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Critical effects on vibrational dephasing in CH4 diluted in CO2
Volume 179,
CHEMICALPHYSICSLETTERS
number4
26 April 199I
Critical effects on vibrational dephasing in CH4 diluted in CO2 M.A. Echargui
’ and F. Marsault-Herail
Laboratoire de Spectrochimie Mokulaire, UR4 5 08, Universit6Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05. France Received 12 January 1991;in final form
I I February 1991
The Raman isotropic v, bandof CH4 diluted in CO1 hasbeen studied in the supercritical fluidphase,especially along the critical isochore of the mixture down to the liquid-vapour critical point. The comparison with published data on pure CH, shows that, in spite ofthe large vibrational band shift due to environmental fluctuations, the critical mhomogcneous broadening in the CH4/ CO2mixture is considerably attenuated.
1. Introduction A critical inhomogeneous broadening due to the density fluctuations has been evidenced in the isotropic Raman spectra of some pure fluids [ I-61 near the liquid-vapour critical point. It is well established [ 7-91 that the vibrational shift plays a predominant role in the manifestation of such an effect. For binary mixtures two kinds of critical effects have been considered. On the one hand, for a liquidliquid critical point, there is no evidence (experimental [ lo] or theoretical [ 111) that concentration fluctuations give rise to spectral critical effects. On the other hand, in the case of a liquid-gas critical point, density fluctuations. similar to those in pure fluids, are expected to induce a critical broadening of the isotropic Raman bands. Such a phenomenon has been observed for the Q lines of Hz and HD diluted in argon [ 121 and for the uI band of CH4 diluted in CD4 [ 91. In this last case the slight decrease of critical effects with respect to pure CH, was explained by the absence of resonant transfer and by the decrease of vibrational dephasing. For CH, diluted in C04, which is the subject of the present investigation, absence of resonant transfer should be counterbalanced by an increase of environmental fluctuations. As a consequence the critical ’ Present address: Laboratoire de Physique Moltkulaire, F.S.T. Campus Universitaire, 1060 Belvedtre, Tunis. 0009-26 14/91/$
03.50 Q 199 I - Elsevier Science Publishers B.V.
effects are expected to he important. However this hope will be deceived, the critical inhomogeneous broadening being much weaker for the CO2 solution than for pure methane.
2. Experimental The Y, Raman band of CH, diluted in COz was recorded using the experimental device previously described [ 51. The Raman shift measurements were carried out by scanning the neon line at 5869.82 8, in the same run. The frequency accuracy is 0.2 cm-‘. The spectral slit width being 0.25 cm-’ for an apparent bandwidth of the order of 2 cm-‘, the apparent band profile was identified to be the true one. The error on the half width at half maximum Av,,, is $0.1 cm-‘. The gas mixture was prepared in a tank according to tht= procedure described in ref. [ 61; the CH4 molar fraction in CO1 was fixed to 8.5 ? OSW in order to use the mixture p VTdata of ref. [ 13 1,For the band shift measurements, the gaseous mixture was confined in the scattering cell [ 61 at 3 11 K and cooled at constant volume along isochoric lines ( 119 <
317
Volume 179, number 4
CHEMICAL PHYSICS LETTERS
removing the gaseous mixture, so that the position of the meniscus remained unchanged (constancy of the liquid and vapour volumes); then the cell was closed at the critical point. This method leads to a precise value of the critical temperature but only to a rough determination of the critical density. Since we had already observed that the critical density effect is not so drastic as that of the critical temperature [ 61, a slight deviation from pc is not significant. The ratio (T-T,)/T, is estimated with a precision of 1V3. 2.1. Band shift The temperature effect on the vI frequency at a given density is negligible in the density range studied here. Fig. 1 compares the values for the solution and the pure liquid as a function of density at 301
26April1991
K. In both cases the curves V,=f(p) are well fitted by a parabolic law: v10+up+bp2. But in the same conditions of density and temperature, the red-shift is significantly more important in CO1 than in pure methane, as expected from the Lennard-Jones potential constants (T[ 151 and t/k (3.82 8, and 137 K or 3.90 A and 16 I K, for pure CH4 or CH,/CO,, respectively). In fig. 2 we have plotted the Y, frequency of CH, in CO1 and in pure CH, versus the reduced density p* =pa3 at the same reduced temperature T*=kT/c. It appears that, in spite of the absence of resonant transfer, the band shift in the COz solution is the same as in pure CH,. Accordingly, considering the large value of the vibrational dephasing, significant inhomogeneous broadening is expected in the COz solution near the liquid-gas critical point.
