J . Phys. Chem. 1991, 95, 10115-10123 hosts of the inclusion compounds, for instance cyclodextrin, are organic and contain protons. For such host compounds with relatively small holes or channels, deuterium heteronuclear dipolar interactions with protons can become significant.
lolls
Acknowledgment. I thank Prof. M. Bloom for helpful discussions and suggestions. I thank Dr. E. Sternin for communicating his preliminary proton decoupling experiments to me, and NSERC/NATO for a postdoctoral fellowship.
Dipolar Solvation as a Signature of Dielectric Responses in Supercooled Liquids Ranko Richert* and Achim Wagener Fachbereich Physikalische Chemie und Zentrum f u r Materialwissenschafen, Philipps Vniuersitat. 3550 Marburg, Germany (Receiued: May 31, 1991)
Time-resolved Stokes shifts of phosphorescence bands are investigated by monitoring the solvation dynamics of electronically excited probe molecules embedded at low concentrations in organic supercooled liquids of varying polarities. The long-lived T,states of the solutes give access to dipolar equilibration of the glassy medium near TG on a millisecond to second time scale. Coincidence of solvation and glass transition temperatures over a large TG range relates the spectral shift to the a process of the glass with only minor sensitivities to the specific probe molecule. Emission energy data for the Franck-Condon and equilibrated solvent configurationsallow determination of the change in dipole moment upon T, -So excitation in agreement with theoretical predictions. Relative polarities of the glasses as quantified by the positive solvatochromism of quinoxaline are highly correlated to the corresponding values for the liquid state at 20 OC. The observed solvation dynamics map the dielectric response to a motion of charge and can be rationalized in terms of dielectric dispersion, importance of microscopic solvent behavior, and an excess cooperativity of longitudinal relaxations.
I. Introduction The absorption and emission energies of molecules in condensed media are subject to variations relative to the energies of the counterpart isolated state. Most obvious features are the Stokes shift and line broadening observed upon going from the gas phase of a molecule to its dissolved state in a liquid solvent and the effect of solvatochromism in the case of polar solvents.’ Upon excitation a molecule can undergo significant changes in its permanent dipole moment and polarizability? thereby forcing surrounding solvent dipoles to readjust to establish equilibrium conditions again. This solvation and concomitant impact on energy levels of a chromophore are due to the polarization of the surrounding solvent which results either from electronic contributions only (nonpolar solvents) or, additionally, from the alignment of permanent solvent dipoles (polar solvents). The pure electronic part of the solvent polarization is established on the time scale of an electronic transition, e.g., SI Soabsorption. In contrast, the contribution of solvent dipoles involves molecular reorientation, leaving it a priori open whether the static polarization is completed within the time between absorption and emission processes. If so, as is true for most low-viscosity liquids at ambient temperatures, the emission occurs from the excited state which is lower in energy compared to the initial Franck-Condon excited state. In situations where the lifetime of the emitting state and the time needed for rotational alignment of solvent dipoles become comparable, the depopulation of the excited state must be accompanied by a gradual decrease in emission energy as experimentally verified by Ware’ employing picosecond time resolution. Subsequently, the emission energy (in general the mean energy of the emission band) has been used for monitoring the dynamics of solvation. It has been shown that the mean energy directly maps the solvation coordinate if the conditions of linear responses are s a t i ~ f i e d . ~ The typical experiment for resolving solvation dynamics involves a fluorescent solute dissolved at low concentration in a liquid
-
( I ) Reichardt, C. Solvents and Solvent Effects in Organic Chemistry; VCH: Weinheim, 1988, and references cited therein. (2) Liptay, W. In Excited Stares; Lim, E. C.. Ed.;Academic Press: New York, 1974; Vol. I . (3) Ware, W. R.; Chow, P.; Lee, S. K . Chem. Phys. Lett. 1968, 2, 356. (4) Maroncelli. M.; Maclnnis, J.; Fleming, G. R. Science 1989, 243, 1674.
solvent of low viscosity. The emission band is then scanned by recording the temporal decays of the fluorescence with picosecond resolution at fixed spectral positions. The temperatures of interest are confined to a range in which the time scale of solvation dynamics falls approximately within the span between temporal resolution of the detector and fluorescence lifetime. For focusing on the temporal progress of solvation it is convenient to normalize the energetic decay u ( t ) to the limiting values u(0) and u ( m ) , leading to the Stokes shift correlation function C(t) defined by Theoretical approaches to predicting time dependences for C(t) are based on the dielectric properties of the solvent under study. For the simple cases of Debye systems, manifested by an exponential response of polarization or by Lorentzian loss curves no wider than 1.14 decades, the dielectric is characterized by the static and optical constants cs and e, (.=nZ),respectively, and the dielectric relaxation time rD which refers to the results of the common impedance analysis technique. These typical dielectric data are obtained under the conditions of an external electric field which remains unaffected by the progress of polarization. Solvation is also a process of polarization, albeit one that is restricted to the vicinity of a probe molecule by virtue of a sudden change of the local field induced by the dipole moment transition pE pG. In the latter case the charge distribution rather than the field is constant, which allows the polarization to lower the effective field by screening. The response of a continuum dielectric under these conditions proceeds according to the relaxation time rLS-’ with TL = ( L / % ) T D (TL 5 TD) (2) For the first solvent shells screening is ineffective so that solvent dipoles in the vicinity of the solute are expected to relax within T D . This is the basis of Onsager’s “inverted snowball picture”,* stating that solvation is governed by time scales ranging from sL (short times, continuum) to T~ (long times, first shells). This
(5) Frohlich, H. Theory of Dielectrics; Clarendon: Oxford, U.K., 1958. (6) Kivelson, D.;Friedman, H. J . Phys. Chem. 1989, 93, 7026. (7) Friedman, H . J . Chern. SOC.,Faraday Trans. 2 1983, 79, 1465. (8) Onsager, L. Can. J . Chem. 1977, 55, I8 19.
