J. Phys. Chem. 1989, 93, 753-758 Pd(Cp)(C3H,) lead to the deposition of Pd. This fact is quite clear from the X-ray electron spectroscopy (XES or EDAX) spectra we have collected previously.6 From Auger electron spectroscopy no appreciable oxygen contamination was found, while carbon contamination after Ar+ sputtering to remove surface impurities was less than 10%. With use of close contact masks, as outlined elsewhere,6 photolysis of Pd(Cp)(C3H,) can be used to deposit Pd in submicron features as shown in Figure 4. While the actual squares in the figure are only 20 X 20 pm, ultimate resolution should be better, if use is made of the diffraction patterns seen. As previously mentioned, the mask-substrate distance in Figure 4a was calculated to be around 60-300 pm on the basis of the spacing of the fringes. If these patterns resulted from physical blockage of surface sites by the mask, it would then be too close for the diffraction pattern in Figure 4a to be produced. The diffraction subpatterns thus support our conclusion that the decomposition of this moolecule takes place on the surface and is truly photolytic in nature rather than pyrolytic. If pyrolysis were the driving force, laser-heated areas would surely not remain so distinct during a several hour deposition (see ref 6 for more detailed arguments on the subject). Since the neutral decomposition of Pd(Cp)(C3H5)to Pdo(g) requires 5.5 eV, as illustrated in Figure 3, the complete photolysis of Pd(Cp)(C3H5)cannot be a gaseous reaction. Such a process would have to be a two-photon process at 3.68-eV photon energy, and at a photon flux of around 6 photons/(A*/ns) this two-photon process is unlikely (similar flux per femtosecond would be necessary). Therefore, we can conclude that the deposition of Pd from the photolysis of Pd(Cp)(C3H,) occurs either from incomplete dissociation of the ligands or from the fact that the surface species are sufficiently long-lived to permit two-photon dissociation processes to occur. A third possibility is that the surface acts as a catalyst, lowering the bond energies in the molecule. Regardless of which of these processes is taking place, it is certain that photolysis of surface species must provide better pattern resolution than gaseous decomposition.
753
The photolysis of Pt(Cp)(C3H5)with 308-nm laser radiation has recently been demonstrated to lead to the deposition of Pt on quartz," with a thin-film composition of 24% C, 76% Pt. Auger electron spectroscopy of our coatings, in marked contrast, shows almost no carbon (much less than 5 1 0 % ) . This suggests either that photolysis of the allylcyclopentadienylplatinum is incomplete or that decomposition of the ligands occurs. The energetics of decomposition for Pt(Cp)(C3H,) is currently under investigation by methods similar to those reported herein. V. Conclusions We have constructed the thermodynamic decomposition cycle for gaseous allylcyclopentadienylpalladium, Pd(Cp)(C3H5). Both electron-induced ionization and photoionization were used to obtain appearance potentials with a high degree of confidence. With the use of literature data, both the ionic and some neutral parts of the cycle could be derived. This cycle and relative abundance information were used to draw the conclusion that the decomposition of Pd(Cp)(C3H5)would be relatively "clean" for photon energies above 5.5 eV. Photodeposition leading to thin-film formation is more likely to be a surface-nucleated reaction with the proper choice of photon energy (less than 5.5 eV). This surface selectivity may be very useful for obtaining the ultrafine line resolution in such demand in the semiconductor and other industries, and it is observed to result in the deposition of very clean Pd films.
Acknowledgment. This work was funded by the US.DOE through Grant No. DE-FG-02-87-ER-453 19, the Deutsche Forschungsgemeinschaft/Sonderforschung Bereicht 6 (DFG/SFB 6), the Syracuse University Senate, and Engelhard Corp. We thank G. 0. Ramsayer for his assistance in obtaining the AES results. Registry No. Pd(Cp)(C,H,), 1271-03-0. (17) Rooney, D.; Negrotti, D.; Byassee, T.; Macero, D.; Chaiken, J.; Vastag, B., submitted for publication in J . Electrochem. SOC.
