Raman study of vibrational relaxation of cyclohexane in benzene solutions

chemical Physics83 (i984)293-302 North-Holland, Ams~eidam~‘

-

- .C

RAMAN STUDY OF VlBtiTIONAL _. IN BENZENE SOLUTXONS H. ABRAMCZYK

RELAXATION

OF CYCLOHEXANE

_

-

and W. REIMSCHriSSEL

Institute of Apphed Radratron Chemistry, Technrcal Universrg tddi. Poland Received 16 May 1983

The Raman proftles of the vs mode (802 cm-‘) of cyclohexane, vs (723 cm-‘) of cyclohexane-d,, and vz (992 cm-‘) of benzene and its deuterated analogs have been measured as a function of concentration in the benzene-cyclohexane liquid system. The vtbrattonal time correlation functions of cyclohexane m benzene solutions have been calculated by Founer inversion of isotropic band contours The concentration dependence of the experimental vtbrattonal correlation times computed from theoretically for Knapp-Frscher for the va mode

the correlation functions and from the half width at half height have been compared with that predicted various mechanisms of band broadening We have tested the Ftscher-Laubereau dephasmg model and the concentration-fluctuatron model. We have found that the latter model reproduces well expertmental data only of benzene in solutron.

1.Introduction The understanding of the mechanisms of line broadening gives valuable information about the interaction of the reference molecule with its environment and about the structure and the dynamics of the bath. Mechanisms of vibrational relaxation may be probed by varying the temperature, pressure or solvent. There are a few theoretical mod& to examine the concentration dependence of tie vibrational linewidth in liquid binary mixtures. A most useful approach to thrs problem is the Fischer-Laubereau dephasing model [l] modified for use in binary mixtures [2,3]. Recently, Knapp and Fischer [4] have developed a theoretical description which accounts simultaneously for the static and dynamical aspects of concentration fluctuations at the reference molecule. This model is based on the stochastic lineshape theory of Kubo [S] for the case of many-state jump modulation_ In this- paper, we attempt to determine the broadening mechanism pf the isotropic Raman bands of both components in the benzenecyclohexane system. Reorientational and vibrational relaxation in liquid benzene and cyclohex-

ane has been investigated exhaustively using infrared Raman, Rayleigh and NMR methods, while the benzene-cyclohexane system has received little attention [6] and has not yet been investigated through Fourier analysis of the Raman lineshape. The benzene-cyclohexane liquid system exhibits very interesting thermodynamic and transport properties. The benzene-cyclohexane system has a positive deviation from ideality and it has exceptionally large values of excess functions in comparison with other non-polar systems: enthalpy He [7], free enthalpy G’ [8], volume v [9] and self-diffusion coefficients of the components [lO,ll]. This suggested, that the interaction between like molecules in the solution is stronger than interaction between molecules of different components. We thought that it would be interesting to examine whether these properties are reflected in the concentration dependence of vibrational relaxation For this purpose, the Raman bandshapes of the totally symmetric us mode of cyclohexane, the v, mode of cyclohexane-d,, and the vz mode of benzene have been-measured as-a function df solution concentration. The fundamental v, mode of cyclohexane represents the C-C stretch in the ring

0301~0104/84/$03.00 0 Elsevier Science Publishers B-V. (North-Holland Phystcs Publishing Division)

294

H_ Abramc=,k.

W RemschiiweI

/ Vibrurionnl relaxanon of c_wlohe_wne In benzene so~%iSons

plane while the uz mode of benzene is associated with the C-H stretch in the ring plane_

formula: A’ l/2

2. Experimental Spectrograde benzene, cyclohexane (Merck), benzene-d, (99.7%; OPIDI, Poland) and cyclohexane-d,? (99.4%; Isocommertz, GDR) were used without further purification. The compositions of the mixtures were determined by weighing. RdrfKIn bands were measured with a Coderg model PHO spectrophotometer with a double monochromator and a Spectra Physics 164 argon laser operating at 4880 A. All experiments were done using 90” scattering_ The polarization analyser was pIaced in the path of the scattered beam before the entrance slit of the double monochromator. The slit opening of the monochromator corresponded to 2 spectral slit width of 0.5 cm -’ for all measured profiles. Corrections for fmite slit wtdth have been estimated usmg the

Fig 1. Polarized (I,, ) and depolamed (I,

= A;,z [ 1 - 2( s/A&)‘]

*‘z.

