Resonant vibrational dephasing investigated by high-precision femtosecond CARS

Resonant vibrational dephasing investigated by high-precision femtosecond CARS

CHEMICAL PHYSICS LETTERS Volume 191, number 1,2 27 March 1992 Resonant vibrational dephasing investigated by high-precision femtosecond CARS M. Fic...

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Volume 191, number 1,2

27 March 1992

Resonant vibrational dephasing investigated by high-precision femtosecond CARS M. Fickenscher,

H.-G. Purucker

and A. Laubereau

Physikalisches Institut, Universitdt Bayreuth, W-8580 Bayreuth. Germany

Received 2 December 199 1; in final form 15 January 1992

Using three-colour coherent anti-Stokes Raman scattering on the femtosecond time scale, the concentration dependence of the dephasing time Tz of the v2 mode of acetone is carefully studied at room temperature for isotopic dilution and the solvent CCL+. Theoretical arguments suggest that the measured isotopic dilution effect of 10.8f 1% represents the contribution of resonant energy transfer via the repulsive part of the intermolecular potential to the total dephasing rate of the neat liquid. The steric factor S accounting for the smaller efficiency of non-collinear interactions as compared to head-on collisions is determined from the experimental data to be S= 0.12 f 0.01, in agreement with theoretical expectations.

1. Introduction Compared to the wealth of spectroscopic information derived from infrared and Raman techniques, the understanding of vibrational dephasing is rather scarce #‘. An explanation of this fact may be the complexity of the physical situation in molecular liquids with a variety of superimposed mechanisms. Isolation of individual relaxation channels is highly desirable under such conditions. The isotopic dilution technique is one of the experimental possibilities in this respect and may provide quantitative insight in dephasing dynamics [ 21. Large concentration effects were reported in the past for a number of strongly infrared-active vibrational modes and related to transition dipole-transition dipole interaction [ 3-61. A contribution via the repulsive part of the potential was also considered by several papers [7,81.

In this Letter the high accuracy attainable with coherent Raman spectroscopy in the time domain is exploited for a study of resonant dephasing. The relaxation of a symmetric mode with small transition dipole moment is investigated; i.e. the v2 vibration of acetone in isotopic dilution and dissolved in carbon tetrachloride. Evidence is presented for reso*’ For recent reviews, see ref. [ 11. 182


nant energy transfer of this vibration via the repulsive part of the intermolecular potential. A dominant non-resonant contribution is inferred from the study of the mixture with CCL,.

2. Experimental A schematic of the experimental system for threecolour CARS on the femtosecond time scale [ 9 ] is depicted in fig. 1. A special dye laser with pulsed operation is applied, details of which were reported elsewhere [ 9 1. Hybrid mode-locking, a linear cavity (mirrors M 1-M4) and two dye jets for the gain medium (rhodamine 6G) and nonlinear absorber (DODCI) are used to generate trains of intense femtosecond pulses at 568 nm [ lo]. Single pulse selection and amplification is performed in a triple pass amplifier stage pumped by a small Nd: YAG laser [ 111. The major part of the dye laser pulse (40 uJ, z 200 fs, bandwidth 2.6 nm) is focused into a water cell for continuum generation [ 12 1. Two additional synchronized pulses with tunable frequency position are derived from the broadband emission simply by adjustable interference filters (IFl, IF2) and subsequent amplification in separate dye amplifier stages ( pyridine 1 and rhodamine 10 1, respectively) [ 13 1. For the present experiment pulses are generated at 05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.

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Fig. 1. Schematic of the apparatus for three-colour CARS with femtosecond time resolution. The three synchronized input pulses are produced by a hybrid-mode-locked (HML) dye laser and continuum generation with subsequent dye amplifier stages; second harmonic generation SHG, mirrors Ml-M4; interference filters IFI-IF3; fixed delay FD, variable delay VD; nonlinear absorber cell NA; polarizers Pal 1,Pol2; aperture A; filter F; photomultiplier PM.