Importance of Molecular Size on the Dynamics of Solvent Relaxatlon Shyh-Gang Su and John D. Simon*,+ Department of Chemistry B-041, Institute of Nonlinear Studies, University of California at San Diego, La Jolla, California 92093 (Received: June 27, 1988)
The time evolution of the Stokes shift of the twisted intramolecular charge-transfer emission from (dimethy1amino)benzonitrile (DMABN) and (diethy1amino)benzonitrile (DEABN) is examined in 1-propanol solution. Over the temperature range from -10 to -50 OC the Stokes shift correlation function, C(t),is nonexponential with an average relaxation time, ( T J , different from that predicted by theories that model the solvent as a dielectric continuum. In addition, ( T ~ for ) DMABN is faster than for DEABN, clearly showing that the solvent relaxation measured by C(t) is dependent on the size of the solute. The data are compared with recent mean spherical approximation (MSA) models for ion and dipole solvation that take into account the relative sizes of the solvent and solute. The ion-MSA theory provides a reasonable fit to the data; however, the dipole-MSA theory significantly underestimates the time scale of the solvent relaxation. Comparison with related studies on the solvation ) in the order C153 > DEABN > DMABN, opposite to of Coumarin 153 (C153) in 1-propanol reveals that ( T ~ decreases that predicted by the MSA models.
Introduction Dielectric continuum models are commonly used to gauge solvent fluctuation time scales in polar solvents.'** In particular, with a continuum model, the relevant time scale in electrontransfer processes is given by the longitudinal relaxation time, TL ( 7 = ~ ~ ~ c = , / t ~ ) . ~Whether -~ dielectric continuum theory is able to accurately gauge solvent relaxation times has prompted several 'National Science Foundation Presidential Young Investigator 1985-1990, Alfred P. Sloan Fellow 1988-1992.
0022-365418912093-0753$01 SO10
experimental studies aimed at measuring the microscopic dynamics of solvent relaxation. These studies have focused on measuring the time-dependent Stokes shift of a probe molecule dissolved in the polar solvent of i n t e r e ~ t . ~ - 'The ~ time-dependent spectral (1) (2) 1949. (3) (4) (5)
Kivelson, D.; Madden, P. A. Annu. Rev. Phys. Chem. 1980, 31, 523. Frohlich, H. Theory of Dielectrics;Oxford Univ. Press: Oxford, U.K., Sumi, H.; Marcus, R. A. J. Chem. Phys. 1986,84, 4859. Rips, I.; Jortner, J. J. Chem. Phys. 1987, 87, 2090. Sparpaglione, M.; Mukamel, S . J . Chem. Phys. 1988.88, 3263.
0 1989 American Chemical Society
754
The Journal of Physical Chemistry, Vol. 93, No. 2, 1989
relaxation is quantified by calculating the correlation function C(t)
where u ( t ) , u ( O ) , and u ( m ) are a characteristic frequency of the emission spectrum a t time t , zero, and infinity, respectively. Dielectric continuum theory predicts that in the case of a Debye solvent, C ( t ) decays exponentially with a time constant of T L . ~ Previous studies from several research groups clearly show that the solvation dynamics are much more complicated. In contrast to the predictions of dielectric continuum theory, the time dependence of C(t) is usually nonexponential with an average decay constant that is between T L and 71). These deviations have been attributed to molecular aspects of the solvation process that are not accounted for by simple dielectric continuum models. From a simple electrostatic picture, the majority of the relaxation is