Fluorescence studies of solvation and solvation dynamics in ionic

J . Phys. Chem. 1991,95,9095-9114

9095

Fluorescence Studies of Solvation and Solvation Dynamics in Ionic Solutions Curtis F. Chapman and Mark Maroncelli* Department of Chemistry, I52 Davey Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802 (Received: April 29, 1991; In Final Form: June 21, 1991) We have employed steady-state and time-resolved emission spectroscopy to study static and dynamic aspects of the solvation of polar aromatic solutes in ionic solution. Several common solvatochromicprobe molecules (Cu102, Cul53, Prodan, 4-AP) were examined in a wide range of ionic solutions consisting of a variety of salts (mainly Li+, Na+, Mg2+, Ca2+,SrZ+,Ba2+ perchlorates) in a number of nonaqueous solvents (tetrahydrofuran, acetone, propylene carbonate, acetonitrile,dimethylformamide, dimethyl sulfoxide, methanol, 1-propanol, and formamide). The presence of ions causes shifts in the spectra of these probe solutes similar to those observed in pure solvents of varying polarity. As a function of increasing salt concentration or time, the primary spectral change is a frequency shift with little accompanying change in the spectral shape or width. Ion-induced frequency shifts in steady-state spectra are typically in the range of several hundred cm-’ in 1 M salt solutions. The magnitudes of these shifts decrease as the strength of solvent-solute interactions increases. They depend little on the identity of the anion but are approximately proportional to the charge-to-size ratio of the cation of the salt considered. The ionic solvation dynamics measured by time-resolved fluorescence take place on a I-IO-ns time scale. The kinetics is significantly dependent on excitation wavelength, especially for excitation on the red edge of the absorption spectrum. The rate of spectral shift is proportional to salt concentration and inversely proportional to viscosity for concentrations of 1 M or less. When these two factors are accounted for, the observed solvation rates are found to decrease with solvent polarity and decrease with the charge-to-size ratio of the cation. A number of the above results are inconsistent with the commonly used description of solute-ion interactions in terms of a diffuse ion atmosphere. To rationalize our observations we propose a model based on equilibrium among a limited set of solvates distinguished by the number of cations in the first solvation shell of the probe.

I. Introduction

In recent years considerable effort has gone into understanding the dynamical aspects of polar solvation and how a noninstantaneous solvent response influences reaction kinetics.’” One line of research has examined the connection between rates of solvent relaxation and rates of electron- and other charge-transfer reactions. Although this connection has been well established theoretically, its experimental verification has been reported only in a modest number of cases. A second area of effort has involved measuring solvation dynamics with nonreactive probes, and attempting to understand the observed dynamics in terms of simple theoretical models of the solvation process. The current status of this work is in some ways reverse from that of the former area. Solvation times”, the times required for relaxation of the solvation energy after a change in the solute (reactant) charge distribution, have been measured by using the timedependent Stokes shift that wcurs in fluorescent probes after electronic excitation. Through the efforts of several groups, a wide variety of pure polar solvents have been studied, and as a result the dynamics are empirically well described. Available theoretical models of the dynamics are not yet capable of predicting the observed dynamics; however, the situation is rapidly improving. Through the interplay between experiment, computer simulation, and theory, a fundamental understanding of solvation dynamics in simple liquids is beginning to emerge.&” The present work represents an extension of our previous studies on (nonreactive) solvation dynamics into the realm of ionic solutions. The same considerations that motivate study of solvation dynamics in pure polar solvents apply equally well here, and given (1) A number of excellent reviews on the subject of solvation dynamics and its affect on charge-transfer reactions are available. References 2-5 list several that provide useful entries into the literature of this area. (2) Weaver, M. J.; McManis, G. E. 111 Arc. Chem. Res. 1990, 23, 294. (3) Barbara, P. F.; Jarzeba, W . Adu. Photochem. 1990, 15, 1. (4) Bagchi. B. Annu. Rev. Phys. Chem. 1989,40, 115. ( 5 ) Maroncelli, M.; Maclnnis, J.; Fleming. G. R.Science 1989, 2443, 1674. (6) A very recent review is Maroncelli, M. J . Mol. Liq., in press. Some of the most recent original papers are refs 8-12. (7) Chandia, A.; Bagchi, B. Chem. Phys., in press. (8) Raineri, F. 0.; Zhou, Y.;Friedman, H. L.; Stell, G. Chem. Phys. 1 9 9 1 ,

152, 201. (9) Jarzeba, W.; Walker, G. C.; Johnson, A. E.;Barbara, P. F. Chem. Phys. 1991, 152, 57. (IO) Carter, A. E.; Hynes, J. T. J . Chem. Phys. 1991, 94, 5961. ( I I ) Fonseca, T.;Ladanyi, B. M. J . Phys. Chem. 1991, 95, 21 16. (12) Maroncelli, M. J. Chem. Phys. 1991, 94, 2084. ( I 3) Levy, R. M.; Kitchen, D. B.; Blair, J. T.;Krogh-Jespersen, K. J. Phys. Chem. 1990, 94, 4470.

0022-3654/91/2095-9095%02.50/0

their relevance to biological processes, ionic solutions are certainly an important reaction medium. In some ways, ionic solutions can be viewed as simply more polar versions of their pure solvent counterparts. They might therefore be expected to influence reactions in a similar manner. Dynamically, however, ionic solutions may be rather different from pure polar solvents. Whereas dynamics in a pure solvent involves primarily reorientation of solvent molecules, in ionic solutions the time dependence of ionsolute interactions should arise from translational ion motions. This distinction might be expected to produce characteristic differences in the dynamics which would imply differences in the nature of the solvent-reactant coupling in these two types of solutions. In the work reported here we explore such differences in simple nonreactive systems with the goal of broadening our data base on dynamical solvation and thereby providing further insight into the molecular mechanisms of the dynamics observed in both types of solution. Until recently, modification of reaction rates by ionic solutions had only been considered with respect to equilibrium solvation effects. In mmt cases, rate changes were related to the differential solvation of reactants versus the transition state, as in the classic Bronsted/Debye-Huckel model and its ~ a r i a n t s . ’ ~ JIn~ these models, the free energies (activities) of the reactants and transition state are modified from those in the pure solvent by the presence of an ion atmosphere surrounding each of the various species. In many cases the effects produced by this ion atmosphere can be predicted by the Debye-Huckel which is appropriate to the limit of weak ion-ion interactions and a continuum solvent. At higher concentrations, or when multiply charged species are involved, ion association causes departures from the Debye-Huckel description, and alternative treatments of the free energies must be invoked.” Besides modifying reactive barriers, an ionic atmosphere can also significantly alter rates of diffusion-influenced reactions by changing the interaction potentials between charged species. This aspect of the ionic influence has been recently studied experimentally and theoretically by several Here (14) Bronsted, J. N.; Delbanco, A. Z . Anorg. Allg. Chem. 1925,144,248; as discussed in: Hammett, L. P. fhysicul Urganic Chemistry, McGraw-Hill: New York, 1960; Chapter 7. (15) Davies, C. W. Prog. React. Kine?. 1961, I , 161. Olson, A. R.; Simonson, T.R. J . Chem. Phys. 1949, 17, 1167. (16) Debye, P.; Huckel, E. Phys. Z 1923, 185. (17) Robinson, R. A.; Stokes, R. H. Electrolyte Solufions; Academic Press: New York, 1959. (18) Harned, H. S.;Owen, B. B. The Physical Chemistry of Elecfrolyre Solutions; Reinhold: New York, 1950.

0 199 1 American Chemical Society

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The Journal of Physical Chemistry, Vol. 95, No. 23, 1991

Chapman and Maroncelli

again, interactions are most often viewed in terms of the Debye-Huckel model for the ion atmosphere.21 Even in these latter studies, where the solvent influence comes through modification of diffusion rates, its effect is modeled assuming a stationary ion atmosphere. That is, all of these approaches neglect the fact that the ion atmosphere set up around a reactant cannot respond instantaneously to its motions, but rather must lag behind the reactive motion to some extent. This lag can cause a retarding force on the reaction in the same way that it does in pure polar solvents. Several recent theoretical studies have addressed this dynamical aspect of the influence that an ion atmosphere exerts on a reaction.22-24 Sridharan et a1.22performed a Brownian dynamics simulation to examine the diffusion-controlled reaction of two oppositely charged univalent ions in a 0.1 M 1-1 electrolyte. Relaxation effects were found to be rather small in this particular system. Only modest departures from the behavior predicted by a static Debye-Huckel ion atmosphere model were observed, and these could be ascribed to modification of the ion atmospheres of the two reactant ions upon close approach. In a related study, Ibuki and Nakaharaz3 considered the influence of ion atmosphere relaxation on diffusion-controlled reactions between an ionic and a neutral reactant. These authors numerically solved the generalized diffusion equation in the inertia-free limit using several models for the time-dependent friction. The friction model of most interest was taken from the Debye-Falkenhagen (DF) theory of conductivity and dielectric dispersion in electrolyte solutions.25 The latter theory is one among an impressive arsenal of theories on the effects of ion-ion interactions on equilibrium and transport properties that were developed during the first half of the cent ~ r y . ' ~ * Although ' ~ , ~ ~ these theories did not focus on chemical reaction dynamics, the ion-atmosphere-relaxation effects considered there in relation to ion mobilities are directly transferable to the problem of diffusion-controlled reactions. In the DebyeFalkenhagen theoryZ5the frequency-dependent friction caused by the lag between a probe ion's motion and that of its ionic atmosphere was calculated in the dilute limit assuming a Debye-Huckel picture. lbuki and NakaharaZ3used the D F result for this ion atmosphere friction to calculate its impact on the short-time kinetics of diffusion-controlled reactions. They predicted that observable departures from Smoluchowski behavior (i.e., the time-independent friction case) should result from this ion-atmosphere effect, and they pointed out possible manifestations in the recent fluorescence quenching experiments of Eads et al.27 Further experimental studies of this sort are needed in order to verify such an interpretation. The final theoretical study of dynamical ion-atmosphere effects on reactions is work by van der Zwan and H y n e ~ In . ~ contrast ~ to the two previous studies, these authors considered the impact of ion dynamics on a reaction with a substantial reactive barrier, using as a model a dipole isomerization considered previously in the polar solvent case.28 To derive analytical results, van der Zwan and Hynes again employed a Debye-Falkenhagen type approach for describing the friction. Since these authors considered a dipolar rather than ionic reactant, they first derived results analogous to those of the DF theory but for the case of the ionic atmosphere

surrounding a point dipole solute. They were careful to point out that such a theory is only applicable in the limit of dilute solutions of low-valence ions in highly polar solvents, Le., in situations where ion aggregation is negligible. With this caveat, they demonstrated that ion-atmosphere-relaxation effects can significantly alter the rates of barrier-limited reactions. In their discussion van der Zwan and Hynes also emphasized the fact that there is a simple and direct connection between solvation dynamics as measured by time-resolved Stokes shift experiments and the friction operative on the dipole reaction examinedaZ9 They pointed out that results of such measurements could therefore be used in place of theoretical descriptions of the ion-atmosphere friction in cases that are beyond the limited scope of the Debye-Huckel approach. This point is an important one for the present study. Similar to the situation prevailing in the initial stages of work on pure polar solvent effects, theories such as that of van der Zwan and Hynes are beginning to model the connections between reaction rates and friction caused by ionatmosphere relaxation before much is actually known about the nature of such relaxation. Even though a substantial part of the early history of physical chemistry revolved around measuring and interpreting ion c o n d u c t i ~ i t i e s , ~including ~ J ~ , ~ ~ the effects of ionic relaxation, these measurements provided only a relatively indirect test of ion-atmosphere theories. Time-resolved fluorescence experiments, on the other hand, provide a direct probe of ion-atmosphere-relaxation processes. Thus, in addition to measuring the friction relevant to certain kinds of reactions, these experiments should also provide stringent tests for theories of ion-atmosphere r e l a ~ a t i o n . ~ ~ *It~ is ~ Jwith " this goal in mind that we have undertaken time-resolved fluorescence measurements of ionic solvation dynamics. During the course of our studies, reports of similar work by Huppert and co-workers have appeared.3'-32 These authors made time-resolved fluorescence Stokes shift measurements on the probe solute coumarin 153 (see Scheme I) using the single-wavelength method.33 Solutions of LiC104 in ethyl acetate3' and more recently acetonitrile and propylene carbonate32 were studied. Huppert and co-workers observed nanosecond time scale relaxations of the fluorescence frequency that varied with salt concentration and solvent. These observations are in agreement with ones we have made on similar systems.34 However, the interpretation given by these authors is rather different from the one that we will offer. Huppert and co-workers discussed the spectral relaxation within the context of the Debye-Falkenhagen theory of ion-atmosphere relaxation. On the basis of conductivity measurements, these authors noted that extensive ion pairing exists in the solvents and concentration ranges studied. They therefore ascribed the (slower than expected) relaxation observed to translational dynamics of ion pairs rather than of the individual ions assumed in the DF theory. Although ion pairing also undoubtedly exists in the solutions we have studied, our explanation of the dynamics is not directly related to such ion pairing but rather involves association between ions and the probe solute. The work reported here consists of steady-state and time-resolved fluorescence measurements of several representative solvatochromic probes in a variety of ionic solutions. Because little

(19) Chiorboli, C.; Indelli, M. T.; Scandola, M. A. R.; Scandola, F. J . Phys. Chem. 1988, 92, 156. Scandola, M. A. R.; Scandola, F.; Indelli, A. J . Chem. Sac., Faraday Trans. 1 1985, 81. 2967. (20) Pines, E.; Huppert, D.; Agmon, N . J . Phys. Chem. 1991, 95, 666. (21) More molecular approaches have been adopted in: Lee, J . J . Am. Chem. Sac. 1989, 1 1 1 , 421; J . Phys. Chem. 1990, 94, 258. (22) Sridharan, S.; McCammon, J. A,; Hubbard, J . B. J . Chem. Phys. 1988, 90, 237. (23) Ibuki, K.; Nakahara, M. J. Chem. Phys. 1990, 92, 7323. (24) van der Zwan, G . ; Hynes, J . T. Chem. Phys. 1991, 152, 169. (25) Debye, P.; Falkenhagen, H. Phys. Z . 1928,29, 121. English translation in: The Collected Papers of Peter J . W . Debye; Interscience: New York, 1954. (26) Falkenhagen, H.; Ebeling, W.; Kraeft, W. D. In Ionic Interactions; Petrucci, S . , Ed.; Academic: New York, 1971; Vol. 2, p 61. (27) Eads, D. D.;Dismer, B. G . ; Fleming, G. R. J . Chem. Phys. 1990,93, 1136. (28) van der Zwan, G . ; Hynes, J . T. Chem. Phys. 1984, 90, 21, and references therein.

(29) van der Zwan, T.; Hynes, J. T. J . Phys. Chem. 1985, 89, 4181. (30) Kim, H. J.; Friedman, H. L.; Raineri, F. 0.J . Chem. Phys. 1991.94, 1442. (31) Huppert, D.; Ittah, V. In Perspectives in Photosynthesis; Jortner, J., Pullman, B., Eds.; Kluwer Academic: Netherlands, 1990; p 301. Huppert, D.; Ittah, V.; Kosower, E. M. Chem. Phys. Lett. 1989, 159, 267. (32) Ittah, V.; Huppert, D. Chem. Phys. Lett. 1990, 173, 496. (33) Nagarajan, V.; Brearley, A. M.; Kang, T.-J.; Barbara, P. F. J . Chem. Phys. 1987.86, 3183. (34) Although our studies are very similar to those of Huppert and coworkers [refs 31 and 321, there is no direct overlap between their work and the primary results reported here. For completeness, we did attempt to make a direct comparison to their results for Cu153 in acetonitrile. We were unable to reproduce the single-wavelength measurements described by these authors. However, in a 0.2 M LiClO,/acetonitrile solution, the average relaxation time of the spectral shift ( ( T ) , see section VI) measured by use of the full spectral reconstruction was in reasonable agreement with the results reported using the former method (3.9 versus 4.4 ns).