(1)

where the subscripts t and a denote “true” and “apparent” full half widths at half height A,,, and s is the slit width. Spectra were recorded at room temperature. The scan speed was 2.5 cm-‘/mm with a time constant of 1.6 s. These settings minimize any possible mechanical and electronic distortions of the bandshape. Typical polarized and depolarized profiles of natural and deuterated cyclohexane in benzene solutions are shown in figs. 1 and 2, respectively_ The vs bands of cyclohexane and cyclohexane-d,, are slightly asymmetric due probably to the presence of the hot bands of the 13C species. The contour obtained after graphical resolution is given by the dotted curve in fig. 1. It is seen that the htgh-frequency half of the v5 band is not dtsturbed, so it is used for calculations of vibrattonal

) hne profile of :he vs band of cyclohcrane

ii. Abramczyk,

W. Rermschiisset / fibrationaf relaxation of cyclohexane m benzene sohions

295

%

Ill00 90

80 70 60 50 LO

30 20

732 -------

10

1

722

7:2

3 (cr41

0 Fig. 2 Polarized (I,, ) and depolarized (I,

correlation

) hne profile of the v5 band of cyclohexane-d,,

times. In benzene, hot bands occur on side of the vz band. An additional Raman band exists also in the far wing of the band but it does not interfere significantly. The contour used for calculations obtained after graphical resolution of the overlapping contours into the constituent vt (O-l) and other bands is the same as in ref. [12]. AlI bands studied are not overlapped by bands of the second component. The base lines are absolutely flat and horizontal. The vibrational time correlation functions a,( r ) for neat cyclohexane and for cyclohexane in benzene were obtained using the usual procedure by the

applying:

high-frequency

a,(t)

=jW i,,(w) -00

e-‘Or do,

(2)

where i,,,(w) is the normalized isotropic part of the scattermg tensor and o is the angular frequency. The vibrational correlation functions of neat cyclohexane and of cyclohexane in benzene for several concentrations are presented in fig. 3. It is seen that the experimental vibrational correlation functions are weIl approximated by a simple exponential for times longer than 3 ps. So, the vibrational correlation times q may be calculated from the experimental correlation functions using

Ii_ Abramcqk,

296 0.e

1.6

2.4

W. RermchiiErP:

3 2

4.0

/

Vtbrarional refaxarmn 4 a

of qdohexane

5.6

7.2

in be&-em soluz~onr

a.0

a.0

In@”

[PSI 7

-0.2 -

-06-

FIN 3 Vlbrattonal correlation functtons of neat cyclohexane (1) and of cyclnhexnne m bcnzrnr for benzne 0 570 (3) and 0 820 (4).

3. Results

the relation:

= it@,

mote fracttons 0 424 (2).

dr+lr

e-“‘dr. T

where T 1s an arbitrary division between the shortand long-time dependence of the vibrational correlation function. The first integral of eq. (3) was evaluated numerically using Simpson’s rule in steps of 0.02 ps over T = 7 ps and the second term was solved analytically. The vibrational correlation times of the components were also computed from the widths of the bands:

(4) where “;“/_ is the half width at half height of the isotropic profile. Numerical calculations were carried out on an Odra 1305 computer according to a programtn written in AIgol 1900. All statistical errors reported in this work are calculated at a confidence IeveI of 0.95.

