- Email: [email protected]
Raman study of the orientational dynamics of liquid H2S and D2S
142 (1986)547-550 Elsevier Science Publishers B.V., Amsterdam -Printed
547
Journal of Molecular Structure,
in The Netherlands
RAMAN STUDY OF THE ORfENTATIONAL DYNAMICS OF LIQUID H2S AND D2S
M.PERROT and M.BOUACHIR Laboratoire de Spectroscopic Infrarouge (UA 124) Universite de Bordeaux I 33405 TALENCE-Cedex,France
ABSTRACT The analysis by numerical simulation of the experimental% Raman vibrational bandshapeof H S and D2S in the gaseous and liquid phases between room temperature and the me !ting point gives important information on the orientational dynaT mics of these asynnnetricrotors molecules and also on the temporal local structure of the corresponding liquids. For the liquid phase, application of the Gordon's J model extended to asymmetric rotors yields the angular momentum correlation time TV, in agreement with almost free rotational dynamics on a 0.1 picosecond timescale and close to the time between molecular collisions deriired from Chandler's macroscopic model. From this we conclude that the possibly existing hydrogen bonds between H2S molecules in the liquid state do not have a sufficiently long lifetime to perturb the monomolecular orientational dynamics. INTRODUCTION Even though isolated H2S and H20 molecules have close geometrical and electrical characteristics(ref.1,2),they give rise to liquids of very different properties (ref.3,4). This is generally attributed to the presence of a strong, hydrogen-bonded intermolecularnetwork in the condensed phase of H20 and its absence in H2S (ref.4,5). The wings of depolarized Rayleigh scattering (25-500 cm-') of liquid water exhibit two characteristic structural bands associated to the bending (Q 60 cm-1 ) and the stretching (C 180 cm-') of the intermolecularO---B,..0 hydrogen bond (ref.6,7). On the other hand, nothing similar is detectable in the spectra of liquid H2S which are essentially of induced origin and related to dipole-induced dipole (DID) and dipole-quadrupole (Collision-InducedRotational Scattering, CIRS) intermolecular interactions. This type of profile implies almost free rotation of the H2S molecule in the liquid state (ref.8,9). In order to obtain more information on the structure of liquid H2S, it is convenient to precisely study the mechanism of its
molecular reorientational
dynamics. Because of recent developments of theoretical models extended to the case of asymmetric rotors (ref.10) and the improvement of computer/spectrometer couptlingtechniques, Raman vibrational spectroscopy is now especially well suited for this type of study.
0022-2860/66/$03.50
0 1986 Elsevier Science Publishers B.V.
548 METHOD AND RESULTS From the experimental IW
and Ivh Raman spectra, one obtains the isotropic
and anisotropic profiles which are related to the vibrational and the orientational dynamics of the molecules (ref.11,12,13).For the H2S molecule although the three normal modes are Raman active, only the well-isolatedv2 bending mode -1 may be used for a precise bandshape analysis, as v, and v3 appear at 1183 cm in the same spectral domain around 2600 cm-' (ref.14).
-
I vv
I
\ I
I
800
1 1300
I
I
I 1800
Fig.1 . Experimental Raman Ivv and Ivh spectra of the V2 vibrational mode of liquid H2S (T = 22OC, P = 18 atms.). From the complete set of experimental results between room temperature and melting point for neat H2S, D2S, and an isotopic mixture of H2S 50X, l-IDS 40 X and D2S IOX, one observes that - the spectra are not affected by intermolecularassociation, - the very narrow isotropic spectrum (FWHH Q, 3 cm-') originates mainly from monomolecular vibrational dynamics, -1 - the very broad (FWHH Q,250 cm 1 anisotropic spectrum, which is temperature dependent and follows the detailed balance relationship, reflects essentially the monomolecular orientationaldynamics. These conclusions permit us to study the mechanism of the orientationalmolecular dynamics of liquid H2S directly from the analysis of the anisotropic profile since this profile is the Fourier transform of the monomolecular orientational correlation function (G (t) : m ='P2 Ianiso(~) = F.T. G2R(t) = < ok2* (0) ui2 (t) > c m = -2
(1)
549
'2 where cI is an element of the spherical tensor associated with the derivative m of the molecular polarizability of the corresponding vibrational mode (ref.10, 15). For the case of the
v2
mode of the H2S molecule (A, symmetry, C2" molecule), '2 equation 1 is simplified as the elements cx+,are zero and the simulation of the bandshape of the gaseous state leads to a term IX;'negligeable compared to Cxlz (ref.9). Thus, the anisotropic profile of this v2 mode reflects essentially the dynamics of the soleo
tensorial element.
