Rotational diffusion of coumarin 102 in trifluoroethanol: the case for

1496

J . Phys. Chem. 1993,97, 1496-1501

Rotational Diffusion of Coumarin 102 in Trifluoroethanol: The Case for Solvent Attachment R. S. Moog’ and D. L. Bankert Department of Chemistry, Franklin and Marshall College, Lancaster, Pennsylvania 1 7604

M. Maroncelli Department of Chemistry, 152 Davey Laboratory. Pennsylvania State University, University Park, Pennsylvania 16802 Received: September 15, 1992; In Final Form: November 13, 1992

The rotational dynamics of Coumarin 102 (C102) in pure decalin and pure trifluoroethanol (TFE), and of a 1:1 C102:TFE complex in decalin, are examined using time-resolved fluorescence anisotropy measurements. The rotation of C102 in decalin is well-described by the Debye-Stokes-Einstein hydrodynamic model with slip boundary conditions as is the 1:1 complex. The reduced rotation time, T r / q , of C102 in pure TFE is significantly larger than its value in pure decalin but is indistinguishable from that of the complex in decalin. These results suggest that the rotation of C102 in TFE can be interpreted as the rotation of a 1:1 ClO2:TFE complex following the hydrodynamic model with slip boundary conditions.

Introduction Since Eisenthal and Drexhage’ reported the first direct observation of rotational reorientation of molecules in liquid solutions using picosecond laser pulses in 1969, the examination of the effects of solvents on the rotational motion of mediumsized solutes has been an active field of study. An important goal of much of this work is an understanding of the source and nature of the friction experienced by the rotating body. The magnitude of the friction coefficient, [,is related to the rotational diffusion coefficient, D, about a given axis by

D = kT/( (1) where k is the Boltzmann constant and Tis the temperature. The earliest experiments were generally analyzed using the DebyeStokes-Einstein (DSE) hydrodynamic theory of rotational diffusion2J and modifications thereof,e7 in which the solute is modeled as a sphere or symmetric ellipsoid and the solvent as a continuum of viscosity q. Previous workers5-*have summarized the relationship between the observed rotational reorientation time, T,, and the principal diffusion constants of the model solute. The general result is that, for spheres and many ellipsoids, the rotational motion can be characterized within experimental error by a single diffusion constant and thus also a single reorientation time given by

= qVFC/kT

(2) where Y is the solute molecular volume, F is a parameter that accounts for the shape of the model solute and is a function of the ellipsoid axial ratio, p, and Cis a parameter that is determined by the hydrodynamic boundary condition. Under stick hydrodynamics, the first layer of solvent ‘sticks” to the rotating body, thereby retarding its motion through the bulk viscosity. In this case, C = 1. For slip boundary conditions, there is no tangential force exerted on the rotating body by the solvent. The rotational motion is retarded only by the solvent which must be displaced as the body rotates. In this case, Cis a function of p and has a value between 0 and 1.6.7 Note that, for a given molecule modeled as an ellipsoid, T,/V is predicted to be proportional to 1/ T for a constant boundary condition. Prior to the mid-l980s, the experimental work in this field predominantly involved measuring the rotation times of both charged and neutral solutes in a variety of solvents (protic and aprotic) and interpreting the results in termsof this hydrodynamic model. Fleming’s monograph provides an excellent review of T,