We have found that the observed isotropic Raman full Ime-width at haif height of the v5 mode is 2.2 + 0.1 cm-’ for neat cyclohexane and 2.6 f 0.1 cm-’ for neat cycIohexane-&. The latter value IS in good agreement with that reported by Tanabe [13] (2.5 t_ 0.1 cm-‘) while the former is drastically different (1.6 f 0.1 cm-‘). The reason for this discrepancy is unknown, because Tanabe does not give all experimental conditions, for example spectral slit width. The vibrational correlation time of neat cyclohexane determined from eq. (3) was found to be 4.92 _+ 0.28 and from eqs. (1) and (4) 5.06 -C 0.15 ps. We see that both methods give good agreement. The vibrational correlation times of neat cyclohexane-& and benzene calculated from the half width were found to be 4.47 _C0.20 and 4.78 f 0.48 ps, respectively. Figs. 4 and 5 show the concentration dependence of the vrbrational correlation time rV of cyclohexane in benzene and in benzene-d, solutions, respectively. Fig_ 6 shows the concentration dependence of ?; of cyclohexane-d,, in benzene_ In aI1 cases studied, the vibrational correlation time

H. Abramayk.

W. Reimschi&se~-/ Vtbratmd

rda_&icn of cychhexane in~betueneduhs

[PSI

5.0.

k.0.

hli’l 801.0

800.0

On0

0.2

Fig. 4 Vtbrational

0.L

0.6

correlation

times

0.8

800.0

1.0

~~(0, A) and sluft

of the

peak frequency Pu (0) of the vs mode of cyclohexane m benzene. A: r, obtamed from eq. (3); 0: 7” obtained from eq approximated parabolic curve for experimental (4); -: data (n) (see table 1); ----: dephasing model (without anharmomctty). - - - -: dephastng model (with anharmonicity concentration-fluctuation model (R = 0): effect), - - -: O-t3concentratton-fluctuatton model R = 0 2288-O 3512(1 - x,)+0 2748(1~a)‘).

of cyclohexane

a benzene

in benzene reaches a maximum

mole fraction

for 0.5 and 0.6.

between

Experimental data are rather well approximated by the paraboiic equations given in table 1. In figs.

Table 1 Least-squares constants hexane solutions

of the equation

(%)e

Gd-h-C6H,

4.92&0.28 b, 5.06~0.16 =) 5.06&0.16 4.47 *0.20 47g+o4g

C&,-C~DI, a’ b’ =) d,

I 0.0

a’

(5),, is the average value for the neat solute. 7” calculated from eq. (3). 7, calculatefl from eq. (4) For benzene in Ceffe-CsDta we have used the linear equation-

XB I

I

I

I

0.2

0.4

0.6

0.8

799.0 1.0

Fig. 5. Vtbrattouaf correlation tune r_(0) and shift of the peak frequency AP (0) of the vs mode of cyclohexane ut benzene+ -expenmental curve (table I); ----: dephasing model (without anharmonicity); anharmonicity effect): -. -_

- - e-* dephasing model (with concentration-fluctuation model

(R=O).

we also present the peak frequency shift Av = v - v,,, where v, is the frequency of &he neat solute.

4-6

Although small, a trend to a change of the position of the maximum for the v, modes is observed with

7” = (~“)e + ax + bx2 of the experimental

Solute-solvent

C&,-C&i C.&,-C&f,

801.0

vtbrational

correlation

hmes

P

b

2.51 2.91 2.43 1.73 1.37

-222 - 3.04 - 2.40 -171 - 6)

‘rv = (7v)e + a(1 - xa).

for benzene-cyclo-

H

298

Abranrcq k. W. Remrrchiirrel /

Vrbratronal relaratron of cyclohexane in benzene solurrons

increasing benzene mole fraction_ In fig. 7 we present the vibrational correlation time and the shift of the peak frequency of the v2 baud of benzene as a function of concentration of the C,H,-C,H,, system. One may suppose that the vibrational correlation time of benzene increases linearly shift

with decreasing

is observed

benzene

of the benzene

mole fraction.

line center

No

upon

drlution.