Solvation and Solvation Dynamics in Ionic Solutions SCHEME I

&o

e. 0

R

" \

CU10.2 R=CH3 C ~ 1 5 3R&F3

I

\

'N

j?'J$:-"

I

0

H

"Prodan"

4-AP

work of this type has been previously performed, we have tried to survey the behavior in as wide a range of conditions as possible, by varying the probe solute and the solvent, as well as the concentration and identity of the ions involved. After the probe molecules and methods employed are described, the results are presented in four sections. Section 111 concerns steady-state absorption and emission studies. Spectral changes as a function of added salt appear to reflect a continuously varying solvation state of the same sort assumed to exist as a function of solvent polarity in pure polar solvents. However, the magnitudes of the shifts and the trends with solvent and ion identity are not consistent with a simple ion-atmosphere picture of the type assumed by most t h e o r i e ~ . * ~Instead, - ~ ~ * ~a ~more discrete, molecular representation of solvation in terms of multiple association equilibria between the probe solute and the cationic component of the solution provides a better account of the equilibrium spectral data. In section 1V we describe the general features observed in the time-resolved fluorescence spectra of these systems. Similar to the findings of Huppert and c o - w ~ r k e r s , ~we * *observe ~~ that the solvation dynamics resulting from ion motions is surprisingly slow; it typically occurs on a I-ns time scale at room temperature. We show that such slow dynamics cannot be due to purely diffusive dynamics, as has been previously assumed, but must involve activated dynamics, which we interpret as ion/solvent rearrangements in the first solvation shell of the probe. With this picture in mind we then discuss the systematic trends in the dynamics observed as a function of solvent, ion identity, and concentration in section V. In this section we also show that the observed kinetics are inhomogeneous; that is, they depend significantly on the excitation wavelength used to initiate the dynamics. We explain this behavior in terms of quantitative models of ion-probe association equilibria in section VI. 11. Experimental Section

The fluorescence probes coumarin 102 (Cu102) and coumarin 153 (Cu153), obtained from Eastman Kodak, and Prodan (6propionyl-2-(N,N-dimethylamino)naphthalene),from Molecular Probes Inc., were used as received. 4-Aminophthalimide (4-AP Eastman Kodak) was recrystallized from methanol. The solvents dimethyl sulfoxide, methanol, 1 -propanol (Aldrich, HPLC grade), acetone, formamide, tetrahydrofuran (Aldrich, spectrophotometric grade), acetonitrile (Aldrich or Fischer HPLC grade), and ethanol (Quantum Chemical Corporation) were used without further purification. Dimethylformamide (Aldrich, spectrophotometric grade) and propylene carbonate (Aldrich) were distilled over molecular sieves at 20 mmHg. All solvents were stored over molecular sieves. The anhydrous salts sodium and barium perchlorate (Aldrich), tetrabutylammonium perchlorate (Fluka), magnesium perchlorate (Alfa), lithium chloride, and sodium thiocyanate (Aldrich) were used as received. Lithium perchlorate, also anhydrous (Aldrich), was found to contain significant amounts of water and was dried before use by heating in vacuum for 24 h at 65 OC. The salts strontium and calcium perchlorate (Alfa) could only be obtained as hydrated crystals. These were dehydrated by heating for several days under vacuum at 180 OC. Water content of the acetonitrile solutions was checked by ' H NMR. In the case of magnesium perchlorate, a 1 M solution was found to contain 1.5 mol % water. In all other solutions no water was detected, implying C0.2 mol 3'% water in these cases. Salt solutions were prepared by dissolving a weighed amount of the desired salt in the appropriate volume of solvent. Viscosities of these solutions were measured using a Gilmont falling ball type viscosimeter immersed in a constant temperature bath.

-

The Journal of Physical Chemistry, Vol. 95, No.23, 1991 9097 Steady-state absorption and corrected emission spectra were obtained with a Perkin Elmer Lambda 6 UV/vis spectrophotometer and a Spex Fluorolog-2 series F212I fluorimeter, respectively. Samples were prepared in I-cm quartz cuvettes by dissolving enough probe into the salt solutions to provide an optical density of 1 for absorption and -0.1 for emission measurements. Such optical densities correspond to concentration in the range 10-4-10-5 M with these probes. Steady-state measurements were made at room temperaiure, which corresponded to 23 f 1 OC. Fluorescence samples were not deoxygenated. Time-resolved fluorescence measurements were made with a time-correlated single-photon counting apparatus previously described.35 The system is based on a synchronously pumped and cavity-dumped dye laser for excitation and microchannel plate detection, and it provides an overall instrumental response of 50-60 ps (fwhm). Fluorescence decays were fit to a sum-of-exponentials function using an iterative reconvolution algorithm. This procedure partially removes the effect of instrumental broadening and increases the effective time resolution to -20 ps in these experiments. Wavelength resolution for the spectral measurements was obtained by collecting emission through a 1 /4-m monochromator (HA-HIO) having a resolution of 4 nm. Time-resolved fluorescence spectra were generated by collecting series of decays at 10-nm intervals over the emission spectrum, usually 12-16 decays. The multiexponential fits to these decays, after normalization to the steady-state intensities, were then used to reconstruct emission spectra at any time (see ref 36 for details). The samples used for the time-resolved experiments were the same as those used in the steady-state fluorescence measurements; however, here the temperature was controlled to f0.2 OC (typically at 23 "C) by means of a circulating coolant. As will be discussed in section V (see for example Figure 16), the dynamics measured in ionic solution depend on the excitation wavelength employed. In such a situation, the optimum choice of excitation is probably at the peak of the absorption spectrum, since this point represents the best guess for equivalent conditions for all systems. Unfortunately, we had performed many experiments before noting this excitation dependence and we have therefore not adopted this convention. (In addition, peak excitation was often inconvenient due to limited laser tuning ranges.) What we have done instead is to excite the different probe molecules at one or two fixed wavelengths on the blue side of the absorption spectrum. The wavelengths employed were Cu102 and Prodan A,, = 362 nm, Cu153 A,, = 380 nm, and 4-AP Acxc = 290 nm (S,excitation). (With a few of the salts and solvents Cu102 was excited at 388 nm.) On the blue side of the absorption spectrum, the time dependence is not a strong function of excitation wavelength (Figure 16). Based on the one case we have studied in detail, Cu102 in 1 M NaC104/acetonitrile, it does not appear that excitation wavelength variations will cause differences of more than 15% in the times reported. Further, they should not significantly affect any of the trends we report. A final experimental detail concerns the measurement of frequencies and widths from the spectra. Prior to analysis both the steady-state and time-resolved spectra were converted to a linear frequency representation. The frequencies reported in this work are average frequencies measured from these spectra. Use of average rather than peak frequencies helps reduce the effects of small shape changes on the results. In nearly all cases the spectra could be well fit by a log-normal line-shape f ~ n c t i o nand , ~ ~in~ ~ ~ such cases averages were obtained as the analytical first moment of the fitted function.36 However, the absorption spectrum of Prodan in all solvents, and the spectra of Cu102 and Cu153 in cyclohexane, presented instances where a log normal line shape did not properly represent the observed spectrum. For these few cases the mean of the frequencies at the upper and lower half-

-

(35) Chapman, C. F.; Fee, R. S.; Maroncelli, M. J . Phys. Chem. 1990. 94, 4929. (36) Maroncelli, M.; Fleming, G. R. J . Chem. Phys. 1987, 86, 6221. (37) Saino, D. B.; Metzler. D. E. J . Chem. Phys. 1%9, 51, 1856. Fraser, R. D. B.; Sujuki, E. In Spectrial Anolysis; Blackburn, J. A., Ed.; Marcel Dekker: New York, 1970; p 171.

9098 The Journal of Physical Chemistry, VoI. 95, No. 23, 1991

Chapman and Maroncelli

TABLE I: Spectral Characteristics of Several Solvatochromic Probes in Pure Solvents and in 1 M NaCIO./Acetonitrile Solutions (23 "C) A. Pure Solvents

polar shifts (chex-DMSO) probe

cu 102 CUI53

Prodan 4-AP

A%,' I .47 1.84 1.45 2.40

A%n"

PAP

2.94 3.85 3.7 1 3.60

1.47 2.01 2.26 1.20

acetonitrile solutions' ns 0.20 0.28 0.24 0.23

Yata

rata

"em

rem

26.82 24.31 (28.17) 28.29

3.52 3.83 (4.90) 4.44

21.50 18.11 21.46 20.94

2.97 3.41 3.17 3.57

B. 1 M NaClO,/Acetonitrile Solutions S.S.

orobc CUI02 CUI53

Prodan 4-AP

-AY-~ 0.47 0.36 (0.38) 0.50

Arab 0.08 0.00

(0.19) 0.32

time-resolved fluorescence

differences (1 M - 0 M)d -Au.0.84 0.57 0.94 I .55

Ar.-

AAJ

rn.Jns

4 0 ) - v(m),R 10' cm-'

0.05 -0.02

0.37 0.21 0.55 1 .os

4.58 5.48 3.57 21.1

0.55 0.40 0.73 1.11

0.10 0.14

(r).g

ns

1.25 0.8 1 1.48 0.83

a Frequency shifts Au ( IO3 cm-I) in steady-state absorption (abs) and emission (em) spectra between cyclohexane (chex) and dimethyl sulfoxide (DMSO) solvents. AAu is the relative Stokes shift AAu = Auem- Ayah. These various frequency shifts measure the relative sensitivity of the probes to solvent polarity. bAverage solvation times (as defined by eqs 17 and 18) measured in I-propanol at 253 K. 'Frequencies Y (IO3 cm-I) and bandwidths r (full width at half-maximum; IO3 cm-l) in acetonitrile solutions. The values in parentheses denote the fact that the lowest frequency absorption spectrum of Prodan consists of two overlapping bands, making the measurement of frequencies and widths less certain. dDifferences in frequencies and bandwidths of steady-statespectra in 1 M NaClO,/acetonitrile solutions relative to pure acetonitrile solvent. Units are all IO3 cm-I. To the extent that the shifts due to ions and the pure solvent can be separated, these numbers reflect the relative sensitivity to the probes to solvation by ions. 'Differences ( I O 3 cm-I) in the steady-state Stokes shifts in 1 M NaClO,/acetonitrile solutions and pure acetonitrile solvent: AAu A Y ~ ~ - A UTo , ~ .the extent that the pure solvent and ionic contributions are separable, this Stokes shift difference represents the amount of shift expected in timer resolved fluorescence. /Total (wavelength integrated) fluorescence lifetimes. These values were determined from broad-band measurements of emission decays. EMagnitudes u ( 0 ) - u ( m ) (IO3 cm-') and average relaxation times ( 7 ) (eq 18) of the time-resolved fluorescence shifts. These values were obtained from single-exponentialfits to u ( r ) data (see text).

height points was used as the average frequency. The steady-state frequencies reported here were reproducible to within f10 cm-I, and the time-resolved frequencies ( v ( 0 ) and v ( m ) ) to f 3 0 cm-I in most cases. The relative uncertainties when comparing different salt solutions or concentrations are considerably greater (f70 cm-I) due to small changes in spectral shape.

111. Steady-State Spectroscopy We begin our discussion with a general description of steadystate absorption and emission spectra. Typical data are illustrated in Figure I , which contains spectra of the probe Cu102 in NaClO,/acetonitrile solutions at a series of salt concentrations. Both the absorption and emission spectra shift to the red as the concentration of NaC10, is increased. The shifts appear to reflect a continuous change in solvation environment as a function of salt concentration. There is very little change in width or spectral shape as one proceeds from the pure solvent to the saturated salt solution. In this respect these shifts are similar to those observed with Cu102 in a series of solvents of increasing polarity. In addition, there is no evidence of an isosbestic point in the spectra that would argue against a simple continuous change of solvation as a function of ionic strengths3* The general features of the spectra illustrated in Figure 1 are also observed with Cu102 in other salt/solvent systems as well as with other solvatochromic probes. In most cases studied, the only significant change ions produce on the probe spectrum is an overall shift. Of course, the magnitude of this shift depends on a number of variables. The first is the identity of the probe solute. Table I lists results for four common solvatochromic probes in I M NaClO,/acetonitrile solutions. Here we compare static and dynamic characteristics of Cu102, Cu153, Prodan, and 4-AP (Scheme 1) in this representative ionic solution, in the pure acetonitrile solvent, and in other pure polar solvents. The four probes examined share the characteristic that both their absorption and emission frequencies depend strongly on solvent polarity. As a measure of this sensitivity we have included in Table I the frequency shifts, AuJchex-DMSO), observed between cyclohexane

1.0

I

0.8

0.6

0.4

0.2 w

330. 3 5 0 . 3 7 0 . 390.

430

Wavelength ( r i m )

420. (38) In a few special cases, however, such as with red-edge excitation experiments on dilute Mg2+/acetonitrile solutions, one can observe evidence for the decomposability of the spectrum into contributions of distinct species. Such behavior is the exception rather than the rule.

410.

450.

480.

510.

540.

Wavelength (nm) Figure 1. Steady-state (a) absorption and (b) emission spectra of Cu102 in NaCIO,/acetonitrile solutions as a function of NaCIO, concentration.

The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9099

Solvation and Solvation Dynamics in Ionic Solutions and dimethyl sulfoxide. These two solvents were chosen for reference since they define the endpoints of the popular A* solvatochromic polarity scale.39 Also listed are the corresponding differences in the Stokes shifts between emission and absorption, APu(chex-DMSO) I( Au,,(chex-DMSO) - Auab,(chexDMSO)]. It is useful to digress momentarily in order to consider the content of these various frequency shifts, since analogous quantities will be used throughout the remainder of this section. In the approximation that the dominant change brought about by an electronic transition is a change in the dipole moment of the solute, frequency shifts caused by solvent polarity can be expressed asB*@

(3) In these expressions the u’s refer to 0-0 transition frequencies, and transitions are assumed to begin from an equilibrium solvation condition (see below). Thefs in eqs 1-3 represent the (assumed) linear response of the medium to a dipolar solute. Within such a description, the solvent-solute interaction is through a reaction field, R = fp. at the site of the solute dipole p. The two response factorsf,,, and fm respectively denote the total polarity response of the solvent and the infinite frequency or electronic response (that part of the response that is able to follow the electronic transition). The dipoles po and pl are those appropriate to the ground and excited states of the solute, respectively. In a continuum solvent approximation, for a spherical solute of radius a in a pure polar solvent, these factors are given by the familiar function:41 2(x- 1) (4) ”) = a3(2x 1)

+

When evaluatingf,,,, x is the static dielectric constant whereas for fm it is the square of the refractive index of the solvent. In an ionic solution, or in more realistic treatments of pure polar solvents, different expressions for thefs would apply; however, eqs 1-3 would remain unchanged. A few features of these expressions are noteworthy. First, the shifts in absorption and emission individually depend on both the “configurational polarizability” (or what is usually termed the orientational polarizability) of the solvent,f,,, - fm, as well as on the electronic polarizability, f-. However, their difference (eq 3) is only related to the former effect. That is, the difference between emission and absorption frequencies (Le., the Stokes shift) is only related to the noninstantaneous parts of the solvent response, and its behavior as a function of solvent is often simpler than either uab or u, alone. Another important feature of the difference vabs - u,, is that it in fact measures the extent of the time-dependent shift to be expected in time-resolved fluorescence m e a s ~ r e m e n t s .We ~ ~ note that eq 2 is only valid for emission originating from an excited state in equilibrium with its solvent surroundings. In a time-resolved experiment, Y, at t = 0 is equal to uab and it evolves to a u,, described by eq 2 only after times long compared to the characteristic time scales of the solvent response. Thus, this long time value of u,, (what we will later call u ( = ) ) is equal to the steady-state emission frequency only when the fluorescence lifetime is much greater than the solvation time scale. The final comment on the application of eqs 1-3 to experimental frequency shifts is that we do not generally use the (unknown) gas-phase values as references but instead calculate frequency shifts relative to some other more convenient reference. For example, in discussing shifts in pure polar solvents we examine Au,(chex-DMSO), referring the frequencies in the polar solvent DMSO to those in the nonpolar (39) Kamlet, M. J.; Abboud, J.-L.M.; Abraham, M. H.; Taft, R. W. J . Org. Chem. 1983, 48, 2877. (40) Marcus, R. A. J . Chem. Phys. 1965, 43, 1261. (41) See, for example: Frohlich, H . Theory ofDielecrrics; Oxford Univ-

ersity Press: London, 1958; Appendix B.