0022-3654/93/2097- 1496$04.00/0

this work.* Although in some cases the theory could account for the experimental results?J2 deviations were often observed. For alcohol solvents, r r / qwas frequently found to be proportional to 1/ T, but the experimentally determined hydrodynamic volume was found to be significantly larger than that of the model ellipsoid.llJ3-19Inaddition, therotationofmany dyesin hydrogenbonding solvents was found to be much slower than would be predicted on the basis of the rotation times in aprotic solvents.11J4.20 In all of these works, the authors proposed that the observed deviations from the DSE model were due to solvent attachment via hydrogen bonding to the solute,thereby increasing the effective volume of the rotating species. Other results inconsistent with the DSE model were attributed to changing boundary conditions as a function of solvent,20v21 or to specific solvent effects for large alcohols12or at highviscosities.22Several workers11,14,16,21.23noted the difficulty in differentiating between the effects of solvent attachment and a change in hydrodynamic boundary condition in explaining the experimental results. More recently, there has been a shift toward examining dielectric f r i ~ t i o n as ~ ~a tpossible ~~ explanation for the observed deviations from DSE theory. In this case, the rotation of a polar solute in a solvent is slowed by the retarding force of the reaction field present in the polarized solvent, which does not respond instantaneously to the motion of the solute. For the analysis of the experimental rotational reorientation data, the standard approach has been to assume that the total friction experienced by the rotating solute is the sum of the hydrodynamic friction described by the modified DSE model and the dielectric friction. Although this separation of the two types of contributions is not rigorously correct,26this approach provides a simple framework for analysis. Many attempts to provide a theoretical calculation of the dielectric friction contribution have been and considerable e ~ p e r i m e n t a l ~ ~ .and ~ ~ Jc *o ~m~p ~ t a t i o n a l ~ ~ - ~ ~ effort has been expended in testing these theories. For example, Waldeckand co-workershave examined the roleof realisticcharge distributions (as opposed to simple dipoles studied previously) on the rotational f r i ~ t i o n . ~ ~In - ~these l J ~ and other cases, deviations from DSE predictions have been shown to be qualitatively understandable with varying degrees of success using different theories of dielectric f r i ~ t i o n . ~ ~ However, ~ ~ , ~ ~quantitative , ~ ~ . ~ ~ , ~ ~ agreement (in the absence of adjustable parameters) has remained elusive. Although this recent work has emphasized explaining experimental results in terms of dielectric friction, several authors have 0 1993 American Chemical Society

