J. Phys. Chem. 1991, 95, 1979-1987
1979
Conclusions
is kinetically facilitated if the process is electronically diabatic but vibronically adiabatic. We have identified specific van der Waals modes that fulfill these criteria for generalized complexes possessing C,,C,,, and C3, symmetries.
Excitation of intermolecular vibrational modes provides a mechanism for the acceleration of intermolecular electron transfer via an excited intermediate complex. Forward electron transfer
Acknowledgment. This material is based upon work supported by the Division of Chemical Sciences, U.S.Department of Energy, under Award No. DE-FG05-MER-13975.
ronment where intermolecular torsional and shearing motion is restricted.
Long-Distance Charge Recombination within Rigid Molecular Assemblies in Nondlpolar Solvents John M. Warman,* Kenneth J. Smit, Matthijs P. de Haas, Stephan A. Jonker, Radiation Chemistry Department, IRI, Devt University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
Michael N. Paddon-Row, Anna M. Oliver, Department of Chemistry, University of New South Wales, P.O. Box I , Kensington, New South Wales 2033, Australia
Jan Kroon, Henk Oevering, and Jan W. Verhoeven Department of Organic Chemistry, University of Amsterdam, Nieuwe Achtergracht 129, 1018 WS Amsterdam, The Netherlands (Received: June 18, 1990; In Final Form: October 8, 1990)
The lifetimes of the charge-separated states formed on photoexcitation of rigid donor-insulator-acceptor molecules with variable edge-to-edge separation from 5 to 15 A have been measured in the nondipolar solvents trunr-decalin,benzene, dioxane, and their admixtures by using the time-resolved microwave conductivity (TRMC) technique. The lifetime is governed by two recombination pathways: direct to the ground state and indirect via the locally excited donor. The latter becomes increasingly important as the separation distance increases and/or the driving force for charge separation decreases. Very large solvent effects are found. Data are presented on the effects of changing the donor and acceptor groups and of modifying the norbornyl type u-bonded bridges.
Introduction In a recent paper] data were presented on the rates of charge separation and recombination following photoexcitation of a series of rigid donor-insulator-acceptor molecules in which the length of the insulating bridge was varied from approximately 5 to 14 A. For both processes the electron-transfer rate was found to decrease exponentially with edge-to-edge separation distance, Re in angstroms, according to the expression k = u exp(-0.88Re) For barrierless conditions toward charge separation the preexponential frequency factor, uCs, was found to be on the order of lOI4 s-I and only very weakly dependent on the nature of the surrounding medium even in going from saturated hydrocarbons to highly polar acetonitrile. The frequency factor for the charge recombination process on the other hand was found to be extremely sensitive to the solvent, increasing by almost 2 orders of magnitude in going from cyclohexane, for which uCR = 8 X lo9PI, to dioxane, This great sensitivity of recombination kinetics to the surrounding medium prompted the experiments on solverit mixtures which are included in the present work. It was found that a deviation from the exponential dependence, given by the above equation, occurs for the longer bridge compounds in saturated hydrocarbon solvents.l** In fact, the rate of decay of the giant dipole state was actually found cvcntually
-
Paddon-Row, M. N.; Oliver, A. M.;Warman. J . M.; Smit, K. J.; de Haas, M. P.; Oevering. H.; Verhoeven, J. W. J . Phys. Chem. 1988, 92,6958. ( 2 ) Smit. K. J.; Warman, J. M.; de Haas, M . P.;Paddon-Row, M. N.; Oliver, A. M . Chem. Phys. Leff. 1988, 152, 177. (1)
0022-3654/91/2095-1979$02.50/0
to increase with distance for the largest separations. Under these conditions the rate becomes sensitive to the electronic polarizability of the medium so that pronounced differences even between different saturated hydrocarbons are found.* This effect has been attributed to the Occurrence of an additional pathway for charge recombination involving back electron transfer to regenerate the local excited donor state. As expected, the advent of this process is found to be accompanied by delayed donor fluore~cence.~The reason for the effect has been proposed to be the decrease in energy difference between the local excited donor state and the charge-separated state as the latter gradually loses the energy of Coulombic attraction between the charged centers with increasing distance between them. Particular attention will be paid to this “problem”, which limits the maximum attainable lifetime of the charge-separated state, in the present paper. While the rate of charge separation has been found to be relatively insensitive to the dielectric properties of the surrounding medium for the norbornyl-type bridge compounds, it has been shown to be very sensitive to the structure of the bridge i t ~ e l f . ~ . ~ The introduction of only a single “kink” in the all-trans structure is sufficient to produce almost an order of magnitude reduction in the rate of the forward electron-transfer process. This has been taken as evidence for a high through-bond as opposed to (3) Oevering, H. Ph.D. Thesis, University of Amsterdam, 1988. (4) Oliver, A. M.;Craig, D. C.; Paddon-Row, M. N.; Kroon, J.; Verhocven. J . W . Chem. Phys. Left. 1988, 150, 366. (5) Lawson, J . M.; Craig, D. C.; Paddon-Row, M. N.; Kroon. J.; Verhoevcn, J . W . Chem. Phys. Lerr. 1989, 164, 120.
