Picosecond solvation dynamics: The role of the solvent microscopic relaxation time in highly polar aprotic solvents

Picosecond solvation dynamics: The role of the solvent microscopic relaxation time in highly polar aprotic solvents


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Volume 146, number 1,2


29 April 1988


Alain DECLEMY and Claude RULLIERE Centrede PhysiqueMolkulaire Optiqueet Hertzienne, Unit& Asmike au CNRS No. 283, Vniversitkde BordeauxI, 351 Cows de la Lib&ration.33405 TalenceCedex, France Received 16February 1988

The solvation dynamics of a rigid polar probe dissolved in highly polar aprotic solvents has been studied using time-resolved fluorescence techniques. We have observed good correlation between the characteristic solvation time ra and the microscopic relaxation time rM of the individual solvent molecules. Near the probe the “continuum” description of the solvent fails and a microscopic description is necessary.

1. Introduction

The study of the time-dependent fluorescence shift (TDFS) of an excited polar probe molecule dissolved in a polar solvent is a powerful tool for investigating the relaxatiqn dynamics of solvent surrounding the probe. Indeed, when the electronic state dipole moment changes strongly between the ground state and an excited state prepared by optical excitation, the solvent configuration surrounding the excited probe is initially in a non-equilibrium configuration. Due to the dipole moment change in the excited state, the interaction forces between the polar solvent and the polar probe change with respect to the ground state. As a consequence, the solvent surrounding the probe has to relax in order to minimize these new forces, inducing the TDFS of the excited probe. This process reveals the dynamics of solvent relaxation. In two recent papers [ 1,2] we presented our first experimental results on the picosecond TDFS of polar probes dissolved in different polar protic and aprotic solvents at room temperature. These probes had attractive characteristics for TDFS studies since large dipole moment changes ([email protected] 10 D) occur on excitation, However, from recent picosecond TDFS studies [ l-61 it appears that well-defined experimental con-

ditions have to be fulfilled in order to properly relate TDFS studies to solvent relaxation dynamics. The choice of the probe and of the solvent are the key points. It has been shown, for example, that the probe must be as rigid as possible to avoid intramolecular rearrangements [ 51. These processes may also induce a time-dependent evolution of the probe fluerescence spectrum which will be superimposed on the solvent relaxation effects. Under such conditions, TDFS studies will reveal intramolecular processes as well as solvent relaxation. The choice of the solvent is also important [ 2-6 1. In alcoholic (protic) solvents, hydrogen bonds may be formed between the probe and the solvent molecules as well as between solvent molecules. In this case TDFS studies will also reveal specific hydrogen bond effects which will be superimposed on the “pure” polarity effects of the solvent relaxation process. From these considerations it appeared to us very important to perform TDFS studies under near-ideal experimental conditions which simplify the physical situation as much as possible, in order to focus on the specific role of the polar solvent relaxation near a polar probe. This is the aim of this paper, in which we present new experimental results obtained under the near-ideal experimental conditions described below. The selected probe MPQB (3-methyl-2,3,6,7,8-

0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )



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pentahydroquinolizino-4n-( 1,9-g,h)-l-benzoxazine1,4-2-one), shown in fig. 1, is as rigid as possible and displays a large Stokes shift in polar solvents [ 2 ] facilitating TDFS studies. As solvents we selected the polar aprotic solvents DMF (dimethylformamide) and PC (propylene carbonate). These were selected because their dielectric relaxation is well characterised at several temperatures. In particular, the frequency-dependent dielectric response c(o) can be described by a single Debye dispersion regime (see refs. [7-91) with a bulk dielectric relaxation time r,. In section 2 we present the experimental results of our TDFS studies in these solvents. Under these experimental conditions (selected probe and solvent), the currently developed theories predict a single-exponential time development of the TDFS process with a characteristic relaxation time rR approximately equal to rL, the so-called longitudinal relaxation

time of the solvent, defined as

%= (&/%)%I



where E, and e. are the infinite-frequency and the static dielectric constants and zn is the bulk dielec-

tric relaxation time of the solvent. However, the validity of the relationship between rR and rL as defined in ( 1) has recently been questioned [ 6 1. Indeed, such relations are always derived from a “continuum” approach where the polar probe is considered as a point dipole in an Onsagertype cavity interacting with a dielectric continuum. In this paper, in view of the experimental results described in section 2, and as recently proposed by Friedrich and Kivelson [ lo] (in the case of a solvated ion) we propose the following hypothesis: In the presence of strong dipolar solute-solvent interactions, the nearest-neighbour solvent molecules of GROUND

