J. Phys. Chem. 1995,99, 14628-14631
14628
Isodielectric Kramers-Hubbard Analysis of Diphenylbutadiene Photoisomerization in Alkyl Nitriles and Chlorinated Solvents Robert M. Anderton and John F. Kauffman*J Department of Chemistry, University of Missouri-Columbia, Columbia, Missouri 6521 1 Received: June 23, 1 9 9 P
The permittivity dependence of the trans to cis isomerization barrier of diphenylbutadiene (DPB) observed previously in n-alcohols is shown to extend to alkyl nitriles and chlorinated solvents. Kramers' expression predicts the observed DPB isomerization rate constants in these solvents when evaluated by using the barrier height given by the permittivity dependence developed in n-alcohols. In contrast, the observed DPB isomerization rate constants in mixtures of ethanol and hexane were substantially lower than predicted, indicating either differences between the bulk and local composition or differences in the way the mixed solvent orders itself in the vicinity of the solute.
I. Introduction Trans-cis isomerization of diphenylpolyenes is a prototypical reaction used to test models of reaction dynamics in liquids and gases. The photophysics involved in the isomerization of these molecules has been extensively studied, and the subject has been well reviewed.',2 Solvent effects play an important role in the isomerization rate of stilbene and diphenylbutadiene (DPB). At gas densities the isomerization rate increases with increasing density due to collisional activation. As liquid density is approached, the solvent friction begins to impede the isomerization. The reaction rate also increases with increasing solvent polarity, which is a result of the solvent stabilization of the polarizable transition state.2 Since the Arrhenius law neglects the temperature dependence of these solvent effects, it is necessary to apply more detailed methods of analysis. Kramers' theory3has been applied extensively to diphenylpolyene isomerization kinetics. It describes the rate of isomerization in terms of the solvent friction and the parameters which describe the potential energy surface to isomerization as
where k is the isomerization rate constant, is the angular velocity correlation frequency, and w, and ab are the initial well frequency and the imaginary barrier frequency, respectively. Kramers' expression correctly predicts the rate constants for the isomerization in alkanes when a measure of the local friction, such as the rotational correlation time of the solute, is usede4s5 Deviations from the predictions of hydrodynamic approximations of Kramers' expression have been documented, in which the solvent friction is approximated as a function of the bulk v i s ~ o s i t y . ~Grote . ~ and Hynes7have generalized Kramers' theory to include frequency dependent friction, and isomerization rate constants of stilbene8 and DPB9 have been fit using this model. The Kramers expression is a product of an exponential energy term and a preexponential term which depends on solvent friction. On the basis of this model, isoviscosity Arrhenius plots have been constructed within a series of homologous solvents using solvent-temeprature pairs which maintain a constant viscosity, which in principle results in a constant preexponential E-mail address: chemkauf@mizzoul .missouri.edu. should be addressed. Abstract published in Advance ACS Abstracts, September 15, 1995.
