Journal of MolecularLiquids.65/66 ( !995) 49-57
Uitrafast Measurements of the Dynamics of Soivation in Polar and Non-Dipolar Solvents J. Gardecki, M. L. Horng, A. Papazyan, and M. Maroncelli Department of Chemistry The Pennsylvania State University University Park, PA 16802 ABSTRACT The dynamics of solvation of the probe solute coumarin 153 has been measured with -100 fs time resolution using the fluorescence upconversion technique. A wide variety of solvents, including polar aprotic solvents, hydrogen bonding solvents, and non-dipolar solvents have been examined. For all solvents of even moderate polarity (e0>5), the solvation dyna~cs observed follows the predictions simple models based on the solvent's bulk dielectric response. For a number of "non-dipolar" solvents such as dioxane and benzene, for which e o <5, we observe surprisingly large time-dependent shifts, which seem to reflect the solute interacting with the large quadrupole (and higher multipole) moments of the solvent molecules. These dynamics represent a solvation distinct from the dipolar solvation dynamics previously studied and they cannot be modeled in terms of any currently available theory.
INTRODUCTION An understanding of the time-dependence of solvation is a key ingredient in modern theories of chemical reaction in solution . For this reason there has been a great deal of research focused on measuring and building predictive theories of this dynamics [2,3]. The main concern to date has been on polar solvation dynamics, where the interactions are strongest and are predicted to have large effects on electron and other charge-transfer reactions . A few recent studies also begun to consider the dynamics of solvation in nonpolar solvents [4-6]. In either case, the phenomenon of interest is the time-dependent relaxation of the solvation energy subsequent to some step-function change in the solute's electronic structure. This dynamics is most often measured by monitoring the fluorescence of an appropriately chosen solute upon electronic excitation. (Other, less direct methods, are also under current development .)
Coumarin 153 0167-7322/95/$09.50 9 1995ElsevierScienceB.V. All rights reserved. SSD10167-7322 (95) 00844-6
50 In the present report we describe new time-resolved measurements of solvation dynmnics using the probe molecule coumarin 153 (hereafter referred to as C153) . This weft-known solvation probe has been thoroughly characterized in a number of past studies [2,9]. Its main attribute which makes it an excellent solvation probe is that upon electronic excitation its dipole moment changes from a ground state value of - 6 D to a value of--15 D in S1 . Furthermore, its $1 state is well separated from other excited singlet states and there is no indication of the occurrence of any excited-state reaction in most solvents [8,9]. Although the solvation dynamics of this molecule have been measured in a number of solvents previously [2,9], we have undertaken an extensive series of new measurements on more than 24 solvents. Motivation for this study comes from indications by computer simulation and theoretical considerations that earlier studies might have missed an important part of the dynamics due to limited time resolution [ 11]. Computer simulations first pointed to the presence of a prominent ultrafast component of the dynamics in small, highly polar solvents such as water , acetonitrile , and "methyl chloride" . Recent experiments have confinmd the existence of this "inertial" component of the dynamics in a few important cases [ 15,16]. The present work reflects our attempts to more completely characterize such ultrafast dynamics in a broad range of solvents. Compared to earlier studies, we are aided in this pursuit by greatly improved temporal resolution (~ 100 fs FWHM instrument response), as well as having a method of accurately determining the position of the emission spectrum prior to solvent relaxation [ 17]. These two improvements allow us to make what we believe to be highly reliable measurements of the solvation dynamics of C153 in a range of solvents.