solvent cyclohexane. Since we assume that polar interactions dominate the observed solvent shifts, we further assume that the instantaneous, nonpolar, part of the solvent response is the same in all solvents, so that such shifts effectively measure only the polar part of the solvent response in DMSO, Le., Auab(chex-DMSO) = (po - pl).poV;,, - fm). For the probes considered here this approximation should be a fairly good one. A less standard and more questionable choice is made when considering spectral shifts due to ion-solute interactions. Here we report shifts such as Auah(I M-0 M), which refer the frequency observed in ionic solutions (1 M concentration) to the frequencies measured in the pure solvent (0 M concentration). In using these differences we implicitly assume that frequency shifts in ionic solutions can be thought of as being due to separate contributions from probesolvent and probe-ion interactions, and that the former are the same in the presence or absence of added salt. Although similar in spirit to the polarlnonpolar separation, this latter approximation is not always appropriate, as will be discussed in more detail below. For now we take shifts such as Avab( 1 M-0 M) to be at least a rough measure of the isolated effect of ions on the probe spectrum. Returning to the data in Table IA, we can conclude several things about these probe molecules from the pure solvent shifts, Au,(chex-DMSO) and AAu(chex-DMSO). Since substantial shifts are observed in both absorption and emission, all of the probes must have relatively large dipole moments in both the ground and excited states (eqs 1 and 2). For the ground state, semiempirical calculations with the MNDO/AMI Hamiltonian42 support this conclusion, yielding calculated dipole moments of 6.1, 6.0, 4.1, and 4.8 D for the probes 01102, Cu153, Prodan, and 4-AP, re~pectively.4~The signs and magnitudes of the Av values also indicate a substantial increase in dipole moment between So and SI. In Cu102 we estimate Ap N 5 D based on the continuum solvent/spherical solute ( a = 3.8 A) expressions given above. Changes of comparable magnitude are expected for the other probes as well; however, the data in Table I also suggest some quantitative differences. For example, it appears that 4-AP has the strongest ground-state interactions with polar solvents, while the change between So and SIis least for this probe and greatest for Prodan. We also note that, although Cu102 and Cu153 are structurally very similar (Scheme I), they exhibit significantly different solvent sensitivities. Thus, while the probes studied are all typical solvatochromic probes (Le., with large I . ( ~Ap) , they do serve to span a range of possible behavior. Now consider these probes in ionic solutions, represented by the data for 1 M NaClO,/acetonitrile solutions listed in Table IB. As already discussed, the widths of the spectra are not much altered by the presence of added salt. With one exception (4-AP absorption, whose change is 7%) the widths of both the absorption and emission increase by 54% between the pure solvent and the 1 M salt solution. Variations of this order are also seen when comparing the widths of spectra in different polar solvents. Frequency shifts between ionic solutions and the corresponding neat solvent can also be compared to the pure solvent shifts discussed above. The main conclusion to be drawn from such comparisons is that there is relatively little correlation between the two types of solvatochromic shifts. Absorption shifts between 1 M salt solutions and the neat solvent, Auab( 1 M-O M), are seen to be on the order of 20-30% of the cyclohexane-DMSO shifts. In absorption, the ordering of probes with respect to shift is roughly the same in the two sets of data. The emission shifts are much more variable, with the magnitude of Aue,(l M-0 M) being between 15 and 45% of the neat solvent shifts, Au,(chex-DMSO). Here, whereas the largest emission cyclohexane-DMSO shift was observed with Cu153, the shift of this probe between a 1 M NaC104 solution and the neat acetonitrile solvent is actually the smallest of the four. Looking at the relative Stokes shifts, AAu(chex-DMSO) and AAu( 1 M-0 M), the correlation is even (42) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J . Am. Chem. SOC. 1985, 107, 3902.

(43) Maroncelli, M. Unpublished results obtained by using the MOPAC program suite (Quantum Chemistry Program Exchange, MOPAC 5.0, No. 589).

9100 The Journal of Physical Chemistry, Vol. 95, No. 23, 1991

Chapman and Maroncelli

TABLE 11: Solvent Properties and Speetrrl Characteristics of Cul02 in Pure Polar Solvents (23 "C)

solvent properties" Cu102 s.s spectral characteristics* solvent ** eo 8", J'12 cm-3/2 AG,, kJ/mol us,, rdm Yem rem I tetrahydrofuran 0.58 7.6 19.0 27.44 3.47 22.53 2.90 acetone 0.72 21 22.1 (9) 26.97 3.43 21.74 3.03 2 propylene carbonate 0.81 65 21.8 14.6 26.68 3.54 21.37 2.94 3 4 acetonitrile 0.85 36 24.1 15.1 26.82 3.52 21.50 2.97 dimeth ylformamide 0.88 37 24.1 -9.6 26.71 3.51 21.48 2.97 5 6 dimethyl sulfoxide 1.oo 46 26.6 -13.4 26.48 3.49 21.22 2.94 7 methanol 0.60 33 29.3 8.2 26.17 3.55 20.48 2.98 8 formamide 0.97 111 39.6 -8 25.77 3.48 20.36 2.93 "Various solvent properties relevant to the energetics of solvation of dipolar and ionic solutes. T * is the solvatochromic polarity scale developed by Kamlet and co-workers (see: Kamlet, M. J.; Abboud, J. L. M.; Abraham, M. H.; Taft, R. W. J . Org. Chem. 1983, 48, 2877). eo is the static dielectric constant (from: Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Soluenfs; Wiley: New York, 1986). 6, is the Hildebrand solubility parameter, a measure of the cohesive energy density of the solvent (values from tabulations in: Marcus, Y. fon Soluafion;Wiley: New York, 1985). AGlr is the free energy of transfer of Na+ from water to the solvent of interest. Relative values indicate relative free energies of solvation of the Na+ ion in these solvents. which can be taken as a (crude) relative measure of the ion solvation energies of interest. The values of AGtr listed here are from the selected compilations in: Marcus, Y. Pure Appl. Chem. 1983, 55, 977. The value for acetone is much more uncertain than the rest. bFrequencies Y and bandwidths r (10' cm-I) of steady-state absorption and emission spectra of Cu102 in the pure solvent. no.

worse. CAP has the smallest relative Stokes shift in pure solvents, but its Stokes shift upon addition of 1 M NaC104 to acetonitrile is nearly a factor of 2 larger than that of the other probes. From the above lack of correlation we conclude that the ionsolute and ion-polar solvent interactions responsible for these spectral shifts do not scale in the same manner with solute. That is, they cannot both be described simply in terms of probe dipole moments as done in eqs 1-3. Such a result is not surprising; similar behavior is found when comparing these probes in polar aprotic and hydrogenbonding solvents. For example, even though 4-AP shows the smallest Stokes shift in simple polar solvents, the Stokes shift in alcohols is much larger with 4-AP than with either Cu102 or CUI53. This similarity to hydrogen-bonding solvents is the first suggestion that the probe-ion interactions being measured here are more specific than the interaction of a dipolar molecule with its ion atmosphere. Some perspective on the nature of the probe-ion interaction can be gained by comparing the relative magnitudes of the shifts observed in pure polar solvents and ionic solutions to what is expected on theoretical grounds. The treatment of van der Zwan and H y n e yields ~ ~ ~ predictions for solvatochromic shifts in ionic solutions using continuum solvent/spherical dipole solute approximations identical with those used in deriving eqs 1-4. As already mentioned, the equilibrium aspects of the ionic part of the problem are based on the same basic picture and approximate solution as the original Debye-Huckel theory of ion activities.I6 lnstead of the atmosphere of an ion, the van der Zwan and Hynes theory treats the ionic atmosphere surrounding a dipolar solute. The model assumes the solvent to be a structureless continuum fluid and is solved in a limit appropriate to dilute solutions of low valence ions in high dielectric constant solvents, just as is the Debye-Huckel theory. The equilibrium free energy of a point dipole solute of radius a is given in this theory by

comparison between shifts in ionic solutions and those in pure solvents. The ratio of the two shifts is given by Au(ion atmosphere) Au(po1ar solvent)

-

(7)

where n is the refractive index of the solvent. Using this expression with values appropriate to 1 M solutions of NaCIO, in acetonitrile (eo = 36, n2 = 2 at 293 K), the ion-atmosphere shift is predicted to be only -3% of the polar solvent shift. Equation 8 applies to the difference in frequencies between emission and absorption as does eq 3 and it is therefore best viewed as a prediction for the experimental ratio AAu( 1 M-0 M)/AAu(chex-CH,CN). In Cu102 this experimental ratio is -3O%, an order of magnitude larger than calculated. Similarly large values are found with the other solutes. One could justifiably object to the use of a Debye-Huckel type model at concentrations as high as 1 M. In l M acetonitrile the Debye length, which sets the scale for the decay of the ionic atmosphere, is only K - I 2 A. Since this value is smaller than the solute radius, the assumptions of a continuum solvent and a diffuse ionic atmosphere are clearly inappropriate. However, even at 0.1 M concentration, where comparison to the theory is more reasonable, the calculated ratio is still more than an order of magnitude less than that observed: 0.8% versus 20% in C ~ 1 0 2 .Thus, ~ the magnitudes of the spectral shifts observed here cannot be accounted for by a continuum ion-atmosphere treatment of this type. We will see later that the dynamics predicted by such models are also far from the spectral dynamics observed in experiment. Why is this theory inapplicable to the systems of interest here? One could cite ion-pairing effects, present in virtually any solvent but water, as the cause of departures from the theory. However, reducing the ion concentration down to levels where ion pairing should be of minor concern still does not yield agreement with the theoretical predictions. Another possible problem is the fact that these probes are poorly approximated by the hard-sphere, point-dipole solute employed in the theory. While this is true, the same applies to the treatment of the pure polar solvent shift, and by considering only the ratio of the two shifts one would expect that this source of error would largely cancel. The most likely origin of the discrepancy lies in viewing the ion-probe interactions in terms of a continuous ion atmosphere. We will show presently that it is more fruitful to treat the probe-ion interactions in terms of specific association between the probe and ions in the form of

In these expressions N A is Avogadro's number, k , Boltzmann's constant, e the electronic charge, and C~and ziare the concentration (M)and charge of ion i. The first and second terms in eq 5 are respectively the free energy of solvation due to the polar solvent and to the ion atmosphere. This separability makes for an easy

(44) We note that a concentration of 0.1 M may still not be safely within the low-concentration limit for a solvent such as acetonitrile (eo 36). However, by the time "safe" concentrations are reached, the theory predicts unobservably small shifts in the spectra. For example, even at 0.1 M the ratio of 0.8% means a shift of only 15 cm-I.

-'I F ++

3 w

1

€0 (5) 03 1)(2to + 1 + ceg) 2(2ro + 1)(2Q g)j = a3 2to + 1 where p is the solute dipole moment, eo the solvent dielectric constant, and y is related to the inverse Debye length, K ,

G=

K2

z

+

(.....)z,,

103tokBT

+

i

-

-

5

The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9101

Solvation and Solvation Dynamics in Ionic Solutions

TABLE 111: Spectral Cbracteristics of CulOZ in 1 M NaCI04 Solutions in Various Solvents (23 “C) time-resolved fluorescence differences ( I M-O M)O no. solvent - A b Ar.b -Avm Arm A A d 0.93 0.07 1.50 0.26 0.57 tetrahydrofuran 0.05 0.38 0.51 0.05 0.89 acetone propylene carbonate 0.47 0.05 0.60 0.12 0.11 0.47 0.08 0.84 0.05 0.37 acetonitrile dimethylformamide 0.15 0.01 0.31 0.07 0.17 0.11 0.01 0.18 0.05 0.07 dimethyl sulfoxide 0.16 -0.00 0.23 0.03 0.07 methanol 0.06 0.03 0.05 -0.00 -0.00 formamide

-

u(0)

S.S.

v:cP ~0,dns 0.96 4.36 0.66 4.53 6.9 4.72 0.79 4.58 1.9 4.12 4.7 4.07 0.82 5.01

ns

T ~ :ns

~ ( 0 ) ) :

T ~ :

IO3 cm-l

(u,, %)

1.07 0.69 -0.6

3.24 (27%) 0.94 (81%) 6.2 (71%) 1.36 (88%) 1.17 5.03 (30%)

(u,, %)

(7):

ko/ ns CPns-1 ~~

0.55

0.25 0.20 (0.58)

0.65 (73%) 1.35 0.10 (19%) 0.78 0.1 (29%) - 5 0.06 (12%) 1.21 1.17 0.83 (70%) 2.09

(0.05)

(0.05)

0.80 0.96 -2

0.63 2.0 2.0

(20)

ODifferences in the frequencies ( u ) and band widths (r)of steady-state spectra of Cu102 in 1 M NaCIO, solutions relative to those in the pure solvents. Units are all IO’ cm-’. *Differencesin the steady-state Stokes shifts of Cu102 in 1 M NaC104solutions relative to those in the pure solvent: AAu Au,, - Aunk To the extent that the pure and ionic contributions are separable, this Stokes shift difference represents the amount of shift expected in the time-resolved fluorescence spectrum. Viscosity of the ionic solution (i10%). dTotal (wavelength integrated) fluorescence lifetimes. These values were determined from broad-band measurements of emission decays. e Parameters characterizing the time-dependent frequency shift v(r). The ~ ( i )data were fit a multiexponential function of the form v ( r ) = u ( m ) + Iu(0) - u ( - ) ] [ u lexp(-r/rl) + u2 exp(-r/T2) + ...I. In almost all cases a single- or double-exponentialfit was sufficient to describe the u ( t ) relaxation. The results listed here are the time constants, T,. and amplitudes, a,, in parentheses. ( T ) is the average tims given by (7)= alii + 0 2 7 2 + ... . ’Reduced relaxation rates, ko (see eqs 19 and 20). The values here are our best estimates for these rates obtained from fitting both the average frequency data (listed here) as well as peak frequency data. 27.5

4

h

Q

0 w

d I

400 1 200.

O. I

800.1 4

0

0

.

1

(DMF) , , , , ,

1

,

, ,

(DMSO)

0. 25.6

26.0

26.4

26.8

27.2

27.6

Figure 3. Steady-state (a) absorption and (b) emission shifts, Au -= v ( l M) - u(0 M), of Cu102 in 1 M NaCIO, solutions in various solvents

-

plotted against the absorption frequency in the pure solvent, unh(O M). The curves drawn on these plots are only suggestive. (See also Tables I1 and 111.) 22.1

E 0 21.6$

\

7

20.1 0.

7

1.

2.

“CIO4

1 (MI

e

” 1

e 1

3.