expected to take place in the first few solvent shells. Thus, the details of the local solvent structure and intermolecular interactions will determine the solvation process. Along these lines, several workers have recently addressed the role of solute/solvent size in the dynamics of solvation. Both analytic theories and molecular dynamics simulations have been reported. lGZ3 Tfhese theoretical studies demonstrate that the solvent molecules near the solute do not respond on a time scale of T~ but restructure on a longer time scale similar to T D . On the molecular level, the exact time scale of the response depends on the distance from the molecular solute. Using the mean spherical approximation (MSA), Wolynes19 proposed a model for ion solvation that takes into account the relative sizes of the solute and solvent. The solute is modeled as a point charge in a hard sphere and is embedded in a dipolar hard sphere solvent. The time dependence of the solvation energy was found by replacing the static dielectric constant, eo by the experimentally measured frequency-dependent dielectric constant, e(w). To a good approximation, the dynamics could be accounted for by two relaxation times, T~ and a second, slower relaxation time that takes into account the motions of the solvent near the solute. Even though this treatment focuses on ion solvation, it is reasonable to assume that the general physical conclusion will apply to the case of molecular solutes. Rips et aLZOand Nichols and Calef2' extended the ideas of Wolynes and derived analytic solutions for ion and dipole solvation dynamics within an MSA model, respectively. In a recent paper, Maroncelli and Fleming compared the ion-MSA model and time-dependent Stoke shift data for Coumarin 153 in several solvents.23 In general, good agreement was observed between experiment and theory. However, the ability of MSA theories to account for changes observed by varying the solute/solvent properties in a controlled manner has not been tested. In order to address the effect of molecular size on the solvation dynamics observed in polar solvents, we have examined the time-dependent spectral relaxation of the twisted intramolecular charge-transfer state of (dimethy1amino)benzonitrile (DMABN) (6) Simon, J. D.; Su,S.-G. J . Chem. Phys. 1987,87, 7016. ( 7 ) Su,S.-G.; Simon, J. D. J . Phys. Chem. 1987, 91, 2693. (8) Simon, J. D. Acc. Chem. Res. 1988, 21, 128. (9) Maroncelli, M.; Fleming, G.R. J . Chem. Phys. 1987, 86, 6221. (10) Castner. E. W., Jr.; Maroncelli, M.; Fleming, G. R. J. Chem. Phys. 1987,86, 1090. ( 1 1 ) Kahlow, M. A.; Kang, T. J.; Barbara, P. F. J . Chem. Phys. 1988,88, 2312. (12) Nagaragan, V.; Brearley, A. M.; Kang, T. J.; Barbara, P.F. J . Chem. Phys. 1987,86, 3183. (13) Mazurenko, Y . T.; Bakhshiev, N . G.Opt. Spectrosc. 1970, 28, 490. (14) Bagchi, B.; Oxtoby, D. W.; Fleming, G. R. Chem. Phys. 1984, 257. (15) van der Zwan, G.; Hynes, J. T. J . Phys. Chem. 1985, 89, 4151. (16) Friedrich, V.; Kivelson, D. J . Chem. Phys. 1987, 86, 6425. (17) Calef, D.; Wolynes, P.G. J . Chem. Phys. 1983, 78, 4145. (18) Loring, R. F.; Mukamel, S. J. Chem. Phys. 1987, 87, 1272. (19) Wolynes, P.G. J . Chem. Phys. 1987, 86, 5133. (20) Rips, I.; Klafter, J.; Jortner, J. J . Chem. Phys. 1988, 88, 3246. (21) Nichols, A.; Calef, D. J . Chem. Phys. 1988, 89, 3783. (22) Karim, 0.;Haymet, A. D. J.; Banet, M.; Simon, J. D. J . Phys. Chem. 1988, 92, 3391. (23) Maroncelli, M.; Fleming, G. R. J . Chem. Phys. 1988, 89, 3519.