METHODS Emission decays were obtained from a fs Ti:sapphire laser/fluorescence upconversion spectrometer whose construction is reported elsewhere . Here we only note that the overall temporal response used in these studies was between 112-125 fs as measured by the FWHM of the cross correlation between the pump and gate pulses. Decays (0-200 ps with a variable step size) were collected at a series of ten emission wavelengths (8 nm [email protected]
) which were then used to reconstruct time-evolving emission spectra in the manner described in Refs. 8 and 9. From these spectra the solvation dynamics was extracted in the form of the spectral response function, s~(t)-
v(t)-v(oo) , v(0)-v(--)
where v(t) denotes the frequency of the peak of the emission specmun at time t (see Refs. 8 and 9 for details). All dynamics were measmed at room temperature, 23:1:2 C. DYNAMICS IN P O L A R SOLVENTS Figure 1 illustrates typical time-resolved emission spectra of C153 observed in the solvents acetonitrile, chloroform, and 1-pentanol. Also shown (dashed curves) arc the steady-state emission spectra (equal to the time infinity spectra in most cases) and the estimated time-zero spectra, the spectra expected prior to any solvent relaxation. (The latter were obtained through comparison of steady-state spectra in the solvent of interest and in a non-polar reference solvent as described in Ref. 17.) A few features of these spectra are noteworthy.
First, with the current time resolution, we are able to capture the full spectral evolution. That is, in nearly every solvent studied, the observed spectrum at t=0 agrees, to within roughly the accuracy of the time-zero method (--200 cm -i for C153), with the predicted time-zero specmml. Second, the time-evolution observed in all of the solvents studied involves a simple time-dependent shift with little change in shape or width. This behavior is indicative that we are indeed observing a continuous solvation process without interference from other excited state processes. The extent of the observed shift depends on solvent polarity. It ranges from --700 for weakly polar solvents such as chloroform to slightly over 2000 for strongly polar solvents such as acetonitrile. The magnitudes of these shifts can be reasonably correlated to the usual reaction field factors expected on the basis of dielectric continuum models . Fmally, as illustrated by the three solvents portrayed in Fig. 1, the rate at which the emission specmun shifts with time varies over an impressive range as a function of solvent.
/// \\\ .i 16.
0 I .05
( 1 0 3 c m -1 )
F'gure 1. Time-resolved spectra of C153 in acetonitfile, chloroform, and l-pentanol (connected points). Times in ps are indicated on the figure: the spectra evolve toward lower frequency with increasing time. The dashed curves are the steadystate emission spectra (red curve) and the spectrum expected prior to any solvent relaxation (blue curve: see Ref. 17).
F'~gure 2. Soivation response functions observed (solid curves) and calculated using the DMSAi theory (dashed curves; see text) for the solvents acetonitrile, methanol, chloroform, and 1-pentanol.
52 Figure 2 shows the spectral response functions (Sv (t), Eq. 1) derived from the spectra of Fig. 1. In order to adequately display data for these varied solvents, whose dynamics occur on very different time scales, we employ a logarithmic time axis. Such a representation is also useful because a number of solvents, especially the alcohols, show highly dispersive response functions. For example, one observes in methanol significant relaxation taking place over 3-4 decades in time. (Multiexponential fits to the methanol data yield roughly equal contributions from components with time constants of 0.2, 2, and 12 ps). Even in simple, non-associated solvents such as acetonitrile, one seldom observes Sv(t) functions that decay exponentially in time. Most often, biexponential fits are required to describe the observed relaxation. This biexponential behavior does not reflect any clear separation between fast inertial dynamics and slower diffusive dynamics in most solvents. Rather, the observed spectral shift usually appears to simply be a continuous non-exponential process. That is not to say that ultrafast inertial relaxation does not occur in many solvents, just that there is no clear time scale separation observed. Of the 18 polar solvents observed to date, a number of them do show prominent fast components that are probably inertial in origin. For example, in the solvents water , formamide, acetonitrile, acetone, dimethylformamide, dimethylsulfoxide, and nitromethane , we find that more than half of the solvation response involves components with time constants of <~00 fs. The dynamics observed in polar solvents can be readily modeled in terms of simple theories based on the bulk dielectric response (~(o~)) of the solvent. Although there are now a variety of more sophisticated theories currently available , we will only consider the "simple continuum" (SC)  and the dynamical MSA (DMSA) models . The simple continuum theory assumes that the solute is a spherical cavity containing a point charge or point dipole. It interacts with the solvent only through the latter's bulk dielectric dispersion ~(r which is assumed to be known empirically. This limiting theory, which should be exact in the absence of specific interactions and in the limit of a solute of macroscopic size, forms the benchmark to which all other theories are compared. Previous studies have shown that predictions of the SC theory provide a useful guide to the dynamics observed in many real molecular systems [2,3]. However, the fact that the solvent is not a continuum fluid, but is in r e ~ t y composed of discrete molecules comparable in size to the solute, should cause deviations from the SC predictions. The DMSA theory corrects for some of the deficiencies of a continuum description by explicitly accounting for the fact that the electrical field generated by a molecular solute changes significantly on a length scale comparable to solvent molecule dimensions. This finite size effect causes a slowing of the solvation response compared to simple continuum predictions to an extent which depends on the solute/solvent size ratio [ 19]. The slow-down is much greater when one considers the response to a change in the solute's dipole moment compared to a change in its net charge (because of the difference in range of the electrical fields involved).
