J. Phys. Chem. 1987, 91, 2693-2696
2693
Solvation Dynamics in Ethanol Shyh-Gang Su and John D. Simon*+ Department of Chemistry, University of California at San Diego, La Jolla, California 92093 (Received: February 1 I , 1987)
Solvation dynamics in ethanol were studied by measuring the time-resolved Stokes shift of the emission from the twisted intramolecular charge-transfer state of bis(4-(methylamino)phenyl) sulfone (DMAPS). The time scale of the spectral relaxation, T ~ was , determined from 0 to -60 OC. Near 0 OC,T~ is comparable to the longitudinal relaxation time of the solvent, T L , in agreement with predictions based on dielectric continuum models. However, with decreasing temperature, sS falls between sL and the Debye rotational relaxation time, T ~ The . deviations of the solvation times from that predicted by a continuum model for the solvent are discussed in terms of molecular details of the solvent which are not included in the simple continuum descriptions.
Introduction The role of solvent motion in chemical reaction dynamics has received considerable attention in the past few years.'-I2 However, to date, a detailed understanding of the dynamic influence of the solvent remains elusive. Studies on intramolecular electron transfer clearly show that, in strongly coupled systems, solvent motion can play a deterministic role in the reaction These studies suggest that the time scale gauging the solvent motion can be approximated by the longitudinal relaxation time, sL(= E , / ~ ~ T T D is the Debye relaxation time and c, and c, are the high-frequency and static dielectric constants of the solvent). The longitudinal time reflects the relaxation of the polarization of a dielectric continuum subjected to a constant charge perturbation. I3-I Another approach for studying solvent coupling is to create an environment of nonequilibrium solvation around a probe molecule and measure relaxation dynamics. Electronic excitation of molecules can produce such nonequilibrium species, and the solvation dynamics can be monitored by measuring the timedependent Stokes shift of the emission spectrum.'2$16-1s The change in solvent environment, reflected by the gradual Stokes shifting of the emission band, has been treated theoretically by several workers. In particular, treatments by Bagchi, Oxtoby, and FlemingIg and van der Zwan and HynesZ0define a Stokes shift correlation function, A(t), to quantify the spectral shift. This function is defined as follows
where v(t), v ( m ) , and v ( 0 ) are the emission maxima at time t , infinity (fully relaxed), and zero, respectively. If a continuum description of the solvent and a single Debye relationship for the dielectric constant are used, A ( t ) decays exponentially with a time constant of sL.Results in agreement with these predictions have recently been observed by Fleming and co-workers for the dye LDS-750 in a variety of simple polar fluids at room temperature.12 Recently, we reported time-resolved emission data for the intramolecular charge-transfer state (TICT) of several aminophenyl sulfones.2Lq22The time- and wavelength-resolved emission behavior indicated that the photophysics of these molecules in alcohol solutions could not be completely described in terms of a simple two-state model in which emission originated from a locally excited state and a single lower energy TICT state. Wavelength-dependent rise and decays times observed in the TICT part of the emission spectrum indicated that the emission from the dipolar state was undergoing a time-dependent spectral shift. Comparison of the wavelength-dependent emission dynamics of several aminophenyl sulfones supported the conclusion that the spectral evolution reflected the restructuring of the solvent to stabilize this charge-separated state. In this Letter, we focus on the details of NSF Presidential Young Investigator 1985-1990.