~ '
Su and Simon and (diethy1amino)benzonitrile (DEABN) in alcohol solution as a function of temperature. The molecules studied were chosen for two important reasons. First, the direction of the dipole moment of the twisted intramolecular charge-transfer state is the same as that of the ground state.24 This is important, as it is possible that if the direction of the permanent dipole moment of the molecule is changed following excitation, the misalignment with the surrounding solvent structure could cause a forced rotation ~ of ~ the solute. In this case, the dynamics measured by C(t) contain both solvent and solute relaxation processes. Such effects have been reported for Coumarin 153.9 Rotational anisotropy studies revealed a fast component that showed an excellent correlation with the transient solvation times measured by C ( t ) . With the direction of the dipole moment held constant, C ( t ) should only reflect the solvent motions. Second, in a comparison of molecular systems, a linear response picture is always assumed. However, it has not been experimentally proven that the solvent response is independent of the magnitude of the dipole moment change. For DMABN and DEABN, the magnitude of the dipole moment change is essentially identical.24 Thus, if any differences are observed in the C(t) plots for these two molecules, the changes must be attributed to the difference in molecular size. From the van der Waals radiiZ5were calculated the molecular volumes of DMABN and DEABN, which are =95 and ~ 1 2 A3, 2 respectively. Thus substitution of the diethyl group for the dimethyl group changes the molecular volume by ~ 2 5 % . Experimental Section A Rhodamine-6G dye laser (Coherent 702- 1) synchronously pumped by a mode-locked continuous wave Nd:YAG laser (Quantronix Model 116) produced 1-ps (fwhm, Inrad 5-14) pulses at 600 nm with a repetition time of 78 MHz. The laser output was amplified at 20 H z by a three-state longitudinally pumped pulsed dye amplifier driven by a nanosecond Nd:YAG laser (DCR2-20). The amplified pulses were =l mJ/pulse. The red light was frequency doubled (KDP), producing 100 WJat 300 nm. This light was used to excite the sample. Fluorescence was detected 90' from the direction of excitation, directed through a polarizer set at magic angle with respect to the polarization of the excitation beam, and focused on the input slit of a Hamamatsu C979 streak camera. The streak camera output was digitized by an intensified Reticon (EGG Model 1420); data collection was controlled by an LSI- 1 1/23 computer. The streak traces were transferred to a SUN-3/110 computer system for analysis. Intensity nonlinearities were corrected by using emission traces of dilute solutions of R6G in methanol. Time calibration was determined by using variable spaced etalons. Wavelength selection nm fwhm) interference filters. was done with narrow band (4 Static fluorescence spectra were recorded with a 1/4-m monochromator (SPEX minimate) coupled to a Reticon detector. The sample was held in a temperature-controlled brass block. The temperature of the sample was measured by a thermocouple and was stable to f 0 . 5 'C. DMABN (Aldrich) and DEABN (Aldrich) were purified by repeated recrystallization form ethanol. 1-Propanol was dried over 3-A molecular sieves and checked for background emission. Sample concentrations were between 1 P and M. All samples were degassed and sealed. Results and Discussion The general procedure for determining the time-dependent emission spectrum from which C(t) is derived is a multistep process that has previously been described?,26 It is important to note that in order to determine C(t) a particular wavelength of the spectrum must be chosen. In recent studies, both the emission maximum and the mean emission wavelength have been used. Unfortunately, the choice of wavelength can lead to slightly different functional behavior of C(t) depending on how the shape of the emission (24) Lippert, E.; Rettig, W.; Bonacic-Koutecky,V.; Heisel, F.; Miehe, J. A. Adv. Chem. Phys. 1987, 68, 1 .
(25) Bondi, A. J . Phys. Chem. 1964, 68, 441.
The Journal of Physical Chemistry, Vol. 93, No. 2, 1989 755
Effect of Molecular Size on Solvent Relaxation
c
1.08.00
0.25
0.50
0.75
1.00
1.25
I
I
1.50
Time (ns) Figure 1. Width of the twisted intramolecular charge-transfer emission of DMABN plotted as a function of time. The width increases during the first 50 ps and then remains essentially constant. This data shows that the width dynamics occur much more rapidly than the solvent relaxation measured by C(t). The temperatures plotted are -30 OC (-) and -50 OC (---).
L
I
0.50
1
1.oo
1 1.50
2.00
Time (ns) Figure 2. Stokes shift correlation function, C(t),plotted as a function of time for DMABN (-) and DEABN (---) in propanol at -50 “C (upper traces) and -30 OC (lower traces). C(f) decays faster in the case of DMABN than in the case of DEABN, showing that the size of the solute molecule is important in determining the solvation dynamics.