DISCUSSION The experimental orientational correlation function G2k(t) derived from numerical Fourier transformation of the anisotropic spectrum (Eq.1) shows that the molecules rotate almost freely for 0.1 picosecond in liquid H2S and that the intermolecular interactions influence the orientational dynamics only for times longer than 0.15 picosecond. This result, confirmed by the analysis of the memory function which is also directly obtainable from the experimental profiles (ref.161, shows that the molecular reorientation does not undergo fast modulation. Starting from these results, one may try to apply the Gordon J orientational diffusion model extended to asymmetric rotors (ref.l0,17).In this model the molecules rotate freely for periods terminated by hard collisions that randomize both the direction and the magnitude of the angular momentum. The only parameter used in this model is the time 'rJbetween collisions, since the time duration of a collision is assumed to be negligible. The agreement between the experimental profiles and the profiles derived from this model is good (except for the values around 0.1 picosecond, which is very low temperatures) and leads to T J the time between two successive molecular collisions strong enough to perturb the free rotation of the molecules. It is important to check if time TJ is compatible with the Enskog time Te between two molecular collisions in a liquid ; T e may be obtained using molecular kinetic theory (ref.18). For uncorredated binary collisions in a liquid of hard spheres, one may calculate 'reand relate it to the time T. according to .j 'ce=a(T)*
T J
(2)
where a(T) is a roughness parameter characterizing how efficient is the collision in modifying the molecular angular momentum (ref.19). For liquid H2S at all temperatures, our results give T always greater than the corresponding .I re, indicating that all molecular collisions are not strong enough to significantly modify the free rotation of the molecules.
550
CONCLUSION From the analysis of the Raman profiles associated with the V2 vibrational mode of H2S and D2S, we conclude that the molecules rotate almost freely in the liquid phase since the time between intermolecularcollisions modifying the angular momentum is about 0.1 picosecond. This result, which agrees with previous NMR spin-rotationrelaxation times (ref.20), shows that the possibly existing hydrogen bonds in liquid hydrogen sulfide do not have a sufficiently long lifetime to perturb its monomolecular orientational dynamics, in contrast to the case of liquide water.
ADKNOLEDGMENTS We are obliged to Doctor J.C.LEICKNAM (Universityof Paris VI) for the numerical calculations of the theoretical profiles using the extended J model and to Doctor J.L.BRIBES for the simulation of the gaseous state profile.
REFERENCES
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
C.W.Kern and W.Karplus in "Water, a Comprehensive Treatise" p.21 Vol.I, F.Franks Ed.Plenum Press New-York (1972). R.L.Cook,F.C. de Lucia and P.Helminger J.Mol.Structure,28, 237 (1975). G 1. S Kell in "Water a Comprehensive Treatise" p.363, Vol.1 F.Franks Ed. Plenum Press New-Y&k (1972). F.Feher in "The Chemistry of non-aqueous Solvents" p.219, Vol.111 J.J.Lagowski Ed.Academic Press New-York (1970). C . N . R . Rao in "Water a Comprehensive Treatise" p.93, Vol.1 F.Franks Ed. Plenum Press New-Yolk (1972). G.E.Walrafen in "Water, a Comprehensive Treatise" p.151, Vol.1 F.Franks Ed. Plenum Prss New-York (1972). M.Brooker and M.Perrot J.Chem.Phys. 74, 2795 (1981). V.Maszacurati,M.A.Ricci,G.Ruocco and M.Nardonne Mol.Phys. 50, 1083 (1983). M.Bouachir Thesis University of Bordeaux I (1985). J.C.Leicknam and Y.Guissani Mol.Phys. 42, 1105 (1981). S.Bratos and E.Mar&hal Phys.Rev.A4,1078 (1971). F.J.Bartoli and T.A.Litovitz J.Chem.Phys. 56,404,413 (1972). L.A.Nafie and W.L.Peticolas J.Chem.Phys. 57,3145 (1972). H.W.Schrotter and H.W.Kluckner in "Raman Spectroscopy of Gases and Liquids" Topics in Current Physics, Vol.11, Springer Verlag Berlin (1979). M.E.Rose in "Elementary Theory of Angular Momentum", John Wiley and Sons NewYork (1957). R.L.Mountain J.of Research of the NBS 78A, 413'(1974). R.G. Gordon J.Chem.Phys. 44,183O (1966). J.O.Hirschfelder,C.F.Curtiss and R.B.Bird in "Molecular Theory of Cases and Liquids" John Wiley and sons, New-York.(l954). D.Chandler J.Chem.Phys. 60,3500,3508 (1974). J.Hauer,E.W.Langand H.D.Ludemann Chem.Phys.62,195 (1981).