Figure 2. Summary of (a) absorption and (b) emission frequencies of Cu102 in NaC10, solutions in various solvents as a function of NaC10, concentration. Numbers denote solvents as listed in Table 11.

discrete 1:l and higher order complexes. To see why, we now consider how the observed shifts depend on the identity of the solvent and the salt. From this point forward we focus exclusively on the probe solute Cu102. Tables I1 and 111 and Figures 2 and 3 illustrate how the spectral shifts vary with solvent, using NaC104 as the added salt. In Figure 2 we plot the absorption and emission frequencies of Cu102 solutions in six

solvents (see tables) as a function of NaCIO, concentration. In all solvents, both the absorption and emission frequencies tend to decrease monotonically with increasing NaC104 concentration. The functional form of these curves will be discussed in more detail later. For now we make the following observations. In most solvents, an approach to some limiting value is suggested, although since solubility restricts the range of concentrations, this behavior is not always obvious. With the possible exception of formamide (no. 8) the shifts from the pure solvent values are always greater in emission than in absorption. Finally, we note from Figure 2 that the magnitude of the frequency shifts appear to correlate with the initial value of the frequency in the pure solvent. For example, the largest and smallest frequency shifts as a function of ion concentration are seen for the solvents tetrahydrofuran (no. 1) and formamide (no. 8), the two solvents in which Cu102 exhibits respectively the highest and lowest frequencies in absorption and emission. To examine this last observation more closely, we can compare shifts observed at a fixed ionic concentration, which we choose to be 1 M in NaC104. Relevant spectral data for Cu102 in pure solvents, along with various solvent characteristics, are summarized in Table 11, and corresponding data for 1 M NaCIO, solutions are given in Table 111. The results are also displayed graphically in Figure 3, where the shifts Av,( 1 M-0 M) are plotted versus the absorption frequency in the pure solvent, v,JO M). (The curves drawn in this figure are only suggestive.) Although two out of the eight solvents deviate from the suggested behavior, the general trend with v,bs is clear. We will discuss possible

9102 The Journal of Physical Chemistry, Vol. 95, No. 23, 1991

Chapman and Maroncelli

TABLE IV: Spectral Characteristics of Cul02 in 1 M Solutions of Variolls Salts in Acetonitrile utd DimethyHoPmrmidt (23 "C)

4.94 4.00 1.02 1.02 0.74 1.36 1.16 1.00 0.72

time-resolved fluorescence differences ( I M-O M)C v ( 0 ) v(m)! TI! ns T2! ns 7,bcP - A u , ~ Arlb -Aum AI',, A A 4 in/ ns IO3 cm-' (u,, %) (u2,%) Acetonitrile (2.97) 3.70 0.37 (3.52) 0.15 -0.01 0.02 3.97 0.13 0.12 0.15 -0.03 0.19 -0.03 0.03 0.84 0.05 0.37 4.58 0.55 1.42 (86) 0.06 (12) 0.79 0.47 0.08 0.74 0.51 0.1 1 0.87 0.06 0.36 4.74 0.55 1.07 0.15 5.24 0.66 2.83 (77) 0.45 (23) 0.61 1.03 0.05 1.18 0.12 0.25 5.24 0.86 7.53 (82) 0.09 (17) 1.31 1.13 0.08 1.37 0.13 2.19 -0.32 0.88 1.77 -0.11 -0.42 5.71 0.24 30 (70) 0.25 (30) 1.74 -0.18 1.25 1.56 -0.09 -0.18 5.38 0.28 7 (70) 0.10 (30) 2.17 -0.31 1.37 1.72 -0.11 -0.48 5.69 0.33 30 (60) 0.05 (40)

1.02 0.74 0.74

0.88 1.94 1.65 1.61

-

S.S.

salt'

(DMF) N a+ Li+/C104Li+/CI-

r+?A

0.15 0.25 0.19

(3.51) 0.01 0.03 -0.03

0.31 0.33 0.29

Dimethylformamide 3.81 (2.97) 0.07 0.17 4.12 0.08 0.08 4.32 0.08 0.10 4.15

0.25 0.41 0.37

1.17 6.88 (56) 9.37 (53)

ko? ( ~ ) / n s CP ns-I

0.07 (44) 0.11 (47)

1.23 1.02 2.28 6.23 (20) (5) (20)

0.63 0.73 0.21 0.18 (0.1) (0.3) (0.1)

1.17 4.31 5.02

2.0 0.49 0.41

"All salts are perchlorates unless otherwise specified. r+ denotes the cation radius. Values for most salts are effective ionic radii of the six-coordinate species obtained from: Shannon, R. D.; Prewitt, C. T. Acfa Crysfallogr. 1970, 826, 1076. Values for the tetraalkylammonium ions were taken from: Robinson, R. A.; Stokes, R. H. Elecfrolyfe Solufions: Academic Press: New York, 1959. *Viscosity of the ionic solution (*IO%). CDifferences in the frequencies ( u ) and band widths (r)in steady-state spectra of Cu102 in 1 M NaCIO4 solutions relative to those in the pure solvents. Units are all IO' cm-l. To the extent that the shifts due to the ions and the pure solvent can be separated, these numbers reflect the relative perturbing power of the various ions. "Differences in the steady-state Stokes shifts of Cu102 in 1 M NaCIO, solutions relative to those in the pure solvent: AAv Av,, - Avlb. To the extent that the pure solvent and ionic contributions are separable, this Stokes shift difference represents the shift expected in time-resolved fluorescence. 'Total (wavelength-integrated) fluorescence lifetimes. These values were determined from broad-band measurements of emission decays. /Parameters characterizing the time-dependent frequency shift v(r). The v ( t ) data were fit a multiexponential function of the form v ( r ) = v ( m ) {v(O) - u ( m ) l [ u , exp(-f/rl) + u2 eXp(-f/r2) + ...I. In almost all cases a single- or double-exponential fit was sufficient to describe the v(r) relaxation. The results listed here are the time constants, T,, and amplitudes, ai, in parentheses. ( T ) is the average time given by ( 2 ) = aITI + u 2 q ... For the ions Sr2+,Ca2+, and Mg2+ the small shifts and long time constants make accurate determination of relaxation times difficult (see text). The values listed for the long times are only rough estimates. EReduced relaxation rates ko (see eqs 19 and 20). The values here are our best estimates for these rates obtained from fitting both the average frequency data (listed here) as well as peak frequency data. The values in parentheses (Sr2+,Ca2+, and Mg2+) are only order of magnitude estimates.

+

+

explanations of this trend with solvent after first describing the dependence of the steady-state spectra on the identity of the ions involved. We have studied how the steady-state spectra and dynamics vary as a function of ion by examining the behavior of Cu102 in solutions of a variety of salts in acetonitrile and dimethylformamide (DMF) solvents. The results for 1 M solutions are summarized in Table IV. Two main observations can be made about the steady-state shifts as a function of salt. The first is that the shifts are primarily a function of the cation and depend little on the identity of the anion involved. Due to limited solubilities we could make only two direct anion comparisons. These are between the pairs NaCIO4/NaSCN in acetonitrile and LiC104/LiCI in DMF (Table IV). In the first case the values of Auab and Au, between the two salts both differ by -30 cm-I, which is less than 10%of the magnitude of the shifts involved. In the LiCIO,/LiCI comparison the maximum difference is larger, -60 cm-'in Au,,. This difference, which amounts to -30% of the (small) shift observed, is near to our frequency uncertainties and is smaller than differences typically observed when the cation is varied. (Note also the small rate changes shown in the last column of Table IV.) However, it may be that the CI- anion does affect the spectrum noticeably more than the CIOL anion. More convincing evidence for the minor role played by the anion, at least in the CIO; salts most studied here, is available from observed cation dependence of shifts. The second key feature of the data in Table IV is that a simple correlation exists between the spectral shifts observed and the charge-tesize ratio of the cation involved. The dependence is plotted in Figure 4 using data on C104- salts of eight cations in acetonitrile. As shown here, the shifts relative to pure solvent, Ausb(l M 4 M) and Au,( 1 M-O M), appear to be approximately linear functions of q/r, where q and r a r e the charge and radius of the cation. We note that if the C104-anion contributed significantly to the solvation, a nonzero intercept would be expected in these plots. The fact that the tetrabutylammonium perchlorates (q/r 0.2 au/A) show very small frequency shifts rules out the possibility that the anion contributes appreciably to the shifts in

-

1500.1 v

g

a LI

t 1000. 5

0 0. 0.

0

.

v 1,

,

,

,

, 2.

,

,

,

,I 3.

Figure 4. Steady-state (a) absorption and (b) emission shifts, Au = u( I M) - v(0 M), of Cu102 in 1 M solutions of various perchlorate salts in acetonitrile plotted against the charge-to-radius ratio of the cation of the salt. The lines are only suggestive. (See also Table IV.)

any of the solutions. In absorption, a linear relationship appears to hold for all of the cations except for Sr2+( q / r = 1 .7),45while in emission the shifts fall short of a linear dependence at the highest values of q/r. As will be discussed later, the emission shifts appear to saturate in this way because as q / r increases, the dynamics slows down and equilibrium solvation ceases to be realized during the probe lifetime. We note that the particular choice of q/r for these (45) The behavior of Sr2+in absorption (as well as in emission) appears to be anomalous. The absorption shift is much larger than would be expected based on the other members of the alkaline earth family studied: Ba2+,Ss+, Ca2+, and Mg2+. The dynamical results with this ion are also somewhat unusual. We are unaware of Sr*+being anomalous in other situations and it is unclear why we should observe such behavior here. These shifts and the dynamics observed are, however, reproducible.

Solvation and Solvation Dynamics in Ionic Solutions correlations is somewhat arbitrary. We also considered dependences of the general sort, Au a q / ( r u)p, and found reasonably linear correlations for values of a in the range 0-2 A and values of p between 1 and 3 . The simplest function, q / r , did however, give the best fit to a linear relation. Whatever the precise dependence, the behavior illustrated by Figure 4 clearly implies the importance of structural aspects of the solvation neglected in ion-atmosphere-type models. These observations suggest that spectral shifts in ionic solutions result from some sort of close association between cations and the probe solute. With these ideas in mind, we propose a simple model that is able to account for most of the spectroscopic behavior of the systems studied. This model, based on the idea of ion-probe association, will be elaborated more quantitatively in section VI, when we consider the dynamics of the solvation process. Here we use it to provide a qualitative explanation of the trends in spectral shifts with solvent and ion identity described above. We first assume the existence of a multistep association between ions (I; actually cations) and the probe solute (P) of the form PSJO ==? PS,,II = ... PSWjIj... PS,I,I e= PSOI, (9)

+

There are a total of n "sites" available for ion-probe contact in the first solvation shell of the probe (P). They can be occupied by either a cation ( I ) or a solvent molecule (S). Equilibration among the various species, which is how we will later interpret the spectral dynamics, involves activated interchange of ions and solvent molecules. At the present time we can only speculate as to the actual nature of the association in these systems, i.e., what sort of 'sites" are available, their relative energetics, etc. In Cu102 (Scheme I) the carbonyl oxygen atom should possess a large negative charge and be readily accessible to solvent or ions. One might assume that this would therefore be one particularly favorable site for cation binding. The entire ?r system would also be expected to interact favorably with a positive ion and thus provide additional sites for association. However, beyond these guesses we do not know what a reasonable value of n should be or how different the various sites are. The model embodied in eq 9 should therefore be viewed as merely a caricature of the real physical situation. Its two key ingredients, which should survive future refinements, are (i) the focus on interactions in the first solvation shell and (ii) the assumption of the discrete nature of the association process. Further support for the necessity of these aspects of the model will be given later. In order to describe the spectral shifts we make the simplest possible guess concerning how the probe spectrum varies with association numberj. We assume that the only effect of replacing a solvent molecule with an ion is to cause a shift in the frequency of the probe spectrum. We further assume that the frequency of a particular solute is a linear function of the number of ions with which it is associated, i.e., that the frequency, vj, of the PS,Ij solvate is simply uj = u0 j 6 v (10)

+

The spectrum observed is then given by a weighted superposition of the spectra of individual j solvates, and the average frequency of this spectrum is

which, using assumption 10 becomes

- vo = ( j ) b u

(12) (In section VI we will show that, in addition to describing the shifts in average frequencies, the spectral shapes produced by this sort of superposition provide a good representation of the observed spectra.) Since the frequency of the j = 0 solvate, vb is identically the frequency of the pure solvent spectrum, shifts such as Avab( 1 M-0 M) are therefore interpreted as Uok

AYab(l M-0 M) = (j)'6~,,

(13) From this expression we see that the spectral shift at a particular concentration reflects a product of two factors: one factor

The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9103 specifying the shift of the transition frequency produced by a single solvent-ion exchange ( S U , ~ ) , and the other describing the distribution over probe environments in terms of the average number of ions (j) at that concentration. The superscript 0 in this expression denotes that in absorption the relevant ion distribution is that in equilibrium with So. For emission it would be the distribution appropriate to SI. For a given salt/solvent pair it is the variation of (j) with ionic concentration that gives rise to the curves shown in Figure 2. In section VI we will show that specification of reasonable models for the equilibrium constants involved in eq 9 can reproduce the sort of concentration dependence observed. Here we will discuss in general terms how eq 13 qualitatively explains the dependence on solvent and ion shown in Figures 3 and 4. To motivate discussion of the energetics, consider the interactions involved in one step of the multistep sequence described by eq 9. In terms of pairwise interactions, the "bonds" that are lost and formed can be schematically described by

+

P-s I-s P - I and the energy involved expressed as A€'' = em''

+ s-s

+ CIS- €pi''

- ess

(14)

(15)

The tIJ here are "bond energies" (considered positive) for the various interactions in this double displacement "reaction", and the superscripts a denote the fact that the probe can be in either the So or SI state and that its interactions will vary accordingly. Equations 14 and 15 are only a crude representation of the energetics involved in the real system; however, they suffice to describe the main features of the experimental trends discussed above. The equilibrium constant for reaction 14 will depend on some type of Boltzmann factor, involving the net energy charge, K 0: exp(-Ac"/kT), and this factor will control the (j) term in eq 13. The change in transition frequencies for a single ion-solvent exchange, 6ux, is related to these energies by buab = (A€'

- Ae0)/ hc

= 4 t P I - fps) In writing the last expression we have assumed that changes between the ground and excited states of the probe are such as to scale the energies tps and cpl in the same manner. (For SImore polar than So a < 0.) Finally, we can express the observed shifts as Auab( 1 M-O M)

=z

~ ( j ) ' ( c p I- tps)

~ ( j ) ~ ( t p l tpS)

(1 6a)

( 16b) Avem(1 M-0 M) where the average number of ions in probe state a,(j)", depends on the various equilibrium constants as some increasing function of the total energy difference A P . Consider the solvent dependence of the shifts displayed in Figure 3 in light of eq 16. The incremental shift caused by an ion, bv, 0: (epl - em), depends on solvent by way of the probe-solvent interaction energy e=. Since the transition frequencies in the pure solvents (in particular vab(O M)) should be linearly related to em, if the 6v factor in eq 13 dominates the solvent dependence we would anticipate a linear Au,( 1 M-O M) versus vab(0 M) relationship. That the correlation shown in Figure 3 is not linear can be ascribed to the fact that the equilibrium distributions (i.e., the (j) terms) will also change as a function of solvent, via changes in em as well as in the other energies eIs and es. In general, (j) is a complicated nonlinear function of these energies. To the extent that elS and e= contribute significantly to the variation of Ae with solvent one might not expect any simple correlation to exist between the observed shifts and eps (or uabS(OM)) alone. From Figure 3 we see that such a correlation does indeed exist. This observation can be rationalized by the fact that the strength of ionsolvent and solvent-solvent interactions, cIs and cs, like cpS are roughly related to the solvent "polarity" such that these energies also tend to follow vab(0 M). Some relative measure of the latter energies

9104 The Journal of Physical Chemistry, Vol. 95, No. 23, 195’1

is provided by parameters b ~ and , AG,, listed in Table 11. The Hildebrand solubility parameter bH measures the cohesive energy of the pure solvent4 and is thus a reflection of %, It is interesting that this solubility parameter correlates with both the absorption and emission frequencies of Cu102 in a wide range of solvents, including nonpolar, polar, and hydrogen-bonding solvents.4’ With respect to the data in Table 11, bH shows the same ordering as uabS(0 M). the only exception being propylene carbonate.48 The more important energetic differences among solvents probably arise from the els term, which is represented in Table I1 by the free energies of transfer AG,, of the Na+ cation from water to the solvent of interest. These free energies should provide a fairly direct measure of relative ionsolvent interaction energies in this series of solvents. The correlation between AG,, and uabS(0M) is much poorer than for bH, due in part to the large uncertainties associated with these free energies. Nevertheless, a correlation does seem to exist for all of the solvents except dimethylformamide (DMF) and dimethyl sulfoxide (DMSO). These two particular solvents have AG,, values that are much more negative than would be suggested by the AG,, versus uabS(0 M) correlation formed by the other solvents. It is just these two solvents that also lie off of the general correlation of ionic shift versus uab(0 M) in Figure 3. What we conclude is that D M F and DMSO are better able to solvate Na+ ions (Le., tls is greater) than their “solvatochromic polarity”, u,k(O M), would indicate, and this effect results in their departure from the general trend shown in Figure 3. The above model also easily explains the ion dependence of the shifts (Figure 4). The terms in eq 15 that change upon varying the cation are cpl and tlS. It is reasonable to expect that these energies both vary as some function of the charge-to-size ratio of the cation, and thus correlate with q / r . The apparent linear dependence suggests that the main determinant of the shifts is the frequency term (epl - eK), rather than the population term

ci).