spectrum evolves during the relaxation process. In a study on Coumarin 153: the spectral width was found to decrease by -20% on a faster time scale of solvent relaxation. As a result different C(t) curves could be generated depending on the particular wavelength chosen. Before the wavelength to be used for calculating C(t) for DMABN and DEABN was defined, the evolution of the spectral shape was examined. In Figure 1, the width of the emission spectrum in propanol is plotted as a function of time. For temperatures ranging from -10 to -50 OC, the width increases rapidly during the first a 5 0 ps and then remains essentially constant. In addition, the dynamics of this spectral broadening show only a mild dependence of the temperature. Similar results are observed for DEABN. Due to the constant spectral shape observed for delay times greater than 50 ps, the dynamics revealed by C(t) on this time scale are independent of the characteristic wavelength chosen. In Figure 2, C(t) is plotted for DMABN and DEABN at two different temperatures in propanol solution. For these calculations, the emission maximum was chosen in constructing C(t). In all cases, t h e relaxation function for DMABN decays faster than that for DEABN. The difference between the two molecules becomes more pronounced at lower temperature. Similar results are observed in other alcohol solutions. The time-dependent behavior of C ( t ) is dependent on the parameters used for u ( 0 ) and u ( - ) . Extrapolation of the data to find v(0) is straightforward and has been discussed in detail in several recent paper^.^,'^.^^ With the
The three Debye relaxation times are commonly associated with different molecular motions of the solvent: rotational motion of ; rotation, TD2; and hydrogen bond the terminal OH, 7 ~ 3monomer breaking in molecular cluster, 7~1.For linear alcohols, sufficient experimental data for all three Debye relaxation times and their associated dielectric constants have only been reported for 1The dominant contribution to the dielectric (27) Su, S.-G.;Simon, J. D. J . Chem. Phys., in press. ( 2 8 ) Garg, S. K.; Smyth, C. P. J. Phys. Chem. 1965, 69, 1294. (29) Davies, M. In Dielectric Properties and Molecular Behauior; Hill, N.
E., Vaughan, W. E., Price, A. H., Davies, M., Eds.; Van Nostrand: London, (26)
Phys.
Su,S.-G.; Simon, J. D., to be submitted for publication in Chem.
1969.
(30) Davidson, D. W.; Cole, R. H. J . Chem. Phys. 1951, 19, 1484.
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The Journal of Physical Chemistry, Vol. 93, No. 2, 1989
function over the temperature range studied results from the third region of Debye dispersion; thus it has become common to use the dielectric parameters for this region of dispersion to calculate the solvent relaxation time T ~ .In Figure 3 , data for DMABN in propanol at -40 "C are compared to predictions based on a dielectric continuum treatment of the solvent. The calculated curve is the prediction of a dielectric continuum model of the solvent using eq 2 for e(@). The inclusion of the fast motions (represented by the higher frequency terms in eq 2) dramatically affects the calculated dynamics compared to those of a simple Debye solvent; C ( t ) no longer decays exponentially. However, the predicted relaxation is much faster than the experimental data. In addition, identical relaxation rates would be expected for DMABN and DEABN, in contrast to the data displayed in Figure 2. These results are not surprising and are consistent with Stokes shifting measurements of a variety of molecules in alcohol solution. The differences in C(t)curves for DMABN and DEABN result from the detailed molecular interactions between the solute and the surrounding solvent. The MSA models that have been recently proposed address the role of solute/solvent size on the solvation '~ was shown dynamics. In the initial work by W ~ l y n e s ,solvation to occur on a range of time scales. However, to a good approximation, the dynamics could be modeled as a sum of two exponentials. The time scales were given by T~ and second relaxation time TG: TG-'
=
1 + f/z(rc/D,)(eo+ 3 ) TD-'
1
+ 1/(rc/DJ(L + 3 )
Su and Simon
1 1 .oo
I
2.00
3.00
4 00
Time (ns) Figure 4. S ( t ) calculated for (- - -) a single spherical ion whose volume is the same as that of DMABN and (-) the linear superposition of two
spherical ions whose volumes are equal to those of the dimethylamino and cyanophenyl groups of DMABN. The curves are essentially identical. The average solvation times are 680 and 720 ps, respectively.
(3)
The importance of T o to the solvation process was dependent on the polarity of the solvent, eo, and the ratio of the radius of the ion, rc, to the diameter of the solvent, D,. For rc/Ds >> 1, T~ becomes similar to T ~ .However, for rc C D,, 76 can become comparable to TD. Rips and co-workersZOextended the ideas of Wolynes and derived an analytic expression for calculating ion solvation within the MSA approximation. In this model, the response function, which is analogous to the experimentally measured C ( t ) ,is given by S ( t ) :
(4)
I
0.50
1
1.oo
I
1.50
2.00
Time (ns) Figure 5. Experimental C(t)curve for DMABN in propanol at -40 "C (-) is compared with that from the ion-MSA theory (- - -). The dielectric continuum prediction (---) as well as the approximate MSA model derived by Wolynes (- - -) is shown for comparison. These data show that the ion-MSA theory provides a superior fit to the data than
dielectric continuum models. where E ( t ) is the time-dependent energy of interaction between the ion and the solvent polarization. The calculation of S ( t ) is carried out by using a Laplace transformation and the relationship between E ( t ) and the complex admittance, x(p) of the system.