681 and 612 nm (1 uJ, 300 fs, 2.8 nm width) that serve as Stokes-shifted excitation (vs) and probe pulses (v), respectively. The remainder of the original dye laser pulse is used as the second excitation pulse (“laser”, vL, 10 pJ ) . The two synchronized pump pulses are directed with horizontal linear polarization and a small intersection angle ( z 1.5” ) into the sample cell of length 2 mm. By proper frequency setting of the Stokes pulse, the molecular vibration (r+,) of interest is driven close to the difference frequency resonance, vex vL- vs. The probing pulse passes a variable delay line VD, a A/2 plate for vertical polarization and a nonlinear absorber cell NA (DCI-2 in ethylene glycol); the latter discriminates background radiation of the probe beam. The pulse is coupled into the sample under phase matching conditions with the help of a Glan polarizer (see fig. 1). The coherent anti-Stokes scattering (frequency v+ vO) is measured in a small solid angle in the phasematching direction and with vertical polarization plane (analyzer Pol2 ). Suitable dielectric fil-

ters (5 19 nm, bandwidth 8 nm ), carefully calibrated neutral filters and a sensitive photomultiplier serve for the signal detection. Similar to CARS in frequency domain spectroscopy the excitation process is operated in the low-gain regime of stimulated Raman scattering (negligible amplification of the Stokes pulse) because of the moderate laser intensity and the short sample length. A large dynamic range of < lo6 and high measuring sensitivity are accomplished; this is due to a careful discrimination of background signals by three factors: small solid angle of detection ( < 10e5 sr), special polarization geometry (pump I probe) and proper frequency setting of the probe pulse (three-colour CARS) [ 91. The latter point removes the common frequency degeneracy between the anti-Stokes probe scattering of interest and undesirable anti-Stokes production of the excitation pulses [ 14,151. In addition, coherent pump-probe coupling is avoided perturbing the signal transient for temporal overlap of the pulses. Samples are of spectral grade purity. Isotope purity of acetone-d, is 2 99OXMeasurements are taken 183


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at 295 K. The concentrations of mixtures were prepared with an accuracy of better than ?- 1%.

3. Results An example for the observed signal transients is depicted in fig. 2a. The v2 mode of neat acetone (full points) is investigated for resonant excitation, vL- us ~2925 cm-‘. The measured time-integrated antiStokes scattering Scoh(tn) of the probe pulse is plotted on a logarithmic scale versus time delay; t,=O

I -







1 i



.5 I 8



z Ei G






,o a ‘r E r”







Delay Time




Fig. 2. High precision femtosecond CARS in neat Ccl4 and acetone: (a) Coherent probe scattering signal versus delay time; open circles: non-resonant scattering of Ccl., measuring the instrumental response function with 80 fs time resolution; full points: resonant CARS signal from the CH3 mode v2 of acetone at 2925 cm-‘; calculated curves. (b) Ratio of the experimental and calculated signal amplitude for the data of (a); the small experimental error of the data points for a variation of signal amplitude over six orders of magnitude is noteworthy.