Chapman and Maroncelli

0.5

1.0

1.5

< u 3 > ( 1 0 ’ ~cm13 ) Figure 5. Fluorescence decay rates ( k ” ) versus the average cubed fluorescence frequency ( v 3 ) of Cu102 in various pure solvent (0)and ionic solutions (X). The data shown here include pure solvents as diverse as hexane, dimethyl sulfoxide, and trifluoroethanol as well as ionic solutions of NaCIO4 in various solvents and a variety of different salts in acetonitrile. kn is the rate of decay of total (wavelength integrated) fluorescence, and (v3) was obtained through numerical integration of the fluorescence spectrum, F(v),via: ( u 3 ) = { l F ( v ) dv)/(SF(v)v-’ dv].

n v,

+ C I-

3

It is finally worth pointing out that eqs 16 should not be taken

too literally. The energetic assumptions break down to some extent

when the most interactive ions are considered. For example, Table IV shows that in Mg2+ the absorption shift AuabS(1 M-O M) is larger than the corresponding emission shift. Even if there were no ion reorganization within the lifetime of the probe, the steady-state fluorescence transition frequency (u,,) could at most be equal to the absorption frequency, not greater than it. The fact that the shift relative to pure solvent is greater in absorption means that the energetic consequences of replacing solvent molecules by ions in the first solvation shell of the probe cannot be purely additive as has been assumed. At least for the ions with the highest charge-to-radius ratio, interactions between first solvation shell ions and solvent molecules must also be accounted for in a quantitative model.

IV. Time-Resolved Fluorescence: General Aspects We now consider the time-resolved fluorescence of probes such as Cu 102 in ionic solutions. We begin with the overall fluorescence decay rate, which illustrates an important point concerning the nature of the probe-ion interactions involved. Figure 5 shows the (wavelength integrated) fluorescence decay rate, kn, plotted as a function of the average cubed fluorescence frequency, ( u 3 ) , in a variety of pure solvents and ionic solutions. We have previously (46) See, for example, the discussion: Barton, A. F. M. Chem. Reu. 1975, 75, 731.

(47) Kamlet et al. (Kamlet, M. J.; Carr, P. W.; Taft, R. W.; Abraham, Am. Chem. Soc. 1W1,103, 6062) have previously shown that 6, correlates reasonably well with the i ~ scale * of solvent polarity. Since the absorption and emission frequencies of Cu102 are linear functions of I* in polar aprotic solvents, it is not surprising that we find this correlation with 6,. What is most interesting is that a single correlation between Y and bH appears to hold in nonpolar, aromatic, polar aprotic, and hydrogen-bonding solvents. (48) Propylene carbonate is somewhat anomalous in its behavior. Probe frequencies in this solvent do not show the same good correlation with in this solvent that they do in other solvents. Furthermore, the width of the absorption spectrum is significantlydifferent from the width in other solvents. We conjecture that these anomalies may result from the acidity of propylene carbonate.

M. J .

18.5

19.5

20.5

21.5

22.5

23.5

F r e q u e n c y (lo3 cm-’ ) Figure 6. Time-resolved emission spectra of Cu102 in a 2 M NaClO,/acetonitrile solution. The points and dashed curves represent the “raw” spectra and the solid curves are the log normal fits to these data. The times shown are 0, 0.3, I , and IO ns from right to left.

shown that the radiative decay rate is an approximately linear function of ( v 3 ) for the case of Cu102 in a wide range of pure s0lvents.4~ Since the quantum yields are near unity and vary little with solvent for this probe, the total decay rates can be used in place of radiative rates for simplicity in the present comparison. Figure 5 demonstrates that the same relationship between decay rate and frequency exists in pure solvents (0)and in ionic solutions (X). The data in this figure spans a range of pure solvents from hexane to trifluoroethanol and includes solutions of a number of different ions in acetonitrile and other solvents. The fact that a single correlation applies to both the pure solvents and the ionic solutions indicates that the nature of the probe-ion interactions is not fundamentally different from the probesolvent interactions already present in pure polar solvents. That is, quenching effects are negligible, and there are no unusual electronic perturbations caused by ion-probe association in these systems. Typical time-resolved fluorescence spectra are illustrated in Figure 6, which contains results obtained with Cu102 in a 2 M (49) Fee, R. 5 170.

S.;Milsom, J. A.; Maroncelli, M. J . Phys. Chem. 1991,95,

Solvation and Solvation Dynamics in Ionic Solutions

The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9105

NaCIO4/acetonitrile solution. As in the steady-state spectra, the time-dependent emission is well described in terms of a spectrum of constant width and shape that undergoes a continuous frequency shift with time. In 1 M salt solutions, the magnitudes of the time-dependent shifts are typically on the order of 500 cm-I, whereas width changes are typically 1100 cm-', or 120% of the shifts. These features of the time-dependent spectra are similar to what is observed in pure polar solvents. By analogy to the latter case we characterize the observed dynamics in terms of a spectral response function, C(r),defined by C(t) =

d t ) - 4-w) 40) - 4 m )

-21.51

,

'

'

I

'

, I

r

-

0

4

c20.51

(17)

where v ( t ) is some measure of the emission frequency at time t , etc. In order to determine this C(t) function we first fit the 12-16-point experimental spectrum at a given time to a log-normal line ~ h a p e . ~ ~"Raw" J' data and representative log normal fits are illustrated in Figure 6 by the points and the continuous curves, respectively. The frequency measure we use for v ( t ) is the average (first moment) of the spectrum calculated analytically from the fitted function. Use of the peak frequency yields similar C(t) functions in most cases, but the former measure is preferable in light of the spectral modeling considered below. Before proceeding, it is useful to comment on the use of this C(t) function to monitor solvation processes occurring in ionic solutions. Although the shifts appear continuous, there are many indications that the best description of our results is in terms of association equilibria among discrete probe-ion complexes, as already described. If such discrete species are present, it might be preferable to measure the spectral kinetics in a way directly related to the growth and decay of these distinct species, rather than as a continuous frequency relaxation process. We have investigated this alternative by attempting to fit the fluorescence decays to a two-state kinetic model, an approach consistent with the scheme given in eq 9 for the case n = 1. One characteristic of such two-state kinetics is that just two unique time constants appear in the fluorescence decays; only the relative amplitudes of the exponentials associated with these times should vary as a function of wavelength.N In some cases, primarily when the spectral shift is small, an entire decay series can be reasonably fit by only two time constants in this manner. But in the general case, and especially for large frequency shifts, more than two time constants are needed to fit the data at all wavelengths. Thus, the time-resolved emission data, like the steady-state spectra, indicate that solvation is generally more complex than can be modeled by a two-state equilibrium. This does not of course exclude the possibility of higher order equilibria, and the addition of even one further step (n = 2)does appear to be capable of explaining all of the features observed experimentally (see section IV). Unfortunately, without more knowledge of the details of the associations involved, it is not fruitful to attempt fitting to a higher order kinetic scheme, and we thus rely on a description in terms of the overall spectral movement, i.e., C(t). The relationship between the usual continuous description used in discussing the dynamics in pure solvents and the association scheme described in the last section is that here we picture our "solvation coordinate" as being the time-dependent average number of ions, ( j ( t ) ) . Examples of v ( t ) data and corresponding spectral response functions are provided by the NaCIOJacetonitrile concentration series shown in Figure 7. The limiting frequencies v ( 0 ) and v ( - ) both decrease monotonically with concentration (Figure 7a). The semilogarithmic plots of the C(r) functions plotted in Figure 7b show that the response times also decrease with increasing salt concentration. Except for some small-amplitude fast dynamics that is present for concentrations 11 M, the response functions observed in NaC104/acetonitrile solutions are exponential. In pure polar solvents, decay of c(t)tends to be clearly nonexponentiaL3s5so that this behavior at first seems unusual. The exponentiality exhibited by the NaC104/acetonitrile data probably (SO) See for example the treatment by: Laws, W.R.;Brand, L. J. f h y s . Chem. 1979.83.195.

L

L

L

-

\

(b)

- 4 e \

-5.'

"

"

"

'

'

X

2. 3. 4. 5. Time (ns) Figure 7. (a) Time dependence of the emission frequencies, v ( t ) , and (b) spectral response functions, C(t),of Cul02 in NaClO,/acetonitrile sclutions at various salt concentrations. From bottom to top the concentrations are 0.1, 0.25, 0.5, 1.0, and 2.0 M. 0.

1.

does reflect a fundamental difference in the dynamics underlying the spectral shifts in the two types of solutions; however, exponential c(t)functions are not always observed. Many solutions, for example in LiCIOJacetonitrile and NaC104/THF (Figure lo), show response functions that are far from exponential. In order to characterize the overall time scale of the solvation response in a consistent way, we therefore make use of an (integral) average time, (7)

JmC(t) df

(18)

The most obvious feature that distinguishes between solvation dynamics in ionic solutions and pure polar solvents lies in the average times involved in the respective relaxations. In most pure polar solvents at room temperature, spectral shifts due to solvation dynamics occur on a 1-100-ps time scale. For example, in pure acetonitrile ( 7 ) < 1 ps,' which is much less than our instrumental resolution. In the NaC104/acetonitrile solutions of Figure 7 on the other hand, (7)varies between 800 ps and 5 ns. The ionic dynamics in all of the solutions we have studied occurs on this much slower, nanosecond time scale. Before discussing possible interpretations of the observed dynamics, it is useful to first investigate the extent to which the dynamics due to the solvent itself can be separated from that of the ionic component of the solution. Solubility constraints require that we work in relatively polar solvents, solvents in which probes such as Cu102 exhibit spectral dynamics even in the absence of added salt. Thus, in principle, the time-dependent shifts illustrated in Figure 6 do not reflect ionic motions alone but also contain a part due to the same sort of polar solvent dynamics present in the pure solvent. Forunately, the large time scale difference between these two aspects of the overall dynamics renders them approximately separable. In fact, since we generally work in solvents such as acetonitrile, whose solvation dynamics are (for us) unobservably fast in the pure state, the time-dependent shifts we do observe can be considered to arise solely from ion dynamics. This point is illustrated in Figure 8, where we plot the concentration dependence of v ( 0 ) and v ( m ) as measured in our photon-counting experiments, along with an estimate of the "truen u ( 0 ) that would be observed with sufficient temporal resolution. The latter value is estimated from the steady-state absorption spectrum using the idea that at t = 0 the origins of absorption and emission must c ~ i n c i d e . ~ 'In the pure acetonitrile solvent no time-resolved Stokes shift is observed, Le., the apparent v ( 0 ) is equal to ~ ( 0 0 ) . The absorption frequency, however, indicates that a shift of 1710 cm-l takes place undetected by our experi(51) Fee,

R. S.;Maroncelli, M. Manuscript in preparation.

9106 The Journal of Physical Chemistry, Vol. 95, No. 23, 19'91

Chapman and Maroncelli

"true" v(0)

V

2

22.1

1 1

W

~

CH,CN

dynamics

1

1 1

I

s 12oo.A

a, 3 0a,

20.9 20.3

I , , ,p

-I

'\

dynamics

0.

1.

1 .o

2.0

3.0

4.0

2

Figure 8. Limiting frequencies of the time-depcndent emission of Cul02 in NaClO,/acetonitrile solutions at various salt concentrations. u(0) and

refer to extrapolated frequencies at times zero and infinity obtained from multiexponential fits to the U ( Y ) data. The curve labeled "true u(0)" is an estimate of the Y = 0 frquency that would be obtained with infinite time resolution (see text). v(-)

ments. If this 1710-cm-' shift is subtracted from the "true" v(0) values at the different NaC10, concentrations, the dashed curve in Figure 8 results. This curve coincides with the observed v(0) curve towithin the relative uncertainties in these measurements. Such agreement (with -100 cm-I), while not universal, is also observed in a variety of 1 M solutions of various other ions and solvents. We interpret such coincidence to mean that, at least in the majority of cases, the contribution of solvent molecules to the dynamics is similar enough in the pure solvent and ionic solutions that it provides a constant and unobservable background component to the spectral shifts. Thus, the much slower timedependent shifts we do observe involve "only" the dynamics of the ions, and these can be viewed as being "independent" of solvent molecule motions. There is, of course, no strict separability of ion and solvent dynamics. As already stated, our interpretation of the "ion" dynamics actually involves exchange of ions and solvent molecules in the first coordination sphere of the solute, which by necessity entails solvent as well as ion motion. What is meant by separability here is that solvent dynamics of the sort operative in the pure solvent is so fast that it merely provides an adiabatic 'dressing" for the local, more specific, ionsolvent exchange dynamics taking place in the probe's immediate vicinity. Further support for this idea of separate ion and solvent dynamics comes from the one example in which we have been able to observe the dynamics of both the ionic and molecular components of a salt solution simultaneously. The system is LiC104 in I-propanol, illustrated in Figure 9. In this figure we compare the time-dependent frequency shifts observed with Cu102 in pure propanol (solid curves) and in a 1 M LiC104/propanol solution (dashed curves). Two different frequency measures are shown here, the average frequency, v,,, and the peak frequency, uPk We include both frequency measures and plot the data using a logarithmic time axis to emphasize the differences in the behavior of the ionic versus the pure polar solution at long times. In pure propanol CUI02 is observed to undergo a time-dependent Stokes shift with an average relaxation time of 50-60 ps, so that the spectral shift is essentially complete within a few hundred picos e c o n d ~ . (The ~ ~ very small changes in vav at longer times reflect (52) Since this time is comparable to the width of our instrumental response function, we do not completely resolve all of the dynamics, and the true relaxation time is therefore somewhat shorter than this value. Using the steady-state absorption spectrum5' we estimate that -30% of the shift (500-700 cm-I) is missed in this case. In the LiC10, solution, because the *solvent" part of the dynamics has slowed considerably, less of the fast dynamics is missed (-2046). When this difference is accounted for, the solvent contribution to the total dynamics is the same in the pure solvent and ionic solution to within experimental uncertainties.

Figure 9. Time dependence of the frequency shifts Au(t) of Cu102 observed in pure I-propanol (solid curves) and a I M UC1O4/1-propanol solution (dashed curves). Panel a shows the frequency of the peak of the spectrum and panel b the average frequency. The shifts have been arbitrarily defined relative to 4 2 0 ns) = 0 in order to better compare the data in the two solutions.

slight width and shape changes that are within the uncertainty of these measurements.) Several differences are evident when LiCIO, is added. The most important is the appearance of a slow component to the spectral shift, which can be seen as the long-time tails of the dashed curves in Figure 9. Because the contribution of this long component to the total relaxation is small, its decay time is not well determined; however, it is at least several nanoseconds. We attribute this slow component to the ionic contribution to the solvation dynamics. The more prominent, fast component is then ascribed to the same sort of solvent dynamics present in the pure solvent. As noted above for cases where the solvent dynamics are unobservably fast, in this example as well, the magnitudes of the two components suggest that the ionic shift adds to an approximately constant background shift due to the solvent.s2 Thus, these data provide more justification for the approximate separability of the ion and solvent dynamics. We note that the fast "solvent" dynamics are not identical in the salt solution and in the pure solvent. The average relaxation time of the fast component is lengthened to 120 ps in the LiCIO, solution, roughly twice its value in pure propanol. Thus, the presence of added salt does influence the dynamics of the solvent as well as provide an additional relaxation mechanism. In the present case, the ion influence on the solvent can be accounted for simply by the change it induces in the bulk viscosity: the ratio of time constants of the fast component (ionic solution/pure solvent) is 2.2 and the ratio of viscosities is 2.1. We now consider the nature of the ion dynamics being observed. As discussed previously, most theoretical treatments of ion solvation dynamics and its effect on reaction have invoked simple ion-atmosphere models. Such models describe the solvation energy relaxation following a change of probe electronic state as the result of translational diffusion of ions in the ion atmosphere of the probe. The solvent is represented by a continuum fluid in which ions diffuse at characteristic rates determined by solvent viscosity. Such simple diffusive dynamics are much too fast to be the origin of the dynamics observed in the present experiments. Several results support this conclusion. First of all, simple calculation^^^ show 1 M, that under the conditions considered here (concentration viscosity 1 cP) the time constant for a diffusion controlled reaction should be 150 ps, not the 1-ns times observed. More sophisticated calculations of ion-atmosphere relaxation, as for example the DebyeFalkenhagen t h e ~ r yor~ its ~ dipole , ~ ~ analogue

-

- -

-

-

(53) Based on the sample Stokes-Einstein expression for fluorescence quenching as discussed in: Birks. J. 9% Phorophysics of Aromoric Molecules; Wiley: New York, 1970; Chapter 10.