0 1991 American Chemical Society
1980 The Journal of Physical Chemistry, Vol. 95, No. 5, 1991
Warman et al.
CN
DUN(l31DCNE
eN DMqll]DVCE
CN
DUYB.blDCNE
CN CN CN
DMN[lO]DCNE
CN CN
CN
CN DMN[lZJDCNE
Figure 1. Molecular structures of the compounds investigated in the present study. In the text the various compounds are referred to in shorthand as D[n,x]A with D and A abbreviated names of the donor and acceptor moieties and n and x signifying the number of u bonds in the bridge and bridge modifications, respectively. These shorthand versions are given in the figure beneath the corresponding molecular structure.
through-space component in the coupling between the states involved in charge separation. These same ‘bent” molecules have been studied in the present work in order to probe the throughbond character of the charge recombination process. In general, much more attention has been paid in the past to the study of the photoinduced charge separation process than to charge recombination. This is due, at least in part, to the experimental difficulties involved in monitoring the charge-separated states formed which are often only weakly fluorescent, if at all. Also, the unequivocal identification and absolute measurement of short-lived radical ion species by their optical absorption, as used by some workers,b8 is often extremely difficult because of concurrent bleaching of the absorption bands of the ground state and formation of strongly absorbing local excited singlet and triplet states. In the present work we have applied mainly the time-resolved microwave conductivity (TRMC) technique9which is only sensitive to those states for which a large change in dipole moment compared with the ground state has occurred. The method is by its nature limited almost exclusively to the investigation of solutions in nondipolar solvents. This limitation has however by no means resulted in a lack of variety in kinetic behavior as the present paper will demonstrate.
Experimental Section The solvents used were tram-decalin (Merck synthetic grade), which was redistilled and passed through activated silica gel, and benzene and p-dioxane (Fluka, UV spectroscopic grade). The benzene was used as received, but the dioxane was passed through a column of activated silica gel immedihtely prior to use. (6) Wasielewski, M. R. In Phofohduced Elecfron Transjrr; Fox, M. A,, Elsevier: Amsterdam, 1988; Part A, p 161. Chanon, M., Me.; (7) Wasielewski, M. R.; Niemczyk, M. P. In forphyrlnr-Excited States and Dynamics; Gouterman, M., Rentrepis, P. M., Straub, K. D., Eds.; ACS Symposium Series No. 321; American Chemical Society: Washington, DC, 1986; p 154. ( 8 ) Sakata, Y.; Nakashima, S.; Goto, Y.; Tatemitsu, H.; Miaumi, S.; Asahi, T.; Hagihara, M.; Nishikawa, S.;Okada, T.; Matap, N. J. Am. Chem. Sot. 1989, I l l , 8979. (9) de Haas, M. P.; Warman, J. M. Chem. Phys. 1982, 73, 35. (IO) Oevering. H.; Vcrhoeven, J. W.; Paddon-Row, M. N.; Warman, J. M. Tetrahedron 1989, I S . 475 1.