U
,.il cm-1
-2
cm-1
916
2914
L: !912
0.15
100
200
p
(mast)
Fig. 1. Density dependence of the ~1 frequency of CH.+in CO2 and in pure fluid at 301 K. ( 0 ) and (-), experimental data and parabolic law fitted on data for CH, in CO,; (---) parabolic law deduced from ref. 191 for pure CH.,.
318
t- I
0.30
PO3
Fig. 2. Reduced density dependence of the P, frequency of CH, in CO1 and in pure fluid at the reduced temperature T* = I .87. (0 ) experimental data for CH, in CO2 and (---) parabolic law deduced from ref. [ 9 ] for pureCH.,.
Volume179,number 4
CHEMICAL PHYSICSLETTERS
2.2. Band profile
In order to show the contribution of the critical effects on the band shape, we measured the bandwidth Av,,~ along the critical isochoric line of the CO1 solution. We also deduced the Lore&an cLand Gaussian cc widths related respectively to the homogeneous and inhomogeneous broadening by fitting a Voigt profile to the experimental one, Lastly we fitted the I+ band shape to the Fourier transform of a vibrational correlation function corresponding to an intermediate regime between slow and fast interaction modulation [ 161.
(1)
In this model previously used for pure CH4 [ 51 and its isotopic solution [ 9 1, d2 and r= are respectively the mean square interaction modulation and the interaction correlation time. The experimental bandwidth Av,,~ and the ratio cc/c, are reported versus ( T- T,)/T, in figs. 3 and 4, respectively. The comparison of these results with those obtained in pure CH, shows no significant
l
.
+
change in band profile for CH4 in CO* in contrast to the striking inhomogeneous broadening for pure CH, as the critical point is approached. The use of the intermediate model (eq. ( 1) ) leads to a value of the mean square interaction modulation A2 which remains constant along the critical isochoric line. A2 is greater for the CO, solution (~0.3~ 1O24sm2) than for pure CH4 (~0.17~10~~ se2) which confirms the enhancement of the vibrational dephasing in solution. The plot of T,, the interaction correlation time, versus ( T-T,) / T,, is reported in fig. 5. r, remains very small in the CO2 solution (fast modulation regime) even when (T- T, ) / T, tends towards zero. This result is strikingly different from that in pure CH4, where rc was shown to increase strongly (very slow modulation regime) at the critical point. All these features demonstrate the weakeness of critical effects on the v, band profile in CO2 solution, in contrast to their importance in pure methane. This difference is unexpected, taking into account the magnitude of the vibrational dephasing, and pre-
1
AW+$rn-’) 2.5
t +* + +
26April1991
+
. +
+
+
Ii
t
12
1.5
0
* 0
0 0 0 0
1
1.
.
.
l
10 20
30
4,O 50
60
7
X1C3
10
.
30
50
yc
P
x10
3
A
Fig.3. Temperaturedependenceof the halfwidthat half maximum,Av~,z,ofv, of CH, in CO2 (0) and in pure fluid ( + )
Fig. 4. Temperature dependence of the ratio c,/c, of the Gaussian to the Lorentzian width of the Voigt profile optimized on the u, band of CH, in CO? (0 ) and in pure fluid (0 ), along the
along the isochoric linepzp,.