0022-3654/91/2095-l0115%02.50/0 0 1991 American Chemical Society
10116 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
prediction has been verified on a more sophisticated and general level by means of the mean spherical approach (MSA) treatment which accounts explicitly for the microscopic structure of the solvent.+12 The numerous results concerning solvation dynamics are subject to various r e v i e w ~ ~ Jand ~ - ' ~will not be resumed in detail at this point. The main conclusion we draw on in the following is that solvation dynamics display dispersive, Le., nonexponential, relaxation patterns even for Debye solvents. If C(t) is analyzed according to the stretched exponential or Kohlrausch-Williams-Watts (KWW) decay type exp[-(t/~)"],"~~the typical dispersion parameter a settles in the range 0.6-0.8 for Debye liquids of low viscosity.22 In cases of protic solvents, e.g., alcohols, solvation dynamics are more complex due to hydrogen bonding and multiple dispersion regimes (non-Debye solvents).23 A certain class of liquids does not tend strongly to crystallize upon cooling below their melting point.24 These glass formers exhibit no abrupt changes of their properties like viscosity, volume, etc. down to temperature where the viscosity of a solid (==lOI3 P) is reached.25 This point crudely coincides with the glass transition temperature TG at which the supercooled liquid is no longer able to attain its thermodynamic equilibrium within typical experimental observation times of several minutes.% Relaxational processes above TGare notorious to follow a Vogel-Fulcher (VF)27 type temperature dependence with pronounced apparent activation energies until, ultimately, the dominant motional process ( a processes) becomes frozen just below TG. The presence of dielectric relaxation in the supercooled state of a liquid indicates that the phenomenon of solvation must be active as well, albeit not accessible using luminescent probes with lifetimes of the order of 10 ns. The success of employing long-lived triplet states for tracing solvation dynamics in the millisecond to second range near TGhas been demonstrated in recent publication^^^-^^ focusing on quinoxaline dissolved as probe molecule in 2-methyltetrahydrofuran (MTHF). The scope of the present paper is to systematically investigate solvation and its dynamics for a variety of probe molecules and supercooled liquids in the vicinity of their glass transition temperatures TG.We are able to show that solvation is a generally occurring feature in supercooled liquids without being restricted to polar solvents or probe molecules subject to large values of pE - p G . The dynamics of solvation in terms of the Stokes shift correlation function C(f) turns out to be virtually unaffected by the specific probe molecule under study, indicating that the re(9)Calef, D. F.;Wolynes, P. G. J . Chem. Phys. 1983, 78,4145. (IO) Wolynes, P. G. J . Chem. Phys. 1987, 86,5133. ( 1 1) Rips, 1.; Klafter, J.; Jortner, J. J. Chem. Phys. 1988, 88, 3246. (12) Rips, 1.; Klafter, J.; Jortner, J. J . Chem. Ph)s. 1988, 89,4288. (13) Kosower, E. M.; Huppert, D. Annu. Reo. Phys. Chem. 1986,37, 127. (14)(a) Maroncelli, M.; Castner, E. W.; Webb, S.P.; Fleming, G. R. In Ultrafast Phenomena V; Siegman, A. E., Fleming, G. R., Eds.; Springer: Berlin, 1986. (b) Maroncelli, M. J . Mol. Liq, 1991, submitted for publication. (15)Simon, J. D. Arc. Chem. Res. 1988, 21, 128. (16)Barbara, P. F. Arc. Chem. Res. 1988, 21, 195. (I 7) Huppert, D. In Dynamical Processes in Condensed Molecular Systems; Klafter, J., Jortner, J., Blumen, A,, Eds.; World Scientific: Singapore, 1989. (18) Barbara, P. F.; Jarzeba, W. In Advances in Photochemistry; Volman, D. H., Hammond, G. S., Gollnick, K., Eds.; Wiley: New York, 1990:Vol. 15.
(19)Kohlrausch, R. Pogg. Ann. Phys. 1847, 12,393. (20)Williams, G.; Watts, D. C. Trans. Faraday Soc. 1970, 66,EO. (21)Williams, G . ;Watts, D. C.: Dev, S. B.; North, A. M. Trans. Faraday Soc. 1971, 67, 1323. (22)(a) Maroncelli, M.; Fleming, G.R. J . Chem. Phys. 1987,86,6221. (b) Maroncelli, M.; Fleming, G. R. J. Chem. Phys. 1990, 92,3251. (23)Bagchi, B.; Oxtoby, D. W.; Fleming, G. R. Chem. Phys. 1984, 86, 257. (24)Elliot, S.R. Physics of Amorphous Solids: Longman: London, 1983. (25)Wong, J.; Angel, C. A. Glass Structure by Spectroscopy; Dekker: New York, 1976. (26)Jackle. J. Rep. Prog. Phys. 1986, 49, 171. (27)Fulcher, G.S. J . Am. Chem. Soc. 1925,8, 339. (28)Richert, R. Chem. Phys. Lett. 1990, 171. 222. (29)Richert, R. In Dynamical Processes in Condensed Molecular Systems; Blumen, A., Klafter. J., Haarer, D., Eds.; World Scientific: Singapore, 1990. (30)Wagener, A.; Richert, R. Chem. Phys. Lett. 1991, 176, 329.
Richert and Wagener TABLE I: Solvents Together with Their Abbreviations and tbe Parameters Polarity ETN(from Ref l), Solvation Temperature Ts (for tbe Solute QX), and Class Transition Temperature Tc abbrev solvent EP TqIK TrIK 3MP 4MH TEA MTHF 3BP NMEC NBOH
PDOL MEOH
3-methylpentane 4-methylheptane triethylamine 2-methyltetrahydrofuran 3-bromopentane N-methyl-t-caprolactam I-butanol 1,3-propanediol methanol/ethanol (4:l)
0.006 zo.01 0.043 0.179 0.213 0.336 0.602 0.747 =0.760
7756 io4 110 94 115 176 119 158 108
10157
105" 905* 1104 11556 16OS9 =11060
laxation process is a linear response controlled by solvent properties. The normalized relaxation patterns deviate strongly from exponentiality as expressed by aKWW i= 0.4, in accord with the MSA prediction based on the Cole-Davidson type dielectric behavior of glassy systems. A linear relation between the solvent polarities near TG and at 20 OC is revealed by the positive solvatochromism of quinoxaline. Regardless of the inability to measure the TI So absorption energies, the spectroscopic data allow for delineating the change pE - pG in dipole moment for the T, So transitions of the probe molecules in perfect agreement with theoretical calculations for pE - pG. The recent discussion on whether the observed Stokes shifts are actually due to solvation or to an inhomogeneous distribution of emission lifetime^^',^^ will be excluded in the present paper. Due to the large shifts of the fluorescence spectra of dyes in polar liquids, a minor contribution to apparent spectral shift arises from the direct ( u - ~ ) - I energy dependence of radiative lifetimes33 as confirmed quantitatively by Maroncelli et a1.34,35 In accord with the comparatively small Stokes shifts of triplet probes in supercooled liquids, the above (u-~)-I effect as well as inhomogeneities does not contribute to the present findings as previously demon~trated.~~
-
-
11. Experimental Conditions The solvents compiled in Table I were distilled and dried prior to use. Naphthalene (NA),quinoline (QI), and quinoxaline (QX) served as probe molecules as commercially available. The variety
naphthalene (NA): X = X'= CH quinoline (01):X = N: X' = CH quinoxaline (QX): X = X' = N
of usable solvents is restricted through the conditions of glassforming materials at practical cooling rates of =IO K/min and transparency in the range 500-300 nm. The solute/solvent concentration was 2 X mol/mol in every case, assuring that coupling among probe molecules is negligible and spectral shifts due to energy migration are sufficiently suppressed. Excitation of the chromophores is accomplished with the 308-nm line of a XeCI-filled excimer laser (Lambda Physik, EMG 500) operated at a repetition period of at least 3 7 p H , f P H being the phosphorescence lifetime o f the probe molecule. I n all cases, NA, QI, and QX, population of the TI electronic state proceeds via absorption within the singlet manifold, vibrational relaxation, and intersystem crossing. The TI population process is spontaneous with respect to the time scales of detection and assures an energetically random occupation within the inhomogeneous density of states. Energetic selectivity would require a correlation between SI and TI levels which is absent in these s y ~ t e m s . ~ ~ , ~ ~ (31) Agmon, N.; Hopfield, J. J. J. Chem. Phys. 1983, 78, 6947. (32)Agmon, N.J . Phys. Chem. 1990, 94,2959. (33)Birks, J. B. Photophysics of Aromatic Molecules; Wiley: London,
I.9711 __ .
(34)Maroncelli, M.; Fee, R. S.; Chapman, C. F.; Fleming, G. R. J . Phys. Chem. 1991, 95,1012. (35) Fee, R. S.; Milsom. J. A.; Maroncelli, M. J . Phys. Chem. 1991, 95, 5 170.