~ ;
this solvation process in ethanol solutions. Unlike simple polar fluids, Le., Me2S0, linear alcohols are generally described by three regions of Debye relaxation behavior.23 The three time scales obtained reflect the rotation of the terminal C-OH group ( T =~ 1-2~ ps), monomer rotation (7D2 = 20-30 ps), and the making and breaking of hydrogen-bonded aggregates ( T >~ 100 ~ ps). In solvents characterized by multiple relaxation regions, more complicated behavior for A(t) is predicted.19 For ethanol more than 75% of the solvent molecules are hydrogenbonded at room temperature. N M R experiments show that with decreasing temperature the amount of free alcohol monomer also decreases.24 As a result, dielectric dispersion studies of ethanol show that the solvent is reasonably well characterized by a single region of Debye d i s p e r s i ~ n .Thus, ~ ~ exponential behavior for A(t) might be expected. As stated above, if one assumes a macroscopic Debye continuum model where the solvent dipoles relax by rotational diffusion, an exponential decay of A ( t ) with time scale sL is predicted. van der Zwan and H y n e ~ ~have ~ , ~recently ' reported that relaxation
(1) Velsko, S. P.; Waldeck, D. H.; Fleming, G. R. J . Chem. Phys. 1983, 78, 249. (2) Kosower, E. M.; Huppert, D. Chem. Phys. Lett. 1983, 96, 433. (3) Huppert, D.; Kanety H.; Kosower, E. M. Faraday Discuss. Chem. SOC. 1982, 74, 161. (4) Sumi, H.; Marcus, R. A. J. Chem. Phys. 1986, 84, 4894. (5) Kosower, E. M. J. Am. Chem. SOC.1985, 107, 1114. (6) Calef, D. F.; Wolynes, P. G. J . Chem. Phys. 1983, 78, 470. (7) Zusman, L. D. Chem. Phys. 1980,49, 295. ( 8 ) Brunshwig, B. S.; Ehrenon, S.; Sutin, N. J . Phys. Chem. 1986, 90, 3651. (9) McGuire, M.; McLeson, G. J . Phys. Chem. 1986, 90, 2549. (10) Mazurenko, Y. T.; Bakhshiev, N. G . Opt. Spectrosc. 1970,28,490. (11) Weaver M. J.; Gennett, T. Chem. Phys. Lett. 1985, 213, 213. (12) Castner, E.; Maroncelli, M.; Fleming, G. R. J . Chem. Phys. 1987,86, 1090. (1 3) Frohlich, H. Theory ofDielectrics; Oxford University: Oxford, 1949. (14) Friedman, H. Trans. Faraday SOC.1983, 79, 1465. (1 5) Onsager, L. Can. J. Chem. 1977, 55, 18 19. (16) Safaradeh-Amiri, A. Chem. Phys. Lett. 1986, 125, 272. (17) Halliday, L. A.; Topp, M. R. Chem. Phys. Lett. 1977, 48, 40. (18) Okamura, T.; Sumitani, M.; Yoshihara, K. Chem. Phys. Lett. 1983, 94, 339. (19) Bagchi, B.; Oxtoby, D. W.; Fleming, G. R. Chem. Phys. 1984, 86, 257. (20) van der Zwan, G.;Hynes, J. T. J. Phys. Chem. 1985, 89, 4181. (21) Su, S.G.; Simon, J. D. J . Phys. Chem. 1986, 90, 6475. (22) Su, S. G.;Simon, J. D. Chem. Phys. Lett. 1986, 132, 345. (23) Garg, S. K.; Smyth, C. P. Phys. Chem. 1965, 69, 1294. (24) Sukai, Y.; Sadoaka, Y.; Yamamoto, T. Bull. Chem. SOC.Jpn. 1975, 46, 3515. (25) Davies, M. In Dielectric Properties and Molecular Behauior; Hill, N. E., Vaughan, W. E., Price, A. H., Davies, M., Eds.; Van Nostrand: London, 1969.
