8 September 1989
CHEMICALPHYSICSLETTERS
Volume 16f, number 2
VIBRATIONAL DEPHASING IN HIGHLY COMPRESSED LIQUID NITROGEN STUDIED BY TIMERESOLVED STIMULATED RAMAN GAIN SPECTROSCOPY Ron KROON a, Rudolf SPRIK a and Ad LAGENDIJK a*b a NatuurkundigLaboratoriumder UniversiteitvanAmsterdam,Valckenierstraat 65, IO18XE Amsterdam,The Netherlands b FOMInstitute for Atomicand MolecularPhysics,Kruislaan407. 1098 SJ Amsterdam,The Netherlands
Received 24 June 1989
In liquid nitrogen at 295 K the minimum in the variation of the vibrational dephasing rate Tr’ with density is observed at p= 2.15 x 1022cm3. The observedbehaviour showsgood agreementwith the results of previously published molecular dynamics
simulations.
Combining highpressure techniques, such as the diamond anvil cell (DAC), with timeresolved spectroscopy offers a good opportunity of studying the dynamics of microscopic processes in molecular dense phases over a wide density range. Vibrational relaxation can be studied by following the decay of a coherent vibrational excitation due to the fluctuating environments of the individual molecules. Recently the first applications of picosecond stimulated Raman scattering in a DAC were demonstrated [ 1,2]. In ref. [2] we described the sharp rise of the vibrational dephasing rate of liquid nitrogen at 295 K over a density range of (2.32.9) x 10” cm3, corresponding to a pressure range of 0.92.4 GPa, where it solidified. The observed variation of Tr’ at these high fluid densities was in marked contrast to its behaviour at low fluid densities (~5 1.6~ 10z2 cm3) where a decrease of T, ’ with density was observed [31. In this Letter we describe an experimental study of the intermediate density regime of liquid nitrogen at 295 K, p= (1.702.47) x 10” cmM3,corresponding to pressures of 0.261.2 GPa. We show that in this density regime the high and low density behaviour of T, ’ is seen to match, yielding a minimum value for T, ’ as a function of density. The results are compared to other experimental and theoretical work. We first present a concise discussion of the theory on vibrational
relaxation.
For dense phases the Hamiltonian of a vibrational oscillator can be written as H=&+HB+V,
(1)
where Ho is the vibrational Hamiltonian for the isolated molecule, HB the Hamiltonian describing the rotational and translational degrees of freedom of the bath, and V the Hamiltonian which couples the oscillator to the bath [ 4 1. In Raman scattering studies on vibrational relaxation, one usually probes the correlation function of the normal coordinate Q. Whenever the coupling between the oscillator and the bath is weak the normal coordinate correlation function is given by
= (Q(0)2> ew[i(w+
(a> ItI w(WA
(2)
where ( } denotes an ensemble average over the bath degrees of freedom and ( o) is the average shift in vibrational frequency of a molecule with respect to the unperturbed oscillator due to interaction with the bath [ 51. The vibrational dephasing rate i”j I is then given by m Tr’ =
I
dt(Awi(0)Awi(t))
= ( Awi(0)2)r,
(3)
0
with
Aw,(t)=&;(t)(w)
and
do;(t)=fi’
x [ V, , (1)  VW( t ) 1, where r, is the correlation time
0 0092614/89/$ 03.50 0 Elsevier Science Publishers B.V. (NorthHolland Physics Publishing Division )
