Volume 101, number 4.5 CHEMICAL PHYSICS LETTERS 28 October 1983

EVIDENCE FOR SOLVATION STRUCTURAL DEPENDENCE

OF ROTATIONAL DIFFUSION ANISOTROPY

1M.J. SANDERS and M.J. WIRTH Department of chemistry. University of Wisconsin-Madison. Madison. Wisconsin 53706, USA

Received 6 March 1983; in fmal form 12 August 1983

The rotational diffusion behavior of tetracene in ethylene glycol and u-dodecanol was studied by fluorescence depolari- zation spectroscopy. The data show that the convolution of the anisotropy function with the instrument response has op-

posite signs for the two solvents. Computer simulations of the anisotropy functions indicate that the relative values of the diffusion constants must be solvent dependent. Tetracene exhibits much faster reorientation in its molecular plane in ethyl- ene glycol than in dodecanol. These results suggest that solvation structure, in addition to solute geometry, influences the relative values of the diffusion constants.

1. Introduction

Knowledge of the mechanisms of rotational diffu- sion is crucial to the understanding of liquid dynamics. The Debye-Stokes-Einstein model [ 1] describes the rotational diffusion behavior of large molecules in continuum fluids. This model appears to be accurate for many chemical systems, and it is convenient be- cause the predicted decay curves are exponential [z] and the relative values of the diffusion constants about the solute axes are approximated from the lengths of the axes by the Perrin equations [3]. Frequently, the rotational diffusion constants of organic molecules are larger than those predicted by the Debye model, presumably due to weaker solvent-solute interac- tions. Rotational diffusion in this case is described by applying the “slip” boundary condition [4,5] to the Debye model, with the strong interaction behavior described by the “stick” boundary condition. Dif- ferent behavior is possible for viscous solvents, in which reorientation occurs through large angle mo- lecular jumps [6] _

The additional complexity of anisotropic, equilib- rium solvation environments is not accounted for by the Debye model. Experimentally, the existence of anisotropic solvation environments would be observed as a deviation from the Debye behavior, and the rela-

tive values of the reorientation rates for the three axes would be solvent dependent_ Observation of the effects of solvation structure is complicated by the fact that the slip boundary condition, which appears to prevail for non-polar solutes, also gives rise to changes in the relative values of the diffusion constants. Additionally, experimental resolution of the multiple exponential decays for a general ellipsoid of revolution is difficult_ Deviations of the experimentally determined diffusion constants from predicted values are generally attrib- uted to solvent attachment or to slip behavior, and

any possible effects of solvation structure are ob- scured.

The purpose of this work is to determine whether solvation structure affects the rotational diffusion of the large aromatic molecule tetracene. Fluorescence depolarization measurements are used to determine reorientation anisotropies. The approach used to avoid ambiguous interpretation due to slip behavior is to identify a solvent for which the reorientation behavior departs greatly from that predicted by molecular ge- ometry using either stick or slip boundary conditions. If such an effect were solvent dependent, this would be strongly suggestive of a solvation structure contri- bution to the rotational diffusion process. A means of identifying a change in axes of rotation isoutlined from the theory of fluorescence depolarization behavior_

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Volume 101. number 4.5 CHEMICAL PHYSICS LETTERS 28 October 1983

2. Theory

The theory for the relationship between the rota-

tional diffusion constants and fluorescence depolariza- tion behavior is well understood. and has been described by Tao [2] and Chuang and Eisenthal [7]. The fluo- rescence polarization anisotropy. R(t). is defined as folIo\~s:

R(r) = [I,(f) - -I~Cmw&J + ~l,Wl - (1) The exact dependence of R(t) on the diffusion con- stants is determined by the relationship between the molecular absorption and emission axes. To identify changes in the approximate rotational symmetry axis. ir is important to select a suitable absorption axis of tetracene. Our designation of the tetracene ases is given in fig. 1. For absorption into the x-polarized. third ex- cited singlet state. and emission from the),-polarized. lowest excited singlet state. the fluorescence depolari- zatlon is described by Eisenthal [7]_ as follows:

R(r)= ${(a -f )esp[-(6D + ?A)r]

-(a-+;)esp[-(6D - ?a)?]), (2)

(Y=(D_~+D~,+D;)/~A. D=;(Dx+DF+Dz).