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the probe (roughly the first shell) relax in an individual manner with their own microscopic (molecular) relaxation time TM. This time TM has been shown to be related to solvent macroscopic parameters, according to [ 111 TM=[(~~o+~,)/~~o~KI~D,


where gK is the Kirkwood factor, which is of the order of unity (gKx 1) in DMF and PC.

In section 3 we discuss this new hypothesis and show that it is consistent with the experimental results of section 2. We conclude that this new interpretation allows some discrepancies appearing in the literature between “continuum” theories and TDFS experimental studies to be explained.

2. Experimental results TDFS has been experimentally studied using a “picosecond” fluorimeter described elsewhere [ 12 1. It enables the time evolution of the whole emission spectrum (between 4000 and 8000 A) of the excited probe to be studied. All measurements were made at the “magic” angle to avoid depolarisation effects and the temperature was kept constant to f 1“C using a Specac Cryostat P/N 21000. Under these conditions we observed (as illustrated in fig. 2) that the general spectral shape of the emission spectrum does not change as a function of time, but that the whole emission spectrum shifts to longer wavelengths with time. Only a small change in the bandwidth emission spectrum appears at short times. As in our previous work [ 1,2], we characterise the




&E =

Fig. 1. MPQB probe.




-\ \



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Volume 146, number 1,2
















Fig. 2. Illustration of the time evolution of the emission spectrum probe.MPQBinPCatT=-50°C. (l)t=25ps, (2)t=450ps.

TDFS process by the time evolution of the wavelength of the emission maximum as given by the spectral-shift function: [email protected](f)[email protected](t)--F(~-+co),


where 9E (t) and i$ (t+oo) are respectively the wavenumber of the maximum of the emission spectrum at time t after the optical excitation and at longer times where the spectrum does not evolve. Note that tg (t-~oo) is normally equal to the wavenumber of the maximum of the emission spectrum

obtained under steady-state experimental conditions. Under these considerations, fig. 3 shows a set of experimental curves [email protected] (t) obtained at different temperatures in PC. The problem now is to fit these experimental curves to a theoretical model. However, given a theoretical function for the TDFS, we have to take into account the duration of the laser pulse 6t which may influence the experimental TDFS curves. We have characterised our laser pulses and they can be described by a Gaussian with a fwhm lit= 40 ps. In these conditions, at each time t, during the window observation time St, the TDFS spectrum is a superposition of different spectra corresponding to different molecular systems at different relaxation stages. These different molecular systems are created at different times t (0 c t-c i3t) due to the finite duration of the excitation pulse. To take into account the influence of pulse duration, we have developed a numerical procedure which enables us to simulate the observed emission spectrum at any time t. In this way, for any given shape of the emission spectrum (constant as shown in fig. 2) and for any given relaxation law we can easily simulate the expected Aa? (t) curves and compare then with the experimental curves [email protected] (t). The simulations display interesting features, showing an important “integration” effect on the resulting kinetics at short times. For example, if the

I gem-q













Fig. 3. The evolution of i$’ (t ) under different experimental conditions in PC. The continuous lines are tits obtained under the conditions described in the text.


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Volume 146, number 1,2

Table 1 Solvent parameters and characteristic parameters of the TDFS as observed for MPQB. tu: static dielectric constant of the solvent. em= n’: infinite-frequency dielectric constant of the solvent. gu: Kirkwood factor of the solvent calculated from the Kirkwood-Onsager formula [13],withe,- -II 2 and solvent parameters from the cited references. T,, (in ps): bulk dielectric relaxation time of the solvent. r,_ (in ps): longitudinal relaxation time of the solvent calculated from ( 1). T, (in ps): microscopic relaxation time of the solvent calculated from ( 2). fR (in ps): experimental time constant of the picosecond observable part of the TDFS as explained in the text. [email protected] (t=O): amplitude of the slow component of the TDFS associated with ~a. fi”;”( t-+w ): wavenumber (in cm- ’ ) of the maximum of the relaxed emission spectrum of MPQB Solvent