Dipolar Solvation in Supercooled Liquids
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 10117
170 -0lOl
20750
21250 Energy/cm-'
21750
Figure I. (Upper) Temporal evolution of the (C-0) band shown by
tracing selected levels within the lower IO-ms spectrum (identical energy scales). Lines are obtained connecting the spectral positions of coinciding heights for 30 normalized spectra recorded with an incremental delay of n X 20 ms and 20 ms time window. (Lower) Normalized phosphorescence spectrum of QX/MTHF recorded 10 ms after excitation at 94.4 K including every second intensity level of the upper contour plot. Samples are held in a vacuum-sealed cuvette within a liquid N, cryostat of 0.1 K thermal stability and approximately f0.5 K temperature reading accuracy. The detector receives the luminescence via an optical fiber coupled to a polychromator (PTI, Model 01-002) with holographic 2400 L/mm grating whose output is recorded with an optical mutichannel analyzer (EG&G, O.M.A. I11 with the 1024 channel gatable camera 1421-R-1024-G). For the present purposes no correction regarding the spectral sensitivity was necessary as data from the outermost region of the MCP/ diode array has been disregarded. Gating the camera with a pulser (EG&G, Model 1303/1304)determined the temporal resolution of the spectra for times 1 2 0 ms relative to the laser pulse. Sequential readouts of 116.6ms/scan between laser pulses allowed for resolving the range 20 ms-2 s. Averaging over 100-2000 excitations was necessary to achieve a satisfactory S / N ratio. By comparing emission spectra over the entire temperature range before and after excessive laser irradiation (doses higher than otherwise used), it turns out that sample degradation reduces the intensity to 10% of its initial value, albeit without affecting the spectral profile within their reproducibility. Possible explanations for this presently irrelevant effect are photochemical degradation of solutes and loss of optical clarity within the sample, likely to occur at temperatures above TG due to partial crystallization.
Ill. Results All of the following experimental results are based on a large set of spectra, each recorded under a different condition. The necessary parametrization of the data is facilitated by means of the following reasonings. The vibronic progression of the highenergy (0-0) phosphorescence peak remains unaltered within the present time and temperature scales and will not be referred to in the following. Mean energies u are obtained via integration of the peak within a spectral region of negligible contributions from the adjacent peak. The profiles are of Gaussian shape as determined by least-squares analysis of the high-energy wing. Section 111.1 covers data to be presented on the absolute energy scale. Data related to the dynamics of solvation will be handled in terms of the spectral correlation function C(t),i.e., normalized to the limiting energies, as done in section 111.2. 1. Spectroscopic Data. A typical TI So (0-0) emission spectrum of QX in MTHF and its temporal evolution are shown
-
(36) Suter, G. W.; Wild, U. P. Chem. fhys. 1988. 120, 131. (37) Suter, G. W.; Wild, U. P.; Holzwarth, A. R.Chem. fhys. 1986,102, 205.
100
90 TIK
110
-
Figure 2. Thermally induced lowering of the mean TI S, ( 0 4 ) energy ( u ) for QX/MTHF in the vicinity of To of MTHF (upper). The data are based on spectra recorded in the time window 1-2 ms after excitation. The lower part indicates the simultaneous broadening of the emission profile in terms of u obtained by Gaussian profile analysis. Thermal broadening is superimposed by a peak at temperatures where solvation is active. Lines serve as guides only. The figure also clarifies the characteristic solvation parameters u(O), u(-), Au, u(O), a ( = ) , ut,, and Ts used in the text.
*-*-
37
*15t
5 215,
I
E,N (20°C)
Figure 3. Variations of the mean emission energies o(0) and u ( m ) with solvent polarity ETN(at 20 "C)for the solutes NA, QI, and QX as indicated. Lines are least-squaresfits to the data points; their slopes are stated in units of cm-I. Only QX shows a significant positive solvatochromism.
in Figure 1. The basic feature of the contour plot in Figure 1 (upper panel) which disregards the decay in intensity is qualitatively representative for the spectral behavior of all samples. It is evident that the emission band undergoes a gradual Stokes shift on the time scale while, apart from a slight broadening, the profile remains unchanged as it shifts to lower energies. The temperature range where such spectral shifts are active within experimental resolution of -500 ~ s - 1 s extends over a few Kelvin only. At temperatures outside this range the mean emission energies are independent of time and indicate no systematic temperature dependence within IO K (see Figure 2). The two limiting mean emission energies will be denoted u(0) and u ( m ) , anticipating that the higher energy u(0) is temperature invariant if observed for t = 0 and that the lower value u ( m ) is approached for all temperatures in the long time limit. These values will be used to normalize u ( t ) according to eq 1. In every case reported here we observe the temporal progress of u ( t ) decaying in the range u(0) to u ( m ) at intermediate temperatures, Le., in the transition region of u( T ) in Figure 2. Characteristic temperature dependences of the mean emission energy u and the spectral width u for a fixed
-
Richert and Wagener
10118 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 TiK
NA/4MH NA/MTHF NA/3BP NA/NBOH NA/MEOH
21203 21 251 21 181 21 210 21210
90 110 98 84 96
21 21 21 21 21
145 IO9 167 I69
75 115 103 92 94
53 106 72 43 41
104 92 115 119 107
QI/MTHF Q1/3BP QI/NBOH QI/MEOH
21925 21877 21911 21927
126 140 131 114
21785 21730 21782 21840
140 163 147 130
140 147 129 87
93 115 119 108
QX/3MP QX/4MH QX/TEA QX/MTHF QX/3BP QX/NMEC QX/NBOH QX/PDOL QX/MEOH
Z21349 21 362 21 325 21 290 21 273 21 230 21 198 21 063 21 172
106 147 158 195 230 210 260 200
21 294 21 300 21 128 21 051 20 942 20 968 20 802 20 592 20641
92 108 160 165 215 255 230 270 220
255 62 197 239 331 262 396 471 531
104 110 94 115 176 119 158 108
I50
I10
180
160
140
TIK
130
Figure 5. Thermally induced depression of the normalized mean TI
-
S, (0-0) emission energy detected within 10-20 ms after excitation. Data points refer to QX in various solvents as indicated. Lines are included for clarity. Solid and open symbols refer to the lower and upper tem-
perature scales, respectively.
'Energies u and u refer to the Stokes shift and are stated in cm-I. Explanations of parameters are given in Figure 2.
I
90
-
200
TIK
I
' " ; I ~;: OO
,
200
,
400
,
I 600
A Y / cm-I
Figure 4. (Lower) Correlation of the spectral width u(0) to the spectral shift Au of solvation for all solute/solvent combinations. The line represents a least-squares fit which extrapolates to u = 84 cm-l at Au = 0. (Upper) Same as lower plot but for the estimated inhomogeneous part uhhof the experimental widths u(0). q n h is approximated by subtracting 0.8 cm-I/K for the homogeneous contribution to the line width (see eq 9) assuming a linear uhom(7') relation. The corrected data extrapolate to uinh = 0 (Au = 0), and, simultaneously, the correlation improves, especially for data points related to high values of Ts. Data in parentheses (QX/MEOH) are subject to a high uncertainty.