Rotational Diffusion of Coumarin 102 in Trifluoroethanol

The Journal of Physical Chemistry, Vol. 97, No. 8, 1993 1497

3.0 pL of alcohol was added to the remaining volume, resulting in an alcohol concentration of approximately 2 mM. A second 3.00-mL aliquot was then removed and examined. This process was repeated, resulting in increasing alcohol concentration, with effectively no change in the C102 concentration. Steady-state absorptionand fluorescencespectra were obtained using Perkin-Elmer Lambda 6 and Spex Fluorolog 111 spectrometers, respectively. Fluorescencespectra were corrected for instrumental response. Time-resolved experiments were performed using a single-photon counting instrument, with sample Coumarin 102 excitation from a synchronously pumped dye laser and microchannel plate detection.50 The instrument response time of the system was about 65 ps (fwhm). Fluorescence emission was collected through a polarizer set parallel, perpendicular, or at the magic angle (54.74’) to the polarization of the exciting pulses and then through a 1/4-mmonochomator (ISA H-10) having a band-pass of 16 nm. For all experiments,the sample temperature TFE was held constant (h0.5 “C) by circulating liquid from a thermostat4 bath through an appropriate metal sample holder. Figure 1. Structureof C102 (upper left) and space-filling representations of C102 with the first model oblate ellipsoid (see text and Table 11). Also The general method for determination of rotation times from shown is a space-filling representation of TFE (lower right). time-resolved fluorescence measurements has been described in detail previ~usly;~?~ therefore, only a brief description will be given noted the difficultyin experimentallyseparatingthe hydrodynamic here. The fluorescenceemitted through a polarizer oriented either and dielectricfrictioncontributionsto rotational motion.27v31-3638p47 parallel (Ill) or perpendicular (II)to the polarization of an initial For example,Dutt and D ~ r a i s w a m have y ~ ~ reported that although short pulse of light is measured as a function of time. Assuming a dielectric friction model adequately describes the rotational that the rotational diffusion may be approximately characterized motion of a cationic probe (Oxazine 720) in some mixed solvents, by a single diffusion constant (a reasonable assumption in the it is not sufficient to explain the observed behavior of the anionic present case5p8),the fluorescencedecays have the functional forms proberesorufin. They propose that an additional effect of solvent attachment, resulting in an increase in the effective size of the rotating body, must be invoked to account for the observed results in alcohol/water mixtures. In addition, other recent results are viewed as consistent with solvent a t t a ~ h m e n t . 3 ~ ~ 3 5 ~ 3 ~ ~ ~ ~ ~ ~ ~ The goal of the present work is to examine whether solvent where 7f is the fluorescence lifetime, Ai is the overall amplitude attachment alone is sufficient to explain quantitatively the rotational behavior of a polar species in a protic solvent. This of each decay, and ro is the initial anisotropy. In theory, molecules question has not been unambiguously answered in past studies, whose absorption and emission dipoles are parallel should give in large part due to the uncertainty in the size and/or shape of ro = 0.4; in practice, this theoretical maximum is rarely observed. the “rotating species” in a strongly hydrogen bonding solvent. Values for the initial anisotropy, rotation time, and lifetime were Our conceptual approach is to first examine the rotational obtained by a simultaneous fit to both I&t) and I L ( t ) . The fits dynamics of an uncharged polar probe in a nonpolar, noninterwere accomplished by convolving trial decays with the instrument acting solvent and then experimentally measure the effect of response function and then employing a least-squares fitting attaching a single alcohol molecule to the probe through a procedure. The fits to the C102:TFE complex data were not as hydrogen bonding interaction. These results will provide us with well-defined as for the pure solvents, and the value of 7, for a a model of the size and shape of the rotating 1:1complex. Finally, given pair of decays was observed to depend upon ro. Therefore, we examine the rotation time of the probe in the pure alcohol and for the complex, the initial anisotropy was not varied but was set determine whether the results may be adequately explained using at ro = 0.35, equal to the value in the pure solvents. In all cases, the experimentally obtained 1:1 complex model and including 7f was also obtained for each sample from the magic angle only the hydrodynamicfriction as described in the modified DSE fluorescence decay, and these values were consistent with those approach. Although this approach seems obvious, it is not an obtained from the fits to the corresponding pair of polarized easy one to implement experimentally and to our knowledge has fluorescence decay. not been applied previously. In the present work we rely on the Results and Discussion spectral properties of Coumarin 102in 2,2,2-trifluoroethanol (see Figure 1) to accomplish this goal. Rotation Times in Pure Solvents. Rotation times of C102 in decalin and TFE were obtained at 272 K. Temperatures lower Experimental Section than ambient were used to increase the solution viscosity,thereby Laser grade Coumarin 102 (C102) was obtained from Kodak. increasing the observed rotation times to enable more precise Anhydrous decalin (decahydronaphthalene, 99+%, mixture of determinations. Fluorescence lifetimes and rotation times are cis and trans isomers), NMR grade trifluoroethanol (TFE, reported in Table I, and typical results for the parallel and 99.5+%), and hexafluoro-2-propanol (HFP, 99.8+%) were perpendicular fluorescence decays are shown in Figure 2. purchased from Aldrich. 2-(Trifluoromethyl)propanol-2(TFMP) Although the total fluorescence is well described by a singlewas obtained from PCR. All reagents were used without any exponential decay for the pure decalin solution and for the further purification. complexes, in pure TFE the overall fluorescence decay is All samples were prepared under a nitrogen atmosphere in a biexponentia1.5’ This is attributed not to any intrinsic inhomoglovebag to exclude water. To obtain a series of solutions with geneity of the TFE solutionbut rather to the well-known dynamical varying alcohol concentration, a 2 1.OO-mL stock solution of C 102 Stokes shifting52-54of the fluorescence in this polar solvent. The in decalin of appropriate concentration (approximately 5 X 10” rotation time of C102 in TFE is seen to be significantly longer M) was first prepared. A 3.00-mL aliquot was removed and than that in decalin; however, the viscosity of TFE at this used to measure the absorption of the pure decalin solution. Then temperature is also greater than that of decalin. According to

Moog et a].