0022-3654/87/209 1-2693%01.50/0 0 1987 American Chemical Societv
2694
The Journal of Physical Chemistry, Vol. 91, No. 11, 1987
by translational motion can become important when the time scale of rotational relaxation is long. The relative importance of translational motion, referred to as polarization diffusion, is gauged by the ratio DTD/u~, where D is the self-diffusion constant and a is the cavity radius of the solute. For ratios greater than 1, translational diffusion is predicted to play a dominant role; in this limit the relaxation dynamics will not be exponential and will occur on a time scale much faster than T~ Assuming that a = 4 %., a reasonable value for bis(4-(methylamino)phenyl) sulfone (DMAPS), and a self-diffusion constant of 2.0 X cm2 s-l, for ethanol at room temperature, the ratio DTD!a2 = 2.1. This result suggests that polarization diffusion will be important in the solvation process of the TICT state of DMAPS in ethanol. Both of the above models are derived from a macroscopic continuum picture of the solvent. Hubbard and Onsager28demonstrated that as a result of dielectric friction, an electrolyte solution should possess an infinite number of relaxation times, all smaller than T D which ~ can give rise to an observed relaxation time for the pure solvent which is less than T ~ More , recently, the importance of T D in determining solvation dynamics in water has been discussed by Robinson and c o - w o r k e r ~ . ~Molecular ~ dynamics simulations of Fleming30 also support the importance of a range of relaxation times between T D and TL. In addition, Calef and Wolynes31examined solvent relaxation around a charge using a Vlasov-Smoluchowski approach in which they model the positions and orientations of the solvent dipoles by a nonequilibrium density distribution. This model reveals the importance of a range of time scales in the solvation process. Model calculations in ethanol show that the average solvation time falls between T~ and T ~ A. general theoretical treatment which clearly demonstrates the importance of a range of relaxation times in the solvation process has recently been reported by Loring and Mukame1.32 In this paper, the Stokes shift correlation function, eq 1, is generated from the time-dependent emission of DMAPS in ethanol from 0 to -60 OC. The solvation times obtained are compared to those predicted by the above theories. The DMAPS structure is 0
\
//O
1
Experimental Section A cQmplete description of the experimental apparatus will be published at a later date.33 Picosecond pulses are generated by synchronously pumping a R6G dye laser with the second harmonic of a CW mode-locked Nd3+:YAG laser (Quantronix 116 modelocked at 38 MHz). Autocorrelation traces of the dye laser output (InRad 5-14) indicate that the pulses are on the order of 1-2-ps fwhm. The dye laser pulses are amplified by a three-stage longitudinally pumped pulsed dye amplifer. The output pulse energy is =l mJ/pulse, i 20% peak-to-peak fluctuations, with amplified spontaneous emission suppression of better than 100:1. (26) van der Zwan, G.; Hynes, J. T. Physica A (Amsterdam) 1983, IZIA, 227. (27) van der Zwan, G.; Hynes, J. T. Chem. P h p . Lett. 1983, 101, 367. (28) Hubbard, J.; Onsager, L. J . Chem. Phys. 1977, 67, 4850. (29) Robinson, G. W.; Thistlethwaite, P. J.; Lee, J. J. Phys. Chem. 1986, 90, 4224. (30) Maroncelli, M.; Castner, E. W., Jr.; Webb, S. P.; Fleming, G. R. In Ultrafast Phenomena F; Siegman, A. E., Fleming, G. R., Eds.; SpringerVerlag: New York, 1986; p 303. (31) Calef, D. F.; Wolynes, P. G. J. Chem. Phys. 1983, 78, 4145. (32) Loring, R. F.; Mukamel, S., submitted for publication in J. Chem. Phys. (33) Su, S . G.; Simon, J. D., to be submitted for publication.
Letters
0.0
0.0
Figure 1. Time evolution of the emission spectrum of DMAPS in ethanol at 0 "C (top) and -60 "C (bottom). For 0 OC > T > -60 "C the spectra clearly show the rapid decay of the local excited state (A,,, = 360 nm). At 0 OC, there is a rapid spectral relaxation of the TICT emission. The band shape and position of the TICT emission are constant for t > 50 ps. However, at -60 "C, the emission spectrum of the TICT state clearly undergoes a time-dependent Stokes shift. With increasing time, the maximum emission wavelength shifts to lower energy; relaxation to equilibrium solvation (A,,, = 470 nm) is not attained on the time scale plotted.
The red light is frequency-doubled (KDP = 5 1 0 % efficiency) to 300 nm and used to excite the sample. The remaining red light is delayed and used as a timing marker for signal averaging of the streak camera data. Fluorescence is detected 90" from the direction of excitation and focused on the input slit of Hamamatsu C979 streak camera. A 1-cm cell was masked so that emission over the central 0.2 cm was detected. The streak camera output is recorded by an E.G.G. Intensified Reticon (Model 1420) which is interfaced to an LSI- 11/23+ computer. The computer software is designed so that data can be accepted by the computer the prepulse examined for both intensity and position, and the acceptable data are shifted and added into memory at the laser repetition rate of 20 Hz. Time calibration was determined with etalons. Intensity nonlinearities were corrected by measuring decay curves of dilute R6G in methanol. Wavelength selection was accomplished with parrow-band interference filters (ESCO, 5-nm fwhm). From traces of the laser pulses, an instrument response of =lo ps is obtained. The resulting data are transferred to a Celerity C-1260 computer system for kinetic analysis. All decay kinetics were determined by convolving the desired functional forms with the prepulse recorded by the streak camera. M. In general, 5000 Sample concentrations were lo4 to laser shots were averaged for one decay. Bis(4-(methylamino)phenyl) sulfone was synthesized by using previously reported procedure^.^^ The product was purified by repeated recrystallization from dioxane. Results and Discussion The procedure used to determine v,(t), from which the Stokes shift correlation function A ( t ) is derived, involves several steps and will be discussed in detail in a future p ~ b l i c a t i o n . Decay ~~ (34) Rettig, W.; Chandross, E. A. J . Am. Chem. SOC.1986, 107, 5617.