observation time are depicted in Figure 2, which also clarities the notations of u(O), u ( m ) , a(O), a(=), ulr, Au, and Ts. These parameters are compiled in Table TI for all samples. Figure 3 shows a graphic representation of the spectroscopic data as a function of the solvent polarity at 20 OC in terms of ETN.' A fairly linear relation of the parameters o(0) and o(-) vs ETNis obtained, with only QX being subject to a pronounced solvatochromism. Figure 4 indicates a significant correlation between the Gaussian width u(0) of a TI So (0) emission spectrum and the total Stokes shift Au = u(0) - u ( m ) observed for the same sample. Obviously, a single relation holds for all solute/solvent combinations. 2. Spectral Correlation Data. Following common practice, the energy data in the context of solvation dynamics will be reduced to the scale 0-1 of the spectral correlation function C ( t ) (see eq I). Figure 5 indicates the relative Stokes shifts of QX in various solvents expressed by the thermal course of C (1 5 ms), i.e., based on spectra recorded within the (arbitrary) time window 10-20
-
100
95
Figure 6. Plot as in Figure 5 but for various solutes in MTHF and on an enlarged temperature scale. The characteristictemperatures Tsare equal within 2.5 K. BN denotes the solute I-bromonaphthalene(7zpH= 20 ms). TABLE Ilk KWW Fit Results and the Related Thermodynamic Data (kJ/molb system aKWW 7S(TS) EA(7S) EA 101 254' 0.40 0.21 s QX/NBOH ~~~~
~
QX/3BP
QX/MEOH QX/MTHFc QI/MTHF
0.35 0.35 0.43 0.40
1.3 ms 0.12 s 2.3 s 1.1s
168 130 152 149
1oob
92d 92d
Extrapolated from dielectric relaxation data.55 From dielectric relaxation data>6 CDatafor QX/MTHF is taken from ref 28 with an improved calibration of energy (+0.5 nm) and temperature (+0.5 K). From viscosity data.$' ms. The "solvation temperature" Ts,given by C (I5 ms) = 0.5 at T = Ts,maps the appropriate glass transition temperature To to a g o d approximation ( Ts = TG 4 K; see also Tables I and 11). An analogous plot for different probe molecules in the solvent MTHF is given by Figure 6, suggesting that the progress of solvation as a function of T is not specific for a certain probe although the absolute energies and Stokes shifts differ drastically. The solvation dynamics in terms of C(t)have not been acquired for all samples listed in Table 11. A typical C ( t ) data set for a variety of temperatures is shown in Figure 7 which emphasizes the marked temperature dependence and nonexponential decay pattern characteristic of the solvation dynamics observed near To. The experimental resolution of C(t) rules out an unambiguous identification of the underlying decay function. To a first approximation, KWW fits yield satisfactory representations of most of the curves. Due to data uncertainties, analyzing the decays separately would result in a scattering of dispersion parameters cyKww(T ) of as much as f0.06within several Kelvin for a single sample. To avoid this unreasonable effect, we chose to select an appropriate temperature-independent cyKWW with T entering only
+
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 10119
Dipolar Solvation in Supercooled Liquids Ttmelms
20
10
30
LO
So solvated
5
0.4 06 Timels
08
10
Figure 7. (Upper) Splined data of the normalized energetic relaxation C(r) and simultaneous transient broadening (u) on a common time scale. Data were obtained from QX/MTHF at 96.7 K. (Lower) Calculated C(r)curves parametric in temperature based on QX/MTHF data. C(r) decays are KWW fits with a common aKWW = 0.43. The f K W W ( r ) dependence in this plot corresponds to the least-squares fit to the actual iKwW(r) data (see Figure 8).
120
110
TIK
"
sOivated
Figure 9. Schematic energy diagram of a probe molecule in solution for the cases of So and TI being the fully solvated states. Dashed lines indicate the temporal progress from left to right on a time or solvation coordinate after excitation, including the Stokes shift of u(r). The population path of the TIstate via vibrational relaxation and ISC is oversimplified.
aIw ,063
0.2
I
100
L
related to its macroscopic counterpart a,the solute polarizability, by the Clausius-Mosotti formula a = a3(ec - I)/(cc + 2) (4) where 4*a3/3 is often identified with the van der Waals volume, assumed to be impenetrable to thermal collisions.39 The dipole moments of interest are pG = p(So) in the ground state and pE = p(TI)in the excited triplet state. The transient population of SI upon excitation is expected to decay within less than 1 ns and may be disregarded in view of the present time scales. The usual experimental approach to pE- pG is based on the relation of the difference of mean absorption and emission energies to the solvent parameters cs and n240
with the vacuum velocity of light c, Planck's constant h, absolute dielectric constant eo (set 4aeo = 1 for CGS units) and assuming cc = 1. For arbitrary tC eq 5 may be generalized to23 ( Auab) - ( Auem) =
8
9
I
10 11 103~1~ Figure 8. Temperature dependence of solvation times ss in an Arrhenius representation for QX in various solvents. The two probe molecules QX and QI in MTHF reveal indentical temperature dependences. The apparent activation energies are given in Table 111 as taken from the slopes of the least-squares fits (lines). Longitudinal (+) and transversal (X) dielectric relaxation times for 3BP are included for rCD data of ref 45 translated to rKWW values. into rKww( 0. Table 111 compiles the KWW fit results by stating ~KWW,TKWW(TS) and the mean solvation time constant rs( Ts) for C(t)
7s =
(~)KWW
c(t)
T K W W / ~ K W W ~ ( ~ / ~ K (W 3 4W )
eXp[-(f/rKWW)aKWW]
(3b)
The temperature dependences of rS are depicted in a log ( r s ) vs 1 / T representation in Figure 8. Although a simple activation according to the Arrhenius law is not expected in the supercooled state, the experimental temperature ranges are insufficient for identifying the course of rs( 71. The apparent activation energy of solvation varies with the solvent but not with the solute molecule, which is an expected result on the basis of the C (15 ms) vs T functions in Figures 5 and 6. IV. Discussion 1. Solute Effects. In the context of solvation the solute dipoles are commonly considered as point dipoles centered in a spherical cavity of radius a with the cavity dielectric constant eC. cc is (38) Lindsey, C. P.; Patterson, G. D. J. Chem. Phys. 1980, 73. 3348.
In practice, dipole moments can be obtained via calculation of the mean slope M of ( Auab) - (AU,.,,) vs F =Ats)-An2),with f ( x ) denoting the reaction field function F =Ats) - f ( n 2 ) A x ) = ( x - 1)/(2x + ec) (7) and using M = 2(& - ~ ) 2 / ( 4 7 r w h a 3or) lpE - $1 = O.OI(MU~)'/~, where M in cm-' and a in A yield the change in dipole moment in Debye? Due to the vanishing small transition strengths of TI So absorptions for the solutes under study, the values for ( Auabs)are inaccessible. On the other hand, the two emission energies u(0) and u ( m ) carry the same information regarding the sensitivity to solvent parameters as do ( Auabs)and ( Au,). Equation 5 is usually applied to steady-state spectra of fluorescence probes in lowviscosity solvents, where solvation is fast compared to the emission lifetime. AD,& and Au,, detected under these conditions relate to the energy differences Auab = u[Sl(So)]- u[So(So)] and Aue, = u[SI(Sl)]- u[So(Sl)],where the state in parentheses denotes the electronic state for which the configuration of the environment represents equilibrium conditions. In this notation So(So) and S,(S,) are relaxed states, whereas So(Sl)and Sl(So)are the corresponding Franck-Condon states. As schematically illustrated in Figure 9, the situation is analogous for the energies 40) = ~[TI(SO)I- ~[SO(SO)l (8a) u ( - ) = U[Tl(Tl)I - U[SO(TI)I (8b)
-
(39) Bondi, A. J . Phys. Chem. 1964, 68, 441. (40) Lippert, E. Z.Naturforsch. 1955, IOa, 541
10120 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
I
uuul POOL
4",
,
,
,
,
,
I
.2 .3 f ( ~ $ 1 f- (n2) (20°C) Figure 10. Plot of the total Stokes shift Av for QX vs the static reaction field function F as in eq 7, where F is taken from 20 OC solvent data and assuming cc = 1. The slope of the least-squares fit is M = 1400 cm-'. Taking the actual cc into account yields M = IO00 cm-' and (pE- pG) = +1.6 D for quinoxaline (see text).