isochoriclinepep, 319
Volume 179, number 4
CHEMICAL PHYSICS LETTERS
r
26 April 1991
References
Wps)
-6
0
-5
I 2
i
0
20
40
60
a0
[ I] M.J. Clouter and H. Kiefte, J. Chem. Phys. 66 ( 1977) 1736. [Z] M.J. Clouter, H. Kiefte and R.K. Jain, J. Chem. Phys. 73 ( 1980) 673. [3] M.J. Clouter, H. Kiefte and N. Ah, Phys. Rev. Letters 40 (1978) 1170. [4] M.J. Clouter and H. Kiefte, Phys. Rev. Letters 52 (1984) 763. [5] M.A. Echargui and F. Marsault-Herail, Mol. Phys. 60 (1987) 605. [6] M.A. Echargui, These d’Etat, Paris (1989). [7] H.L. Strauss and S. Mukamel, J. Chem. Phys. 80 (1984) 6328. [S] M.J. Clouter, H. Kiefte and C.G. Deacom, Phys. Rev. A 33 ( 1986) 2749. [9] F. Marsault-Herail and M.A. Echargui, J. Mol. Liquids, in pE%.
Fig 5. Temperature dependence of the r, parameter deduced from cq. ( I ) optimized on the vi band of CH, in CO, ( l ) and in pure fluid (0 ), along the isochoric line p=pc. The parameter A* is zO.3~10~~s-~inCO~and ~0.17x1024s-2inpurefluid.
vious results obtained in other solutions [ 9,121. A systematic study of the influence of concentration and of the nature of the solvent is necessary to sift out general rules about the critical inhomogeneous broadening of isotropic Raman spectra in mixtures near a liquid-vapour critical point.
320
[IO] J.R. Petrula, H.L. Strauss, K.Q.H. Lao and R. Pecora, J. Chem. Phys. 68 (1978) 623. [ 111 BP. Hills, Mol. Phys. 37 ( 1979) 949. [ 121 M.A. Echargui, F. Marsault-Herail and J.P. Marsault, to be published. [ I 3 ] H.H. Reamer, R.H. Olds, B.H. Sage and W.N. Lacey, Ind. Eng. Chem. 36 (1944) 88. [ 141 M. Chatelet, A. Tardieu, W. Spreitzer and M. Maier, Chem. Phys. 102 (1986) 387. [ 15 ] M.E. Alikhani and J.P. Perchard, J. Phys. Chem. 94 ( 1990) 6603. [ 161 W.G. Rothschild, J. Chem. Phys. 65 (1976) 455.
CHEMICALPHYSICSLETTERS
number4
26 April 199I
Critical effects on vibrational dephasing in CH4 diluted in CO2 M.A. Echargui
’ and F. Marsault-Herail
Laboratoire de Spectrochimie Mokulaire, UR4 5 08, Universit6Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05. France Received 12 January 1991;in final form
I I February 1991
The Raman isotropic v, bandof CH4 diluted in CO1 hasbeen studied in the supercritical fluidphase,especially along the critical isochore of the mixture down to the liquid-vapour critical point. The comparison with published data on pure CH, shows that, in spite ofthe large vibrational band shift due to environmental fluctuations, the critical mhomogcneous broadening in the CH4/ CO2mixture is considerably attenuated.
1. Introduction A critical inhomogeneous broadening due to the density fluctuations has been evidenced in the isotropic Raman spectra of some pure fluids [ I-61 near the liquid-vapour critical point. It is well established [ 7-91 that the vibrational shift plays a predominant role in the manifestation of such an effect. For binary mixtures two kinds of critical effects have been considered. On the one hand, for a liquidliquid critical point, there is no evidence (experimental [ lo] or theoretical [ 111) that concentration fluctuations give rise to spectral critical effects. On the other hand, in the case of a liquid-gas critical point, density fluctuations. similar to those in pure fluids, are expected to induce a critical broadening of the isotropic Raman bands. Such a phenomenon has been observed for the Q lines of Hz and HD diluted in argon [ 121 and for the uI band of CH4 diluted in CD4 [ 91. In this last case the slight decrease of critical effects with respect to pure CH, was explained by the absence of resonant transfer and by the decrease of vibrational dephasing. For CH, diluted in C04, which is the subject of the present investigation, absence of resonant transfer should be counterbalanced by an increase of environmental fluctuations. As a consequence the critical ’ Present address: Laboratoire de Physique Moltkulaire, F.S.T. Campus Universitaire, 1060 Belvedtre, Tunis. 0009-26 14/91/$
03.50 Q 199 I - Elsevier Science Publishers B.V.
effects are expected to he important. However this hope will be deceived, the critical inhomogeneous broadening being much weaker for the CO2 solution than for pure methane.