'
The Journal of Physical Chemistry, Vol, 91, No. 11, 1987 2695
Letters
o-lr
5
I
-0. 4
4
c 4
-0. 8
-1. 6
1
-2
0 1.6
1.8
2
2 . 2 2 . 4 2 . 6 2 . 8
200
0
3
Figure 2. Example of the log-normal spectral fit to the data. The data shown are for DMAPS in ethanol at -40 O C . The times plotted are (*) 50 ps, (X) 200 ps, and (0)600 ps. The solid lines are the best fit of the log-normal distribution to the data. The shift of Y,, to lower energy with time is clearly revealed by these data.
600
400 Time
Wovonumber (~10' 1
(PO)
Figure 3. The log of the Stokes shift correlation function, In [ A ( t ) ] ,is plotted as a function of time. The solvation times were determined by the best fit of a single exponential to the A(t) function. The temperatures for the various plots are as follows: (-), 0 OC;(--), -20 OC;(---), -30 " C ; (-*-), -40 OC;(---), -60 OC. Temperature (X)
curves are collected in 10-nm intervals from 340'to 600 nm, covering the entire emission spectrum. The data are then fit to a sum of exponentials by using an iterative nonlinear least-squares convolution and comparative analysis. The resulting functions are then normalized by scaling the peak intensity such that the integrated area is equal to the intensity of the steady-state corrected emission spectrum at the wavelength of interest. The results from this treatment are shown in Figure 1 for DMAPS in ethanol at 0 and -60 OC. From these plots, the time evolution of the emission spectrum can be examined. In both cases, rapid decay of the local excited state is observed in the blue edge of the spectrum. The relaxation dynamics of the TICT emission can be seen by examining the region from 400 to 560 nm. At 0 OC, there is a rapid relaxation of the TICT emission. For t > 50 ps, there is no change in band shape or band position. However, at -60 OC, the Stokes shift in the TICT emission can clearly be seen. Even at 600 ps, the longest time plotted in Figure 1, the emission spectrum is still evolving in time. Emission spectra like those given in Figure 1 provide intensity information in IO-nm intervals. This is not sufficient for an accurate generation of the correlation function A(t). To overcome this limitation, these data were fit to the l o g - n ~ r m aline l ~ ~shape function. Examples of this fit are given in Figure 2 for the TICT emission of DMAPS in ethanol at -40 OC as a function of time. The log-normal function provides an excellent fit to the experimentally determined intensities and enables a more accurate determination of the emission maximum. The emission maximum of the fully relaxed emission spectrum v(-) was determined by constructing the spectrum between 2 and 3 ns after excitation. Over this time range, the maximum is found to be constant. Using v(t) and v ( m ) , one can determine the Stokes shifting correlation function. In Figure 3, the log of the correlation function, In [ A ( t ) ] ,is plotted as function of time. To a good approximation, the decays are exponential over the temperature range studied. Some curvature and oscillatory behavior are observed. However, considering the limited dynamic range of the detection system, it is difficult to state whether the deviations are significant. To gauge the solvation times, the data presented in Figure 3 were fit to single exponentials. The results are shown in Figure 4. For comparison, the values of T~ and T~ are also given. T~ was calculated from the expression T~ = ~ , ~ / E ~ T where D, is the high-frequency dielectric constant associated with the dominant region of Debye dispersion. Sumi and Marcus36have argued that for alcohols the square of the index refraction should be used for (35) Siano, D. B.; Metzler, D. E. J. Chem. Phys. 1969, 31, 1856. (36) Sumi, H.; Marcus, R. A. J . Chem. Phys. 1986,84,4272.