0' 0
1
TABLE I V Theoretical and Experimental Values for the Change in Dipole Moment pE - between the States TIand S, for NA, QI, and QX Ifin - fiA D system MNDO HF/3 exP NA QI QX
0.053 0.024 0.524
0.153 0.012 1.305
=O EO
1.6
which also monitor the TI-So energies for the differing solvent configurations. Applying eq 6 to Au = u(0) - u ( m ) instead of ( A U , ~-) (Au,,) implies the advantage of canceling the energy offset inherent in ( A U , ~-) ( Auem) which is also present a t F = 0 and which itself might depend slightly on solvent polarity. The correlation of Au with F (ec = 1 and at 20 "C) is shown for QX in Figure IO and points toward a linear dependence of Au on F. Estimation of lpE- pol, denoting the length of the vector A p , via eq 6 actually requires knowledge of the solute property tC and solvent parameters fs and n2 at temperatures at which the energies are determined, Le., near TG in our case. The appropriate lowtemperature data for F (eq 7) are available only for 3BP, resulting in F(TG)= 0.23-0.27 for the range 1.5 ItC I2, which is reasonable for simple conjugated organic compounds. For the solvent 4MH F = 0 results readily from the lack of a permanent dipole moment. Focusing on QX we arrive at a slope M = 1000 cm-I for tc = 1.75. Taking the van der Waals radius a(QX) = 3 A39 into account leads to IpE- pCl = 1.6 D, which results in (pE p ~ =) 1.6 D according to the positive solvatochromism. The weak dependence of the emission energies u(0) and u(-) on solvent polarity for the solutes N A and QI in Figure 3 suggests negligible permanent dipole moment changes upon excitation for these molecules. Calculations of the ground (So)and excited (TI) state dipole moments for the isolated molecules NA, QI, and QX have been carried out by Frenking4I employing the program Gaussian 90.42 Optimization of molecular geometries using the semiempirical MNDO method43 for the T,electronic state reveals alterations of the atomic coordinates upon excitation with a significant impact on the resulting dipole moments. Charge distributions for the calculated geometries of the ground (So) and excited (T,) states have been obtained by semiempirical (MNDO) and by ab initio (HF/3-21 G ) techniques for the MNDO-optimized geometries. The calculated dipole moment changes pE - are listed in Table 1V. The directions of dipole vectors are practically maintained in every case. Comparing the ab initio results with those from the MNDO calculation shows that the relative values for the different molecules are the same, while the absolute dipole mo-
+
(41) Frenking, G. Unpublished results. (42) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foreman, J. B.; Schlegel, H . B.; Raghavachari, K.; Robb, M.; Binkley, J . S.;Gonzales, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A,; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J . J. P.; Topiol, S.; Pople, J. A. Gaussian 90, Rev. F.; Gaussian Inc.: Pittsburgh, PA, 1990. (43) Dewar, M. J. S.;Thiel, W. J . Am. Chem. SOC.1977, 99, 4899 and 4907.
Richert and Wagener ments shift slightly with different level of the quantum mechanical technique. It is gratifying to note that experimental and theoretical A p results agree perfectly for NA, QI, and QX within their accuracy (see Table IV). The above results for N A and QI, namely A p = 0, deserve further attention. Although Figure 3 rules out significant changes of p upon excitation of these two solutes, we observe (time-resolved) Stokes shifts with average values of 63 and 126 cm-I for N A and QI, respectively (see Figure 3 and Table 11). We conjecture that the electronic polarizabilities differ for the So and T I states of the solutes, which initiates solvation with a minor Stokes shift, yet being otherwise identical to the process caused by permanent dipoles. Observation of indistinguishable solvation dynamics for QI and QX in MTHF with respect to C(t)and ss(V (see Figures 6 and 8 and Table III), although A p (and thus the driving force) varies a t least by 1 order of magnitude, clearly indicates the validity of linear responses for the present findings. 2. Solvent Effects. The impact of a solvent to the solvation of a probe molecule derives from several aspects. One is the temperature range in which reorientation of permanent solvent dipoles occurs on the time scale of the present experiments, Le., on the order of milliseconds to seconds, which is slightly faster than typical times of =lo0 s for determining TG by DSC technique~.*~ Activation energies of relaxational processes in supercooled liquids near TGare generally high, and it is observed that solvation dynamics are faster than diffusional relaxation.2z4 We thus expect solvation of a triplet probe to be observable at temperatures slightly above T,, given the experimental time scale as limited by the radiative lifetime. This behavior is observed for the solvation of QX in eight different glass formers via coincidence of the solvation temperature Ts, where C (1 5 ms) = 0.5 or u (15 ms) = [u(O) + u ( m ) ] / 2 ,with TG + 4 K (see Figure 5 and Table I). This definition of Ts yields an arbitrary but convenient quantity for delineating a characteristic temperature of the solvation process. As is obvious from the above coincidence, solvation is closely related to the a process of the glassy medium. The solvent polarity is by its (empirical) definition a property that affects the extent of solvation. A large number of scales exist for gauging the relative influence of more or less polar s o l ~ e n t s . l * ~ ~ One being directly derived from the solvatochromism of a suitable dye is the ETNparameter proposed by Dimroth and Reichardt.' The content of polarity scales goes beyond those of microscopic properties of solvent molecules (e.g., dielectric characteristics) in the sense that it encompasses the solute-solvent coupling in an empirical fashion. A direct comparison between the pronounced solvatochromism of QX (Figure 3), Le., solvent dependence of u(0) and u ( m ) at T = 95-175 K, and independent polarity data is impossible, because literature data are available only for the liquids at 20 "C. Taking u ( m ) for the solute QX itself as polarity scale PQ at the glass transition reveals a fairly linear correlation to ETNdetermined at 20 "C as evident in Figure 3. Deviations among these relative polarities PQ (==lo0K) and ETN(293 K) are within the scattering of different scales, e.g., x* and ETN, obtained for equal temperatures. The above result agrees well with the notion that the static contribution to the reaction field functional F is almost independent of temperature (for 3BP see ref 46). The above-mentioned effects of solvent polarity on electronic energies of the probes are significant only if the probe molecule possesses dipole moments that interact with the polar medium (compare NA and QX in Figure 3). The overall sensitivity of a certain probe to the medium in terms of the energies is best expressed by the total Stokes shift due to solvation, Le., Au = u(0) - u ( m ) . In the absence of dielectric saturation, a strong coupling between solute and solvent should simultaneously yield a large shift Au and an increased sensitivity of the transition energies to the inhomogeneous distribution of solvent configurations inherent ~
~~~~~
~~
(44) Nickel, B.; Ruth, A. A. J . Phys. Chem. 1991, 95, 2027. (45) Kamlet, M. J.; Abboud, J. L. M.; Taft, R. W. Prog. Phys. Org. Chem. 1981, 13, 485. (46) Berberian, J . G.; Cole, R. H. J . Chem. Phys. 1986, 84, 6921.