A=(D_;+D;+D;-D_yD,. -D,,Dz -D2Dx)1~3_

Eq. (2) describes the anisotropy for a general. asym- metric rotor. Changes in the relative values of the dif- fusion constants can change the sign of R(r) if the es- citation and emission axes are appropriately selected. The conditions under which this sign changes can be more readily seen by reducing eq. (2) to describe the anisorropy for a symmetric top. If the x axis is the rot;ltional diffusion symmetry axis, then the equation

R(r) = -+ exp(-6Dzr) (3)

Fig. 1. .&MS and transition dipoles for tetracene. So + S1 is _r-polarized at 475 nm; SO + S3 isx-polarized at 294 nm. Di- mensions are 14.2 _S (x aG.s), 7.3 E\ (_v alis), 3.2 A (s 3G.s).

is obtained: similarly, if the z axis is the symmetry axis. then the equation

R(f) = -A exp[-(2Dx + 4Dz)t] + & exp(-6D,t) (4)

is obtained. From these relations it is clear that the predicted behavior for the z-axis rotor is much dif- ferent from that for the x-axis rotor. If Dz SD,, then the opposite signs of the pre-exponential terms in eq. (4) result in a change in sign of the fluorescence aniso- tropy during the decay.

We have determined from numerical integrations of the Perrin relations for tetracene modeled as a general ellipsoid. as described by Small and Isenberg [S], that its behavior is expected to be that of a prolate sym- metric top with fast rotation about the long axis. If tetracene instead reorients fastest in its molecular plane, as is the case for anthracene and other aromatics [9,10], this behavior would be observed as a positive sign in the anisotropy function. Further. a solvent dependence of the sign of the anisotropy function would be evi- dence for an influence of solvation structure on the solute rotational diffusion constants.

As noted above, the rotational diffusion model is not expected to apply to the reorientation of tetracene in viscous solvents. so that eqs. (Z)-(4), which were derived for rotational diffusion. may not be valid. How- ever_ Zinsli [ 1 I] has shown that the use of the rota- tional jump model leads to an equation similar to eq. (2), with the diffusion constants replaced by average jump angles. It is straightforward to show that R(t) for tetracene behaves similarly for jump diffusion and small-angle diffusion_ Thus. a positive sign in R(t) still indicates that the z axis is the fastest axis, without re- quiring the strongly damping diffusion limit to hold in these viscous solvents.

3. Experimental

The optical arrangement was that of conventional 90” fluorescence depolarization experiments. The ex- citation source was a cavity-dumped rhodamine 6G dye laser, synchronously pumped by I W from the 5 14.5 nm line of an argon ion laser mode locked at S2 MHz. The cavity dumping repetition rates was typi- cally 82 kHz. After being frequency doubled to 294 nm, the excitation beam was passed through a Glan- laser prism. Fluorescence in the parallel and perpen-

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Volume 101, number 4,s CHEMICAL PHYSICS LETTERS 28 October 1983

dicular directions was observed through a high extinc- tion polaroid. Powers were kept less than 0.1 mJ per pulse to avoid saturation and non-linear spectroscopic

processes. The decay constants of tetracene are significantly

faster than the instrument function, thus optimiza- tion of the instrument reproducibility and noise prop- erties is important. A squirrel cage lP2SA photomul- tiplier, wired for -1 S ns rise time [ 121, was used in the analog mode, and its output was detected by a Tektronix 7000 series oscilloscope with an S4sampling plug-in. Contributions to the response function due to trigger drift were minimized by optical triggering, in which a small portion of the beam was split off and focused onto a TIED-56 photodiode. The sampling was triggered on the sharp rising edge of the photodiode pulse. The noise on the sampled waveforms was mini- mized by signal averaging with a CBM microcomputer interfaced to the sampling oscilloscope_ Data was ana-

lyzed using a combination of the method of moments

deconvolution [ 131 and least-squares curve fitting. The

tails of the parallel and perpendicular curves were matched and the sum of the experimentally deter- mined curves. I;(f) + 21;(t), was analyzed for the fluo-

2 4 6 6 10 I2 14 zi

Timebs)

Fig. 2. Typical photomultiplier response function, along with simulated fluorescence curve 1; (short dashes) andfi (long dashes). The curves were calculated from eq. (3) for a value of D, = 1.39 X log s-t_ This would correspond to a value of TAR = 120 ps if the molecule were spherical.

rescence decay time using the method of moments. Then the difference I;(t) - I;(t) was analyzed for re- orientation time constants using least squares. This procedure was reiterated until a self-consistent solu- tion was obtained. A typical response function for the system is shown in fig. 2, along with simulated paral- lel and perpendicular fluorescence curves. These curves were calculated for a reorientation anisotropy described by eq. (3), with a fluorescence lifetime of 5.0 ns and a diffusion constant D = 1.39 X log s-l_ For a spheri- cal molecule, this would correspond to a reorientation time constant of 120 ps. The system was tested by measuring the rotational diffusion constant of rhod- amine B in n-propanol, which has a decay constant similar to that of tetracene. The measured value of 3 10 f 70 ps is in agreement with the 250 ps value re- ported in the literature from picosecond experiments for the excited-state reorientation [ 141.