* Author to whom correspondence @
0022-365419512099-14628$09.0010
term. Assuming that the activation energy is constant across the solvent series, the slope of these plots should be the same for any value of viscosity. Isoviscosity plots for DPBlo." and stilbeneI2 in alkanes exhibit consistent slopes at all viscosities. Isoviscosity Arrhenius plots of tilb bene,'^,'^ DPB,'' and dimethoxystilbeneI6in alcohols have different slopes at different viscosities, which we attribute to two effects. The first is that the relationship between the bulk viscosity and the local friction is not constant across the series of solvents used in each plot due to changes in the relative sizes between the solute and solvent molecule^.'^ The second is that the barrier to isomerization depends on the solvent permittivity which changes across the span of each plot.'* Evidence of the permittivity dependence of the barrier to isomerization of dimethoxystilbene and stilbene was noted by Sivakumar et al.I9 They observed that isoviscosity plots of these solutes in alkyl nitriles yield consistent slopes at all viscosities, but isoviscosity plots in n-alcohols have different slopes at different viscosities due to a much steeper dependence of the solvent permittivity on the temperature. The temperature and viscosity dependence of DPB isomerization in n-alcohols was examined by Keery and Fleming20by fitting the temperature dependent rate constant data to a hydrodynamic form of Kramers' expression. Since each fit was conducted in a single solvent over a temperature range, this analysis involved the assumption that the large change in solvent permittivity over the studied temperature range did not have any effect on the potential energy surface to isomerization. A novel approach addressing the effect of solvent polarity on the barrier to stilbene isomerization was demonstrated by Hicks et aL2' They measured the isomerization rate constant in mixtures of a polar and a nonpolar component of similar bulk viscosities such that the polarity of the mixture could be scaled by varying the composition while maintaining isoviscous conditions. The rate data were fit to an Arrhenius type rate expression, where the activation energy was assumed to be a linear function of the Et(30) parameter. This approach was successfully applied to p-(dimethy1amino)benzonitrile (DMABN) isomerization2' but was reported to be unsuccessful when applied to stilbene isomerization in neat n-alcohols and alkyl nitriles.22 In a previous paper,'* we presented the results of a study which separated the effects of solvent friction from the effect of solvent permittivity on the rate of DPB isomerization in n-alcohols by performing fits to Kramers' expression, eq 1, 0 1995 American Chemical Society
Analysis of Diphenylbutadiene Photoisomerization under isodielectric conditions. The /3 term in Kramers' expression is a function of the friction imposed by the solvent and may be related to the rotational correlation time of a probe molecule by the Hubbard r e l a t i ~ n ? ~ 6kT
B =I T ' where Z is the moment of inertia and z, is the rotational correlation time of a solute molecule in the solvent. This approach assumes that the friction that opposes the isomerization reaction scales linearly with the friction felt by the rotating molecule, as both a function of solvent and temperature. This isodielectric Kramers-Hubbard (IKH) analysis does not require any assumptions regarding of the functional form of the dependence of the potential energy surface parameters on the solvent permittivity. Our previous study indicated that the DPB isomerization barrier decreases linearly in n-alcohols with increasing solvent permittivity over the range of permittivities examined (e = 10-20). The IKH method is performed by choosing solvent-temperature pairs to maintain a constant solvent permittivity over a series of analogous solvents containing at least six different solvents. The temperature dependence of a solvent's permittivity is described by the parameter a, where
Because alcohols have large a values, their permittivities can be varied dramatically over a relatively small temperature range. Conducting IKH fits in other solvent systems is precluded by the small a values found in other polar solvents, which results in little overlap in solvent permittivity across a given analogous solvent series within an easily attained temperature range. The purpose of the present study is two-fold. First, we test whether Kramers' expression predicts the rate of isomerization in other polar solvents when Kramers' parameters are assumed to be given by the permittivity dependence determined in alcohols. Second, we perform the same test in mixtures of ethanol and hexane. Our motivation for this portion of the study was to test whether this method could be extended to a wider permittivity range by the use of solvent mixtures. The result presented below indicates that the IKH method can be extended to other neat polar solvents but cannot be applied directly to solvent mixtures.