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 10121
Dipolar Solvation in Supercooled Liquids
in the glassy phase. The latter effect is experimentally accessible via the line width a(0) of the emission profile. The expected (linear) relation of ~ ( 0 to ) Au is observed as shown in the lower plot of Figure 4. More accurately, the spectral width cr results from the convolution of an inhomogeneous spreading q n h and the homogeneous line width ahom a selected molecule is subject to. Consequently, only the contribution Qinh should vary systematically with Au. To derive q n h from the observed a(0) values, we make use of the crude estimate that ahom increases linearly with T a t approximately 1 cm-’/K and then “deconvolute” by subtracting 0.8 cm-’/K of the temperature Ts, which is within several of the temperatures at which a(0) has been obtained. This result of dinh according to Qinh
U(O)
- 0.8 cm-I
X
(Ts/K)
(9)
is plotted in the upper part of Figure 4 and indicates two features if compared to the a(0) vs Au data. The inhomogeneous contribution to o(0) extrapolates to din,, = 0 at Au = 0, and, simultaneously, the correlation ~ ( A u has ) improved, mainly due to subtraction of the large a h o m for the two solvents of high TG, PDOL ( Ts = 158 K) and NMEC ( Ts = 176 K). We conjecture that the varying inhomogeneous spectral spreading is a signature of the dipolar coupling between solute and solvent as is Au, instead of a reflection of varying degrees of orientational disorder among the different solvents. Due to the geometrical similarity of the probe molecules NA, QI, and QX, the above notions hold when all data points in Figure 4 are considered or when only those for QX (dots) are considered. An unambiguous discrimination between the linear dependence ai,,h(h) and qnh2 = (kT/2h)Au, as proposed by Loring$’ would call for a more precise evaluation of qnhnot achieved at present. The spectral widths a ( - ) measured above Ts (see Figure 2) are =IO cm-’ above the corresponding u ( 0 ) values and do not display a systematic dependence on Au, T, or solvent. Most probably, a(m) - cr(0) reflects an increase of a h o m as a consequence of the onset of molecular mobility above TG . 3. Solvation Dynamics. Up to this point we have disregarded the temporally resolved progress of the Stokes shift which monitors the equilibration process of solvent molecules initiated by electronic excitation of the probe. The previous subchapters have covered the influence of solute (Ap) and solvent (ETN,TG) parameters on the spectroscopic data u(O), u ( m ) , and u(0). We now address the temporal progress of solvation in terms of the spectral correlation function C(r),irrespective of the absolute energy scales. The temperature dependences depicted in Figures 5 and 6 indicate that the observed solvation processes are governed by properties of the solvent, the specific probe being of minor relevance for the C(t) results. This is emphasized by the high correlation of Ts with TG(Figure 5; Table I) and the low sensitivity of C (1 5 ms) vs T to the specific probe molecule (Figure 6) and supported by the analogous feature in the Arrhenius plot of rs in Figure 8. According to the MSA theory,I2 C(t) depends only on the molecular geometries as far as the solute is concerned, which agrees with the obvious interchangability of the fairly equal sized solutes NA, QI, and QX. While the Stokes shift u ( t ) in the range u(0) and u ( m ) is in progress, not only the mean emission energy but also the width of the profile depends on time. Figure 2 indicates the increase of a( T ) with T a t a fixed time window of observation, superimposed by a peak of q n h at temperatures where solvation proceeds within that time window. The amount of this transient increase ulr (see Figure 2) is proportional to the shift Au (utr= 0.08Au) and together with d i n h = 0.28Au from Figure 4 the relation ut,
0 . 0 8 A ~ 30% uinh
(10)
is obtained. Figure 7 displays the analogy of this effect on the time scale and is virtually identical with results obtained in liquid solutiona and with effects indicated by ~imulations.4~It is seen (47) Loring, R. F. J . Phys. Chem. 1990, 94, 513. (48) Maroncelli, M. Unpublished results for Cul02/NMP.
that a(?)approximately returns to its initial ( t = 0) value after the solvent has equilibrated, i.e., if C(t) = 0. The transient broadening is easily rationalized by noting that relaxation of the solvent involves a multitude of small steps down the energy scale, with the elementary processes being subject to a wide distribution of event times. At intermediate times some accidentally fast sites will be closer to equilibrium than others, which results in the broadening until, ultimately, complete relaxation at all sites restores the initial width. This picture of a transient inhomogeneous broadening of site energies is strongly supported by the scaling of qtrwith q n h . The spectral narrowing at long times is not seen in Figure 1 because C ( t = 0.6 s) is still as high as 0.22 in this case. Temporal changes of the emission spectrum apart from the shift itself imply the problem of an ambiguity in extracting a characteristic energy u ( t ) to calculate C(t). Following common practice of experimental as well as theoretical work, we use the average emission energy as u ( t ) . It is a common feature of the glassy state that all relaxational processes exhibit dispersive, Le., nonexponential, decay patterns.2s Equally widespread is mapping the relaxation patterns in glasses by the KWW function, mainly with the aim for gauging the degree of dispersion in terms of aKWw. This empirical decay type is notorious to yield good fits to experimental data, especially in cases where the process is of hierachical natureSoas is true for most relaxations (not reactions). In view of the uncertainties of C(t) data, we follow the practice of an empirical KWW fit serving as gauge for the dispersion and as basis for determining temperature dependences. Typical aKWw parameters near TGrange from 0.4 to 0.6 with no indication of significant changes in the vicinity of TG,463s1 which leads us to anticipate a temperature-invariant value for aKWw for one sample within the narrow temperature intervals of observation. The results for C(r) fits are compiled in Table 111 and can be rationalized along the following lines. Glass-forming liquids that exhibit Debye type dielectric relaxation in the low-viscosity regime tend to show dispersive relaxation patterns upon cooling.46 If measured in the frequency domain, the dispersion is manifested in the broadening of the dielectric loss curve beyond the 1.14 decades wide Lorentzian characterizing a Debye system. Dispersion may then be evaluated by means of a Cole-Davidson fit with dispersion parameter &Des2 PcD can be translated into the dispersion parameter aKWw of the time domain on a least-squares basis.38 Only for one of our glass formers are reliable dielectric data available at TG given by Berberian and Cole for 3-bromopentane (3BP). Their average result for the range 108-1 12 K is PcD = 0.6, corresponding to aKWW (diel.) = 0.7. This significantly lower dispersion compared to our aKww(soIv.)= 0.35 for 3BP is qualitatively realistic because solvation dynamic decays are dispersive also for Debye (&. = 1) solvents. These nonexponentialitiesof solvation in Debye liquids are understood to originate from differently responding solvent shells, depending on their mean distance to the solute,12 whereas dielectric dispersion is a bulk property of the system. Thus, to a first approximation, the distribution of event times of solvation dynamics in non-Debye solvents should result from the convolution of the two independent sources of dispersion. On a quantitative level, the MSA theory” predicts a C(t) pattern characteristic of aKww = 0.44 for the ionic solvation, on the basis of the dielectric parameters tS,e,, and flcBc0of 3BP at TGand assuming equal radii for the ion size (rs) and solvent size (Ri),Le., p = rs/Ri = 1. The remaining discrepancy in aKWW may arise from the MSA theory by assuming a pure dynamic origin of the dielectric dispersion and experimental uncertainties in determining C(t),which are higher for 3BP and the alcohols. The functional form of the decay pattern as predicted by the MSA displays no significant sensitivity to p within the range 0.1 I p I 10 or to the difference between ionic and dipolar solvation.12 A discussion of the time scales of (49) Maroncelli, M. J . Chem. Phys. 1991, 94, 2084. (50) Palmer, R. G.; Stein, D. L.; Abraham, E.; Anderson, P. W. Phys. Rev. Left. 1984, 53, 958. (51) Ngai, K. L.; Rendell, R. W.; Plazek, D. J. J . Chem. Phys. 1991.94, 3018. (52) Davidson, D. W.; Cole, R. H. J . Chsm. Phys. 1951, 19, 1484.