2. Experimental The Y, Raman band of CH, diluted in COz was recorded using the experimental device previously described [ 51. The Raman shift measurements were carried out by scanning the neon line at 5869.82 8, in the same run. The frequency accuracy is 0.2 cm-‘. The spectral slit width being 0.25 cm-’ for an apparent bandwidth of the order of 2 cm-‘, the apparent band profile was identified to be the true one. The error on the half width at half maximum Av,,, is $0.1 cm-‘. The gas mixture was prepared in a tank according to tht= procedure described in ref. [ 61; the CH4 molar fraction in CO1 was fixed to 8.5 ? OSW in order to use the mixture p VTdata of ref. [ 13 1,For the band shift measurements, the gaseous mixture was confined in the scattering cell [ 61 at 3 11 K and cooled at constant volume along isochoric lines ( 119 <
317
Volume 179, number 4
CHEMICAL PHYSICS LETTERS
removing the gaseous mixture, so that the position of the meniscus remained unchanged (constancy of the liquid and vapour volumes); then the cell was closed at the critical point. This method leads to a precise value of the critical temperature but only to a rough determination of the critical density. Since we had already observed that the critical density effect is not so drastic as that of the critical temperature [ 61, a slight deviation from pc is not significant. The ratio (T-T,)/T, is estimated with a precision of 1V3. 2.1. Band shift The temperature effect on the vI frequency at a given density is negligible in the density range studied here. Fig. 1 compares the values for the solution and the pure liquid as a function of density at 301
26April1991
K. In both cases the curves V,=f(p) are well fitted by a parabolic law: v10+up+bp2. But in the same conditions of density and temperature, the red-shift is significantly more important in CO1 than in pure methane, as expected from the Lennard-Jones potential constants (T[ 151 and t/k (3.82 8, and 137 K or 3.90 A and 16 I K, for pure CH4 or CH,/CO,, respectively). In fig. 2 we have plotted the Y, frequency of CH, in CO1 and in pure CH, versus the reduced density p* =pa3 at the same reduced temperature T*=kT/c. It appears that, in spite of the absence of resonant transfer, the band shift in the COz solution is the same as in pure CH,. Accordingly, considering the large value of the vibrational dephasing, significant inhomogeneous broadening is expected in the COz solution near the liquid-gas critical point.
U
,.il cm-1
-2
cm-1
916
2914
L: !912
0.15
100
200
p
(mast)
Fig. 1. Density dependence of the ~1 frequency of CH.+in CO2 and in pure fluid at 301 K. ( 0 ) and (-), experimental data and parabolic law fitted on data for CH, in CO,; (---) parabolic law deduced from ref. 191 for pure CH.,.
318
t- I
0.30
PO3
Fig. 2. Reduced density dependence of the P, frequency of CH, in CO1 and in pure fluid at the reduced temperature T* = I .87. (0 ) experimental data for CH, in CO2 and (---) parabolic law deduced from ref. [ 9 ] for pureCH.,.
Volume179,number 4
CHEMICAL PHYSICSLETTERS
2.2. Band profile
In order to show the contribution of the critical effects on the band shape, we measured the bandwidth Av,,~ along the critical isochoric line of the CO1 solution. We also deduced the Lore&an cLand Gaussian cc widths related respectively to the homogeneous and inhomogeneous broadening by fitting a Voigt profile to the experimental one, Lastly we fitted the I+ band shape to the Fourier transform of a vibrational correlation function corresponding to an intermediate regime between slow and fast interaction modulation [ 161.
(1)
In this model previously used for pure CH4 [ 51 and its isotopic solution [ 9 1, d2 and r= are respectively the mean square interaction modulation and the interaction correlation time. The experimental bandwidth Av,,~ and the ratio cc/c, are reported versus ( T- T,)/T, in figs. 3 and 4, respectively. The comparison of these results with those obtained in pure CH, shows no significant
l
.