Figure 3. Solvation functions in dimethylsulfoxide. ,\
2 .82 2.0 MSi
3 3.~ 4.9 MSd
4 2.5 3.8 SC*
curve ("0") is the obsen~ ~ and the dashed curves 1-4 are calculations using various models described in the text. The number of short dashes in the line pattern ctmeslxmd to the numbers wovided on inset tabulation of the characteristic times of these mslxmse functions: 1--SC (ion), 2ffiDMSA
0 .65 1 . 6 0 b s 1 .27 .80 SCi
neglecting the unobserved uitrafust part of e(o~) (see tex0.
,...~,- ~ . ~
Figure 3 compares the experimentally observed solvation response of C153 in dimethylsulfoxide (#0, solid curve) to the predictions made by simple continuum and DMSA theories. The inset to the figure tabulates the 1/e times (t,,) and the average or integral correlation times (< %>) of the various response functions. These data show that the SC prediction for the response to a charge perturbation (#1) is too fast compared to the observed dynamics by a factor of approximately two. (The SC prediction for a dipole jump is sinfilar to that for a charge jump.) The DMSA prediction for a charge jump (#2; "DMSAi") is very close to the observed dynamics whereas the DMSA prediction for a change in solute dipole CDMSAd") is more than two-fold slower than the observed response. These observations concerning the performance of the various theories are quite general, as we will show presently. However, before doing so, we must make an important point regarding the use of dielectric data in such comparisons. The solvent response measured in time-resolved emission studies involves all solvent motion occurring on time scales slower than that of the electronic transition itself, i.e. slower than optical frequencies. Dielectric data, even those from recent experiments that, as in the case of DMSO , extend to the 100 GHz range, do not include all relevant nuclear motions of the solvent. For example, the dielectric data for DMSO used in Fig. 3 was reported to follow a Davidson-Cole distribution with parameters ao--46.40 ande..--4.16. The fact that some of the nuclear polarizability of the solvent is missed by this parameterization is indicated by the fact that at optical frequencies eop,--nv2=2.19. The difference e . . - nv2=1.97 reflects the contributions of nuclear responses in the FIR CPoley absorption") and IR regions (intramolecular vibrations) not captured in the dielectric data. Although this neglected part may seem small compared to the total polarizability of E0--46.40, the effect of these contributions on the computed solvation dynamics can be considerable, as illustrated by curve #4 in Fig. 3. This curve is a SC (ion) calculation which ignores such
54 contributions. The t~, and < ~ > times are slower than the same SC calculations that include these effects by factors of 9 and 5 respectively[ Although DMSO is an extreme example (in most solvents e . - no 2 is smaller than in DMSO), the difference is an important one, and proper comparisons must include the fast part of the nuclear response not directly observed in dielectric measurements. In the calculations described here we have treated this contribution as if it were a single relaxation m r m with a longitudinal time constant of 0.1 ps. This particular form of the time-dependence is arbitrary and is certainly an over simplification of the real dynamics. Luckily however, as long as the term describing the unobserved part of s is assumed reasonably rapid, its particular form and time scale do not appreciably affect the calculated values of t~, and < 1:>.