Tetracene, n-dodecanol and ethylene glycol were used without further purification. Concentrations were kept below 10 --4 M to avoid possible complications due to aggregation. No concentration effects were ob- served in the range 10-4--10-6 M.

4. Results and discussion

Representative fluorescence depolarization data are shown in fig. 3 for tetracene in ethylene glycol and in tz-dodecanok The observed positive and negative aniso- tropies are small but reproducible. For both solvents tetracene was excited into the S, level at 294 nm. The time-dependent fluorescence intensities, I, and IL of eq. (I), are shown to be convoluted with the relatively broad photomultiplier response, shown in fig. 2. Des- ignating the convoluted curves as 1; and 1;. the ex- perimentally determined anisotropy is plotted in fig_ 3 as 1; - I;, where it is shown that this function changes sign with solvent. Throughout the discussion. the term “experimental anisotropy” refers to the difference Z; -I;, rather than the true anisotropy defined in eq. (1). To determine whether the sign change in 1; - Z; corresponds to a sign change in R(r) requires exami- nation of the convolution integral. The photomulti- plier response, c(r). convolutes Ir and I1 individually; however, due to the additive nature of the convoh:- tion theorem, the function I,, -IL is convoluted, as shown below:

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Volume 101. number 4.5 CHEhlICAL PHYSICS LETTERS 28 October 1983

Time@rs)

Time&)

tion oscillates. For the two solvents studied, ethylene glycol distinctly exhibits a positive sign indicative of the oscillating function. For n-dodecanol, a negative sign is observed. which indicates behavior either ac- cording to eq. (3) or to eq. (4) with significantly dif- ferent relative D values. In either event, the sign change in the experimental anisotropy with solvent indicates that the relative values of the diffusion constants of tetracene differ for these two solvents.

The amount by which the relativevalues ofthe dif- fusion constants change with solvent can be estimated from simulations of the experimental anisotropy. These data were simulated by convoluting the instru- ment response function with eq- (4) for several values of Dz/DX. These simulations are plot ted in fig. 4, where it is shown that a ratio of Dz/DX less than 3 results in a negative value for f; --I;. DzIDx must be at least 6 for the experimental anisotropy to have no negative portion. The simulations thus show that there must be at least a factor of 2 change in the relative values of the diffusion constants to account for the experimen- tal decay curves. We note that the factor of 2 depends

Pig. 3. Parallel (short dashes) and perpendicular (long dashes) fk~~rrs~~ncc CII~WS, and the difference 1i - ii (solid fines) for tetraccnc in dodrcxtol (upper) and ethylene gIycoi (Iower). excited af 294 nm. The diffcrenrc curve is calculated from the rJ\v data. vv ithow deconvolution.

I;(f) - I;(f) = j- ; ‘,(7’) -I,(T)] C(r - T) d7’. (5) -co

Upon convolution, the behavior of 1; - Z; can be posi- tive. negative, or oscillate. depending upon the rela- tive values of the diffusion constants. and the photo- multiplier time response. A positive sign during any pdrt of the decay is a definite indication that the func-

0 2 8 IO

Fig. 4. Simulations of the convoluted anisotropy function using eq. (4). with varying ratios of 0=/O,. Calculated for constant Dz = 2.78 X 10’s’-‘. (a) Dz,,Dx = 6, (b) Dz/Dx = 5, (cl DzfDx = 3. @I D=fDx = 1. These curves show that DzJDx must be at least 6 for the e.\perimentaIly observed anisotropy function to bepositive throughout thedecay, and thatDz/Dx must be no more than 3 for the observed anisotropy to be negative throughout the decay.