11. Procedure We have measured DPB fluorescence lifetimes and rotational anisotropies in several alkyl nitriles, chlorinated solvents, and mixtures of hexane and ethanol. We compare isomerization rate constants predicted from the dependence of the Kramers' parameters on solvent permittivity determined in n-alcohols with the observed isomerization rates as determined from fluorescence lifetimes. Solvent permittivities of the nitriles and the ethanollhexane mixtures were measured using an instrument of our own construction, in which a temperature controlled liquid capacitance cell acts as the capacitor in an RC oscillator circuit. The frequency of the oscillator is about 4 MHz and depends on the permittivity of the material between the plates in the capacitance cell. The instrument was calibrated with a series of solvents of known permittivity. Fluorescence lifetimes were measured by the method of time correlated single photon counting. Excitation was provided by a synchronously pumped dye laser, pumped by a frequency doubled mode-locked Nd: YAG laser, yielding 7-ps, 600-nm pulses at 82 MHz. The dye laser output was then frequency doubled by a KDP crystal to
J. Phys. Chem., Vol. 99, No. 40, 1995 14629 generate 300-nm pulses which were directed through a UV polarizer and focused onto the sample. The fluorescence was collected by a cooled Hamatsu R2809U-11 microchannel plate after passing through a 370-nm band pass filter and a polarizer oriented at an angle of 54.7O to the excitation polarizer. The instrument response function was collected by scattering off of a very dilute solution of latex particles in water and had a full width at half-maximum (FWHM) of approximately 50 ps. The decay constants were extracted via the method of iterative reconvolution, and the decays were well represented by single exponential model functions. The nonradiative rates were calculated from the fluorescence lifetimes using the value of the radiative rate constant for DPB of 7.7 x los, which has been shown to be relatively solvent independent.I0 Nonradiative relaxation is assumed to be dominated by the isomerization reaction. The nitrile solvents were obtained from Aldrich and multiply fractionally distilled to remove all fluorescence resulting from excitation at 300 nm. Optima grade hexane and methylene chloride were obtained from Aldrich and used as received. Absolute ethanol was obtained from McCormic Distilling Co., Inc., and fractionally distilled. Reagent grade 1,2-dichloroethane was obtained from Fisher and used as I received. The rotational correlation times of DPB in each of the solvents were determined by measuring the steady state fluorescence anisotropy. The rotational anisotropy is given by the Pemn equation,24 (3) where Zplis the intensity of the fluorescence when the excitation and emission polarizers are parallel to one another and zpd is the fluorescence intensity when the excitation and emission polarizers are perpendicular. In the case of single exponential fluorescence decays, the rotational correlation time is then given by (4) where zfis the fluorescence lifetime and ro is the rotational anisotropy in the limit of infinite friction, which we measured for DPB in glycerin at -20 "C to be 0.39 f 0.01. Measurements of r via eq 3 for each solution were used to calculate rotational correlation times via eq 4, and these were used to calculate /3 for each solvent via eq 2. The other parameters in eq 1, Ea, wa, and wb, were calculated from their permittivity dependencies as determined in n-a1cohols.ls
E, = -8.6736 x lo-*€
+ 3.8463
+
ma = -4.636 x 1 0 " ~ 1.2267 x lOI4 Ob= 2.0 x
1oI2
(5a)
(5b) (5c)
These parameters, along with p, were used in eq 1 to calculate predicted nonradiative rate constants, which were compared to the measured nonradiative rate constants in each solvent.
III. Results and Discussion Table 1 presents the solvent permittivity, the fluoresence lifetimes, and the rotational Correlation times for DPB in each of the solvents examined in this study at the temperatures indicated. The values of the solvent permittivity we report for
Anderton and Kauffman
14630 J. Phys. Chem., Vol. 99, No. 40, 1995
TABLE 1: Measured Fluorescence Lifetimes and Rotational Correlation Times for DPB in a Range of Polar Solvents at the Temperatures Indicated in the Tabld
ethanol 1-propanol l-butmol 1-pentanol 1-hexanol I-heptanol 1-octanol valerionitrile hexanitrile methylenechloride 1.2-dichloroethane 70 mol % EtOH 80 mol % EtOH 90 mol % EtOH a
B
symbol in temp Figure 1 (“C)
solvent
1 2 3 4 5 6 7 8 9 10 11 12 13 14
60 30.0 20.0 20.0 20.0 20.0 20.0 25.0 25.0 25.0 25.0 25.0 25.0 25.0
E
19.0 19.8 17.7 15.2 13.2 11.6 10.2 20.3 17.8 8.9 10.4 11.8 15.2 19.4
tf(ps) tr(ps) (xlOI3) (x109)
30.3 84.1 147.8 204.6 252.1 297.4 366.5 73.7 95.7 76.0 101.8 128.5 103.5 79.6
28.5 60.8 106.2 133.4 164.1 205.4 238.2 45.7 51.4 32.8 47.2 28.3 33.3 37.9
1.2 2.4 4.0 5.0 6.1 7.7 8.9 1.7 2.0 1.3 1.8 1.1 1.3 1.4
32.2 11.1 6.0 4.1 3.2 2.6 2.0 12.8 9.7 12.4 9.1 7.0 8.9 11.8
The data in neat alcohols are from ref 18.