Solvation and Solvation Dynamics in Ionic Solutions

The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9107

-0.3 -

-1.

I

C

w

:L

Y

U

W

0

0

-3.

0

y

- 4. PC/THF

~~~~

- 5.

0.

-0.6 -

,.

-2. +

A

i z -

i

n

-

1.

2.

4.

3.

-0.9 -1.2

u

--1.8 le5 2.7

2.9

3.1

3.3

3.5

3.7

103 /T

Time (ns) Figure 10. Spectral response functions observed with Cu102 in three solutions. All solutions correspond to 1 M concentrations of the additives methanol (MeOH), propylene carbonate (PC), and NaCIO, in tetrahydrofuran (THF).

treated by van der Zwan and H y n e ~ also , ~ ~predict ion-atmosphere-relaxation times of 100-200 ps (for e,-, N 36). All of these approaches, which assume diffusion through a continuum solvent, predict relaxation that is roughly 10-fold faster than the dynamics we actually observe. A direct experimental demonstration of the nondiffusive nature of these dynamics is provided in Figure IO. In this figure we compare solvation dynamics of Cu102 in 1 M tetrahydrofuran (THF) solutions of the salt NaCIO,, and the two molecular cosolvents propylene carbonate (PC) and methanol (MeOH). The two polar species F T and methanol are more polar than THF and cause red shifts in the fluorescence of Cu102 relative to pure THF. The time-dependent Stokes shift observed in the latter two systems results from a "dielectric enri~hment"~~ of the probe's first solvation shell after electronic excitation. That is, via a translational diffusion process, molecules of the more polar cosolvent add to the immediate vicinity of the excited-state probe. This enrichment occurs on a time scale of -200 ps, in agreement with the above estimates for diffusion-controlled processes. In contrast, solvation dynamics in the NaCIO,/THF solution takes place with an average time constant of 4.4 ns. Thus, we conclude that the ion dynamics observed here are not diffusion controlled in the usual sense. In addition to being much slower than predicted, the observed dynamics also cannot involve predominantly long-range, nonspecific interactions of the sort invoked by ion-atmosphere models for the following reason. We have used fluorescence depolarization measurements to determine the rotation times of probes such as Cu 102 in a number of ionic solutions. The times are in the range of 150-600 ps, which are in general much shorter than the corresponding solvation times. For example, the rotation time of Cu102 in 1 M NaClO,/acetonitrile solution is rr0, 3~~ = 160 whereas the solvation time is 1.3 ns, roughly an order of magnitude longer. Given this disparity in times, long-range in-

-

(54) In addition to the original DF discussion, Friedman and co-workers (ref 30) have explicitly discussed the effect of an ion atmosphere on the time-resolved fluorescence spectrum of a probe solute. Although couched in very different language, the latter treatment is for an ionic solute and for eo >> 1 leads to solvation times identical with the "Maxwell" relaxation time predicted by the DF theory. (55) Suppan, P. Faraday Discuss. Chem. SOC.1988,85, 173. (56) The rotation time determined in fluorescence depolarization measurements is the decay time ( r 2 )of the correlation function (P2(filbr(O)*ficm( f ) ] ) , where fi.b and firm are the transition moment directions for absorption and emission and P2denota the second-order Legendre polynomial. The mast appropriate measure of a rotation time for comparison to the solvation dynamics would be the decay time of the firstsrder correlation function P I . We approximate this time rm by assuming that the motion is purely diffusive, in which case rtO,= 3z2.

Figure 11. Arrhenius plots of the reduced rate ko observed with Cul02 in 1 M NaClO, and LiC104 solutions. In the reduced rate (defined in eqs 19 and 20) the temperature dependence of the viscosity has already been removed. The activation energies corresponding to the least-squares fits shown on the plot are 9.4 and 5.9 kJ/mol for NaCIO, and LiCIO,, respectively.

teractions between the dipolar field of the solute and its ion atmosphere should be averaged out by probe rotation. Thus, the time-dependent spectral shifts we observe cannot arise from changes in such long-range interactions. Rather, the dynamics must involve local rearrangements of ions in the immediate vicinity of the rotating solute. We also note that the relatively slow dynamics observed here imply the presence of significant activation energies beyond those due to solvent viscosity. The presence of such activation energies is confirmed by the temperature dependence of the rates shown in Figure 11. In this figure we plot average solvation rates scaled to solvent viscosity (see section V) in 1 M NaC10, and LiClO,/acetonitrile solutions. Even when the viscosity activation energy (8.7and 4.4 kJ/mol, respectively) is removed by scaling, activation energies of 9.4 (NaC10,) and 5.9 kl/mol (LiC104) are observed. (The actual interpretation of these activation energies is not simple since temperature-dependent changes in both the equilibrium distributions ((j))and the exchange rates are involved.) All of the above observations, together with those already made concerning equilibrium spectra, serve to confirm the general picture developed in the last section. The dynamics evidenced by the spectral shifts involve some sort of activated ion/solvent rearrangement processes in the near vicinity of the probe.

V. Probe, Concentration, Solvent, and Salt Dependence of the Dynamics: Kinetic Heterogeneity We now turn to a description of how the dynamics depends on a number of variables, beginning with the identity of the probe solute. Table IB lists several characteristics of the time-resolved fluorescence of the four probes Cu102, Cu153, Prodan, and 4-AP in 1 M NaC104/acetonitrile solutions. The magnitudes of the time-dependent shifts, v(0) - v( -), track the difference between the steady-state emission and absorption shifts AAv(0 M-1 M) in the expected manner.57 In all of these probes the decay of C(t) is nearly exponential, but the time constants ( 7 ) vary significantly with solute. There is almost a factor of 2 difference between the (57) To the extent that the part of the shift due to solvent alone is a p proximately the same in these 1 M NaCI04 solutions as in the pure solvent, the steady-state (emission-absorption) shifts AAu should provide a measure of the time dependent shift u(0) - v ( m ) as long as the fluorescence lifetime rflis much greater than the spectral shift time ( r ) . If the latter condition is not fulfilled then the two are related by v ( 0 ) - u ( - ) (1 + !z)/~"!AAu(l M-O M). In the case of 1 M NaC104/acetonitrile solutions this relationship appears to be well satisfied, except perhaps in the case of CulS3. In other solutions the observed time-dependent shifts appear to be larger than expected on the basis of AAu(1 M-O M).

-

9108 The Journal of Physical Chemistry, Vol. 95, No. 23, 1991

Chapman and Maroncelli

TABLE V Swctral Characteristics of Cul02 in NaClOJAcetonitrile Solutions of Varying Concentration (23 "C) S.S. differences ( x M 0 M ) b [NaC104],0 i2 ns: M - A u . ~ Arab -Au,, Are, 7:cP in,dns (u2, %)

-

0.00 0.10 0.25 0.50

0.10 0.21 0.32 0.47 0.57 0.68

1.oo

1S O 2.00

(3.52) 0.04 0.06 0.07 0.08 0.07 0.07

0.27 0.44 0.62 0.84 0.95 1.07

(2.97) 0.07 0.07 0.07 0.05 0.04 0.02

0.37 0.39 0.42 0.55 0.79 1.06 1.39

3.70 3.93 4.16 4.35 4.58 4.98 4.99

(1):

5.22 2.77 1.95 1.36(88) 0.06 (12) 1.07 (84) 0.06 (16) 0.92 (84) 0.06 (16)

0.29 0.38 0.45 0.55 0.58 0.59

ns

~k[NaCIO,]/ CP ns-' M-'

4.6 2.6 1.8 1.3 1.1 0.77

0.86 0.64 0.62 0.63 0.63 0.90

'Salt concentration mol/liter (*5 5%). bDifferences in the frequencies ( u ) and band widths (r)in steady-state spectra of CulO2 in the NaClO, solution relative to those in the pure acetonitrile. Units are all IO3 cm-'. 'Viscosity of the ionic solution (*IO%). dTotal (wavelength-integrated) fluorescence lifetimes. These values were determined from broad-band measurements of emission decays. Parameters characterizing the time-dependent frequency shift u(r). The u ( r ) data were fit a multiexponential function of the form v(f) = v ( m ) + (v(0) - u(=))[ol exq(-t/rl) u2 exp(-r(r,) + ..,I. In almost all cases a single- or double-exponential fit was sufficient to describe the v ( t ) relaxation. The results listed here are the time constants, T ~ and , amplitudes, u,, in parentheses. (7)is the average time given by (1) = u17,+ u2i2+ ... 'Rates k = (i)-' scaled by viscosity and concentration. The constancy of these values indicates the extent to which the simple relation k = k O I I ] / qis valid.

+

n

I

1.5

.~

;

W

.

1.0

-

Y

Y

F

I

0.5I 0.0

0.5

1.0

1.5

2.0

P

T

1

2.5

[salt1 ( M I Figure 12. Viscosity scaled rates, kq, as a function of ion concentration for three ion/solvent systems. The lines drawn on these graphs are the best fit lines to the data below 1 M concentration which pass through the origin, and they define the reduced rate ko for these systems.

times in the fastest and slowest cases. This variability is greater than is observed among different probes in the same pure polar solvent. (Examples of the range typical in the latter case are provided by the propanol solvation times listed in Table IA.) Since the energetics of association (i.e., elP and csp) depend on the identity of the probe, it is not surprising that the dynamics should also. We will not explore this probe dependence further and will henceforth consider only the dynamics of Cu102. The dependence on ion concentration is illustrated for three ion/solvent systems in Figure 12. Listings of the NaC104/ acetonitrile data are also provided in Table V. Average rates, defined as k = ( 7 ) - l , are not themselves simple functions of Concentration. In some cases, for example, NaCIO, in dimethylformamide, the rates are nonmonotonic functions of salt concentration. However, this behavior seems to result from the fact that the solution viscosity changes appreciably with the concentration of added salt. For example, as shown in Table V, the viscosity of NaC104/acetonitrile solutions increases by almost a factor of 4 between 0 and 2 M. When this variation is accounted for through use of viscosity-scaled rates, kv, the dynamics are seen (Figure 12) to be simply proportional to ion concentration, at least for concentrations below I M. In some cases the proportionality breaks down at higher concentrations, possibly due to nonnegligible changes in ion activities at these concentration^.^^.^^ We have (Sa) It would be desirable to examine the dynamics as a function of cation activity rather than as a function of concentration as we have done here. Unfortunately. little data is readily available on ionic activities in the nonaqueous solvents used. Examination of mean activities in water (ref 5 9 ) suggests that activities and concentrations (M) should agree to within -20% or so for most of the salts studied in aqueous solutions of (0-2 M). The agreement in other solvents is likely to be worse.

26.4

27.6

27.0

v O b s(io3 c m - ' ) Figure 13. Reduced rates observed with Cul02 in 1 M NaCIO, solutions in various solvents. Numbers designate solvents as listed in Table 11.

observed this sort of scaling with viscosity and concentration for a number of ion/solvent systems in addition to those illustrated in Figure 12. Such behavior has also been previously reported by Huppert and co-workers in studies with the Cu153 p r o b e ~ ~ ' 9 ~ ~ It provides a convenient way to compare dynamics in different systems through the use of a reduced rate ko,defined to be the rate that would be observed in a reference 1 M solution with a viscosity of 1 cP. Reduced rates are determined from the experimental data, either from the slope of plots such as those in Figure 12,

or as simply the value ko t

lv(7)-%

M

(20)

at 1 M in cases where a concentration series was not performed.

It is this reduced rate that we will consider in the following discussions of solvent and ion dependence. Table 111 summarizes data concerning solvent variations and their effect on the relaxation observed with Cu102 in NaCIO, solutions. Reduced rates are also plotted as a function of uab(O M) in Figure 13. Consider first the magnitudes of the timeresolved shifts, u ( 0 ) - v(m), listed in Table 111. These shifts parallel the steady-state shifts AAv( 1 M-O M) as a function of solvent; however, in several cases the time-resolved shifts are larger than anticipated from the AAu values.57 For example, when account is made of the nonzero value of ( 7 ) / 7 0 , in acetonitrile and di( 5 9 ) Pitzer, K. S . ; Mayorga, G . J . Phys. Chem. 1973,77, 2300.

The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9109

Solvation and Solvation Dynamics in Ionic Solutions 21.5 I

I

n

-

E 0

Y

0

I

20.5

i 1

'.

7

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I \

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.c

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6.

8.

10.

'

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0.8

'

'

'

'

c's

'

'

' ' ' ' ' '

'

'

'

1.9

'

'

3.0

Time (ns) Figure 14. Time-dependent frequencies, v ( r ) , of Cut02 in various 1 M

perchlorate solutions.

methylformamide the two types of shift agree to within their uncertainties. In tetrahydrofuran and acetone, on the other hand, the u ( 0 ) - Y(-) values are respectively 320 and 250 cm-I larger. In the latter solvents, the solvent contribution to the dynamics appears to be reduced noticeably from its pure solvent value, in contrast to what is typically found (i.e., Figure 8). That this behavior should be observed for those solvents having the weakest interactions with the solute (and ions) is not surprising. In the case of methanol, the time-resolved shift is much larger than anticipated from PAY. On the basis of the very fast time scale observed, -50 ps, we attribute this shift to solvent rather than ion dynamics. That is, although the solvation dynamics in pure methanol occur faster than our experiment can adequately detect, the presence of salt slows these dynamics sufficiently that we begin to pick up a part of the spectral movement. However, based on the frequency of the absorption spectrum, we appear to only be observing a rather small fraction (-25%) of the total shift. The only estimate that we can make of the solvation time in 1 M NaC104/methanol solution is 12 < ( T ) < 50 ps. Such a ( T ) for the solvent part of the dynamics is reasonable in light of the value ( T ) = 6.2 ps in pure methanola and the fact that the viscosity of the 1 M solution is roughly double that of the pure solvent. Unlike the LiC104/propanol case (Figure 9), we were not able to detect any slow component to the spectral shift. We conclude that in methanol, as in formamide, no ionic contribution to the dynamics is observable. When it can be observed, the ion dynamics is found to vary considerably with solvent. In some cases (acetonitrile, dimethylformamide) the spectral shift is exponential in time, while in others (tetrahydrofuran, dimethyl sulfoxide) it is markedly nonexponential. What differentiates these solvents is not clear. Average solvation times also vary with solvent. As illustrated in Figure 13, there may be some correlation between the reduced rate, ko, and the solvating ability of the solvent, as gauged by uab(O M). Based on the solvent/cation exchange models discussed below it would be reasonable to expect the rate to increase with increasing uabr (Le., as the strength of solvent-solute and also solvent-ion interactions increase). Thus, to the extent that there is a trend in this data, it is not in the anticipated direction. We note that similar "unobvious" behavior is observed with respect to residence times of several of these solvents in the first solvation shell of transition-metal ions.61 Changes in the dynamics as a function of ion identity can be discussed with respect to the data listed in Table IV and displayed in Figures 14 and 15. In Figure 14 we plot the v ( r ) curves (60) Kahlow, M. A.; Jarzeba, W.; Kang, T. J.; Barbara, P. F. J . Chem. Phys. 1989, 90, 15 I . (61) See for example the data compiled in: Burgess, J. Metal Ions in Solution; Ellis Horwwd: New York, 1978; Chapter I 1.

Figure 15. Correlation of reduced rates, &",with charge-to-sizeratio of the cation. The solid line and filled squares correspond to rates in acetonitrile solutions and the dashed line and open circles are in dimethylformamide solutions. The lines drawn here are only used to visually separate the two sets of data. The points in parenthesis are highly uncertain and are shown here only for completeness.

observed with Cu102 in six perchlorate/acetonitrile solutions. Biexponential fits of these curves are provided in Table IV. Most of the u(t) decays contain a fast (50-100 ps) component in addition to a slower component which accounts for most of the relaxation. LiC104 presents the main exception to this general behavior, having a v ( t ) that can be fit by two relatively long time constants. As far as the dynamics is concerned, the cations studied can be divided into two sets having low and high values of the chargeto-size ratio q / r . In the low q / r set (Na+, Li+, and Ba2+)the magnitude of the time-dependent shift increases and the reduced rate decreases monotonically as a function of increasing q / r (Figure 15). For the remaining ions (SrZ+, Ca2+,and Mg2+)which have higher q / r values the situation is less clear cut. All of these latter ions produce much smaller time-dependent shifts than the lower q / r ions. Because of the small magnitude of the shifts and the long time constants involved, the times for these ions are poorly defined (due to difficulty in assigning ~ ( 0 3 ) ) . The values listed in Table IV and plotted in Figure 15 are therefore highly approximate. However, the rates in this case are generally in keeping with a trend of decreasing ko with increasing q / r . For example, in Mg2+ the average decay time is ( T ) 17 ns. Since this is 3 times the fluorescence lifetime of Cu102, this value is only an order of magnitude estimate. However, it is still clear that Mg2+ relaxes much more slowly than Na'. (Using the 4-AP probe, which has a -20-11s lifetime, we measure a value of ko 0.3 ns-' in MgC104, compared to 0.95 ns-' in NaC104.) From the point of view of an association model of the dynamics, the observed behavior with respect to ion identity is roughly as expected. The ions which are mast strongly bound to the probe and solvent exhibit the slowest dynamics. The large decrease in the magnitude of the time-dependent shift produced by "low" and "high" q / r ions is also understandable in terms of effects already discussed in section I11 (see also section VI). As q / r increases, the shift per ion (6u in eq 12) increases, which acts to increase u ( 0 ) - v ( - ) . However, the average number of ions (j) already solvating the ground-state solute also increases. If there is a maximum number of ions ( n ) that can be accommodated around a probe, then a t some point (j) will begin to saturate (Le., when ( j ) O = (j)' = n), and a t this point the spectral shift will decrease. That this "saturation" does indeed occur between Ba2+ and Mg2+ can be surmised from plots of absorption shift versus concentration like those shown in Figure 2a (and Figure 18). Fits (see section VI) to such data for Mg2+ in acetonitrile show that at 1 M concentration the absorption shift has already achieved 93% of its limiting value, meaning that maximal solvation is already achieved by 93% of the molecules in the ground state. Thus, even though 6u is