I

4. Discussion

hi']

Ax’

Tanabe and Jonas [14] have studied the Raman lineshapes of six totally symmetric bands of liquid cyclohexane as a function of pressure and temperature. They found that the dephasing theory predicts satisfactorily the temperature and pressure dependences only for the high-frequency v, (2938 cm-‘) and u-) (2852 cm-‘) bands while for lower frequencies (also for the vs mode studied in this paper) the experimental data could not be interpreted in terms of the simple dephasing model. They suggest that for lower-frequency modes, for

720.0 --_

OO --so

-.+.

719 0

--_.

t

I

L OL

I 02

00

Xi3

718 0

L 08

I 06

10

Ftg 6. Vtbratlonal correlation tzme 7, (0) and shaft of the psak frequency AP(O) of the vs mode of cyclohexane-d,a MI benzene. -I expertmental curre (see table 1). - - -- dephasing model (utthout anharmomctty): -- dephastng model

(wth

anharmomclty

fluctuatton model

(R

effect).

----f

which

conccntratron-

= 0)

[PSI 6.0

\ -\

-4

---A-_

8

-1.

--4 --

----..a

\

It is known that the binary mixtures may processes such as pure tion fluctuations [4,16], depopulatron [17] and

l

0.0

(tie

Z-Z-kT)

vibrational shape m liquid be broadened by several dephasing [15], concentraintra- and inter-molecular resonance energy transfer

0

-.-.-.a.-.-._.

4

8

0

0

of this theory

nism.

-
0

the basic conditron

is no longer valid the vibrational motion may be strongly coupled to the bath. whereas the dephasmg theory assumes that the vibratronal and rotational degrees of freedom do not couple with each other. This stimulated us to examine the effect of dilution on the vS mode of cyclohexane and the v2 mode of benzene m benzene-cyclohexane systems. In our opinion, studying the dilution effect in two-component systems may often be useful to determine the vibrational band-broadening mecha-

I

1

0.2

0 L

xB

I

I

0.6

0 8

1.0

Fig 7 Vtbrational correlation ttme T,(O) and shift of the peak frequency L(O) of the vz mode of benzene MI the benzene-cyclohexane-d,, system - - dephasing model (wtthout anharmonicity). - - --_ dephasing model (with anharmomcity effect); - - -: concentratton-fluctuatton model (R=O).

H. Abramczyk,

W. Relmschiissel / Vibrational relaxatron ofcyclohexane

[18]. In order to determine the mechanism responsible for the concentration dependence_ of the vibrational correIation time of both components in the benzene-cyclohexane system, we have first tested the dephasing model modified for use in binary mixtures [2,3]. In binary mixtures, the bandwidth due to dephasing may be expressed as: %h = (%h )solute-so,ulr + (%h)solutr-,c.,\&

(5)

Ol-

‘jTph

=

(l&h),,

(6)

+(‘&.h),,*

where the subscripts I and J denote solute and The rates of dephasing solvent, respectively. (l/~r~),, and (l/-r,,),, can be expressed as follows:

(7) for k = I (solute) or j (solvent). All symbols have their usual [1,2]. The factor (1 - - meaning where f is the force constant, mfL,pfYQLYv eludes the anharmonicity effect. The contact values of the radial distribution functions were obtained from the expression g,, (a,, ) = fESY( a,, ) + Mr?

e,, )7

(8)

where g,‘,‘( u,~) is obtained from the Percus-Yevick equation [19], while g,“x” (u,~) IS calculated from the scaled-particle theory [20]. The density of the benzene-cyclohexane system was taken from ref. [21] and for benzene-&cyclohexane from ref. [22]. There are no data for the density of the benzene-cyclohexane-d,2 system. The dephasmg theory presented by Fischer and Laubereau can describe only relative changes of the vibrational correlation time, but not the absolute values of the dephasing rates, because the chotce of the molecular parameters M, y and f are somewhat arbitrary for polyatomic molecules. An advantage of studying dephasing processes in two-component systems as a function of concentration, is the possibility to normalize the de-