547
Journal of Molecular Structure,
in The Netherlands
RAMAN STUDY OF THE ORfENTATIONAL DYNAMICS OF LIQUID H2S AND D2S
M.PERROT and M.BOUACHIR Laboratoire de Spectroscopic Infrarouge (UA 124) Universite de Bordeaux I 33405 TALENCE-Cedex,France
ABSTRACT The analysis by numerical simulation of the experimental% Raman vibrational bandshapeof H S and D2S in the gaseous and liquid phases between room temperature and the me !ting point gives important information on the orientational dynaT mics of these asynnnetricrotors molecules and also on the temporal local structure of the corresponding liquids. For the liquid phase, application of the Gordon's J model extended to asymmetric rotors yields the angular momentum correlation time TV, in agreement with almost free rotational dynamics on a 0.1 picosecond timescale and close to the time between molecular collisions deriired from Chandler's macroscopic model. From this we conclude that the possibly existing hydrogen bonds between H2S molecules in the liquid state do not have a sufficiently long lifetime to perturb the monomolecular orientational dynamics. INTRODUCTION Even though isolated H2S and H20 molecules have close geometrical and electrical characteristics(ref.1,2),they give rise to liquids of very different properties (ref.3,4). This is generally attributed to the presence of a strong, hydrogen-bonded intermolecularnetwork in the condensed phase of H20 and its absence in H2S (ref.4,5). The wings of depolarized Rayleigh scattering (25-500 cm-') of liquid water exhibit two characteristic structural bands associated to the bending (Q 60 cm-1 ) and the stretching (C 180 cm-') of the intermolecularO---B,..0 hydrogen bond (ref.6,7). On the other hand, nothing similar is detectable in the spectra of liquid H2S which are essentially of induced origin and related to dipole-induced dipole (DID) and dipole-quadrupole (Collision-InducedRotational Scattering, CIRS) intermolecular interactions. This type of profile implies almost free rotation of the H2S molecule in the liquid state (ref.8,9). In order to obtain more information on the structure of liquid H2S, it is convenient to precisely study the mechanism of its
molecular reorientational
dynamics. Because of recent developments of theoretical models extended to the case of asymmetric rotors (ref.10) and the improvement of computer/spectrometer couptlingtechniques, Raman vibrational spectroscopy is now especially well suited for this type of study.
0022-2860/66/$03.50
0 1986 Elsevier Science Publishers B.V.
548 METHOD AND RESULTS From the experimental IW
and Ivh Raman spectra, one obtains the isotropic
and anisotropic profiles which are related to the vibrational and the orientational dynamics of the molecules (ref.11,12,13).For the H2S molecule although the three normal modes are Raman active, only the well-isolatedv2 bending mode -1 may be used for a precise bandshape analysis, as v, and v3 appear at 1183 cm in the same spectral domain around 2600 cm-' (ref.14).
-
I vv
I
\ I
I
800
1 1300
I
I
I 1800
Fig.1 . Experimental Raman Ivv and Ivh spectra of the V2 vibrational mode of liquid H2S (T = 22OC, P = 18 atms.). From the complete set of experimental results between room temperature and melting point for neat H2S, D2S, and an isotopic mixture of H2S 50X, l-IDS 40 X and D2S IOX, one observes that - the spectra are not affected by intermolecularassociation, - the very narrow isotropic spectrum (FWHH Q, 3 cm-') originates mainly from monomolecular vibrational dynamics, -1 - the very broad (FWHH Q,250 cm 1 anisotropic spectrum, which is temperature dependent and follows the detailed balance relationship, reflects essentially the monomolecular orientationaldynamics. These conclusions permit us to study the mechanism of the orientationalmolecular dynamics of liquid H2S directly from the analysis of the anisotropic profile since this profile is the Fourier transform of the monomolecular orientational correlation function (G (t) : m ='P2 Ianiso(~) = F.T. G2R(t) = < ok2* (0) ui2 (t) > c m = -2
(1)
549
'2 where cI is an element of the spherical tensor associated with the derivative m of the molecular polarizability of the corresponding vibrational mode (ref.10, 15). For the case of the
v2
mode of the H2S molecule (A, symmetry, C2" molecule), '2 equation 1 is simplified as the elements cx+,are zero and the simulation of the bandshape of the gaseous state leads to a term IX;'negligeable compared to Cxlz (ref.9). Thus, the anisotropic profile of this v2 mode reflects essentially the dynamics of the soleo
tensorial element.