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denotes the maxima of the excitation pulses. A rapid signal rise, small delay of the maximum scattering with respect to the pump pulses and a subsequent exponential decrease of the data points are readily seen; the latter starts at tr, z 0.5 ps and extends over a factor > 106. From the slope of the signal decay the dephasing time $T2 = 30 1 + 3 fs is directly obtained. For long delay, t,> 5 ps, some weak signal amplitude survives that originates from a scattering off background components of the probe beam. The solid curve in fig. 2a is calculated from the known theory of the CARS experiment using T2 as the relevant fitting parameter [ 9,16 1. The open circles in fig. 2a indicate the scattering signal for neat CCL, for the same pump and probe frequencies as for acetone representing the instrumental response curve [ 171. A time resolution of 80 fs is indicated by the steep signal descent (broken line) over six orders of magnitude within one picosecond. Fig. 2b illustrates the accuracy of the experimental points; the ratio of measured signal to calculated signal amplitude is plotted. It is interesting to see the small scatter of the data ( z + 10%) in spite of amplitude variations over many orders of magnitude. Each experimental point represents the average of approximately 400 individual measurements. The slope of the signal decay is reproducible in different experimental runs within less than 3 X 1O-3 ( + 0.8 fs for f T, ). An additional systematic error may originate from the calibration of the neutral filters used in front of the photomultiplier to detect the CARS signal. Taking the accuracy of the filter factors into account an overall experimental uncertainty of -+_1% is estimated for the dephasing time. Similar results are presented in fig. 3 for acetone in isotopic dilution with mole fractions of 0.9, 0.7 and 0.6 (full points, open circles and full triangles, respectively). The ordinate values of the signal curves are arbitrarily shifted by factors of ten for better visibility. Values of 4 T, = 304.0, 3 10.3 and 3 12.7 fs, respectively, are deduced from the data with a relative accuracy of approximately + 1 fs; the possible systematic error mentioned above is omitted here since this point has negligible effect on the dilution changes of T2. Similar measurements were carried out for other concentrations and for the solvent CCL. The results are compiled in table 1, again omitting the

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Acetone 2925 cm-

‘0 \


in CCI

> 4

‘h, \





Delay Time




T2 (in

fs) of the u2 mode of acetone

Concentration (vol%)

Solvent GDsO

Solvent cc14

100 90 80 70 60 50 40 30 10 0

601.2+ 1.4 608k 1.7

601.2k 1.4 615.0f 1.5 627.4+ 1.5 64Ok 1.9

620.6 f 2.1 625.4k 1.9

0.5 Mole Fraction


Fig. 3. Same as !ig. 2a for the mixture with acetone-d, and mole fractions of acetone x=0.9 (full points), x=0.7 (open circles) and x=0.6 (full triangles), respectively; experimental points, calculated curves; the ordinate values are arbitrarily shifted for different concentrations for better visibility. The small changes of Tz are readily measured. Table 1 Measured dephasing times

2.5 11 1



” 0

of Acetone

Fig. 4. Dephasing rate of the v2 mode of acetone as a function of concentration for the solvents acetone-d, (full points) and carbon tetrachloride (open circles); experimental points, calculated curves: see text.

tone-d, (full points) and carbon tetrachloride (open circles). A descent of the dephasing rate is noted with decreasing concentration. For the isotopic mixture a linear relationship is found within experimental accuracy. Extrapolation to infinite dilution yields an isotopic change of 10.8 + 1Ohfor the dephasing rate. For the solvent CCL, a slightly non-linear concentration dependence is suggested by the data with an extrapolated total decrease of 2 1.8 rt 1O/bfor x-+0. The extrapolated numbers for T, are included in table 1.

672.4_+1.8 644.6k2.5 653.5 + 2.5 666f7 67454”

703k2.5 749k4 769+6”’

a) Extrapolated.

possible systematic error ( < 1%) for the absolute values of T2. The measured concentration dependences are depicted in fig. 4. The dephasing rate 2/T, is plotted versus mole fraction x of C3H60 for the solvent ace-

4. Discussion A quantitative description of vibrational dephasing in liquids is not available at the present time. A variety of mechanisms was proposed and also compared with spectroscopic observations. The results may be summarized as follows. For a more comprehensive discussion the reader is referred to the literature [ I-8,18-26 ] #‘. w For a review, see ref. [ 27 1.