1498 The Journal of Physical Chemistry, Vol. 97, No. 8, 1993 0.1 I

TABLE I: Fluorescence and Anisotropy Decay Parameters

0.08

32 f 1 56 f 3 51 f 5

Calculated from t) vs temperature relationship given in: Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents, Physical Properties and Methods of Purification, 4th ed.; John Wiley and Sons: New York, 1986. b Fluorescence lifetimeandrotation timeare themean (andstandard deviation) of five determinations; excitation = 384, 387 nm; emission = 430,440 nm. Fluorescence lifetime and rotation time are the mean (and standard deviation) of three determinations; excitation = 384,403 nm; emission = 460, 470 nm. Rotation time was determined by fixing the value of ro at 0.35 (see text for explanation). Fluorescence lifetime and rotation timeare themean (and standarddeviation)of ninedeterminations with excitation from 402 to41 1 nm and emission at 430,440, or 470 nm. The value of zr is also the mean of the two determinations at 406 nm with 430-nm emission. (1

TABLE II: Model EL ids and Reduced Rotation Times for C102 and CIOZ:T&omplex semiaxes (A) c102 c102 ClO2:TFE C102:TFE

.--0

2 2.22 2 2.99

5.27 5 5.91 2.99

5.27 5 5.97 8.0

0.436 0.336 0.455 0.399

1.54 2.22 1.35 1.21

40.0 27.8 58.5 65.1

4.I

1

4.1

I

'

I

v)

a, CT

- 4.

2200.

1650.

: r

I

~1100.~

550-

0.

t

L

Figure 2. Typical time-resolved polarized fluorescence decays of Cl02 in decalin at 272 K. The lower panel shows both the parallel (upper trace) and perpendicular (lower trace) decays, along with the instrument function, which has been shifted in time to provide a clearer presentation. The upper panels show the residuals for the parallel (upper) and perpendicular (lower) decays when simultaneously fit to the functional forms in eqs 3 and 4 with T I = 2930 ps, = 123 ps, and ro = 0.354. For this fit, x 2 = 1.21.

eq 2, the reduced rotation time, rr/q, of a solute of a given size and shape experiencinga given hydrodynamicboundary condition should be constant at a given temperature. Table I shows that there is also a significant difference between the values of r r / 7 in these two solvents. Consistent with many results described previously, the rotation time in the alcohol is significantly slower

g

I

I

bIO.NQ.3 M TFE

d) 0.0085M

w

C102/decalinh 2900 f 70 124 f 3 0.351 i 0.006 3.85 C102/TFEC 6100 i 100 340 f 20 0.348 f 0.005 6.07 3.85 complexd 3400f 70 220 f 20 0.35

I

0.07

TFE

0.06

m 4 II

s

0.05

0'04 0.02

d

0

300

350 400 WAVELENGTH (nm)

450

Figure 3. Absorption spectra of Cl02 in dccalin at 297 K with various concentrations of TFE. There is an isosbestic point at 371 nm, clearly shown in the expanded panel on the right. The systematic increase in intensity on the red side of the band as the concentration of TFE is increasedisattributed totheabsorptionduetothe 1:l C102:TFEcomplex.

than would be expected from DSE theory based on the results obtained in the nonpolar, noninteracting decalin solution, even after correcting for the differences in bulk viscosity. Within the DSE interpretation, this suggests that the size, shape, and/or boundary condition of the rotating species in these two solutions are not identical. The applicability of the DSE model to the rotation of C102 in pure decalin was examined by calculating the reduced rotation time for two oblate ellipsoid models of C 102. Each model ellipsoid was assumed to have a volume equal to that of C102 as calculated from van der Waals increments (233 A3).55 In one case, the minor semiaxis was set to 2 A, a reasonable estimate for the average thickness of C102,56and in the other, the major semiaxis was set at 5 A to represent its average in-plane radius. Figure 1 shows space-filling representations of C102 along with the first model ellipsoid. For each model thevalues of C (for slip boundary conditions) and F may be and they are given in Table I1 along with the calculated reduced rotation times for slip boundary conditions. Note that the predictedvaluesof rr/qunder slip hydrodynamics agree quite well with the experimentally obtained rotation time in decalin. Stick boundary conditions result in calculated reduced rotation times which are much too large for any reasonable model ellipsoids. These results suggest that the model for C102 as an oblate ellipsoid is a useful one and that the rotation of the species in decalin can be well described by the DSE model assuming slip boundary conditions. This is consistent with the notion that slip boundary conditions are most closely approximated by situations in which there is little specific interaction between the solvent and solute and when the solvent molecules are smaller than the rotating solute. Although the size of a decalin molecule is certainly not negligiblecompared to C102, the solvent moleculesare smaller; more importantly, the nonpolar alkane has no specific interactions with the rotating species. As noted previously, the value of rr/q is clearly larger in TFE solution than indecalin. Thus, theremust be a sourceof additional friction in TFE. One possible explanation is that the alcohol solvent provides a boundary condition other than the slipcondition found in decalin. Such a boundary condition would necessarily be intermediate between stick and slip. Alternatively, dielectric friction could be invoked to account for these results. However, rather than consider these approaches,our analysis will investigate whether the results may beexplainedquantitatively by DSE theory in terms of solvent attachment, without proposing intermediate boundary conditions or dielectric friction. Characterizationof the 1:l Complex. Figure 3 shows absorption spectra of a series of solutionsof C102 in decalin to which varying quantities of TFE have been added. In all cases, the amount of TFE is quite small (at most 0.06 ~01%alcohol) and much less than that of the minor component in similar previous studies involving mixed ~olvents.5~-5~ With increasing TFEconcentration, the absorbance on the red side of the band (-400 nm) increases,