The solutes were rigid donor-insulator-acceptor molecules consisting of a donor and an acceptor moiety separated by a completely carbon-carbon o-bonded insulating bridge of linearly fused norbomane and bicyclo[2.2.0]hexane type units. The length of the bridge is varied from 4 to 13 bonds or approximately 5-1 5 A. The structures of the compounds are shown in Figure 1. They are referred to in the text by the shorthand D[n,x]A in which D is the abbreviated name of the donor entity, e.g., DMN = 1,4dimethoxynaphthalene, DMB = 1,4-dimethoxybenzene; A is the abbreviated name of the acceptor, e.g. DCNE = 1,l-dicyanoethylene, DMCE = 1,2-bis(methoxycarbonyl)ethyIene;and [n,x] gives a brief description of the bridge unit with the square brackets indicating rigidity, n the number of u bonds in the bridge, and x special features such as bent (b) and number of ester substituents (nE). The methods of synthesis of the solute molecules have been described The solute concentrations used were on the order of lo4 M, resulting in optical absorbances at the irradiating wavelength of 308 nm of between 0.1 and 1.0. The solutions were deaerated by bubbling with dry C 0 2 , N2, or Ar. The solutions were transferred to a microwave conductivity cell, and changes in the dielectric loss of the solution on flash photolysis were measured by using the time-resolved microwave conductivity (TRMC) technique as described previ~usly.~In the most recent measurements accurate, absolute values of the cell sensitivity factor A9 and the response time of detection could be determined in situ for each solution. The source of excitation was a 5-11s(fwhm)pulse of 308-nm light from a Lumonics HyperEX-400 excimer laser. At this wavelength only the donor moiety was excited (ejo8 = 3.5 X lo3 M-l cm-’ for DMN). The light intensity was on the order of l e 2 0 mJ/cm2. The data were fitted by use of a convolution program that took into account the shape of the laser pulse and the risetime of the detection system and the changing light intensity with depth ( I I ) Oevering, H.; Paddon-Row, M. N.; Heppener, M.; Oliver, A. M.; Cotsaris, E.; Verhoeven, J. W.; Hush, N. S.J . Am. Chem. Soc. 1987, 109,
3258. (12) Paddon-Row, M. N.; Cotsaris, E.; Patney, H. K. Tetrahedron 1986. 42, 1779. Craig, D. C.; Lawson, J. M.; Oliver, A. M.; Paddon-Row, M. N. J . Chem. SOC.,ferkin Trans. I in press. Antolovich, M.; Oliver, A. M.; Paddon-Row, M. N. J . Chem. Soc., Perkin Trans. 2 1989, 783.
The Journal of Physical Chemistry, Vol. 95, No. 5, 1991 1981
Charge Recombination within Molecular Assemblies in the cell? Lifetimes of dipolar intermediates down to 2 ns can be determined with an accuracy of f l ns in this way if the signal-to-noise level is reasonably large and the kinetics are simple, i.e. only one exponentially decaying dipolar intermediate. Where shorter lifetimes are given these were determined from the in-pulse, steady-state microwave conductivity under conditions where the quantum yield and dipole moment were known from other sources or could be assumed with a reasonable degree of accuracy. Values of the lifetime toward charge separation, T~-, given in the present paper were obtained by convolution analysis of the decay of the donor fluorescence using picosecond flash photolysis as described p r e v i o ~ s l y . ~ * 'The ~ * ~unquenched ' lifetimes of the donors, T~ = 1/kb were obtained by using model compounds with a partial bridge attached but without an acceptor group.