(5) and
E(t) = 22 ~ B + i m d p e P t x ( p ) / p 2xi 0-ix(p) in the MSA limit is expressed asZo
x@)
= XMSA@)= 1 - 1/€@)/2Ri[l + A@)]
(7)
where t(p) is the dielectric function of the solvent (p = iw) and Ri is the radius of the ion. The correction term to the ionic radius, A@), is determined from the following function: A(p) = (3r,/Ri)(VTp)J1/3 +
- 2)-]
(8)
where and
In the above expression, r, is the radius of the solvent. Thus, (31) Cole, R. H.; Davidson, D. W. J . Chem. Phys. 1952, 20, 1389.
similar to the approximate solution of Wolynes, the dynamics of S @ ) are completely determined by the dielectric function, e@), and the ratio of the radii of the solute and solvent. In order to determine S ( t ) ,the inverse Laplace transform of eq 5 is needed. This is obtained by using a numerical technique developed by S t e h f e ~ t . ~The ~ . ~time-dependent ~ solvation energy quantified by eq 4 describes ion solvation. In the case of DMABN and DEABN, the intramolecular charge transfer results in separation of charge across the molecule. As a result, these systems may be better modeled as two ions that are in contact. We have examined S ( t ) assuming an ion the size of DMABN and the superposition of the response of two ions (the dimethylamino group and the cyanophenyl group). The results of these calculations are shown in Figure 4. For the calculations shown, the radii of the dimethylamino and cyanophenyl groups were taken to be 1.9 and 2.5 A, respectively. The calculated curves show that similar results are found whether the molecule is modeled as a single ion or two ions in contact. The validity of using an MSA model to describe a pair of ions is not clear. The presence of the second ion will introduce directional dependent interactions which are not included in an MSA model. Since there is little difference in the calculated curves, a single spherical ion with the molecular volume of DMABN (DEABN) will be used in the following discussion. As shown in Figure 5 , calculations along these lines do provide a reasonable fit to the experimentally observed C ( t ) data. For these calculations, all three Debye dispersion regions (32) Stehfest, H.Commun. ACM 1970, 13, 47. (33) Stehfest, H. Commun. ACM 1970, 13, 624.
The Journal of Physical Chemistry, Vol. 93, No. 2, 1989 757
Effect of Molecular Size on Solvent Relaxation TABLE I: Average Solvation Times, temp, K 263 253 243 233 223
(TS),
DMABN 91 166 366 601 1056
for DMABN and DEABN in 1-Propanol as a Function of Temperature' experimental C(t) MSA S(t) DEABN 100 168 441 694 1263
C153 304 661 1340
DMABN
DEABN
continuum
214 300 448 680 1002
210 294 439 661 983
114 162 238 372 612
'These data are compared to average solvation times obtained from both dielectric continuum theory and an ion-MSA theory of solvation. EXperimentally measured ( T ~ values ) for Coumarin 153 (C153)' are also tabulated. All times are in picoseconds.