278
256
238
222
1 '
-20 -21
I
I 3. 6
3. 9
I/T
4. 2 (X1~.3~)
4. 5
Figure 4. The log of various relaxation times are plotted as a function of 1/T (K). The lower line shows the temperature dependence of the longitudinal relaxation time of ethanol, 7L (+). The upper line shows the behavior of the Debye relaxation time, i D(0). The solvation times, T~ (X), are found to fall in between these two limits, 7L < i s< T ~ for , the temperature range studied.
the high-frequency dielectric constant, unless t , , / t , ~ >> ~ 7D2, the > n2 for the Debye time for the monomer rotation. Since alcohols (em1 - n2 = 2.5 for EtOH at room temperature), the value of T~ will vary significantly, depending on the high-frequency constant used. Recent studies of Fleming on solvation in simple polar fluids strongly support the use of eel for calculating T ~ It. is important to point out that, by using eel as the high-frequency dielectric constant, the largest value that T~ can have in the continuum approximation is obtained. Data used for calculating the T~ values shown in Figure 4 were obtained from ref 23, 25, 33, and 31. As can be clearly seen from Figure 4, the solvation times are not described by T~ over the entire temperature range studied. Near 0 O C , T~ = T ~ in, agreement with the predictions from the continuum model. The limiting time resolution of the detection system does not allow us to determine the dynamics at higher temperature. The deviations from T~ observed for T < 0 OC indicate that the predictions from simple continuum models do not provide a complete description of the solvation dynamics. In addition, since T~ > T ~ evidence , of polarization diffusion, or relaxation by translational motion, is not reflected in the solvation (37) Weast, R.C., Ed CRC Handbook of Chemistry and Physics, 64th ed.; CRC: Boca Raton, FL, 1983.
2696
J . Phys. Chem. 1987, 91, 2696-2698
times. Yet, for ethanol, the ratio D r D / a 2is greater than unity, indicating that polarization diffusion effects should be dominant and that solvation should occur much faster than rL. The data suggest that the ratio of D r D / a Zmay not accurately gauge the importance of polarization diffusion effects. On the other hand, the molecularly based theories of Calef and Wolynes" and Loring and M ~ k a m e lthe , ~ ~experimental results of Robinson,29 and the simulations of Fleming30 suggest that a range of solvation times need to be considered. Near the solute, relaxation occurs by rotation motion of the individual molecules, an e\ nt which occurs on a time scale of rD. With increasing distalice from the solute, dipolar interaction serves to shorten the time scale of r e l a x a t i ~ n .The ~ ~ experimentally observed dynamics should reflect the superposition of this range of solvation time and fall between the two limiting dielectric relaxation times. Model calculations reported by both Wolynes31and M ~ k a m e for l ~ the ~
solvation of a charge in ethanol support this conclusion. Similar results would be predicted for solvation around a dipole. Our observation for the solvation of the TICT state of DMAPS in ethanol supports this model. It is important to stress that the observation of solvaton times between rL and r Dcannot be accounted for by a simple continuum treatment of the solvent. We are currently examining the solvation dynamics in several other solvent systems. These results will be reported shortly. Acknowledgment. The authors are grateful for support from the NSF. This work was also supported by equipment donation from EGG Princeton Applied Research and Newport Corporation as matching gifts toward the NSF-PYI grant. We thank Dr. Albert Cross for his advice in the data analysis procedure. We also thank Professor Mukamel for communicating his theoretical work before publication.
Nonlinear Susceptibilities of Finite Conjugated Organic Polymers David N. Beratan,*+$JosG Nelson Onuchic,tl and Joseph W. Perry*' Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91 109, and Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91 125 (Received: February 13, 1987; In Final Form: March 31, 1987)
Tight-binding calculations of the length dependence of the third-order molecular hyperpolarizability for polyenes and polyynes are reported. The *-electron wave functions were determined by exploiting the limited translational symmetry of the molecules. Perturbation theory was used to calculate the longitudinal component of the electronic nonresonant hyperpolarizability. To our knowledge, this is the first two-"band" calculation of third-order hyperpolarizabilities on finite n-electron systems of varying length. In contrast to the results of the one-"band" models, the hyperpolarizability densities increase rapidly and then, after about 10-15 repeating units, approach an asymptotic value.