DMF (-60°C) PC(-15°C) PC (-35°C) PC (-50°C) PC( -60°C) PC (-70°C)

58.3 72.5 81.5

2.15 2.06 2.08 2.10 2.11 2.12

1.oo 1.21 1.21 1.17 1.14 1.12

75.0 84.0 155’ 277 442 769

2.8 2.4 4.0 6.8 10.4 17.6

50.9 47.0 86.3 160 261 464

50+_25 50525 85k35 160+40 250545 470&50

600 400 515 100 900 1200

17615f50 17700-c50 17675+50 17625175 17600+75 17575+75

86.1 89.3


TDFS process obeys a single-exponential law A exp( - t/rR), the integration effect has two consequences on the experimentally observed curves: (i) for rR2 2 fit, the total amplitude of the shift A cannot be experimentally observed; (ii) for rR> 2 at, at earlier times t (t-e 2 St) a “plateau”’ effect appears as illustrated in fig. 3, the length of which depends slightly on rR (and fit). Thus, contrary to our previous observations [ 21, this plateau effect should not be assigned to specific molecular properties of the solvent but directly to the integration effect related to the finite pulse duration. Also our simulations show that under our experimental conditions, it is impossible to measure relaxation TDFS times rR shorter than 40 ps. Bearing the above in mind, we analysed our new experimental results as shown in fig. 3. In all cases the observed [email protected] (t) curves may be simulated with a single-exponential law with characteristic times z, reported in table 1. Also reported are the absolute error in i$ (t-co) and in the intermediate values [email protected] (t, ) (as shown in fig. 3) which directly determine the total error on the two free parameters of the simulations: The characteristic time rR and the associated amplitude of the TDFS (Av”p(t= 0) ).

3. Discussion Also reported in table 1 are the numerical values of r,_ as defined in ( 1). The correlation between tL 4

Ref. 171

18991 [8>91 18791

1891 [8,91

and the measured characteristic time rR is poor. Furthermore, the rL values are too short to be observed with our time resolution: measurement is possible only if 7L r 40 ps. This apparent lack of correlation has already been observed in polar aprotic solvents [4,61. We now focus on the mean forces existing between highly polar probe-solvent systems such as those currently used in TDFS studies. The dipole-dipole interaction ([email protected]/r3) between an excited probe and its nearest-neighbour solvent molecules may be as large as 1OkT and larger than the solvent-solvent interaction. For example, for a solvent molecule with a dipole moment CL = 5 D (as for PC ) lying at a mean distance of 6 8, from an excited probe with a dipole moment p*> 10 D (p*= 15 D for MPQB estimated by means of PPP SCF CI quantum chemical calculations [ 21 and II* = 10 D for Cl53 [4]), the mean diple-dipole probe-solvent interaction is of the order of 5 kcal/mol. On the other hand, the mean dipole-dipole interaction between solvent molecules outside the first shell is less than kT (with kTx 0.6 kcal/mol). Thus the interaction forces between solvent molecules themselves or between the probe and solvent molecules in the first shell are very different. Moreover, near an excited probe - which has to be considered as an extended dipole rather than a point dipole - owing to the molecular scale, the electric field is highly inhomogeneous. Under these conditions (which belong to the high “k” limit [ lo] ), the “con-

Volume 146, number I ,2


tinuum” approach is clearly inadequate to describe the reorientation of the nearest-neighbour solvent molecules of the probe for which we expect the pair correlation function between solvent molecule dipoles to decrease owing to the large interaction with the probe. As a consequence, as shown in ref. [lo], the collective dipolar correlation function reduces to single-particle correlations and the nearest-neighbour solvent molecules of the probe have to reorient themselves in the electric field of the excited probe, ignoring their interaction with the other solvent molecules. In this case the characteristic time of such a process is the microscopic (molecular or individual) relaxation time rM as defined in (2). On the other hand, the solvent molecules of the outer shells, for which the interaction with the probe is weak, reorient themselves taking into account neighbouring solvent molecules. This collective (macroscopic) process will occur with the macroscopic relaxation time rL as defined in ( 1). For MPQB dissolved in DMF or PC, table 1 shows that rL is always faster (by an order of magnitude) than rM. Furthermore, 2; Va]UeS are always SrYKikr than the limit of experimental precision on r, ( > 40 ps). In such a situation the observable part of the TDFS process related to tL appears as an instantaneous shift on our time scale. But for the experi-

Fig. 4. Illustration of the correlation between the longer TDFS characteristic times 7R (deduced from our own experimental results ( 0 ) and from ref. [ 41 ( 0 ) ) and the corresponding microscopic relaxation time 7, calcuated according to expression (2) (see text).