I
I
1
-0.801 0
I
h
1
50
100
150
Time (ps)
were used in defining e(o). The agreement is poor if a single Debye description is used. Both the dielectric continuum prediction and the approximate solution developed by Wolynes are also plotted for comparison. As shown in Figure 3, dielectric continuum theory overestimates the rate of relaxation. The agreement with the Wolynes approximation is comparable to that found with the analytic result. In order to quantify the solvation dynamics, average solvation times, ( 7g),
are calculated from the experimental and theoretical curves. These times are given in Table I. Solvation times obtained by Maroncelli and Fleming for Coumarin 1539 are also listed for comparison. The average solvation time for C153 is generally longer than for either DMABN or DEABN. One of the advantages of the MSA theory over the dielectric continuum approaches is that attention is paid to molecular size. In order to examine the effect of the relative solute/solvent size on the calculated dynamics, S(t) curves for various ratios of the solvent/solute size (k = rs/Ri)are given in Figure 6. For these calculations, c ( w ) is taken to be eq 2 with the parameters for propanol at -20 "C. The calculated curves show that the changes in the relative sizes affect the relaxation observed. As with the qualitative expression derived by Wolynes, eq 3, slower relaxation is expected with decreasing solute size. This behavior is opposite to that observed in Figure 2 and quantified in Table I. The average solvation times for DEABN are -1 5% longer than for DMABN despite the fact that the molecular volume has been increased 30%. Even though the ion-MSA theory provides a more quantitative agreement with the measured C(t) values than that provided by dielectric continuum calculations, it is not able to account for the relative relaxation times found for DMABN and DEABN. Furthermore, both DMABN and DEABN show faster relaxation than C153, even though both molecules are smaller. In addition to the results shown in Figure 5 , qualitative agreement between the above-described ion-MSA theory and
Figure 7. Comparison of C(f) for DMABN in propanol at -20 "C (-) with the solvent response calculated from MSA theories of solvation. The two S ( t ) curves plotted are the ion-MSA (---) and dipole-MSA (---) calculations. Both MSA calculations significantly underestimate the relaxation rate.
experimental C ( i ) curves for Coumarin 153 in alcohol solvents has been observed by Fleming and co-workers. Those studies also examined propylene carbonate and N-methylpropylamide, In both solvents, MSA calculations were in better agreement with the experimental data than was dielectric continuum theory; however, quantitative agreement between the MSA model and the experimental C(t) curves was not observed. In addition, recent femtosecond work by Barbara and co-workers on solvation in small polar aprotic solvents reports that dielectric continuum theory provides a better fit to the experimental c(t)values than the above-described MSA model.34 One source of concern in all of these correlations is that the MSA model discussed is for the solvation of a spherical ion. Recently, Nichols and Calef?' derived an MSA theory for the time-dependent solvation of a dipole. These calculations show that the solvent response is slower in the case of the dipole. The differences in the MSA theory for ion and dipole solvation are shown in Figure 7, in which the two models are compared to the early portion of the experimental C(t) for DMABN in propanol at -20 "C. These data show that while there is poor agreement between both MSA calculations and the experimental C(t) curves, the deviations are greatest for the dipole-MSA theory. This is observed in all of the alcohol solutions we have examined (methanol-hexanol). As an example, in Figure 8 C(t) for DMABN in methanol at -40 "C is compared to dielectric continuum and ion- and dipole-MSA calculations. In this case, c(w) was represented by a single region of Debye dispersion characteristic of the hydrogen bonding motion^.^^-^' Unfortunately, there is little data on the dielectric constant at high fre(34)Barbara, P. F., private communication. (35)Davidson, D. W.Can. J . Chem. 1957, 35, 458. (36) Jordan, B. P.; Sheppard, R. J.; Szwarnowski, S . J. Phys. D: Appl. Phys. 1978, 1 1 , 695. (37)Bertolini, D.;Cassettari, M.; Salvetti, G. J . Chem. Phys. 1983, 78,
365.