Introduction Conjugated organic polymers are currently of great interest for use as nonlinear optical materials.' This is primarily because of the fast time response possible in the nonresonant (transparent) spectral region and the diversity of their optical, chemical, and physical properties which may allow tailoring of a material for particular applications. One goal of much of the research in this area is concerned with the development of such conjugated polymers with enhanced nonlinear susceptibilities, especially the third-order hyperpolarizability. Of particular importance for the nonlinear optical response of these materials are the delocalized electronic states associated with the conjugated a-electrons.* The nonlinear susceptibilities are known to be related to the extent of the electronic d e l o c a l i z a t i ~ n . ~However, ~~ we lack sufficient understanding of these effects to have available a reliable set of molecular design principles. At this stage, it is important to develop a full understanding of the relation of the electron delocalization and the susceptibilities to the molecular structure of the polymer. This would include, for example, the effects of the structure of the repeating units, the number of these units, or the chain length.4 In this Letter we calculate the chain length dependence of the third-order molecular hyperpolarizability of finite polyenes and polyynes. Conjugated polymers of interest have a minimum of one single and one multiple bond per repeating unit. In the limit of a long polymer, the resulting electronic states cluster into groups (or 'Jet Propulsion Laboratory. *Division of Chemistry and Chemical Engineering. NRC/NASA Resident Research Associake at JPL, On leave of absence from the Instituto de Fisica e Quimica de SHo Carlos, Universidade de S5o Paulo, 13560, SHo Carlos, SP, Brazil.
*
0022-3654/87/2091-2696$01.50/0
bands) with forbidden energy regions between them. Systems of interest produce at least two such bands. In this paper we consider only two-band homoatomic systems, although the method can be extended to more complicated repeating units. Previous studies of third-order molecular hyperpolarizabilities have been made with the use of several different model Hamiltonians. Constant and sinusoidal pseudopotentials have been utilized to generate eigenstates and from these the hyperpolari~abilities.~ One difficulty with these models is associated with parametrizing the potentials. Also, for the constant-potential model, the HOMO-LUMO gap decreases with chain length and vanishes for long-chain systems. This is inappropriate for modeling systems with bond alternation. Other models have included molecular details in a tight-binding model but considered only infinite polymer chains.2 The chain length dependence of the hyperpolarizability has also been calculated in the tight-binding limit for a one-band model of p01yene.~These calculations also ( 1 ) (a) Khanarian, G., Ed. Proc. SPIE-Int. SOC.Opt. Eng. 1987, 682. (b) Williams, D. J., Ed. Nonlinear Optical Properties of Organic and Polymeric Materials; American Chemical Society: Washington, DC, 1983; ACS Symp. Ser. No. 233. (2) (a) Agrawal, G. P.; Flytzanis, C. Chem. Phys. Lett. 1976,44, 366. (b) Cojan, C.; Agrawal, G. P.; Flytzanis, C. Phys. Reu. B: Solid State 1977, 15, 909. (c) Agrawal, G. P.; Cojan, C.; Flytzanis, C. Phys. Reu. E : Solid State 1978, 17, 716. (d) Rytzanis, C. In Non-linear Behavior of Molecules, Atoms and Ions in Electric, Magnetic or Electromagnetic Fields; Neei, L., Ed.; Elsevier: Amsterdam, 1979; p 185. (3) (a) Ducuing, J. In International School of Physics, E. Fermi LXIVNonlinear Spectroscopy; North-Holland: Amsterdam, 1977. (b) Rustagi, K . C.; Ducuing, J . Opt. Commun. 1974, 10, 258. (4) (a) Hameka, H. F. J. Chem. Phys. 1977, 67, 2935. (b) McIntyre, E. F.; Hameka, H . F. J . Chem. Phys. 1978, 68, 3481. (c) McIntyre, E. F.; Hameka, H . F. J . Chem. Phys. 1978, 68, 5534.
0 1987 American Chemical Society
