmt,

of the meduun.

poi.irIubdir~

I\ _ I he &ccrnc qtIImi

bmfringencc

X is

of the hght. ,md 111.md p dre the

I\ ~~Ch~th

sdt

hw11g

of rhe pure hquids

respective-

JUiSotropy.

&xc’f.

(11 .md (9) cm of depolanrcd

re-

bc de-

uiJgnetic birefringence studies [ 1Oj. Using the free-molecule qua-

md

drupolc moment. the orientA0n.d correl.ition p.mm&er._c2_ IS c.dcul.~ble from eq. (I): rhc reactIon-field ~1 JClIr’IlI c~~rIcc~IOI1 IS [email protected] ~VheIl die free-

1i1dc~111c qu~drupol~ mnient Lhhl~IOll IIi‘5 01ll>

0t

IIlr’JSUIeIllC11~5. 1hC

SUlCe

11011-diplJkIf

.~ppr~nUll.~~L’

Zrjb ( 1 1JIILI c \pc’r IIWII~S

(2)

SdVeIlt VJ~UCS

bec~uw.

IS der~vcd from infinitethe

rehhc

xIld

PerIllittiVi-

SOhIte

dre

SiIllihr.

ofgZ cdn be obt3ined from Js in other light-scattering

xc used to drternme gl. suitable \AICS s)I &rc** arc rrqmred [ 171: in Jddition. contluuum n~o~Icl~ Jrc in\ol\cd. nhh

3. E\periment.d ~hLrlp~IoIls

pcrmwut.A

of Ihe JppJrJtUS Xld praedure habe been yen

III~‘JSUICIU~‘UIS

wcrc

~.sII,~JIIJl~ricJl-rcJgcIlt

prwr Icr uw.

66

mddr

.a

gr.ide

&%iilS

16.21].

25OC and 632.S liquids

which

of the ex-411 nm.

were

dried

7 January

1983

4. Results and discussion The mohr field-gradient birefringence constants, n,Q, effective polarizability anisotropies, Aaeff, and derived orientational correlation parameters,&, of benzene, hexafluorobenzene, mesitylene and carbon disulphide are given in table 2. Except for mesitylene. for which the vapour-phase molecular quadrupole moment has not been reported, values of g7 were deduced from borh infinite-dilution (omitting sohenteffect correction) and vapour-phase free-molecule quadrupole moments_ The most reliable values of g2 in table 2 3re those derived from the vapour-phase quadrupole moments; the errors arise mainly from the uncertamty in AGff. Results compare favourably with other determinations. for example: CSZ, 1 .I3 f 0.1 1; C6H6. 1.16 + 0.171 C,F,, 2.75 + 038 [lo]: CgH3(Cl13)3, 0.94 f 0.14 Ill]; 311of the foregoing were obtrtined by combining data from the Rayleigh spectrum with me3surements of the Cotton-Mouton effect_ Other v.dues derived by dilution techniques from depolarized Rayleigh scattering 3re: CbH6, 0.99 [24],0.9 [25].O.S [26], CgFg, 2.58 [24], 1.40 [?6] 3nd CS2 1.3 [25]_ Critical discussions of reported g7 vases are given in refs. [ 10,13,27]. The orientstional correlation parameters for benLene, mesitylene 3nd carbon disulphide are effectively umty, apparently reflecting the near-cancellation of (as opposed to absence of) angular correlation between the centr.d molecule and its nearest neighbours [ IO,1 1,X3]. For hexafluorobenzene g2 is significantly larger than unity, implying that 3 more parallel arrdngement of molecules is f3voured. The importance of the sign and m3gnitude of the molecular quadrupole moment in relation to molecular interactions in the vapour, liquid and solid phases of benzene, hexafluorobenzene and 1.3.5trifluorobenzene has been discussed [6]. The qu3drupole moment of hexafluorobenrene is similar to those of benzene and mesitylene, while that of 1.35trifluorobenzene is an order of magnitude smaller 161; however, the orientation31 correlation parameters of hexafluorobenzene and 1,3,5trifluorobenzene 3re identical [24]_ The above suggests that long-range intermolecular forces do not determine the local internal structure of these liquids, although this is not necessarily so for the vapour and solid phases. The g2 values for these similarly shaped molecules h3ve been correlated with the packmg den-

i

Vohune 94. number ?