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A first class of processes termed pure dephasing represents rapid frequency fluctuations of the vibrating molecules interacting with its environment via the repulsive part of the intermolecular potential; here different relaxation channels may be distinguished: (i) V-T coupling via the translational motion [ l&21] and (ii) V-R coupling involving the reorientational motion of nearest neighbours [ 22-241; (iii) pure dephasing also originates from the attractive part of the intermolecular potential with contributions of more distant molecules [ 19,23 1. These effects may be treated in liquid mixtures in terms of concentration fluctuations with a dominant effect by nearest neighbours [ 25 1. A second kind of mechanism involves vibrational energy transfer between quantum-mechanically nondistinguishable molecules, i.e. (iv) resonant transfer (RT) of vibrational energy via the repulsive potential [7,8,20] and (v) via the attractive part of the intermolecular potential (transition dipole-transition dipole coupling) [ 3-6,261. In addition, vibrational energy relaxation may contribute by coupling to other vibrational modes ( V-V), mostly via the repulsive part of the intermolecular potential and involving also rotational ( VR) and/or translation (V-T) motion [28]. In this context it is interesting to distinguish (vi) intramolecular energy redistribution and decay, and (vii) intermolecular transfer of vibrational energy to other modes. The terms intra-, intermolecular here refer to the V-V part of the interaction. We also recall that contributions of different mechanisms are not simply additive in general. The role of interference phenomena, i.e. correlation between relaxation channels is open for discussion. For the processes (i)-(iii) one should note that the time scale (correlation time ) of the interaction determines the character of the line broadening, e.g. homogeneous (inhomogeneous) broadening in the fast (slow) modulation regime [ 21. The isotopic dilution effect was explained by mechanism (v ) for several strongly infrared active transitions [ 2,3-6,26,29]. Contributions of processes (iv) and (vii) may also be important; the latter relaxation paths may be relevant since frequency resonances govern the V-V energy transfer that are effected by isotopic changes. It is discussed in the literature that resonant transfer (v) via transition dipole coupling leads to a vi186

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brational autocorrelation function @with an asymptotic decay of the form [ 21 @(t)aexp[




Eq. ( 1) contains Gaussian and exponential contributions. 72 is the correlation time of the process that may be estimated from the reorientational time (TVx r,) . B denotes a constant factor [ 21 Bx27rp(ap/aQ)4(270%0)-’


(number density p, transition moment per normal mode coordinate ap/aQ, hard-sphere cross section o and vibrational frequency 0). For the present example acetone we estimate negligible dephasing contributions from eqs. ( 1) and (2) since Bt, Bz2 < 10e3 ps- ’ for a measuring interval of t< 10 ps and 72 in the picosecond range or shorter (pz 8.2~ 10” crnw3, ap/aQx18 esu, 0x4.5 A, 0x5.5X5.5XlO’~ s-l). The absence of a Gaussian component in the measured signal decay (compare fig. 2) represents some additional evidence that dipole-dipole coupling according to eq. ( 1) is not effective. The same argument applies for dephasing channel (iii). For our example acetone we introduce the Enskog hard-sphere model for an estimate of the intermolecular collision rate [ 301 and write for the binary mixture of acetone molecules i (mole fraction x) with solvent molecules j [ 8 ] : 2 T =p(x)[x(k,,+k~~)gii(x)+(l-x)k~,gij(x)]



(3) Here k, and k,, represent the combined contributions of processes (iv), (vii) and of (i), (vi), respectively. Mechanisms (ii) and (iii) are neglected (see below). For isotopic dilution, i zj, the number density p and radial distribution functions at contact distance are independent of concentration. (gii = gij= g( a) ) . AS suggested by the isolated binary COGlision model of ref. [ 181 we also have k$ r kg, = k,, (accurate within one or two percent) because of the small changes of effective mass for the isotopic species. A similar argument applies for the contribution of mechanism (vi) to k,,,. A linear concentration dependence results: -