Rotational Diffusion of Coumarin 102 in Trifluoroethanol

The Journal of Physical Chemistry, Vol. 97, No. 8, 1993 1499

TABLE III: Thermodynamic Parameters of 1:l Compkxes complex

\

CIO2:TFE C102:TFMP C102:HFP acetone:TFE acetone:HFP

a+d

Kcqa(M-])W (kcal/mol)

ASo (cal/(mol K))

I10 f 20

-6.8 f 0.9

51 f 9 1400 f 200

-5.7 f 0.7 -7.5 f 1

-13 f 3 -11 f 3 -10 f 3

-5.1'

-13.1'

-6.7'

a Equilibrium constant for complexation experimentally determined at 297 K. Determined over the temperature range 274-297 K,except asnoted. From: Joesten, M. D.;Schaad,L. J. HydrogeitBonding Marcel Dekker: New York. 1974.

350

400

450 500 WAVELENGTH (nm)

550

600

Figure 4. Fluorescence spectra of Cl02 in decalin at 297 K with various concentrations of TFE. The excitation wavelength is the isosbestic wavelength, 371 nm.

while there is a simultaneous decrease in intensity on the blue side (-350nm). 1naddition.anisosbesticpoint isclearlyobserved at 371 nm. In Figure 4, the fluorescence spectra from the same series of solutions are presented. The excitation wavelength is the isosbestic wavelength, 37 1 nm. Systematic changes in these spectra are also observed. As the concentration of TFE is increased, there is a drop in the fluorescenceintensity on the blue side of the spectrum and a corresponding increase in the intensity on the red side. Analogous changes in both spectra (including the presence of an isosbestic point) are observed upon the addition of similar small amounts of TFMP or HFP, although the relative magnitudes of the changes are different for each alcohol. These results suggest that, upon the addition of alcohol to the solutionsof C 102in decalin,a complexis formed whose absorption and fluorescence spectra are red-shifted with respect to the free C102 species. Further evidence for this interpretation is provided by excitation spectra monitored at 384 nm, on the blue edge of the emission spectrum. These spectra (not shown) are all essentially identical in shape, showing that the species in solution emitting at 384 nm is the same in all solutions. Thus, there are substantial numbers of C 102moleculesunaffectedby the presence of alcohol molecules in solution. This strongly supports the proposal that there is an equilibrium established between free C102 species and a hydrogen bonded complex. Since the emission at 384 nm is due solely to free C102, the relative concentration of free C102 in each solution can be calculated from the absorption and emission data.60 Assuming the 1:l equilibrium