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of the (Au/( 0) Awi( t) > correlation function, 6Oi( t) is the instantaneous shift in vibrational frequency of molecule i with respect to the isolated oscillator, and “0” and “1” depict the ground and first vibrationally excited state of the molecule. The time dependence of the matrix elements arises from the bath propagator. In this case eqs. (2) and (3) do not include the population relaxation contribution to the vibrational relaxation process which, for liquid nitrogen, can be neglected relative to phase relaxation processes (T, being 12 orders of magnitude larger than T, at the normal boiling point [ 6,7] ). This remains so even up to the highest pressures where nitrogen at 295 K is still a liquid, as one observes when extrapolating recent data [ 81 on the T, value of nitrogen .(for pressures around 2.4 GPa these values are in the microsecond range). The value of the rootmeansquare frequency fluctuation (Aw,(O)*)‘~* is a measure of the strength of the coupling between the oscillator and the bath while 7c is a measure for the perturbation time scale. Together these parameters determine whether the system shows homogeneous or inhomogeneous broadening in the frequency domain. In the former case (AWES)“* tc& 1 (Lorentzian lineshape). In a molecular dynamics (MD) simulation [ 9 ] it has been shown that liquid nitrogen at its normal boiling point shows homogeneous broadening: 7,~ 0.149 ps, (Ao,(0)2)‘~2=2.32x10” s‘~1.23 cm‘, thus (Aw,(O)~) “27c=0.035 << 1. From this we expect liquid nitrogen at 295 K to be homogeneously broadened over the entire density range studied ( ( 1.72.9) x 1O22cm3). The experimental apparatus used in the timeresolved stimulated Raman gain (TSRG) experiment was described in ref. [ 21. The DAC used in this experiment was described by Baggen et al. [ 10 1. During the experiments the pressure in the sample was carefully measured to an accuracy of + 25 MPa using the welldocumented ruby fluorescence technique [ 111 employing single crystal grains of ruby from a ruby laser rod. Relatively low sample pressures (of the order of 0.25 GPa) were obtained employing a new cryogenic filling technique for our DAC in which the DAC is closed in a saturated nitrogen gas atmosphere at 80 bar and 130 K, instead of in a liquidnitrogen environment [2,10] at 1 bar and 77 138
8 September 1989
K. Sample dimensions were scaled up from 200 x 125 Frn in earlier experiments [ 2 ] to 3 50X 300 p,rn in this work yielding both a more accurate tuning of our sample pressure as well as an improved S/N ratio in the TSRG experiments. The S/N ratio was further improved by selecting a lens combination for our telescope focusing (see ref. [ 21) showing optimal chromatic and spherical behaviour over the frequency range spanned by the twodye lasers (this work: op= 580 nm, w,=670 nm). Using two Wild Heerbrugg Ml microscope objectives, $= 75 mm, placed 0.5 m apart we achieved an effective fourbeam focal overlap region 150 pm long (fwhm), fitting nicely into our sample volume. Thus a typical S/N ratio of 500 was achieved (compared to S/N= 10 in ref. [ 21) which enabled us to accurately observe the rather moderate variation of T 2 ’ with density at intermediate fluid densities. We find that the coherent vibrational excitation in liquid nitrogen at 295 K and intermediate fluid density decays exponentially within the detection range. A typical plot of the TSRG signal as a function of the delay time between the pump and probe pulse pairs is shown in fig. 1. Digital filtering of the experimental data and subsequent background correction have
2
E
10
1 F
6 c
.w
m
1o2F
cs2
163F L
I 0
10
20
30
time
40
50
(ps)
Fig. I. A typical logarithmic plot showing the exponential decay of the stimulated Raman gain signal of liquid nitrogen as a function of the delay time between the pump and probe pulse pairs (measured at 0.625 kO.025 GPa). Also shown is a plot of the instantaneous electronic and Kerr contributions to the TSRG signal of CS2, showing the time resolution of the TSRG measurements (typically l2 ps).