Figure 4. Comparison of ob~rv~ solvation times to predictions of the SC and DMSA theorics. The points show the comparison between the DMSA theory for an ionic solute with polar aprotic solvents denoted by circles and associated solvents by squares. For clarity,
j " ~ - - " .....--'" ........Q ...-'" .......
101 ._E~v i 0 ~ ~
the SC and DMSAd comparisons are only shown
I0 2 101
.j~ ~ '
L~ i 0 o
as the linear fits to the log-log data with the SC predictions being the lower dashed line and the DMSAd the uPl~ dashed line. The solvents represented here are, in order of ~ i n g tie: acetonitrile, acetone, tetmhydrofuran, dimethylformamide, dimethylsulfoxide, propylene carbonate, dimethyl carbonate, chloroform, and benzonitrile (circles) and water , formamide, methanol, ethylene glycol, ethanol, l-prolmnol, l-peatanol, and l-decanol (squares).
Figure 4 compares the characteristic times observed with C153 in a wide range of polar solvents to the predictions of the diele,ctric theories just described. As in Fig. 3, one finds good agreement between the times predicted by the DMSA theory for the response to a charge jump CDMSAi") and the observed dynamics. In contrast, the predictions of the simple continuum (ion) and DMSA calculations for a dipole change in the solute CDMSAd ~176 are r c s ~ v e l y too fast and too slow compared to experiment. The agreement between the observed dynamics and the DMSAi predictions also extends to the shapes of the response functions, as illustrated in the comparisons provided in Figs. 2 and 3. This is rather remarkable agreement, given that it extends over a wide variety of polar solvents, both associawxi and non-associated, whose solvation times span more than 3 orders of magnitude. It demonstrates the basic soundness of theories that link polar solvation dynamics to the solvent's dielectric response. However, it must be recognized that the DMSA theow is not a complete theory for the observed dynamics. If it were, one would expect to find agreement with predictions of the DMSA theory meant to model dipole jumps CDMSAd') rather than
55 with the ion version CDMSAi"), since the lowest-order multipole of the solute that changes upon electronic excitation is its dipole moment, not its charge. Indeed, calculations show that charge distributions of polyatomic molecules such as C153 and their change upon excitation are likely to be more quadrupolar in nature than dipolar . Thus, one would expect that the observed dynamics should be even slower than that predicted by the DMSAd theory. The fact that the observed dynamics is in actuality faster is an indication that some aspect of the real system's dynamics is not properly captured by the DMSA theory. Simulations of lattice solvents  demonstrate that the DMSA theory does accurately predict the dynanfics of both charge and dipole jumps when (as assumed by the theory) the solvent dynamics involves only rotational motion of point dipole particles. What is neglected in the DMSA theory is: i) that solvent molecules translate in addition to rotate and ii) that the solute does not really see a nearby solvent molecule as a point dipole but rather as an extended charge distribution. The effect of translational motions, which contribute an additional relaxation channel for solvation via "polarization diffusion" [2,23] is clearly to speed up the response relative to the DMSA predictions. The effect of the extended charge distribution of solvent molecules is more subtle to gauge but, at least in some cases, this difference has also been shown to hasten the response . We can summarize these results in the following way. The SC model provides useful first estimates for the solvation dynamics observed with a polar solute such as C153. However, due to its complete neglect of molecular aspects of solvation, it predicts response times that are uniformly too rapid. The DMSA approach, when properly applied (i.e. the DMSAd model), predicts too slow a solvation response. This latter model includes some important effects of solvent molecularity which serve to