10122 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 the dielectric responses appears in order. Figures 7 and 8 show the strong dependence of the mean solvation time T~ on temperature, quantified in terms of apparent activation energies EA in Table Ill. Coincidence of E A for QI and QX in MTHF supports the low sensitivity of the solvation process to the specific probe.as emphasized above. Various relaxation aspects of a supercooled liquid, dielectric relaxation, viscosity, Brillouin scattering, etc., are often subject to similar temperature dependence^.^^ The slopes of log ( T ~ vs ) l / T for the supercooled solvent in Table 111 indicate activation barriers that exceed those for other relaxations by a factor of -1.5. This discrepancy holds also for the 3BP data, where dielectric time scales T~ and .zL are available at To. Switching to the longitudinal time constants T ~T() , expected to be more closely related to 7s,4Eo alters the temperature dependence only to a minor extent. The increase in E A upon going from dielectric to solvation data may point toward an increased cooperativity of the underlying process in the case of solvation, especially since field-induced rotational motion of permanent dipoles governs both observables. Such an interpretation is in accord with the faster longitudinal response of the solvent involving an excess cooperativity of solvent dipoles over the transversal (dielectric) process due to screening effect^.^-',^ The difference in activation barriers for T~ and T~ prevents a straightforward judgment concerning the relation of time scales. If this effect were to be explained within the framework of the MSA, one would be forced to assume a drastic increase of p = rs/Ri as the temperature is lowered. On the absolute T scale Figure 8 shows that the relation T L I TS I T~ does hold for 3BP within the experimental temperature range, yet not for a linear extrapolation of the sS data in this plot. For NBOH (TG = 1 19 K) dielectric data are available only down to 135 K, indicative of a significant increase of the apparent activation energy below the melting point.s5 Extrapolating the increase of RT In (u0s) as suggested by Dannhauser and Cole55 yields T~ and T~ data at TG for the slower of the two dispersion regimes, which again encloses the solvation data of QX in NBOH.
V. Summary and Conclusions In summary, we have observed phosphorescence spectra of chromophores in supercooled liquids whose mean energies are sensitive to solvent parameters, temperature, and time. Spectroscopic data of the 0-0 emission bands are obtained by varying the conditions of solvent polarity, 0 -< ETN (20 "C) I 0.75, of sample temperature, To IT I TG + 10 K, and of observation time relative to excitation, 500 ps Ifob I2 s. Although Stokes shifts are small for the triplet probes (- 200 cm-I), data uncertainties seem not to exceed those encountered in solvation dynamics work on fluorescence dyes in liquid solution displaying spectral shifts of up to 2000 cm-I. The reason is that the u-Au relation (Figure 4) also holds for liquid systemsz noting that Au/u critically limits the C(t)resolution. The experimental results, derived from the characteristic data stated in Figure 2 and the time-resolved relaxation u ( 0 ) 1 u ( t ) 1 u ( a ) , are compatible with the features of solvatochromism and solvation in low-viscosity liquids. Unambiguous identification of spectral data for the Franck-Condon and for the equilibrated state of solvent environments yields information regarding the polarity of the glassy medium and permits determination of the change in dipole moment upon excitation of the probe molecule on the basis of emission data. The following conclusions can be drawn. The emission energy u ( a ) of quinoxaline serves as polarity indicator (PQ)usable for supercooled media near TG. In accord with the approximate temperature invariance of the related quantity F i n eq 7,a linear relation between PQ(TG)and ETN(20 "C) is observed (Figure 3); Le., relative polarity scales are maintained when liquids are supercooled. A restriction of polarity scales to liquid media has been previously ruled out by Langhals6I (53) Jeong, Y.H.;Nagel, S.R.; Bhattacharya, S. Phys. Rev. A 1986,34,
602.
(54) Maroncelli, M.; Fleming, G . R. J . Chem. Phys. 1988, 89, 875. (55) Dannhauser, W.; Cole, R. H. J . Chem. Phys. 1955, 23, 1762.
Richert and Wagener
on the basis of polymer data. According to eq 6 , which we apply to the u(0) - u ( m ) results (Figure lo), experimental values for the (vector) difference in dipole moments p(T,) - cc(So) are obtained and strictly confirmed by theoretical (MNDO and HF) predictions for NA, QI, and QX (Table IV). It should be emphasized that the small Ap values calculated for the isolated molecules NA and QI may be distorted significantly in condensed media due to induced dipole moments of up to -0.1 D. A similar aspect concerns the observed solvation in a solvent like 4MH, which may appear unpolar only on a macroscopic scale but not on molecular scales where bond moments of solvent molecules or again induced effects may play a role. The lower plot of Figure 3 clearly indicates that a microscopically unpolar solvent, relating to the intercept of the u(0) and u ( a ) lines at ETN = -0.22 and u = 21 420 em-', is not achieved at ETN= 0. Although we are unable to further quantify the above notions, there is evidence that changes in the polarizability of the solute upon excitation bear an impact on solvation disregarded in eq 6 . The inhomogeneous widths uinhof emission profiles are shown to scale with the total Stokes shift energy Au (qnh= 0.28Au, see Figure 4) for all samples investigated, implying that din,, also gauging the distribution of site energies is controlled by solutesolvent dipolar coupling as is Po, instead of reflecting solventdependent configurational statistics. The spectral width u(0) in the Franck-Condon states of the solvent is restored after equilibration of the environment, although a transient inhomogeneous broadening by ut, = 30% X umh accompanies the relaxation process (Figures 2 and 7) as expected for spectral shifts with a distribution of event times. The observed relaxational processes in terms of C(t) are closely connected to the (Y process of the glassy solvent (Figure 5 and Table I) and are characterized by a marked dispersion with aKWw = 0.4 (Figure 7 and Table 111). C ( t ) profiles turn out to be reproducible with various probe molecules differing in Ap by a factor of > 10, which indicates the relaxations being within the linear response regime and governed solely by solvent properties. As far as appropriate dielectric data exist, solvation dynamics emerge from dielectric relaxation parameters as predicted by MSA theories on a semiquantitative level concerning the mean solvation time and functional form of C(t). It is thus obvious that the dynamic Stokes shift is a direct monitor for the solvent dielectric response to alterations of the charge distribution in the probe molecule initiated by its electronic excitation (see Figure 9). Viewed qualitatively, the solvation in supercooled liquids can be derived from the corresponding findings in normal liquids if the characteristics of glassy systems, as they appear in the dielectric behavior, are properly taken into account. In contrast to solvents of low viscosity where collective motion predominates,62 translational contributions to the solvation energy are unlikely to obscure pure rotational effects in systems of highly cooperative molecular motion active near TG. Although the present findings are considered a promising confirmation that the MSA formalism is also applicable to quasi-static (non-Debye) media, the excess activation energy of solvation (Figure 8 ) prevents a true quantitative test of MSA calculations. One might speculate on the increased cooperativity of the longitudinal (screened) processes, e.g., in terms of an increased rs/Ri for lower Tin the MSA formalism, for rationalizing the higher barriers compared to dielectric relaxation. Clarifying this effect and the relation of absolute time scales calls for more reliable dielectric data, which we defer to a future publication. Experimental solvation data for low-viscosity liquids indicate a discrimination between aprotic and protic solvents, the latter being represented by alcohols. Due to hydrogen bonding and as (56) Wunderlich, B. J . Phys. Chem. 1960, 64, 1052. (57) T. estimated using TG iii 2 / 3 T M(see ref 24). (58) Fischer, G.; Fischer, E. Mol. Photochem. 1977, 8, 279. (59) Murthy, S. S. N . J . Chem. SOC.,Faraday Trans. 2 1989, 85, 581. (60) Barigelletti, F. J . Phys. Chem. 1988, 92, 3679. (61) Langhals, H. Angew. Chem. 1982, 94, 452. (62) Bengtzelius, U.; Gbtze, W.; Sjblander, A. J . Phys. C: Solid State Phys. 1984, 17, 5915.