758
Su and Simon
The Journal of Physical Chemistry, Vol. 93, No. 2, 1989 0 00 $'>\
's,
-3 3 001
\
'>
\ \
\ -4 O 8
00
0 25
0 50
0 75
1 00
Time (ns) Figure 8. Comparison of C(t) for DMABN in methanol at -40 OC (-- -) with the solvent response calculated from MSA theories of solvation. Both the ion-MSA (-) and the dipole-MSA theories predict slower decays than that experimentally observed. Dielectric continuum calculations (---) decay faster than the experimental data. (a
-a)
quencies for this liquid. N M R studies on liquid methanol indicate that the solvent is extensively hydrogen-bonded at this temperature,38 suggesting that modeling the solvent as a simple Debye solvent may be a good approximation. However, as exemplified in Figure 3, contributions to e ( w ) at high frequencies can have a dramatic effect on the calculated response, both in the continuum and MSA models. Once again, as observed for propanol, better agreement is observed with the ion-MSA model than with the dipole-MSA calculations. However, both MSA theories underestimate the solvent response. Dielectric continuum theory, on the other hand, overestimates the response. It is important to note that both the ion- and dipole-MSA theories consider that only time scales between T L and T D contribute to the relaxation process. This results from using a Debye model for e(o) and limiting the solvent response to structural changes created by rotational motions. These models ignore contributions from translational diffusion, librational motions, and other high-frequency responses of the solvent. The contribution of translation motions (polarization diffusion) has been treated.3w2 Within a continuum picture of the solvent, van der Zwan and Hynes41*42 show that these effects become important, and can even ~ In this expression dominate the response, when P = D T ~ / >u 1. D is the self-diffusion constant of the liquid and a is the cavity radius of the solute. For the systems being examined in this paper P 2.5, suggesting that relaxation caused by translational motions of the surrounding solvent may make a significant contribution (38) Sukai, Y.; Sadoaka, Y . ;Yamamoto, T. Bull. Chem. Soc. Jpn. 1975, 46, 3575. (39) Stiles, P. J.; Hubbard, J. B. Chem. Phys. 1984, 84, 431. (40) Colonomos, P.; Wolynes, P. G.J . Chem. Phys. 1979, 71, 2644. (41) van der Zwan, G.;Hynes, J. T.Physicu A (Amsterdam) 1983, IZIA, 227. (42) van der Zwan, G.;Hynes, J. T. Chem. Phys. Lett. 1983, 101, 367.
to the evolution of C ( t ) . In the limit where the relaxation is controlled by these motions, C ( t ) is expected to decay nonexponentially with an average time constant faster than T~ It is reasonable to assume that both translational and rotational motions of the solvent contribute to the C(t) dynamics observed. The absence of these fast motions in the MSA theories could result in a calculated solvent response that is too slow. It is difficult to include these effects in the present theories, as dynamics are , is not a introduced through the dielectric constant, ~ ( w )which measure of these motions. The comparison between C ( t ) and S ( t ) shows that although the MSA theory is attractive in that it takes into account molecular aspects of the solvation process, it fails in two major areas. First, there is poor quantitative agreement between the experimental data and the dipole-MSA theory. Semiquantitative agreement is observed with the ion-MSA theory, yet it is not obvious that this model is appropriate for describing solvation dynamics of i n c e there is substantial DMABN/DEABN or C153 in solution. S charge separation in the excited state, the permanent dipole moment of the TICT state of DMABN/DEABN is appreciable, =15 D, and it would seem to be more appropriate to select a theory for dipole solvation. Second, and most important, the MSA theories predict that the observed relaxation times should be in the order C153 < DEABN < DMABN, in contrast to the experimental data. This failure of the MSA model suggests that a more detailed theoretical understanding of the effect of molecular shape and solute/solvent interactions in the first few solvent shells is needed in order to quantitatively account for the solvation relaxation time measured by C ( t ) . Alternative models to the MSA approach are being examined. Calef and Wolynes" have derived a Smoluchowski-Vlasov equation (SVE) for describing solvent dynamics. In particular, this theory was applied to charge solvation. The results clearly showed the importance of a range of relaxation times and found that the average relaxation time was between T~ and rD,similar to that observed in the C(t) experiments that have been reported to date. Calef2l has extended this approach and finds that both T~ and rD are dependent on distance, with a surprising result that at intermediate wavelengths it is possible that 7L(k) > T D ( ~ ) . Recently, CaleP3 has derived an analytic expression for solvent relaxation processes by using the SVE approach coupled to MSA and LHNC approximations. Detailed comparisons between these models and experimental C ( t ) curves will be presented at a later date.44
Acknowledgment. This work is supported by the National Science Foundation and the donors of the Petroleum Research Fund, administered by the American Chemical Society. We thank Dr. Dan Calef for providing preprints of his work and performing the dipole-MSA calculations. Registry No. DMABN, 1197-19-9; DEABN, 2873-90-7; 1-propanol, 71-23-8; methanol, 67-56-1. (43) Calef, D., to be submitted for publication in J . Chem. Phys. (44) Calef, D.; Simon,J. D.; Su, S.-G.,to be submitted for publication in J . Chem. Phys.