+

C102 TFE F? C102:TFE an equilibrium constant for complexation can be determined.6' Consistentequilibriumconstants are obtained fromsolutions with differing TFE concentrations, with an average value of Kq = 1 10 f 20 M-1 at 24 OC. This value is the averageof 13 determinations performed from a total of five series of experiments. The relatively large deviation is probably due to the uncertainty of TFE concentration in the solutions, arising from the very small (3.0 ILL)quantities delivered during sample preparation. Similar experimentswere performed with TFMP and HFP,and the results are summarized in Table 111. The observed trend in complexation equilibrium constants at room temperature is consistent with the relative hydrogen bond donating strengths of the three alcohols. The strength of the hydrogen bond formed in these complexes is approximatelymeasured by A W for the association. Anestimate ofthisquantity, as well as &So, was obtained from the temperature dependence of the equilibriumconstant measured over the narrow range 274-298 K. These enthalpies, also listed in Table 111, all fall within the range expected for a single hydrogen bond, and their relative magnitudes reflect the expected relative strengths of the hydrogen bonds formed

with these fluorinated alcohols. The negative values of ASoare also consistent with formation of the proposed complex from two independent molecules. In addition, the thermodynamic parameters for the complexation of TFE and HFP with acetone62 are presented in Table 111. These results compare favorably with those obtained in the present study, supporting the interpretation that a 1:1 complex due to a hydrogen bonding interaction is formed between C102 and the fluorinated alcohols, probably at the carbonyl oxygen. In addition, preliminary semiempirical calculations also suggest that the carbonyl oxygen is the preferred site of interaction with TFE.63 Rotation Times of C102:TFE Complexes. Time-resolved fluorescence measurements were made with mixed solutions containing small amounts of TFE at 272 K. The concentration of TFE in these samples was about 0.023 M, which results in 4040% of the C102 present in the form of 1:l complexes. Emission was monitored at either 430, 440, or 470 nm, and excitation was made at several wavelengths from 370 to 41 1 nm. Below 400 nm, there is significant absorption of both the free species and the complex, while at higher excitation wavelengths essentially only the complexspeciesabsorbs. Rotation times using excitation wavelengths between 370 and 398 nm varied from 160 to 200 ps, values which are all greater than I , for C102 in pure decalin. This is reasonable, since at these wavelengths both free C102 and the complex absorb. (The values do not monotonically increase as the excitation wavelength moves to the red, but vary as the relative absorbance of the two species changes across this region.) At 398 nm the absorbance is predominantly due to complex; thus, the rotation time of the complex is expected to be slightly greater than 200 ps. The quantitative estimate of I, for the complex was obtained by averaging the observed rotation times for excitation wavelengths between 402 and 41 1 nm. As shown in Table I, the value is 220 f 20 ps. There appears to be a small systematic rise in the observed rotation time as a function of wavelength in this region, from 206 ps at 402 nm to 220 ps at 406 nm to 240 ps at 41 1 nm. (The uncertainty in these rotation times is about 5%) Based on the calculated equilibrium constant and extinction coefficients for the two species, at most 3% of the absorption at 402 nm is due to free C102, with the percentage decreasing rapidly with wavelength. Thus, the observed rotation time at 402 nm may be a bit too low, due to some absorption by free C102, and the value obtained at 411 nm may be increased slightly by absorption of a small amount of higher order complexes.64 Therefore, 220 f 20 ps seems to be a reasonable estimate of I, for the 1:l complex. In any case, the observed values of r,/s for the rotating speciesin pure TFE and the complex in decalin are nearly identical. Within the DSE interpretation, this suggests that the product FCV is the same for the two cases; that is, that the rotating species has effectively the same size and shape and experiences the same boundary conditions in the two systems. For the 1:1 complex in decalin solution, the site of attachment and the shape of the complex are not known with certainty. Thus, it is not possible to model the rotating species in any definitive way. Still, an argument can be made that the results areconsistent with solvent attachment to the C102, along with slip boundary conditions. Using van der Waals increments,sS the molecular

Is00 The Journal of Physical Chemistry, Vol. 97, No. 8, 1993 volume of TFE is 66 A’, and so the volume of the complex is estimatedto be 299 As. Again, two possible models of the complex are presented in Table 11: one an oblate ellipsoid with a minor semiaxis of 2 A and a second a prolate ellipsoid (based on the proposed attachment of the TFE to the carbonyl oxygen) with a major semiaxis of 8 A. The resulting values for rr/w are in approximate agreement with the observed value. We note that the calculated rotation time is sensitive to the specificdimensions used for these model ellipsoids. However, these calculations, and similarly those previously described for free C102, are not presented in an effort to determine the true shape of the rotating species. Rather, this modeling shows that the experimental result rr = 220 f 20 ps is not unreasonable for a species such as the proposed 1:l complex of C102 and TFE experiencing slip hydrodynamics in decalin solution.