7 Janu~q 1983

CHEWCAL PHYSlCS LETTERS

sity and it was shown that the fluorobenzenes

nificantly closer-packed lene, so that a consistent possible [ Ill_ In our treatment, we induced contribution to highly anisotropic

I

i

c

1 ; I

are sigthan are benzene and mesityinterpretation of results is

have omitted the collision,,,Q and mK, since for the

nondipolar

molecules

considered

here such effects are likely to bc negligible [10.29] _ The neglect of the temperature-independent contribution in eq_ (lc) is justified in the cases of benzene and hexafluorobenzene [S] _ For carbon disulphide, an analysis of the rotational g-value, quadrupole moment and molecular magnetic anisotropy data simihrrly implied that the temperature-independent contribution to the field-gradient birefringence constant is unimportant [7,9] _ The above interpretation of the solvent effect is based on a dipole-induced-dipole mechanism, and is most appropriate to hi&ly anisotropic solutes: as the anisotropy decreases, terms of higher order in T may become significant. A discussion and physical interpretation of the correlation tensors (TL,)) and (T,,). which is relevant to section 2.1, has been given [ 141. The present analysis omits other contributions (for example, molecular hyperpolarizabilities) but it is considered [14] that the anisotropy in the distribution of spherical solvent molecules around an anisotropic solute molecule provides the predominant contribution to the solvent effect on the Kerr, Cotton-Mouton and field-gradient birefringence constants_ The orientational correlation parameters derived from the infinite-dilution birefringence measurements (table 2) are underestimated if the solvent interaction term. &/S(l +D). is assumed to be zero_

Acknowledgement We thank Dr. P-J. Stiles for helpful discussions and the Austrahan Research Grants Committee for fiiancial support.

References ] I] A.D. Buckingham, J. Chem. Phys_ 30 (!959) 1580. 171 AD. Buckingham and R.L. Disch. Proc. Roy. Sm. A273 (1963) 275. [ 31 A-D. Buckmgham, R L. Disch and D.A. Dunmur, J. Am. Cbem. Sot. 90 (1968) 3104. 67

\‘oluIIle

94.

mm1bCr

1

CHEUICAL

141 A D IhJLhmgilJIn .Ind c. GrahJm. hlol Phyc 22 (1971) 335 151 A.D. l~uchm;h.~n~ cd . m UTP ln~crn.~tIonal Rcvievv of S~kncc. i’ii~sic~lCliemictry. Seric\ 1. 1’01 2 (llurrcr~\orth~. London. 197-1) p_ 341. 161 J Vrb.mci~lI .md G.L.D. R:tchIr. J. Chem Sot. 1‘arad.q II 76 ( 1980) 648 171 G L 1). KIIchIc and J. Vrlxmrrcll. J. Ciwn~ Soa. i‘cmda) II 76 ,198O) I?-%5 1h 1 \I K ~~JIIJ&J.A 1) BucLm~h.~n~ Jnd J-11. \VillI.uIls \ 37 (19791 1412 1111 I’ \ \1 Id&w \I K htI@J. T I c-Cl\. K K;. PIerens ,md J. ~~hJlrllliIlr1 Chcrri l’h? P Lcltrr\ 76 (1980) 601

PHYSICS

LEl-l-ERS

7 January

1983

[ 171 T-1 Co\. h1.R. BattaSlIa and P.A. Madden. hi01 Phys 38 (1979) 1539 1IS] M.P. Bopaard. A-D. Buckin~ham and G.L.D. Ritchie, Xl01 Phys 18 (1970) 575. [ 19 j M.P. Bogard. A.D. Buckingham. R.K. PIerens and A.H. White. J. Chem. Sot Farada] I 74 (1978) 3008. [ ZO] hl P BoSaard, A.D. Buckiqham, M.G. Corfield, D A Dunmur and A-H. White. Chem. Phys. Letters 12 (lY72) 558. 1311 J. Vrbancirh, b1.P. Bogaard and G.L D. Ritchic, J Phys Cl4 (1981) 166. I211 J. Timmermans Physico-chemical constants of pure org.mic compounds. Vols l/Z (Elscvier. Amsterdam. 1950/1965). [ 231 X11. Raw. D.A. Horsma, CM. Knobler and P. Perez, J. Ph? s. Chem 73 (1969) 641. [ 24 1 N-41 D. Bro\v II. J T. h&wire and T.L. Swinton. Farada) Diwwions Chcm. Sot. 66 (1978) 244. A K;. RurnlI.mr. G L A11ns .Ind W Il. Flygarc, J. ClIem. l’h\\ 62 (1975) 3289 D.R. Rauer. J-1. Brauman .rnd R. Pccora. J. Chcm. Phys. 63 (1975) 53. 11. VcrwIold. in- Og.mir hquids- structure. dynamIrs end chcm~cal properties. cds A.D. Buchingh.mr. C. LIppcrt and S. Br.Ito\ (Wdey. Ne\r YorA. 1978) 1’. 81. R \V lmpq . PA. M.rddcn and D J. T~ldcslcy. \lol Ph>\ 11(1981) 1319. M_R. ~J~II.I&I. Chcm. Phys Letters 54 (1978) 124