29 April 1988

mentally time-resolved part of the TDFS, a strong and quasi-perfect correlation is observed between rR and rM (see table 1 and fig. 4) in the case of the MPQB probe. This observed correlation strongly supports the above hypothesis. We note that, using another probe ( Cla) and with better time resolution, Fleming et al. observed that the TDFS process can be resolved as a sum of two exponent& with two (a shorter r1 and a longer zz) relaxation times [ 41. For MPQB a good correlation #’ between tM and the longer measured relaxation time ( r2) is observed as shown in fig. 4. Note also that the shortest measured relaxation time 71 falls in the range of r,. This last point will be discussed in a forthcoming publication [ 141.

4. Conclusion We have shown that a picosecond study of the TDFS of highly polar excited probe molecules in polar aprotic solvents reveals the presence of a long characteristic time. This time seems to be related to the microscopic relaxation time of the solvent supporting the hypothesis that this slow component of the TDFS is associated with the individual reorientation of nearest-neighbour solvent molecules due to a strong dipolar interaction with the excited solute, whereas the outer shell solvent molecules reorient in a collective way with a macroscopic relaxation time 7L giving rise to the fast TDFS component. From this hypothesis we might expect the relative contribution of the two relaxation channels ( zL, 7M) to the TDFS to be intimately dependent on the particular solute-solvent system in such a way that in certain situations the observed TDFS may be character&l (at first sight) by a single characteristic time which lies between 7, and rM. Finally, from this hypothesis, we would anticipate that, in the case of a weakly polar excited solute, the TDFS will be essentially dominated by rL, which is associated with weak dipolar solute-solvent interactions.

#I Except in PC at T= - 70°C (where anomalous behaviour occurs since ‘TVis even larger than 7D [4] ).

Volume 146, number 1,2


Acknowledgement Miss M.T. le Bris and Dr. B. Valeur (CNAM Paris ) gratefully acknowledged for providing samples of MPQB. Dr. Ph. Lightfoot is also acknowledged for carefully reading and correcting this manuscript.


References [ 1 ] A. Declemy, C. Rullitre and Ph. Kottis, Chem. Phys. Letters 101 (1983) 401. [2] A. DeclBmy, C. Rulliere and Ph. Kottis, Chem. Phys. Letters 133 (1987) 448. [ 31 Cl. Jones, W.R. Jackson and S. Kanoktanaporn, Opt. Commun. 33 (1980) 315. [ 41 M. Maroncelli and G.R. Fleming, J. Chem. Phys. 86 ( 1987) 6221.

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[ 5 ] V, Nagarajan, A.M. Brearley, J.J. Kang and P.F. Barbara, J. Chem. Phys. 86 (1987) 3183. [ 61M.A. Kahlow, J.J. Kang and P.F. Barbara, J. Phys. Chem. 91 (1987) 6452. [7] S.J. Bass, WI. Nathan, R.M. Meighan and R.H, Cole, J. Phys. Chem. 68 (1964) 509. [ 81 R. Payne and I.E. Theodorov, J. Phys. Chem. 76 (1972) 2892. [ 91 E.A.S. Cavell, J. Chem, Sot. Faraday Trans. II 70 (1974) 78. [lo] V. Friedrich and D. Kivelson, J. Chem. Phys. 86 (1987) 6425. [ 111 D. Kivelson and P. Madden, J. Phys. Chem. 88 ( 1984) 655. [ 121 E. Gilabert, A. De&my and C. Rullibre, Rev. Sci. Instr. 58 (1987) 2049. [ 131 H. Frolich, Theory of dielectrics (Oxford Univ. Press, Oxford, 1958). [ 141 A. Decltmy and C. Rulliere, to be published.