in benzene solutrons

299

phasing time by assuming agreement with the neat solute ( T,“P = Tag)_ The results of calculations of the vibrational correlation times from dephasing theory without inclusion of the anharmonicity rph and with anharmonicity effect ~~~ are given in tables 2-5 and are plotted in figs, 4-7. A simple inspection of figs. 4-7 indicates that the dephasing model does not reproduce satisfactorily the experimental data. To examine the concentration-fluctuation effect we have tested the model recently proposed by Knapp and Fischer [4]_ This model assumes that the spectroscopically active mode of the reference molecule is perturbed by N environmental perturber particles. Knapp and Fischer have shown [4] that the spectral function I(o) can be represented by a linear combination of N + 1 lorentvans:

where i,,(o) IS an mdividual actenzed by two parameters:

lorentzian

char-

cj, = o0 + $NAw + $(2n - N)A;, ~,,=ys+$N(Ay+R)+$(2n-N)Af,

(IO)

where y0 and w0 are the linewidth (hwhh) and the frequency in the neat liquid, respectively. The meaning of the quantities E,, AG and Ap and a detatled discussion of these parameters is given in the paper of Knapp and Fischer [4]. For the time relaxation function G(t) = (f(C)) w h ere C is the full-time-evaluation = (exp(tC)), matrix (C = C,, + R), the sum (9) can be written in closed form to yield Q(f)

01)

= @&)@l(f),

where @o(t)=exp{it[w,+N(l-~)Aw] --t[Yo+Nl-41)’ G,(r)

=

{exp(-rs) x

[cosh( rr) + (s/r)

r = $(A? - iA&),

sinh( rr

)] } Iv,

s=$R+$(u-u)(Ay+iAw).

Table 2 Theoremal

values of the vibrational correlation time of the vs band of cyclohexane

M=0.9798x10-s

g; /=-1XlP

yo=l.l

0,,=800.8cm-‘; -rB

rph

00 0.1 02 03 0.5 0.6 0.7 08

4.92 4.94 490 4.85 478 478 4.64 156 4.46

09

4 36

10

426

04

a’ From ref. [23].

g cm-’

cm-‘;

s-‘;

L,, = 0.306 A; L,

= 0 295 A;

in benzene. o, = 5.52 A *‘; D, = 5.13 A “; 7 = 0 5; N = 5; AS2 = -1.0

cm-‘;

AY=

-0.076

cm-‘;

R=O anh

7Ph

5;rCR = 0)

T-CR f 0)

R

4.92

488 4 83 479 472 4.65

4.92 4.73 4.69 4.66 466 465 469 4.73 4.76

4.92 475 4.71 469 469 467 470 4.76 4.79

0.152 0.135 0.123 0 117 0 117 0 127 0.132 0.148 0.169

4 58 450

484 487”

4 86 4.90 =’

0 196 0 228

4.96

4.95 493

b, From ref. [2]

<) 7Lr= hm,B_,r-,.

t We have obtained the spectral function I(o) as the Fourier transform of @J I)@*( t )_ From the half width of the spectral function we have CdkUlated the vibrational correlation time 7crassocrated with concentration fluctuations. For the ben-

zene-cyclohexane system we have tested both the static (R = 0) and the dynamic (R P 0) approximations_ In the latter case, we have estimated the rate cf particle exchange from the jump diffusion taking into account the model R(c)=6D(c)/r' concentratton dependence of the diffusion coeffi-I-able 3 Thcorcrical values of thr vIbrationacorrelauonume of the ps band of cylohexane m benzene-d,.o, = 5.52 A. 0, = 5 I3 A; y=O.5:M=0.995x10-‘~g;f=-~xx10’Jgcm-’s-~;L,,= 0306~;L,,=O295~;iV=5.M2=-OScm-‘,Ar=-0.005 cm-‘. I&,=SOOScm-‘; -y,=l_O94cm-‘; ‘B 00