-

-

Chapman and Maroncelli

9110 The Journal of Physical Chemisfry, Vol. 95, No. 23, 1991 L O / ,

'

,

"

n

"

'

1 600.

-400.

n v)

-

W

c

v

A k V

I

1 .o

n

8

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2OO.A 0

'

0.0

0.0

330. 350. 370. 390. 410. Figure 16.

Y

430.

Wavelength ( n m ) Time-resolved spectral shift, v(0) - v(-), and average re-

sponse time, ( T ) , observed with Cu102 in 1 M NaClO,/acetonitrile as a function of excitation wavelength. These data have been suprimposed on the absorption spectrum for convenience. TABLE VI: Excitation Dependence of the Dynamics of Cul02 in 1 M NaCIOJAcetonitrile (23 "C) Lc:nm v(O)b v(m)b v(O) - v ( - ) b ( 7 ) ) ns 362 389 404 412 418

21.120 21.093 21.065 21.007 21.007

20.574 20.577 20.572 20.592 20.659

0.546 0.516 0.493 0.415 0.348

1.25 1.21 1.14 1.01 0.82

Excitation wavelength ( a 2 nm). Parameters characterizing the time-dependent frequency shift v(t). These values were obtained from single- or double-exponentialfits to the u ( t ) data. greatest for this ion, there is very little change between the equilibrium distribution of species present in the ground and excited states and therefore only a very small time-dependent shift is observed. A final aspect of these ionic systems, central to understanding their dynamics, is that the spectral kinetics are not independent of excitation frequency. Data for Cu102 in 1 M NaC104/ acetonitrile are summarized in Figure 16 and Table VI. In Figure 16 we have plotted the excitation dependence of the time-resolved shift, v ( 0 ) - v ( - ) , and average relaxation time, (7). Both quantities depend significantly on excitation frequency, varying by 40% and 65%, respectively, over the excitation range studied (Table VI). It is noteworthy that, even with the large variations in (7)with vex,, the v ( t ) decays are exponential except for a small early time component (the 1 M curve in Figure 7 is representative). The meaning of such an excitation dependence can be interpreted by using the potential diagrams shown in Figure 17. These diagrams represent the variation of the free energy with respect to "solvation coordinate" for the probe molecule in its So and SI electronic states. Panel a depicts the situation most often considered. In this rendition there is a single pair of free energy surfaces, identical for all solute molecules. Electronic excitation from the minimum of the So well deposits molecules away from the SIfree energy minimum. The subsequent solvent relaxation toward the S,minimum results in the time-dependent Stokes shift observed in experiment. The dependence of v(0) - v ( m ) on Y, is simply explained in this case when one recognizes that solute molecules occur distributed over a range of solvent configurations in the vicinity of the So minimum. Excitation with different frequencies partially selects from among this distribution thereby giving rise to slightly different starting points on the SI surface, i.e., different v(0) frequencies. One can also rationalize differences in relaxation times on the basis of Figure 17a, but only by invoking a substantial nonlinearity in the solvation response. That is, one must assume that there is a large change in relaxation dynamics depending on how far the system is perturbed from equilibrium.

"Solvation Coordinate" Figure 17. Two possible representations of the solvation free energy

diagrams for ionic systems. Scheme a is the single-well representation commonly used in pure polar fluids. Scheme b shows multiple subminima corresponding to the distinct j-solvates proposed here. Nonlinearity of this sort is not observed in pure polar solvents and therefore could be considered a unique feature of ionic solutions. However, an alternative, and we believe more helpful, representation of the dynamics in the ionic case is provided in Figure 17b. In this scheme we explicitly recognize the discrete nature of the ion-solute association implied by the steady-state results. Instead of a single free energy well, each PI,SWjcomplex (j ions in the first coordination sphere of the solute) is represented by such a well. The distinct j solvates are interconnected by barriers to solvent-ion exchange, as implied by the observed activation energies (Figure 1 I). "Nonlinearity" in the relaxation is interpreted in this more detailed picture as resulting from the fact that the different species j may have different interconversion rates k In the following section we will use this basic picture to model d e results displayed in Figure 16. VI. Kinetic Modeling We apply the idea of multiple association equilibria, embodied in eq 9 and in Figure 17b, to provide a semiquantitative account of the dynamics described in the last section. We will concentrate on one particular system, Cu102 in NaC104/acetonitrile solutions, for which we have a variety of data to explain. Within the context of a multiple association model, there are many more unknown parameters that can be determined from the experimental data. It is therefore not possible to determine physically well-defined kinetic parameters for this system. Our less ambitious aim will be to demonstrate that, with physically reasonable choices for parameters, the observed behavior can be readily reproduced. These calculations mainly serve to further reinforce the underlying picture of ion-probe association in these systems and provide some indication of the nature of the kinetics involved. In both the ground and the excited state we assume an equilibrium of the form PSJO

__ __ ki

k-i

Ki

PS,,I,

k2

...PS",I

k-2

K2

__

,"'

kn

PS,JIn (21)

k-n

...

K"

In this expression the kj and k , are the pseudo-first-order rate constants (kj [I], etc.) for formation and loss of thej-ion solvate (PSwjIj), and the K j are the equilibrium constants, K j kj/k,. As far as the experimental observables are concerned, complete specification of these equilibria requires a set of n ground-state equilibrium constants, {K:], and a set of n equilibrium and n kinetic constants for the excited state, {ICj', kj]. (Since only the excited-state kinetics are relevant here, we denote kj' by kj for convenience.) To connect such equilibria with spectral observables we again make the simplest possible assumptions concerning the spectroscopy. Namely, we assume that the spectra of the different

The Journal of Physical Chemistry, Vol. 95, No.23, 1991 9111

Solvation and Solvation Dynamics in Ionic Solutions

TABLE VII: Parametersa of Model 2 Fits to the CulO2/NaCIOJAcetonitrile Date j uf", IO' cm-' u i m , IO' cm-' K? Kj'

kj

k-j

1 1

0.080

AQb

h'

0.412 0.536 0.052 3.8 X IO-' 2.1 x 10-7

0.038 0.479 0.451 0.032 1.7 X IO-'

0.455 0.561 0.029

0.069 0.637 0.294

n = 4, a! = 0.075 0 I 2 3 4

26.8 I9 26.069 25.318 24.568 23.817

21.500 20.866 20.233 19.599 18.965

0 1 2

26.818 25.980 25.141

21.500 20.735 19.970

1.3 0.10 7.3 x lo-' 5.5 x IO-'

13.0 0.94 7.1 x 10-2 5.3 x 10-3

1 1

1.1

14 190

n = 2; a! = 0.050 1.1 5.7 x 10-2

9.2 0.46

1 1

0.11 2.2

utb"

'Best fits to the experimental data are shown for two choices of maximal ion number, n = 4 and n = 2. and u;" are the frequencies of the absorption and emission spectra of the j-ion solvate, PS,,I,. The K, and k, are the equilibrium and (excited state) rate constants as described in the text. The value of CY was chosen to obtain the best agreement with the experimental emission frequencies ( ~ ( 0 0 ) ) as a function of concentration (Figure 18). bEquilibrium fractions of species in the ground (0) and excited states ( I ) predicted to have j cations in their first solvation shell.

solvates are identical with the spectrum in the pure solvent (j = 0) except for an overall frequency shift. We further assume that this shift is linearly related to j (eq 10). These assumptions then allow us to use the steady-state absorption spectra to determine some aspects of the (KjOI parameter set. Similarly, the steady-state fluorescence spectra (actually the u ( m ) values since the dynamics is not rapid relative to sn) can be used to determine the excited-state equilibrium constants (Kji]. In order to reduce the number of independent parameters in the set {K:,Kjl,ki; j = 1, ..., n] to a manageable level, further assumptions are required. Toward this end, we have examined a variety of possible models for how the constants might be interrelated as a function of j . Two of these, summarized below, serve to illustrate the range of behavior possible: model 1 In, Kio, K I i , k,] Kj = ( (

n - j + 1) nj )Ki n - j + 1)

kj=((

)kl

model 2 In, Klo, KI', kl, a = ao = a') Kj = d l K I

(23a)

kj = k,

(23b)

The predictions of these kinetic models were explored by numerical integratio# of the differential rate equations d P o l /dt = -k1 [Pol + k-l [PI1 d[P,l/dt = +kj[P,-iI

- (k-j+

kj+i)[Pjl + k-u+~,[Pj+ll

d[P"l/dt = +k"[P,ll

(24)

- k-,[P,I

where [Pj] denotes the concentration of the species PS,,Pj, etc. Model 1 was chosen to represent a physical picture of n equivalent sites for ion occupation in the first solvation shell of the probe. The form of the equilibrium constants (eq 22a) results from assuming that the distribution among j solvates is

the energy in this manner, we have implicitly assumed the simple additive scheme described in section 111. The forward and reverse rates in this picture are interpreted in terms of a constant attempt frequency for addition or loss of an ion multiplied by a statistical weight factor depending on the number of sites occupied. Although physically appealing, model 1 is not able to reproduce all of the observed behavior. Its predictions depend only trivially on the maximum association number n. For example, the average frequencies calculated for equilibrium spectra (uabS,u ( m ) ) are all identical with those predicted by a two-state equilibrium:

This functional form (with K1 a [I]) does fit the observed concentration dependence (Le., the data in Figure 2) reasonably well. However, the dynamical predictions of the model are not in agreement with experiment. First, the predicted u ( t ) decays are strictly exponential functions for all parameter choices. Although in the NaC104/acetonitrile system the experimental decays are very nearly exponential, for other ions and solvents they are not. Thus, this model is not generally applicable. More importantly, it predicts no change in relaxation time with excitation frequency and can thus not explain the behavior displayed in Figure 16. Agreement with experiment can be improved by allowing the energy to vary quadratically rather than linearly with j (possibly mimicking ion-ion interactions). However, what is really required to fit the experimental results shown in Figure 16 are rates that vary strongly with j , and this is more naturally achieved with model 2. Model 2 is not based on any particular physical picture. However, of all of the models we have considered, it provides the best overall agreement to experiment. We will therefore make the comparison between this model and the experimental results in some detail. For all orders of the equilibrium in the range 2 I n I 6 the predictions of model 2 are roughly equivalent. For the present discussion we will use results based on the value n = 4 and consider the n dependence later. The equilibrium parameters a,KO, and K' and the spectral parameters byab and 6u, (see eq 13) are determined by fitting the concentration dependence of uab and u,, ( = u ( m ) ) . Since the spectral shape is assumed constant with j , calculation of the average frequency involves only calculating (j),thus making i t the obvious choice for measuring experimental data. Figure 18 shows the results of such fitting, and the parameters so derived are listed, along with the equilibrium in Table VII. As expected, fractions of various species equilibrium constants are larger in SIthan in So. Good fits to the data require that K, decrease substantially with increasing j . Within the representation of the present model one finds a value of a = 0.075, so that each successive K is 13 times smaller than its predecessor. This rapid decrease in K with j means that the j = 3 and j = 4 species are negligibly populated in either So or SI. The population distribution is one in which most solutes have between 0 and 1 ion neighbor in the ground state and between 1 and 2 in the excited state. The spectral dynamics is thus viewed

u,),

In this expressionfl is the fraction of probes in PS, I, aggregates and jAc is the relative energy of such a species. The parameter K I then has the energetic interpretation KI = By writing (62)A fourth-order RungtKutta integration scheme, modified from a routine given in Press, W. H.; Flannery, B. P.; Teukolsky, S.A.; Vetterling, W. T. Numericul Recipes: Cambridge University Press: Cambridge, U.K., 1986,was used for this purpose.

-

Chapman and Maroncelli

9112 The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 0.

E -500. n

8

W

\/

II v1

t

/

P a -1500.

23.0

0.0

0.5

1.0

“CQ

1.5

2.0

1 (M)

Figure 18. Absorption and emission shifts, u([NaCIO,])

2.5

- u(0 M), of

CulO2 in NaCIO,/acetonitrile solutions as a function of salt concentration. The absorption shifts (circles) are from steady-state spectra and the emission shifts (squares)are the v ( - ) values observed in time-resolved measurements. Points are experimental data and the solid curves are the predictions of model 2 ( n = 4; see text and parameters values provided in Table V I I ) . I

I

.-Inr t

c

W +

c -

18.

22.

26.

30.

Frequency (10’ c m - ’ ) Figure 19. Steady-state absorption and emission spectra of Cu102 in acetonitrileand in a 2 M NaClO,/acetonitrile solution. Solid curves are the experimental spectra and the dashed curves are predictions of model 2 ( n = 4; see text).

as resulting from addition of on average one more ion into the probe’s first solvation shell after electronic excitation. One of the features of the experimental data that might seem inconsistent with the presence of multiple species is the fact that the spectral shape and width usually vary little with ion concentration or time. However, the present model is able to reproduce this behavior moderately well. Figure 19, which compares steady-state absorption and emission spectra of Cu102 in NaC104/acetonitrile solutions at 0 and 2 M concentrations, illustrates this feature. Model calculations show that in a 2 M NaC104 solution the equilibrium distribution about a ground-state probe molecule is such that two consecutivej values are roughly equally populated. In absorption their frequencies differ by -750 cm-I, yet the spectrum calculated from summing these individual spectra (plus those of the other j species) has nearly the same width as the spectrum in the pure solvent. In experiment, the excess widths (relative to 0 M) at 1 and 2 M concentrations are both -60 cm-I. The calculated excess widths are 150 and 160 cm-’ at these concentrations, just slightly larger than observed. Thus, the model demonstrates that large changes in spectral shape or width need not necessarily result from a model based on the presence of

25.0

27.0

29.0

vex, ( i o 3 c m - ’ ) Figure 20. Excitation dependence of the (a) time-resolved shifts and average response times (b) observed with Cu102 in 1 M NaCIO,/ acetonitrile. Points are experimental data and the solid curves are the predictions of model 2 (n = 4; see text and parameters values provided in Table V11). The response times have been normalized to unity for excitation at the peak of the absorption spectrum.

multiple species. In emission, the width changes in the experimental spectra are likewise modest compared to the 630-cm-’ shift between successivej solvates. In fact, in the NaClO,/acetonitrile system the widths actually decrease slightly, by 70 and 110 cm-’ in 1 and 2 M solutions, re~pectively.6~The emission spectra calculated for these concentrations broaden by 210 and 180 cm-’. The comparison to experiment is thus not as good in the case of emission (Figure 19). However, fault with the model probably lies in the assumption of constant spectral shape among the different j species, rather than with the central idea of an association equilibrium itself. The fact that the experimental spectra narrow slightly with salt concentration, and especially the large changes induced by Mg2+ ions (Table IV), indicate some narrowing of the fluorescence with j . The dynamical predictions of model 2 are essentially determined once the equilibrium parameters KI0,KIi,and a have been fixed. That is, beyond the assumed form of kj (eq 23b), the kinetics are completely specified by scaling kl to match one experimental time. In general, the calculated time-dependent shifts, v(t) are not simple exponential functions of time within this model. However, for the range of parameters which provide reasonable fits to the equilibrium data, the v(t) functions calculated are very well approximated by single-exponential functions. This feature is in accord with the experimental observation of nearly exponential relaxation in the NaC104/acetonitrile system. We note that, as illustrated by the parameters in Table VII, observation of nearly exponential v ( t ) curves does not necessarily imply simple kinetics in these systems. The overall dynamics actually results from the combined action of substantially different rates, the existence of which is revealed by the excitation dependence of (7). The calculated dependence of (7)and v(0) - v ( m ) on excitation frequency, are displayed in Figure 20. Both aspects of the excitation dependence are reproduced by the model to within experimental uncertainties. As already mentioned, this agreement results from essentially no further adjustment of parameters beyond the fit to equilibrium data. The key kinetic input of model 2 is the assumption that kJ = k l , and it is k l which sets the time scale of the overall kinetics. That is, given parameters fit to the experimental data, for all reasonable vcxcthe rate of spectral shift observed turns out to be within a factor of 2 of k l . The assumption of equal forward rates implies that the reverse rates increase geometrically withj as k , = k,/KJ a &I, and it is actually this (63) These valucs are small enough that they depend on how one chooses to measure the widths. The values given here are the fwhm measured directly from the experimental spectra. They differ slightly from those listed in Tables I, 111, and IV, which were obtained from log-normal tits to the spectra.