DISCUSSION The experimental orientational correlation function G2k(t) derived from numerical Fourier transformation of the anisotropic spectrum (Eq.1) shows that the molecules rotate almost freely for 0.1 picosecond in liquid H2S and that the intermolecular interactions influence the orientational dynamics only for times longer than 0.15 picosecond. This result, confirmed by the analysis of the memory function which is also directly obtainable from the experimental profiles (ref.161, shows that the molecular reorientation does not undergo fast modulation. Starting from these results, one may try to apply the Gordon J orientational diffusion model extended to asymmetric rotors (ref.l0,17).In this model the molecules rotate freely for periods terminated by hard collisions that randomize both the direction and the magnitude of the angular momentum. The only parameter used in this model is the time 'rJbetween collisions, since the time duration of a collision is assumed to be negligible. The agreement between the experimental profiles and the profiles derived from this model is good (except for the values around 0.1 picosecond, which is very low temperatures) and leads to T J the time between two successive molecular collisions strong enough to perturb the free rotation of the molecules. It is important to check if time TJ is compatible with the Enskog time Te between two molecular collisions in a liquid ; T e may be obtained using molecular kinetic theory (ref.18). For uncorredated binary collisions in a liquid of hard spheres, one may calculate 'reand relate it to the time T. according to .j 'ce=a(T)*
T J
(2)
where a(T) is a roughness parameter characterizing how efficient is the collision in modifying the molecular angular momentum (ref.19). For liquid H2S at all temperatures, our results give T always greater than the corresponding .I re, indicating that all molecular collisions are not strong enough to significantly modify the free rotation of the molecules.
550
CONCLUSION From the analysis of the Raman profiles associated with the V2 vibrational mode of H2S and D2S, we conclude that the molecules rotate almost freely in the liquid phase since the time between intermolecularcollisions modifying the angular momentum is about 0.1 picosecond. This result, which agrees with previous NMR spin-rotationrelaxation times (ref.20), shows that the possibly existing hydrogen bonds in liquid hydrogen sulfide do not have a sufficiently long lifetime to perturb its monomolecular orientational dynamics, in contrast to the case of liquide water.
ADKNOLEDGMENTS We are obliged to Doctor J.C.LEICKNAM (Universityof Paris VI) for the numerical calculations of the theoretical profiles using the extended J model and to Doctor J.L.BRIBES for the simulation of the gaseous state profile.
REFERENCES
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
C.W.Kern and W.Karplus in "Water, a Comprehensive Treatise" p.21 Vol.I, F.Franks Ed.Plenum Press New-York (1972). R.L.Cook,F.C. de Lucia and P.Helminger J.Mol.Structure,28, 237 (1975). G 1. S Kell in "Water a Comprehensive Treatise" p.363, Vol.1 F.Franks Ed. Plenum Press New-Y&k (1972). F.Feher in "The Chemistry of non-aqueous Solvents" p.219, Vol.111 J.J.Lagowski Ed.Academic Press New-York (1970). C . N . R . Rao in "Water a Comprehensive Treatise" p.93, Vol.1 F.Franks Ed. Plenum Press New-Yolk (1972). G.E.Walrafen in "Water, a Comprehensive Treatise" p.151, Vol.1 F.Franks Ed. Plenum Prss New-York (1972). M.Brooker and M.Perrot J.Chem.Phys. 74, 2795 (1981). V.Maszacurati,M.A.Ricci,G.Ruocco and M.Nardonne Mol.Phys. 50, 1083 (1983). M.Bouachir Thesis University of Bordeaux I (1985). J.C.Leicknam and Y.Guissani Mol.Phys. 42, 1105 (1981). S.Bratos and E.Mar&hal Phys.Rev.A4,1078 (1971). F.J.Bartoli and T.A.Litovitz J.Chem.Phys. 56,404,413 (1972). L.A.Nafie and W.L.Peticolas J.Chem.Phys. 57,3145 (1972). H.W.Schrotter and H.W.Kluckner in "Raman Spectroscopy of Gases and Liquids" Topics in Current Physics, Vol.11, Springer Verlag Berlin (1979). M.E.Rose in "Elementary Theory of Angular Momentum", John Wiley and Sons NewYork (1957). R.L.Mountain J.of Research of the NBS 78A, 413'(1974). R.G. Gordon J.Chem.Phys. 44,183O (1966). J.O.Hirschfelder,C.F.Curtiss and R.B.Bird in "Molecular Theory of Cases and Liquids" John Wiley and sons, New-York.(l954). D.Chandler J.Chem.Phys. 60,3500,3508 (1974). J.Hauer,E.W.Langand H.D.Ludemann Chem.Phys.62,195 (1981).