30
-1
U
3 0 a g!
10
a
5
0
0
5
10
15
20
25
30
35
Measured Rate Constant (lo’s-’)
Figure 1. Comparison of measured nonradiative rates of DPB with those predicted by Kramers’ theory using the permittivity dependence Cub given by eq 5 and the determined from rotational correlation time measurements. Symbols: n-alcohols (O),alkyl nitriles (v),chlorinated solvents (A),and ethanomexane mixtures (W). The numbered symbols correspond to the solvent numbers in Table 1.
of E,, uarand
the alkyl nitriles are approximately 20% larger than those reported at similar temperatures in the CRC Handbook of Chemistry and Physics,25 which refers to the NBS Circular 514,26which is a table of dielectric constants of pure liquids. It cites a set of measurements made at a frequency of 350 MHZ,~’ at which dielectric dispersion is expected to occur. The values we report in this work represent measurements made at approximately 4 MHz, well within the low frequency regime, and are in good agreement with those measured at low frequency by Laurence.28 The values of the dielectric constants for the n-alcohols, methylene chloride, and 1,Zdichloroethane were taken from the NBS Circular 51426and are in good agreement with our measurements. Table 1 also presents the /3 values derived from the rotational correlation times utilizing eq 2 and a value for the moment of inertia for DPB of 6.5 x kg m2. Figure 1 compares the observed nonradiative rate constants to the rate constants predicted by Kramers’ expression using the solvent permittivity measurements and the rotational cor-
relation times. The solid line in Figure 1 is a line with a slope of 1, which represents perfect agreement between the observed rate constant and the predicted rate constant. An uncertainty in the value of Ea of lo%, or approximately 0.2 kcdmol, leads to an uncertainty of approximately 30% in the predicted rate, which encompasses all of the neat solvents in Figure 1 (symbols 1-11). This indicates that the permittivity dependence of the Kramers’ expression parameters which describe the isomerization of DPB in n-alcohols can predict the isomerization rate in other neat polar solvents within the permittivity range of 1020. This provides evidence that the barrier lowering observed in n-alcohols does not result from specific interactions of the alcohol hydroxyl group with the solute but is instead a result of the solvent reaction field. The predicted nonradiative rate constants of DPB in the ethanolihexane mixtures (symbols 12-14) are much higher than the observed rate constants. This indicates that the activation energies predicted from the measured bulk permittivities are too low and suggests that either the local concentration of hexane is greater than is indicated by the bulk solvent permittivity or that the presence of the hexane disrupts the organization of the ethanol around the DPB. This result is unfortunate because it precludes the use of solvent mixtures as a means of extending the IKH method to the examination of the permittivity dependence of the isomerization barrier into the range not covered by n-alcohols. Solvents having no dipole moment but a large quadrapole moment may also lead to a lower barrier to isomerization than the solvent permittivity suggests. Fits to Kramers’ expression yield a value for the isomerization barrier of 2.0 kcal/mol for DPB in benzene and 2.1 kcaVmo1 for DPB in COz.15The latter value is consistent with the results of Gehrke et aLZ9for DPB in C02 in the high pressure regime. In these solvents the barrier to isomerization for DPB is significantly lower than the 5.9 kcaV mol observed in alkane solvents with similar permittivities. The large quadrapole moments of CO2 and benzene may be responsible for the reduced barrier in these solvents. It has been demonstrated that benzene can stabilize cations through interactions with the n face of the benzene molecule.30 The charge separated transition state of DPB may be stabilized by solvents having low permittivities if they have a significant quadrapole moment over a length scale which corresponds to the distance of the charge separation.
IV. Conclusions The present study indicates that the permittivity dependence of the Kramers parameters to DPB isomerization in n-alcohol solvents successfully predicts the nonradiative rate in other polar solvents. Thus, the linear relationship between barrier height and solvent permittivity extends consistently across n-alcohols, alkyl nitriles, and chlorinated solvents. This suggests that the observed permittivity dependence of the barrier height in n-alcohols is a response to the solvent reaction field rather than specific interactions with the hydroxyl group of the alcohol. Furthermore, we have demonstrated that although Kramers’ expression adequately predicts isomerization rate constants in a wide range of neat polar solvents, it fails in mixtures of ethanol and hexane. This failure indicates that the local composition and solvent structure of the mixed liquid differ significantly from the bulk.