conclusion The rotation times of C102 in decalin and TFE, and of the 1:1 complex of C 102 and TFE in decalin, have been measured using time-resolved fluorescence methods. The rotation of C102 in decalin is adequately described by the DSE equation assuming slip hydrodynamics, as is the C102:TFE complex in decalin for reasonable choices of its geometry. The reduced rotation time, rr/wrof C102 in neat TFE differs widely from its value in neat decalin but is indistinguishable from that of the C102:TFE complex in decalin. This observation suggests that rotation of C102 in neat TFE can be interpreted in terms of rotation via slip hydrodynamics of a 1:l complex. Thus, at least in this strongly hydrogen bonding solvent, the idea of the solvent attachment is able to quantitatively explain the observed rotational dynamics. Of course, other explanations for the present results could also be offered. It is possible, to rationalize why rr/q for C102 differs in decalin and TFE using dielectric friction models or by invoking variable boundary conditions. We have not done so because our goal is not to determine the relative merits of these various approaches in general. Rather our purpose is to show that, for this system, the simple model of solvent attachment, which has a clear molecular interpretation, provides excellent agreement with experimentalresults. Whether this approach would be useful for understanding the dynamics of similar probe/alcohol systems depends on the lifetime of the hydrogen bonds formed to the soluteandthuson thestrengthofthesehydrogenbonds. Although the ClO2/TFE system is special in that the spectroscopy allows the study of isolated 1:1 complexes, the hydrogen bonding strength is not exceptionally high. Thus, the same picture may indeed be applicable to many other systems. Further studies are underway to investigate this possibility.

Acknowledqment. R.S.M. acknowledges a Whitaker Foundation Grant of Research Corporation,the donors of the Petroleum Research Fund, administered by the American Chemical Society, and the Hackman Scholars program of Franklin and Marshall Collegefor their support. D.L.B.also thanks the MerckCompany Foundation’s Undergraduate Science Research Program. M.M. acknowledgesthe Division of Chemical Sciences, Office of Energy Research, US.Department of Energy, for partial support of this work. References rod Notes (1) Eisenthal, K. B.; Drexhage, K. H. J. Chem. fhys. 1969, 51, 5720. (2) Einstein, A. Ann. fhys. 1906, 19, 371. (3) Debye, P. Polar Molecules; Dover: New York, 1928. (4) Perrin. F. Phys. Radium 1934. 5, 497. ( 5 ) Tao, T. Biopolymers 1%9, 8, 609. (6) Youngren, G.K.; Acrivos, A. J . Chem. fhys. 1975, 63, 3846. (7) Hu, C. M.; Zwanzig, R. J. Chem. fhys. 1974, 60, 4354. (8) Fleming, G. R. Chemical Applications of Ultrafast Spectroscopy; Oxford University Press: New York, 1986. (9) Chuang, T. J.; Eisenthal, K. B. Chem. Phys. Len. 1971, 11, 368.

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Rotational Diffusion of Coumarin 102 in Trifluoroethanol (63) Marrone, T. J.; Maroncelli, M. Unpublished results. (64) Carefulexaminationoftheextremerededgeof theabsorptionspectra of the mixed solvent solutions shows that, at the higher concentrations of alcohol and at lower temperatures, there appears to be a very small amount of a third absorption component. presumably attributable to 2:l (or possibly higher order) alcohol:C102 complexes. Although it is difficult to determine quantitatively, we estimate that, under the conditions uscd for measuring the

The Journal of Physical Chemistry, Vol. 97, No. 8, 1993 1501 rotation time of the 1:l complex, the relative absorbance of the higher order complexesincreascswithincreasing wavelength, reachinga maximumofabout 10% at 41 1 nm. In this case, we observe an apparent continuous change in the rotation time with increasing wavelength rather than a multiexponential decay with changing relative contributions of two (or more) components, because the various rotation times are too similar to be resolvable with our instrument.