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as is observed in fig. 3 (full points). Eq. (4) shows that only resonant intermolecular contributions vary with isotopic dilution.We mention here that in a more general derivation, possible contributions by mechanisms (ii) and (iii) can be incorporated in the second term (k,,) in eq. (4). From the experimental data we determine the ratio S= k&k,,p 0.12 f. 0.01. This value is nicely consistent with theoretical expectations. Geirnaert and Gale [ 81 have shown that S represents a steric factor that originates from the smaller effectiveness of non-collinear collisions compared to head-on encounters. Following ref. [ 23]we have &

packed hard-sphere fluids. Taking the literature results ajj=5.10 8, of CC& [ 331 we obtain the value oiiz4.49 8, for acetone used above to estimate the factor S. The numbers give some support to our interpretation of the mixture acetone: Ccl, in terms of non-resonant dephasing via V-T coupling. The same conclusion is suggested by a study of the temperature and pressure dependence [ 341. We note however that the absolute rate of non-resonant dephasing is estimated too small by a factor of 2.4 (without taking into account the additional contribution via the vibrational anharmonicity). 5. Conclusions

(1 -re/w 4( 1+r,/20)

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where r, denotes the length of the molecule. Taking r, = 1.603 A, the distance between the C atoms of the two CHs groups of acetone [ 3 1] and cr= 4.49 8, (see below) we estimate Sx 0.14. The amazingly good agreement with the experimental result gives some support to the conclusion that mechanisms (vi) and (vii) are of minor importance for kRT and Ic,,,, respectively. For different solvent and solute molecules the quantities p, gii and gij in eq. ( 3) become concentration dependent. The corresponding analytical expressions for hard-sphere molecules are derived in the literature and are not repeated here [ 32 1. A nonlinear concentration dependence results in the general case. Such a behaviour is shown in fig. 4 (open circles) for the mixture with CC&. Adopting the results of refs. [ 17,32 ] we have k,,roc(cT/L)~& and find for acetone: Ccl, the simple relation (k”/ kij),+ (“iiloij)2t since the other factors cancel incidentally. Here we introduce oij= f (Oii+ cri) and j = Ccl,; L and p respectively denote the range of the repulsive potential and the reduced mass of the colliding molecules. Using also the experimental value for kRT from the isotopic dilution measurements the dephasing rate can be evaluated from eq. (3) (see dashed curve in fig. 4). The only relevant fitting parameter in the computation is the ratio of hard-sphere diameters; from the data of fig. 4 we obtain qi/ ajj = 0.88 + 0.04. This value agrees well with reported data derived from various methods that range from 0.87 to 0.93 [ 33 1. A similar value, gJcrccarbontet x 0.91 is estimated from density data for densely

The measuring accuracy attainable with high-precision CARS on the femtosecond time scale allows us to study subtle effects on the dephasing of molecular vibrations in liquid mixtures. The isotopic dilution effect for the v2 mode of acetone is explained by resonant transfer of vibrational quanta to nearest neighbours via the repulsive part of the intermolecular potential; the mechanism contributes 10.8 + 1% to the dephasing rate of the neat liquid. The remaining part appears to be predominantly determined by non-resonant coupling to translational motion since the measured concentration dependence for the solvent CC& is fully consistent with theoretical estimates of this relaxation path. The steric factor for off-axis collisions, S= 0.12 + 0.0 1, deduced from experimental data, is found to agree with theoretical expectations.

References [ I] S. Bratos, in: Vibrational spectroscopy of molecular liquids and solids, eds. S. Bratos and R.M. Pick (Plenum Press, New York, 1980) p. 43; J. Yarwood, Rept. Progr. Chem. C 76 ( 1980) 99. [ 2 ] W.G. Rothschild, Dynamics of molecular liquids (Wiley, New York, 1984). [ 3 ] P.C.M. van Woerkom, J. de Blayser, M. de Zwart and J.C. Leyte, Chem. Phys. 4 (1974) 236. [4] G. Dbge, R. Amdt and A. Khuen, Chem. Phys. 21 ( 1977) 53; J. Yarwood, R. Amdt and G. Diige, Chem. Phys. 25 ( 1977) 387; Mol. Phys. 52 ( 1984) 399. [S] J. Schroeder, V.H. Schiemann, P.T. Shark0 and J. Jonas, J. Chem. Phys. 66 (1977) 3215.