J. Phys. Chem. 1991, 95, 10123-10133 many as two or three dielectric dispersion regimes,5s alcohols behave differently compared to simple liquids regarding relaxation dynamics and polarity effects.22 Within the present investigation of supercooled media no such discrimination is found. We consider this result evidence for two characteristic properties of glassy media, cooperative motion and marked dielectric dispersion, obscuring the effects of hydrogen bonding and multiple Debye dispersion in supercooled alcohols, respectively.
10123
Acknowledgment. We thank G . Frenking for kindly conducting the dipole moment calculations and I. Rips for placing the MSA algorithm for ionic solvation at our disposal. We are grateful to J. Klafter and I. Rips for valuable discussions and to M. Maroncelli for the communication of work prior to publication and helpful comments on the manuscript. Financial support by the Fonds der Chemischen Industrie and Deutsche Forschungsgemeinschaft is gratefully acknowledged.
Diffusion of Excited Bianthryi in Microheterogeneous Media Robert B. Pansu*it and Keitaro Yoshihara* Institute for Molecular Science, Myodaiji. Okazaki 444, Japan (Received: March 13, 1991; In Final Form: July 8, 1991)
We studied the time-resolved bathochromic shifting of the fluorescenceof bianthryl (BA) in micelles and bilayered membranes. Whatever the medium, the kinetics are complex but an isoemissive point is observed on the time-resolved fluorescence spectra. The polarized fluorescence and the kinetics of the decay show that, in bilayers (phosphatidylcholines and distearyldimethylammonium chloride), excitation energy transfer and trapping takes place. In micelles, physical diffusion of BA occurs from the core of the micelle to the water interface. We show that the diffusion is controlled by the existence of energy barriers and wells inside the micelles. This potential surface is defined by the variation of the chemical affinity of the probe through the micelle. The kinetics of the decay establishes that, in cetyltrimethylammoniumchloride (CTAC) micelles, BA is localized among polar head groups in a well 1-2 A wide. In sodium dodecyl sulfate, the inner population diffuses at a constant rate of lo8 s-l. This reveals the existence of a skin, not observed in CTAC, that isolates BA molecules from the water.
1. Introduction Due to their importance in catalysis as well as the understanding of intermolecular interactions, microheterogeneous media have been the subject of extensive studies.' Most catalytic reactions occur at the interface with water. The diffusion rate of a reactant to the interface and the escape rate of a product from the reaction site can play a critical role on the overall rate and efficiency of the reactions.2 On the water side, the accessibility of the micelle surface is known to be controlled by electrostatic interaction^.^ However, the time it takes for a solute to travel from the core of the micelle to the surface has not been extensively studied. This time depends on the initial localization of the molecule relative to the interface, on the existence of an energy barrier on the way to the surface, and on the transverse viscosity. In this work, we show that the diffusion of a probe molecule to the water interface is governed by the existence of energy barriers. To measure the diffusion time, we need both a start and stop reference time. For the start time, we produce an excited state using a picosecond laser. For the stop, we use the quenching of this excited state a t the interface. We chose bianthryl (BA) as a probe molecule. BA is one of the TlCT (twisted intramolecular charge transfer) molecule^^*^ whose fluorescence spectrum is sensitive to solvent polar it^.^ BA is expected to have a blue emission in the core of the membrane that turns red as BA reaches the polar interface. In contrast with other TlCT molecules, BA has no polar, acidic, or basic substituent that might induce a localization of the probe in contact with the water phase. We expect that BA will be initially dissolved in the core of the hydrophobic domain. The decay rate of the first excited state varies between 7 ns in alkanes and 34 ns in acetonitrile.' There is a good correlation between the position of the emission maximum and the fluorescence lifetime as shown in Figure 1. This allows us (section 3.3.4) to estimate the fluorescence lifetime of a BA excited state in microheterogeneous media from its fluorescence spectrum. 'On leave from the Physico-Chimie des Rayonements, CNRS URA75, Equipe ENS Cachan, Paris Sud, 91405 Orsay Cedex, France.
0022-3654/91/2095-10123$02.50/0
BA has been used to probe the polarity of microheterogeneous media and the heterogeneity of solubility sites in Vycor glass.* BA has been used in the studies of solvent dynamics around a ~ a l u t e since , ~ it is already twisted in the ground state and the intramolecular movement required for electron transfer is small.IO The electron transfer is thus supposed to be controlled by the solvent reorganization" and is known to last 4 psI2 in propylene carbonate. Exciplex formation with solvent molecules contributes to a spectral shift13 and lasts up to 1 ns in hexanol a t 0 OC.I4 (1) Surfuctunts in solution; Mittal, K. L., Ed.;Plenum Press: New York, 1984. Rleni, M. P. J. Chim. Phys. 1987.84, 1031-5. Buntom, C. A,; Savelli, G . Ado. Phys. Org. Chem. 1986, 22, 213-309. (2) Micellar catalysis of organic reactions. 33. Effect of micellar orientation of the substrate on the magnitude of micellar catalysis. Broxton, T. J., Christie, J. R., Chung, R. P. T. J . Org. React. 19%8, 53, 3081-4. (3) Bunton, C. A. 8th International Symposium of Surfactants in Solution, 1990, Gainesville, FL. ' (4) Grabowski, Z. R.; Rotkiewicz, K.; Siemiarczuk, A.; Cowley, D. L.; Baumann, W. Nouu. J. Chim. 1979, 3, 443-54. ( 5 ) Schneider. F., Lippert, E. Ber. Bunsen-Ges. Phys. Chem. 1968, 72, 115540. Schneider. F.; Lippert, E. Ber. Bunsen-Ges. Phys. Chem. 1970,74, 624-30. (6) Rettig, W.; Zander, M. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 1143-9. Mataga, N.; Yao, H.; Okada, T.; Rettig, W. J . Phys. Chem. 1989, 93,3383-6. (7) Nakashima, N.; Murakawa, M.; Mataga, N. Bull. Chem. Soc. Jpn. 1976, 49, 854-8. (8) Nakashima, N.; Phillips, D. Chem. Phys. Lett. 1983, 97, 337-41. (9) Kosower, E. M. J . Am. Chem. Soc. 1985, 107, 1114. (10) Khundkar, L.; Zewail, A. H. J . Phys. Chem. 1986. 84, 1302-11. Yamasaki, K.; Arita, K.; Kajimoto, 0.; Hara, K. Chem. Phys. Len. 1986,123, 277. (1 1) Nagarajan, A. M.; Bearley, A. M.; Tai-Jong, K.; Barbara, P. F. J . Chem. Phys. 1987, 86, 3183-96. Kahlow, M.; Jarzeba, W.; Kang, T. J.; Barbara, P. F. J . Phys. Chem. 1988,90, 151-8. Kahlow, M.; Kang, T. J.; Barbara, P. F. J . Phys. Chem. 1987, 91, 6452-5. (12) Kahlow, M. A.; Kang, T. J.; Barbara, P. F. J . Phys. Chem. 1987, 91, 6452-5. (13) Visser, R.; Weisenborn, P. C. M.; van Kan, P. J. M.; Huizer, B. H.; Warman, J. M.; de Haas, M. P.; Varma, C. A. G. 0.J . Chem. Soc., Furrrduy Trans. 2 1985, 81, 689-104. (14) Anthon, D. W.; Clark, J. H. J . Phys. Chem. 1987, 91, 3530-6.
0 1991 American Chemical Society