01 02 03 0.4 05 06 07 0.8 09 10

nnh

cients D(c) in the two-component system. In our / calculations we have taken D(c) from ref. [lo] and adopted for r the hard-sphere diameters. The results are given in table 2 and in fig. 4. It is seen that diffusion (R f 0) has a small effect on the vibrational dephasing. The results of the c,aIculation of qr from the concentration-fluctuation model for the remaining systems are given in figs. 5-7. From figs. 4-7 it is seen that the concentrationfluctuation model does not reproduce the experimental data of the vibrational correlation times for Table 4 Theoretical valurs of the vlbrauonalcorrelationtime of the _IJ~ band of cyclohexane-d,2 in benzene. a, = 5.52 A; Q, = 5.13 A; ~=O5:M=1074x10-‘~g;f=-lxlO’Qgcm-’s-~:L,,= 0 306 A. L,, = 0 295 A, N = 5; AD = - 1 1 cm-‘;

R=O

cm-‘.

Ar=

a*

rPh

TPh

7Er

XB

%h

%h

r,r

5.06 5.03 4.98 4.94 488 4.81 4 73 464 4.47 443 4 32

5 06 5 05 5 04 5 02 498 4.94 488 482 467 466 457

506 468 466 461 4.60 4.65 468 469 4.75 4.78 487”

00 01 02 03 0.4 0.5 06 0.7 0.8 09 1.0

4.47 4.43 439 435 4.32 427 423 4 19 4.14 409 405

447 4.45 4.44 4.42 441 439 4 37 4 35 4.33 430 428

447 4 37 4.32 428 426 4.26 426 4.31 4.36 4.44 4.54 II)

a) 7Cr= limX8 _ ,7._

-0.004

o,=720.1cm-‘;y,=l189cm-‘;R=O

a) 7er= lm.-*%f-

A ; I c

Table S ~he~rettca~ values of the vlbrationai correlation time of the y2 band of benzene in cyclohexane-dtz. a, = S 13 A; U, = S S2 A; y=0.5;~=0838x10-~g;f=--1x10’Jgcm~’s~’; L,,= 0285 A; L,,=O.2% ,&; N=S; AG?=O.O cm-‘; AI-= -0302 cm-‘; Wo=989.scm-‘;70=1.13rm-‘;R=0 -VB

%h

$h*

7tr

0.0

5.32

SOS

636”’

0.1 0.2 0.3 0.4 05 0.6 07

5.28 5.23 5.18 5.13 507 5.03 4.%

5.03 5.01 498 4.96 4.94 4.81 4.87

6 12 5.94 5.77 5.57 5.39 5.22 SOS

0.8 09 10

4.90 484 478

485 4 81 4.78

4.92 4.77 4.78

ii) 7.* = hm X,-&

the vS mode of normal and deuterated cyclohexane, whiie good agreement is found for the vg mode of benzene. This model gives satisfactory agreement with the experimental shift of the peak frequency in all cases studied, when calculating the Fourier transform as I(O)

=/Q(r)

exp[i(o

- (~>)t]

dt,

where (L?} = o, + Awx. Now we would like to comment on the contribution of vibrational energy transfer between close-lying vibrational levels to dephasing. Although experiments show that diatomic and triatomic molecules relax on a time scale of nanoseconds or longer and that the vibrational energy relaxation and energy transfer between small molecules are slow enough to determine the vibrational hneshape, this approximation may break down for larger molecules which relax on a picosecond time scale. To examine this pathway of relaxation we have studied the concentration effect on the vibrational correlation time in the deuterated analogs of the benzene-cyclohexane system. If the vibrational energy levels in the system studied were close together one would reasonably expect that during a collision vibrational energy may be transferred to a lower neighbouring energy

level. For the vS mode of cyclohexane two vibra‘tional levels should be taken into account: the v,,(E,) mode at 787 cm- * of cyclohexani [24] and a very weak Raman-active overtone 2w, at 802 cm-* of benzene [25]. Therefore one may expect, that in the benzene-cycl_ohexane system, during collisions, the near-resonance energy conditions would favour the following non-radiative transitions: C,H&;)

+C,H,&3)

+ C,&(V,)

+ C,N,z(~$3)

+ AE(15

CM’)

+ AE(0

cm-‘),

and/or GH&;)