increase the response time compared to the SC predictions, while it neglects certain others that happen to act in the opposite direction. Thus, the agreement between the dynamics observed with the solute C153 and those pwxiicted by the "inappropriate" DMSAi theory should be regarded as partly fortuitous. Nevertheless, the surprising accuracy of the DMSAi predictions makes this simple model of considerable practical value. DYNAMICS IN NON-DIPOLAR SOLVENTS The success of dielectric models in describing the solvation of C153 in polar solvents is quite remarkable. Although, as just discussed, certain aspects of the dynamics are still not quantitatively described by theory, it is fair to say that the basic features of solvation dynamics in polar solvents are well understood. We would like to conclude by observing that the same cannot be claimed for the dynamics in non-dipolar solvents. Figure 5 shows that in the nominally "nonpolar" solvents dioxane and benzene, C153 undergoes time-dependent shifts that are in all respects analogous to the dynamics observed in weakly polar solvents such as chloroform . However, theories of the sort described above, relying as they do on e(co), are inadequate to describe apparently similar solvation dynamics taking place in these latter solvents. Because they lack significant dipole moments, the solvation response predicted on the basis of their dielectric properties (i.e. by e0) is very small . The fact that these and similar non-dipolar solvents we have examined do solvate C153 strongly is a consequence of the large quadrupole and higher-order electrostatic moments these molecules possess. At the short ranges relevant for molecular solvation, these higher moments (or alternatively the
56 charged groups or dipolar bonds) of the solvent molecules are as effective in solvating C153 as are the dipoles of weakly polar solvents. But the long-range dipolar correlations measured by the bulk property E(ca) are virtually absent in these solvents. Thus, to describe the dynamics observed in such solvents one does not have empirical information of the sort contained in e(o~) or an equivalent of the benchmark SC approach available for dipolar solvents. Furthermore, since the range of the interactions between the solvent and solute is shorter in such solvents, one expects that the details of the solvation structure and the effects of wanslational motion should be of much greater importance to the dynamics than in the dipolar solvent case. Thus, we anticipate that these types of solvents should provide a challenging testing ground for the future development of molecular models of solvation and solvation dynamics. l~gare5. Trine-resolvedspeclra of C153 in dioxane and benzene (connected points). The times shown are 0, 0.1, 0.5, 1, 2, and 10 ps from right to left. The dashed curves are the steady-state emission (red curve) and the speclrum expected prior to any solvent relaxation (blue curve; see Ref. 17).
(10 3 c m -I )
ACKNOWLEDGMENTS This research was supported by funds from the Office of Basic Energy Sciences of the US Department of Energy and by the Office of Naval Research. REFERENCES 1. See the reviews: J. T. Hynes, in Ultrafast Dynamics of Chemical Systems, I. D. Simon, Ed. (Klewer, Dordrecht, 1994), pp. 345-381; H. Heitele, Angew. Chem. Int. Ed. Engl. 32, 359 (1993). 2. Reviews of the experimental literature are provided in: M. Maroncelli, J. Mol. Liq. 57, 1 (1993); and P. F. Barbara and W. Jarzeba, Adv. Photochem. 15, 1 (1990); W. Jarzcba, G. C. Walker, A. E. Johnson, P. F. Barbara, Chem. Phys. 152, 57 (1991). 3. Reviews of theoretical and simulation studies can be found in Ref. 1 and B. Bagchi and A. Chandra, Adv. Chem. Phys. 80, 1 (1991); and F. O. Raineri, Y. Zhou, H. L. Friedman, Chem. Phys. 152, 201 (1991). Some of the most recent theoretical developments are described in: F. O. Raineri, H. Resat, B.-C. Perng, F. Hirata~ H. L. Friedman, J. Chem. Phys. 100, 1477 (1994); and B. M. Ladanyi and R. M. Stratt, J. Chem. Phys. (1995).
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