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Volume 101, number 4,5 CHEMICAL PHYSICS LETTERS 28 October 1983

on the magnitude of the D, value used in the simula- tion. These curves were calculated for time constants that demonstrate the smallest possible change in the allowed values of D,/D,. Decreasing the value of D, used in the simulations results in an increase in the change required in Dz/Dg in order to change the sign in the experimental anisotropy. The change in the ratio D,/D, may therefore be much larger than 2. An even more dramatic solvation effect is thus possible, which is a change in the most rapid axis from x to z for ethyl- ene glycol. While x is expected to be the most rapid axis, anisotropy cannot be used to distinguish the two cases.

As noted earlier, eq. (4) was derived from the dif- fusion equation, which may not be valid for a solvent such as ethylene glycol; however, the equation describ- ing reorientation behavior in this case will be similar in form to that of eq. (4). The similarity between the *reorientation behavior of tetracene in ethylene glycol

(fig. 2, lower) and fig. 4a is additional evidence that similar equations describe rotational diffusion and re- orientation in the viscous solvent ethylene glycol. The early parts of both curves remain near zero for a sub- stantial period of time, unlike fig. 4d, in which the curve deviates from zero almost from the start. Recall that the difference I, -IL is convoluted with the photomultiplier response shown in fig. 2. This leads to a smoothing of the anisotropy curve, and the early negative anisotropy which is predicted by eq. (4) is

obscured. It was stated above that the slip limit of rotational

diffusion can result in a change in the relative diffu- sion constants, and does not require invoking solvation structure. It must be detemrined whether this effect can be the cause of the sign change in 1; -I;_ Hu and Zwanzig [4] have determined rotational friction coef- ficients for symmetric tops, and Youngren and Acrivos [ 151 have extended the determination to general el- lipsoids. Therefore it is possible to predict from solute dimensions what the effect of the slipping limit on re- orientation behavior is expected to be. We have car- ried out these calculations for tetracene with the di- mensions given in fig. 1. These calculations show that slip cannot result in a positive experimental anisotropy during any part of the decay curve, thus we conclude that slip does not explain the observed changes in the relative values of the diffusion constants.

An experimental aspect to be considered in the in-

terpretation is local heating of the environment due to excitation into the S3 electronic state. It was neces- sary to select this short-axis polarized state for the anisotropy function to be oscillatory. If the excess spectroscopic energy were instantaneously equilibrated with all degrees of freedom in the solvation environ- ment, the local temperature would rise very rapidly. However, local heating appears to have only a small effect, if at all, on the rotational diffusion constants. as shown in other work [ 16- 1 S]. While it is possible that local heating from excess energy shortens the re- orientation times of tetracene. it would not affect the conclusion drawn from the experimental data: the rela- tive values of the diffusion constants are dependent upon solvent as well as solute.

The data analysis thus reveals that the relative values of the reorientation constants of tetracene change with solvent, and that this change is not accounted for by slip dynamics. This conclusion is contrary to the usual assumption that the relative values of the diffusion constants are determined solely by the solute geome- try,and do not change from solvent to solvent, except for possible solvent attachment. The results thus indi- cate that the structure of the solvation environment has a marked influence on the rotational diffusion be- havior- With these high viscosity solvents, the solva- tion structures can have lifetimes on the order of the rotational diffusion time of tetracene.

Based on molecular geometry and the application of the Perrin relations. tetracene is expected to reorient most rapidly about the x axis and thus have a negative experimental anisotropy. Since the behavior of tetra- cene in dodecanol is consistent with that predicted by the solute shape, and tetracene in ethylene glycol be- haves anomalously, ethylene glycol appears to form an anisotropic solvation structure that allows unusually fast reorientation in the molecular plane. It would be of great interest to determine the solvation structure of ethylene glycol around tetracene, and to under- stand the diffusion behavior of tetracene in this envi- ronment. Improved time resolution will allow a better test of the Zinsli model for tetracene reorientation. Ultimately, the rotational diffusion experiment alone cannot give sufficient information to characterize the anisotropy of the solvation environment_ We are cur- rently emplying two-photon spectroscopic measure- ments [ 191 to provide additional solvation structural information about tetracene.

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Volume 101. number 4.5 CHEMICAL PHYSICS LETTERS 28 October 1983

We are grateful to the National Science Founda- tion and the Graduate School of the University of Wisconsin-Madison for support of this research. We

are also grateful to the Eastman Kodak Company for Fellowship Support for MJS. We wish to thank Drs. Irving Isenberg and Enoch SmaII for help with details of the method of moments and the computer analysis of the data_

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