+C,H,(23,)

+ CeH,2(~g)

+ C,H,(Zv$)

where v;, v; and 2v&, denote excited states. If this mechanism contributes to band broadening it should give a change in the concentration dependence for the C,H,,-C,D, and C,D,,-C,H, systems, because in these isotropic modified systems to a good approximation the potential remains the same but the vibrational spectra change. We have obtained (figs. 5 and 6), however, nearly the same concentration dependences (table 1). This indicates that this mechanism of band broadening is negligible. Finally, we comment on the effect of resonance transfer on dephasing. Normally, if we assume that resonant broadening is independent of other phase-relaxation mechanisms, it would increase the dephasing time upon dilution. Computer-simulation results [26] have shown, however, that the inclusion of cross-correlation terms leads to a decrease of the dephasing time upon dilution_

5. Conclusions The vibrational correlation time of the v2 band of benzene increases upon dilution in cyclohexaned,,. The concentration-fluctuation model of Knapp and Fischer predicts satisfactorily the concentration dependence for this band. The vibrational correlation time of the v, band of both natural and deuterated cyclohexane reach-

302

H_ Abramczyk.

W.

Remmchiiwel/

Vrbratronal rdaxatron of cplohexane

m benzene solutions with a benzene mole fraction of = 0.5-0.6. The experimental data can neither be interpreted in terms of a single mechanism discussed above nor in terms of their combinations. It is possible that observed discrepancies between experimental data and theoretical models for the vibrational time of the y5 mode of cyclohexane arise, according to the conclusions of Tanabe and Jonas [14], from vtbrational-rotational coupling or from the fact that for the lower frequency modes the basic condition tie x- kT is no longer valid. On the other hand, the observed expenmental dependence for cyclohexane may be related structural effects m the to some benzene-cyclohexane system. suggested by the large positive deviation from ideality as mentioned rn section 1. Borodko and Syrkin [6] have found that the intensity of the v1 Raman band of benzene in the benzene-cyclohexane system decreases upon dilution with cycloheuane. They have explained this by self-association in neat benzene. which decreases upon dilution. In recent experiments inhomogeneous broadening in liquid benzene has been found [27] and one possible explanation may be that there are long-hved fluctuations over a time scale of at least 50 ps_ These structural effects in the benzene- cyclohexane system may cause not only repulsive interactions but also different types of slowly varying forces to gtve d contribution to the dephasing. Further experiments wil! be necessary to decide which explanation is correct for the vibrational relaxation in the benzene-cyclohexane system_ We hope that an analysis of the combined results of isotropic spontaneous Raman studies and picosecond coherent probing experiments will be helpful m this respect_ es a maximum

Acknowledgement Our thanks are due to Drs. H. Baranska and A. Labudzinska for their help with the measurements and for useful discussions.

m benzene sohmons

References [I] SF. Fischer and A Laubereau. Chern. Phys. Letters 35 (1975) 6. (21 K Tanabe and J. Jonas, Chem. Phys. Letters 53 (1979) 275 [3] W. Reimschtissel. H. Abramczyk. H. Barariska and A. Labudztftska Chem Phys. 72 (1982) 313. [4] EW. Knapp and S F. Ftscher. J. Chem Phys. 76 (1982) 4730 [5] R Kubo. Advan. Chem. Phys. 15 (1969) 101 [6] J G Borodko and J K Syrkm, Opt. Spectry. 9 (1960) 677. [7] J R. Goates R J Sulhvan and J.B. Ott, J. Phys. Chem 63 (1959) 589 (81 J A Barker. J. Chem. Phks. 20 (1952) [9] A E P Watson.

J A

McLure,

1526

J E. Bennet

and Gr_C. Ben-

[lo]

son. J Phys Chem 69 (1965) 2753 W. Relmschiissel and E Hawhcka. J. Phys (1974) 2307; Ber. Bunsenges Phystk Chem

[ll]

1221. E Hauhcka and W. Retmschussel. Chem 85 (1981) 210.

Chem 78 81 (1977)

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