Acknowledgment. Acknowledgment is made to the donors of The Petroleum Research Fund, administered by the American Chemical Society, for support of this research.
Analysis of Diphenylbutadiene Photoisomerization
References and Notes (1) Allen, M. T.; Whitten, D. G. Chem. Rev. 1989, 89, 1691. (2) Wladeck, D. H. Chem. Rev. 1991, 91, 415. (3) Kramers, H. Physica 1940, 7, 284. (4) Lee, M.; Bain, A. J.; McCarthy, P. J.; Han, C . H.; Haseltine, J. N.; Smith, A. B., 111; Hochstrasser, R. M. J . Phys. Chem. 1986, 85, 4341. (5) Courtney, S. H.; Kim, S. K.; Canonica, S.; Fleming, G. R. J . Chem. Soc.. Faradav Trans. 2 1986, 82, 2065. (6) Rothknberger, G.; Negus, D. K.; Hochstrasser, R. M. J . Chem. Phys. 1983, 79, 5360. (7) Grote, R. F.; Hynes, J. T. J . Chem. Phys. 1980, 73, 2715. (8) Park, N. S . ; Waldeck, D. H. J . Chem. Phys. 1989, 91, 943. (9) Bagchi, B.; Oxtoby, D. W. J . Chem. Phys. 1983, 78, 2737. (10) Velsko, S. P.; Fleming, G. R. J . Chem. Phys. 1982, 76, 3553. (11) Courtney, S. H.; Fleming, G . R. J . Chem. Phys. 1985, 83, 215. (12) Sundstrom, V.; Gillbro, T. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 222. (13) Kim, S. K.; Courtney, S. H.; Fleming, G . R. Chem. Phys. Lett. 1989, 159, 543. (14) Sundstrom, V.; Gillbro, T. Chem. Phys. Lett. 1984, 109, 538. (15) Anderton, R. M.; Kauffman, J. F. Unpublished results. (16) Zeglinski, D. M.; Waldeck, D. H. J . Phys. Chem. 1988, 92, 692. (17) Anderton, R. M.; Kauffman, J. F. J . Phys. Chem. 1994,98, 12117.
J. Phys. Chem., Vol. 99, No. 40, 1995 14631 (18) Anderton, R. M.; Kauffman, J. F. J . Phys. Chem. 1994,98, 12125. (19) Sivakumar, N.; Hoburg, E. A.; Waldeck, D. H. J. Chem. Phys. 1989, 90, 2305. (20) Keery, K. M.; Fleming, G. R. Chem. Phys. Lett. 1982, 93, 322. (21) Hicks, J. M.; Vandersall, M.; Babarogic, Z.; Eisenthal, K. B. Chem. Phys. Lett. 1985, 116, 18. (22) Hicks, J. M.; Vandersall, M. T.; Sitzman, E. V.; Eisenthal, K. B. Chem. Phys. Lett. 1985, 116, 293. (23) Hubbard, P. Phys. Rev. 1963, 131, 1155. (24) Pemn, F. J . Phys. Radium 1934, 5, 497. (25) CRC Handbook of Chemistry and Physics; CRC Press, Inc.: Boca Raton, FL, 1994. (26) Maryott, A. A.; Smith, E. R. In Table of Dielectric Constants of Pure Liquids; NBS Circular 514; U.S. Government Printing Office: Washington, DC, 1951. (27) Schlundt, H. J . Phys. Chem. 1901, 5, 157. (28) Laurence, C. J. Phys. Chem. 1994, 98, 5807. (29) Gehrke, Ch.; Schroeder, J.; Schwarzer, D.; Troe, J.; Voss, F. J . Chem. Phys. 1990, 92, 4805. (30) McCurdy, A.; Jimenez, L.; Stauffer, D. A,; Dougherty, D. A. J . Am. Chem. SOC. 1992, 114, 10314.
JP9517741