+
change in band profile for CH4 in CO* in contrast to the striking inhomogeneous broadening for pure CH, as the critical point is approached. The use of the intermediate model (eq. ( 1) ) leads to a value of the mean square interaction modulation A2 which remains constant along the critical isochoric line. A2 is greater for the CO, solution (~0.3~ 1O24sm2) than for pure CH4 (~0.17~10~~ se2) which confirms the enhancement of the vibrational dephasing in solution. The plot of T,, the interaction correlation time, versus ( T-T,) / T,, is reported in fig. 5. r, remains very small in the CO2 solution (fast modulation regime) even when (T- T, ) / T, tends towards zero. This result is strikingly different from that in pure CH4, where rc was shown to increase strongly (very slow modulation regime) at the critical point. All these features demonstrate the weakeness of critical effects on the v, band profile in CO2 solution, in contrast to their importance in pure methane. This difference is unexpected, taking into account the magnitude of the vibrational dephasing, and pre-
1
AW+$rn-’) 2.5
t +* + +
26April1991
+
. +
+
+
Ii
t
12
1.5
0
* 0
0 0 0 0
1
1.
.
.
l
10 20
30
4,O 50
60
7
X1C3
10
.
30
50
yc
P
x10
3
A
Fig.3. Temperaturedependenceof the halfwidthat half maximum,Av~,z,ofv, of CH, in CO2 (0) and in pure fluid ( + )
Fig. 4. Temperature dependence of the ratio c,/c, of the Gaussian to the Lorentzian width of the Voigt profile optimized on the u, band of CH, in CO? (0 ) and in pure fluid (0 ), along the
along the isochoric linepzp,.
isochoriclinepep, 319
Volume 179, number 4
CHEMICAL PHYSICS LETTERS
r
26 April 1991
References
Wps)
-6
0
-5
I 2
i
0
20
40
60
a0
[ I] M.J. Clouter and H. Kiefte, J. Chem. Phys. 66 ( 1977) 1736. [Z] M.J. Clouter, H. Kiefte and R.K. Jain, J. Chem. Phys. 73 ( 1980) 673. [3] M.J. Clouter, H. Kiefte and N. Ah, Phys. Rev. Letters 40 (1978) 1170. [4] M.J. Clouter and H. Kiefte, Phys. Rev. Letters 52 (1984) 763. [5] M.A. Echargui and F. Marsault-Herail, Mol. Phys. 60 (1987) 605. [6] M.A. Echargui, These d’Etat, Paris (1989). [7] H.L. Strauss and S. Mukamel, J. Chem. Phys. 80 (1984) 6328. [S] M.J. Clouter, H. Kiefte and C.G. Deacom, Phys. Rev. A 33 ( 1986) 2749. [9] F. Marsault-Herail and M.A. Echargui, J. Mol. Liquids, in pE%.
Fig 5. Temperature dependence of the r, parameter deduced from cq. ( I ) optimized on the vi band of CH, in CO, ( l ) and in pure fluid (0 ), along the isochoric line p=pc. The parameter A* is zO.3~10~~s-~inCO~and ~0.17x1024s-2inpurefluid.
vious results obtained in other solutions [ 9,121. A systematic study of the influence of concentration and of the nature of the solvent is necessary to sift out general rules about the critical inhomogeneous broadening of isotropic Raman spectra in mixtures near a liquid-vapour critical point.
320
[IO] J.R. Petrula, H.L. Strauss, K.Q.H. Lao and R. Pecora, J. Chem. Phys. 68 (1978) 623. [ 111 BP. Hills, Mol. Phys. 37 ( 1979) 949. [ 121 M.A. Echargui, F. Marsault-Herail and J.P. Marsault, to be published. [ I 3 ] H.H. Reamer, R.H. Olds, B.H. Sage and W.N. Lacey, Ind. Eng. Chem. 36 (1944) 88. [ 141 M. Chatelet, A. Tardieu, W. Spreitzer and M. Maier, Chem. Phys. 102 (1986) 387. [ 15 ] M.E. Alikhani and J.P. Perchard, J. Phys. Chem. 94 ( 1990) 6603. [ 161 W.G. Rothschild, J. Chem. Phys. 65 (1976) 455.