Solvation and Solvation Dynamics in Ionic Solutions n

--

Y5

\

8oo-.

2.0

/,/q

j

'.'kc-,----"--,

,

,

(b)]

0.0 0.0

0.5

1.0

[NaCIO,

1.5

2.0

2.5

1 (MI

Figure 21. Concentration dependence of the (a) time-resolved shifts and (b) rates observed with Cu102 in NaClO,/acetonitrile solutions. Points are experimental data and the solid curves are the predictions of model 2 ( n = 4; see text and parameters values provided in Table VII). For the experimental rates, the viscosity-scaled rates kq have been used and both the experimental and calculated rates have been scaled to unity at [NaCIOd] = 1 M.

increase in k , with j that produces the observed vex,dependence of the average rate. (It might seem a more natural choice to let the forward rates vary with j rather than the reverse rates. However, since the equilibrium data requires Kj to decrease with increasing j , the fact that the solvation rate increases with uexc and thus j can only be satisfied by k , increasing.) We note that the quality of the fits shown in Figure 20 is fairly sensitive to the value of a. In the present case the value a = 0.075 was chosen to give the best fit to the u,, ( u ( - ) ) data. Only values within the range 0.05 I a I0.10 exhibit large changes in ( 7 ) with u,,, of the sort observed in experiment. Thus, within the confines of model 2, a 10-20-fold increase in k-j with j is needed in order to reproduce the experimental behavior. Model 1, and similar models in which both kj and k , vary in comparable ways with j , do not provide sufficient differentiation between rates of the individual steps to fit the steep ( T ) dependence on u,, observed in experiment. Figure 21 shows that model 2 also reproduces the observed dependence of u ( 0 ) - u ( - ) and ( T ) on concentration. Changes in ion concentration, [I], are assumed to influence the model parameters through a scaling of the pseudo-first-order rate constant kl (and thus K l ) , kl a [I]. The time-dependent shifts, u(0) - u ( = ) , predicted are systematically larger than those observed (due to slightly high values of v(O)), but are still within the accuracy of the relative frequency measurements. An important feature illustrated in Figure 21 b is that the overall rates are predicted to be a linear function of [I], except for very low concentrations. As described previously, a linear relationship is also found experimentally, once viscosity variations have been taken into account. That such a simple dependence should result from a multiple association model is not obvious since not only are the rates kj changing with concentration, but the ground-state distribution of species is also changing with concentration due to changes in the K,. For the conditions considered here, however, the main influence is through the rates, and thus the linear dependence. A final aspect of model 2 is that nearly equivalent results can be generated with a variety of orders n. Although a two-state model ( n = I ) is unacceptable, a three-state (n = 2) equilibrium is able to explain the experimental data almost as well as the n = 4 results described above. The parameters yielding the best fit to an N = 2 model are listed in Table VII. We note that the kinetics of a three-state equilibrium can be solved for analytically, and here one finds that the u(t) decays are strictly biexponential. However, within the relevant range of parameters, one of the time constants dominates such that the u(t) curves are again virtually single exponential. Comparison of the n = 2 and n = 4 parameters

The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9113 shows that the equilibrium constants and equilibrium fractions are similar in the two cases. For example, the average solvation numbers, (j), are found to be 0.64 and 0.62 in So and 1.22 and 1.48 in SI for the n = 4 and n = 2 models, respectively. Since the j = 3 and j = 4 species of the n = 4 model are very little populated at the concentrations considered, this agreement is not surprising. The physical picture provided does not depend significantly on the presence of more than two sites for ion solvation. We conclude this section by considering what the above modeling implies about the nature of the ionic equilibria in these solutions. Because the experimental data are far from sufficient to determine the detailed features of the actual equilibrium, the parameters reproduced in Table VI1 provide merely one plausible description of what occurs in the real system. Further, the assumption of frequences uj that depend linearly on solvation number is an important and unverified simplification of the model. Relaxing this assumption would significantly alter the nature of the distributions derived from the steady-state spectra. Nevertheless, some general conclusions about these equilibria can still be drawn from the calculations. One important observation is that, in order to model the large changes in solvation time with excitation frequency displayed in Figure 16, the equilibrium and rate constants must change substantially withj. Model 1, in which the kj vary by only statistical factors, and similar models that assume only small variations in kj, can provide adequate fits to the equilibrium data, but yield too small an excitation dependence to be acceptable. Such models, especially model 1, are not very different from a continuous solvation picture in the sense that the properties of the different solvates vary only weakly withj. What is required by the kinetic data is a model such as model 2 in which the ki vary strongly with j . Thus, not only do the experimental data imply a discrete association model rather than a continuous solvation process, but the steps in the equilibrium must also be distinct enough so that this discreteness is clearly evident. On the basis of model 2 (and linear vi) we estimate that the initial (i = 1) probe-ion association constant is roughly 10-fold larger than the next largest value. Further, the equilibration rates for steps after the first are at least 10-fold faster than that of the initial step. Since model 2 provides a reasonable fit to all experimental data even for a three-state case (n = 2), one physical interpretation of the model is the following. On a solute such as Cui02 there exists a single highly preferred site for ion association. The energetics of the solvent and ion binding to this site render exchange here relatively slow, and these slow kinetics are essentially what is observed as ko in experiment. Since neither the kinetics nor the equilibrium spectroscopy is consistent with only a single association step, one must also invoke further association to explain the kinetic heterogeneity and make the process appear more continuous spectrally. However, these latter associations, mimicked by t h e j L 2 species in model 2, are considerably faster and energetically less important; they only mask the essential two-state character of the solvation process. This simple viewpoint is attractive in that it yields the convenient interpretation of ko as a measure of the rate kl for the first ion-solvent association step. Unfortunately, it is an oversimplification. The steady-state and time-resolved data indicate that a substantial part of the spectral shift must be due to processes other than the first association step, and thus the real situation is likely to involve important contributions from several association steps. Our best guess for a physical picture of the solvation of a molecule like Cu102 is that it entails something intermediate between a distorted single-ion association and a multi-ion association of the sort offered by model 2 (n = 4). VII. Summary and Conclusions We have measured steady-state and time-resolved emission spectra of several solvatochromic probes in a wide range of salt solutions. These measurements lead to the following generalizations concerning solvation of highly polar aromatic molecules in ionic solution: 1. Although there are quantitative differences as a function of the solute, salt, and solvent considered, ions affect the spectra

9114 The Journal of Physical Chemistry, Vol. 95, No. 23, 1991

of solvatochromic probes in a similar manner in all systems examined. As a function of salt concentration or time, the primary spectroscopic effect of added salt is to induce a frequency shift in the probe spectrum, without substantially changing its shape or width. These frequency shifts appear to be continuous functions of concentration or time and thus resemble analogous shifts observed with the same probes in pure polar solvents. 2. In both static and dynamic measurements, the spectral shifts induced by the ionic component of the solution appear to be approximately separable from shifts due to the supporting polar solvent. Thus, by monitoring such shifts one can measure the statics and dynamics of probe-ion interactions "independently" of the polar solvent's dynamics. 3. Steady-state spectral shifts vary in a systematic way with respect to variations of the salt and solvent considered. For a given concentration of a particular salt, the stronger the solvent-probe interactions, as measured by the probe's absorption frequency in the pure solvent, the smaller the ion-induced shift. In a given solvent, the shifts induced by various salts are primarily a function of the identity of the cation, and these shifts are roughly proportional to the charge-to-size ratio of the cation. 4. The magnitude of the observed spectral shifts are a t least 10 times larger than predicted by Debye-Huckel type ion-atmosphere theories. The magnitudes of the shifts and especially their dependence on ion identity indicate that a more appropriate picture of ionic solvation involves some sort of ion-probe association, rather than a nonspecific interaction of the probe with a diffuse ion atmosphere. 5. Time-resolved fluorescence measurements show that the ion dynamics are slow, typically occurring on a time scale of 1 ns. Such slow dynamics further supports the idea of ion-probe association. Spectral shift times measured in these ionic solutions are roughly an order of magnitude longer than theoretical and experimental estimates of times for diffusion-controlled processes. The temperature dependence of the dynamics also indicates activation energies substantially in excess of the solvent viscosity activation energy. Thus, a Debye-Falkenhagen type description of diffusive relaxation of an ionic atmosphere is not appropriate in these systems. In addition, the spectral dynamics occur much more slowly than rotation of the probe molecule, implying that the interactions responsible must be relatively local. For these reasons we postulate that ionic solvation dynamics in ionic solutions is best viewed as requiring an activated exchange between ions and solvent molecules in the first solvation shell of the probe. 6 . To describe the time evolution of the emission frequencies we employ the same response function, C(t),used to characterize pure polar solvent dynamics. The types of time dependence observed range from being very nearly exponential to highly nonexponential, depending on the salt and solvent studied. Average relaxation rates, k, determined from these C(t) functions appear to scale in a simple manner with solution viscosity (7)and salt concentration ([I]) as k = ko[I]/q for [I] < 1 M. 7. The reduced rates, ko, show systematic trends as a function of the solvent and ions considered. ko appears to increase with increasing strength of probesolvent interactions and it decreases as the charge-to-radius ratio of the cation increases. 8. The kinetics in ionic solutions are not homogeneous; relaxation times depend markedly on the excitation frequency employed. This behavior can be understood in terms of an association equilibrium between cations and the probe solute. Model calculations support the idea that incorporation of a single ion into the first solvation shell of the solute accounts for a large part of the spectral shift observed. We also speculate that the rate measured experimentally may be essentially the rate of achieving equilibrium in this first association step. However, the spectral shifts do not involve merely a two-state equilibrium between the probe and a single cation. The experimental data cannot be accounted for without there also being substantial further solvation, which we view as incorporation of additional ions into the first solvation shell of the solute. It is useful to view these findings in relation to past research on the dynamical aspects of ionic solvation. First we consider the

Chapman and Maroncelli recent time-resolved Stokes shift measurements made by Huppert and co-worker~.~'*~* These authors studied several probe/ion/ solvent combinations quite similar to ones we have studied here, but reached rather different conclusions concerning the nature of the solvation process being observed. Huppert and co-workers interpreted the slow dynamics in terms of slow translational diffusion of ion pairs, which conductivity measurements showed to be the main ionic species present in the nonaqueous solvents they studied. Having the benefit of data from a wider range of ions and solvents, we conclude that, although ion pairing may dominate the conductivity of many of the ionic solutions studied, it does not seem to be immediately relevant to the solvation dynamics of the probe. In our description, the important "pairing" is between cations and the highly polar probe solutes. The nanosecond dynamics observed reflects activated exchange between ions and solvent molecules in the first solvation shell of the probe. Such exchange dynamics have not been previously measured; however, related processes have been observed to occur in this time domain using ultrasonic and NMR technique^.^"^ For example, ultrasound measurements on solutions of NaCIOdMand LiCIOt' in tetrahydrofuran show relaxation occurring on a I-ns time scale, similar to the Stokes shift times we observe in these solutions. In the former measurements the source of the sound attenuation has been ascribed to ion solvation/desolvation dynamics. N M R line-width studies have been used to measure residence times of various solvents in the first solvation shells of many ion^.^'^^^ Although only water exchange times have been measured for the particular ions we have studied, trends with other ions and solvents suggest that exchange times are likely to be in the range that we observe for the probe's solvation dynamics. Thus our interpretation of the dynamics is certainly reasonable in light of what is known of these related processes. We note that time-resolved Stokes shift measurements provide a unique method for exploring labile exchange processes of the sort envisioned here and with much higher time resolution than available from other techniques. Unfortunately, as in ultrasonic measurements, the spectral shifts we monitor are fairly nonspecific quantities. The usefulness of the method therefore rests on obtaining more definitive descriptions of the equilibria actually being observed. Further work in systems where isolated ion-solute complexes can be observed, as well as computational studies of the p r o k i o n interactions involved should prove valuable in this regard. However, even without a complete microscopic description of the solvation process, such measurements have important implications for theories of how ionic solutions influence chemical reactions. For highly polar solutes and in most solvents (water being the obvious possible exception) it is not useful to think of the energetics and dynamics of solvation in terms of Debye-Huckel-like ion atmosphere models. The interactions involved are much stronger and the dynamics much slower than predicted by such models. In many cases, a better starting point for understanding the static and dynamic coupling of reactions to an ionic environment will rather involve recognition of the specific associations of the sort proposed here.

Acknowledgment. We thank Alan Benesi and Alan Freyer for their help in recording the N M R spectra used to determine the water content of our samples, and Richard Moog for a critical reading of this manuscript. We also gratefully acknowledge the Division of Chemical Sciences, Office of Energy Research, U S . Department of Energy, for financial support of this research. Registry No. Cu102, 41267-76-9; Cu153, 53518-18-6; 4-AP, 367685-5; NaCIO,, 7601-89-0; Ba(C104)2. 13465-95-7; Bu,NClO,, 192370-2; Mg(C104)2,10034-8 1-8; LiCI, 7447-41 -8; NaSCN, 540-72-7; LiCIO,, 7791-03-9; Sr(C10,)2, I 3450-97-0; Ca(C104)2, 13477-36-6; Prodan, 70504-01 -7; dimethyl sulfoxide, 67-68-5; methanol, 67-56-1; 1 propanol, 67-64- 1; formamide, 75- 12-7; tetrahydrofuran, 109-99-9; acetonitrile, 75-05-8; ethanol, 64-17-5.

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(64) See the reviews: Petrucci, S.In Ionic lnterucrionr;Petrucci, S.,Ed.; Academic: New York, 1971; Vol 2, p 39. Langford, C. H. fbid; p 1 . (65) Marcus,J . Ion Soloution; Wiley: New York, 1985; Chapter 4. (66) Farber, H.; Petrucci, S. J . Phys. Chem. 1976,80, 327. (67) Jagodzinski, P.; Petrucci, S.J . Phys. Chem. 1974. 78, 917.