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CHEMICAL PHYSICS LETTERS
been performed. The value of the vibrational dephasing rate, together with the associated error, was determined from a leastsquares fit to an exponential decay. This decay was taken to start at delay times > 5 ps to rule out the influence of the laser pulses. The error in the values of T?’ was determined to be &2%. The characteristic system response is obtained through the instantaneous electronic and Kerr contributions to the TSRG signal of C&. It shows that the time resolution of the measurement is typically l2 ps. The variation of the vibrational dephasing rate with density is shown in fig. 2. The fluid density was calculated from the pressure using the equation of state proposed by Mills, Liebenberg and Bronson [ 121. In fig. 2 we have also plotted values for Tz’ obtained by extrapolating data published by Chesnoy [ 31 to 295 K. The TSRG experiments show that at intermediate fluid densities the value of TF’ decreases with increasing density. This behaviour is observed to saturate atp=2.15 x 1O22cme3 afterwhich, at high fluid densities, the dephasing rate shows a steep rise with density. We observe a slight difference between our measured values of T 1’ and those extrapolated up to 295
0.14
I I
r"
0.12
c
0.1

0.08

0.06

‘Lc 
Q
K from lowertemperature data published by Chesnoy [ 31. It may be that this difference arises from the difference in experimental conditions under which the dephasing was measured. We use a lowpower, highrepetition rate laser [ 1,2] while Chesnoy used a highpower, lowrepetition rate laser. The observed behaviour of T; ’ can be understood by separating the intermolecular potential into a purely repulsive (shortrange) part and a dispersive (longrange) part, as shown in a recent MD simulation by Chesnoy and Weiss [ 131. At low fluid densities the longrange forces present the dominant contribution to the dephasing process through their fairly large value of tc (several ps, ten times as large as the correlation time of the shortrange forces). Due to motional narrowing z, decreases with density, giving rise to a decrease in T j ’ since in this density region the decrease of TVis more pronounced than the increase of ( ( Ao,)~) ‘/2. At intermediate fluid densities we observe an interference between the longand shortrange part of the potential which causes the decrease of T, ’ to saturate while at high densities the shortrange forces become dominant, yielding a strong modulation of the vibrational transition frequency of the individual molecules. This leads to a dominance of the frequency modulation over the behaviour of z, and results in a sharp increase of T, ’ with increasing density. The strong repulsive interactions leading to dephasing at high fluid densities prove to be a predominantly binary process [ 2 1. We would like to express our gratitude to Wim Koops for his aid in the experiments. This research
has been supported by the “Stichting voor Fundamenteel Onderzoek der Materie (FOM)“, which is financially supported by the “Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)“.
c4 t
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*
0.04 I
0.021 0.8
_I 1.2
density
1.6
References
.
(1 2oz2 iks3f”
Fig. 2. The measured variation of the vibrational dephasing rate of liquid nitrogen with density: solid circles are from ref. 121, open circles: this work. The solid line is a guide to the eye. n : Variation of T,’ with density obtained by extrapolating the data published by Chesnoy [3] to 295 K.
[ 1 ] M. Baggen, M. van Exter and A. Lagendijk, J. Chem. Phys. 86 (1987) 2423. [2] R. Kroon, M. Baggen and A. Lagendijk, J. Chem. Phys., in press. [3] J. Chesnoy, Chem. Phys. Letters I25 (I 986) 267. [4] J. Chesnoy and G.M. Gale, Advan. Chem. Phys. 70 ( 1988) 297.
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[5] D. Lcvesque, J.J. Weiss and D.W. Oxtoby, J. Chem. Phys. 72 ( 1980) 2744. [6] W.F. Calaway and GE. Ewing, Chem. Phys. Letters 30 (1975) 485. [ 71 A. Lauberau, Chem. Phys. Letters 27 (1974) 600. [ 81B. KbalilYahyavi, M. Chatelet and B. Oksengom, J. Chem. Phys. 89 (1988) 3573.
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[9] D.W. Oxtoby, D. Levesque and J.J. Weiss, J. Chem. Phys. 68 (1978) 5528. [lo] M. Bagmen,R. Manuputy, R. Scheltema and A. Lagendijk, Rev. Sci. Instr. 59 (1988) 2592. [ 111 A. Jayaraman, Rev. Mod. Phys. 55 (1983) 65. [ 121 R. Mills, D.H. Liebenherg and J.C. Bmnson, J. Chem. Phys. 63 (1975) 1198. [ 131 J. Chesnoy and J.J. Weiss, J. Chem. Phys. 84 ( 1986) 5378.