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[6] J. Laane and W. Kiefer, J. Chem. Phys. 73 (1980) 4971. [7] T. Tokuhiro and W.G. Rothschild, J. Chem. Phys. 62 (1975) 2150. [8] M. Geimaert and G. Gale, Chem. Phys. 86 (1984) 205. 191 M. Fickenscher and A. Laubereau, J. Raman Spectry. 21 (1990) 857. [lo] G. Angel, R. Gage1 and A. Laubereau, Opt. Commun. 63 (1987) 259; Opt. Letters 14 (1989) 1005. [ 111 M. Fickenscher, H.-G. Purucker and A. Laubereau, Appl. Phys. B 51 (1990) 207. [ 121 A. Penzkofer and W. Kaiser, Opt.Quantum Electron. 9 (1977) 315; R.L. Fork, C.V. Shank, C. Hirlimann and R. Yen, Opt. Letters 8 (1983) 1. [ 13) J.P. Chambaret, A. DosSantos, G. Hamoniaux, A. Migus and A. Antonetti, Opt. Commun. 69 (1989) 401; A. Migus, A. Antonetti, J. Etchepare, D. Hulin and A. Orszag, J. Opt. Sot. B 2 (1985) 584. 114 A. Laubereau, Chem. Phys. Letters 27 (1974) 600. (15 Yu.S. D’yakov, S.A. Krikunov, S.A. Magnitskii, S.Yu. Nikitin and V.G. Tunkin, Soviet Phys. JETP 57 (1983) 1172; G.M. Gale, P. Guyot-Sionnest, W.Q. Zhengand C. Flytzanis, Phys. Rev. Letters 54 (1985) 823. ]‘6 A. Laubereau and W. Kaiser, Rev. Mod. Phys. 50 ( 1978) 607; A. Penzkofer, A. Laubereau and W. Kaiser, Progr. Quantum Electron. 6 (1979) 55; M. Fickenscher, Thesis (University of Bayreuth, 1990). [ 171 W. Zinth, A. Laubereau and W. Kaiser, Opt. Commun. 26 (1978) 457;


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W. Zinth, R. Leonhardt, W. Holzapfel and W. Kaiser, IEEE J. Quantum Electron. QE-24 (1988) 455. [ 181 SF. Fischer and A. Laubereau, Chem. Phys. Letters 35 (1975) 6. [ 191 R. Lynden-Bell, Mol. Phys. 33 (1977) 907. (201 R.K. Wertheimer, Chem. Phys. Letters 52 (1977) 224; Mol. Phys. 35 (1978) 257. [21] S.1. Temkin and A.I. Burshtein, Chem. Phys. Letters 66 (1979) 52. [22] S.R.J. Brueck, Chem. Phys. Letters 50 (1977) 516. [23] KS. Schweizer and D. Chandler, J. Chem. Phys. 76 ( 1982) 2296. [ 241 P. Aechtner and A. Laubereau, Chem. Phys. 149 ( 1991) 419. (251 E.W. Knapp and S.F. Fischer, J. Chem. Phys. 74 (1981) 89; 76 (1982) 4730. [ 26) D.E. Logan, Mol. Phys. 58 ( 1986) 97; Chem. Phys. 131 (1989) 199. [ 271 D.W. Oxtoby, Advan. Chem. Phys. 40 ( 1979) 1 128) J. Chesnoy and G.M. Gale, Ann. Phys. (Paris) 9 (1984) 893. [ 29 ] G. Diige and D. Lindner, Ber. Bunsenges. Physik. Chem. 94 ( 1990) 408. [ 301 K. Tanabe and J. Jonas, J. Chem. Phys. 67 ( 1977) 4222. [ 3 1] G. Herzberg, Molecular spectra and molecular structure, Vol. 3 (Van Nostrand Reinhold, New York, 1966) p. 658. [ 321 K. Tanabe, Chem. Phys. 38 (1979) 125. [33] K. Tanabe and J. Hiraishi, Mol. Phys. 39 (1980) 1507. [ 341 H.-G. Purucker et al., to be published.