Results and Discussion Several factors can influence the rate of site-to-site electron transfer including the distance over which transfer must take place, the nature of the bulk medium, and the spectral and redox properties of the localization sites. We have attempted to unravel the different contributions of the various parameters by studying molecular assemblies in which one can at least be sure that the geometrical form, including the site-to-site distance and relative orientation, remains invariable during and subsequent to the electron-transfer process. This brings with it however an additional problem in the form of the "inert", rigid bridging unit used to ensure geometrical integrity. It has now been clearly demon~ t r a t e d ,as ~ ,mentioned ~ in the Introduction, that the bridge may in fact not be inert at all, thus introducing a further potential variable. In what follows we present results on the kinetics of the recombination processes that occur subsequent to photoexcitation and charge separation for the compounds shown in Figure 1. In line with the above comments the data will be presented and discussed in four sections: (a) the distance dependence, (b) solvent effects, (c) donoracceptor variations, and (d) bridge modifications. Because of the mutual influence of the different variables on each other, it is in practice almost impossible to keep such a strict division of the data and a certain degree of overlap between the sections will be unavoidable. (a) Distance Dependence. Considerable attention has been paid in previous publications1,2,'0,11 to the distance dependence of the kinetics of both charge separation, process A , and charge recombination, process B, for the series of D M N [ n ] D C N E com-
pounds with n from 4 to 12. One of the main conclusions reached was that, under conditions where the driving force for charge separation is a few tenths of an electronvolt or more, the lifetimes toward charge separation and recombination both increase close to exponentially with the number of intervening u bonds, n, according to the expression T(n) = ~ ( 0 exp[ ) I .9n] (1) From the average increase in edge-to-edge distance, Re, of 1.14
A per u bond, one obtains for the distance dependence of the rates of charge separation and recombination kcs = uCs exp[-0.88Re]
(2)
kDR= Y D R exp[-0.88Re] (3) The theoretical basis of the distance dependence and its quantitative aspects, in particular the relationship to the electronic coupling matrix element between states, Hab,have been discussed previouslylOJ1in terms of the general rate equation for electron transfer: k,, = ( 4 ~ 2 / w , b ( ~ a b ) 2
(4)
In (4) Fabis the Franck-Condon factor for the transition which
10'
3 Y
0.1 0
I
I
2
4
/
I
I
I
8
8
101214
I
I
NUMBER OF SIGMA BONDS Figure 2. Dependence of the lifetime of the chargeseparated state of the DMN[n]DCNE compoundson the number of intervening u bonds, n, for the solvents tramdecalin, benzene, and p-dioxane. The straight lines drawn through the data (extended as dashed lines for benzene and ded i n ) correspond to an exponential dependence of the recombination time on n as given by eq 1 in the text.
0.1 0
4
8
12
NUMBER OF SIGMA BONDS
Figure 3. Dependence of the lifetime of the charge-separated state of the DMN[n]DMCE compounds on the number of intervening u bonds, n, for the solvents benzene, andp-dioxane. For ease of comparison the data for the DMN[n]DCNE compounds in benzene, as presented in Figure 1, are also shown here as filled squares. is expected to be only weakly dependent on site separation if at all. In Figure 2 recombination lifetime data for the DMN[n]DCNE compounds are shown for trans-decalin, benzene, and p-dioxane plotted semilogarithmically against n. Recent, additional results for the n = 13 compound for the last two solvents and for n = 10 and 12 for decalin have been added to previously reported data. The straight lines drawn in the figure correspond to exponential dependences as given by eq 1 with values of ~ ( 0 of) 130, ~ ~15, and 1.5 ps for decalin, benzene, and dioxane, respectively. These values are to be compared with the much shorter value of 9 X s estimated for T ( O ) ~ ~ . ' The deviations from a simple exponential distance dependence, which can be clearly seen in Figure 2 for decalin and benzene, for the longer compounds have already been alluded to in earlier publications.'*2 This aspect of the results, which is attributed to reverse electron transfer for low driving forces, will be discussed at considerable length later following a discussion of the exponential region. In Figure 3 recombination lifetime data are plotted for benzene and dioxane solutions of the D M N [n]DMCE compounds. The straight lines drawn through the points also correspond to an
1982 The Journal of Physical Chemistry, Vol. 95, No. 5, 1991 exponential dependence as given by (1). The values of the preexponential time T ( O ) D R of 6.6 and 0.68 ps for benzene and dioxane, respectively, are seen to differ by a factor of 10 as for the DCNE acceptor compounds. The absolute magnitudes are however approximately a factor of 2 smaller. This decrease in ~(o),, on changing the acceptor from DCNE to DMCE will be discussed in section c. The data in Figure 3 serve simply at this stage to further substantiate the applicability of (1) as a reasonably good general approximation for different solvents and different solutes, at least of the present type. On closer inspection of the data for dioxane in Figure 2, taking into account particularly the new point at n = 13 for which T R = 1.05 ps, it is apparent that a somewhat stronger dependence on bridge length than given by eq 1 would in fact provide a better description of the distance dependence of the recombination lifetime for this solvent. Thus, while eq 1 with ~ ( 0 ) D k= 1.5 ps does predict the lifetime values for dioxane to well within a factor of 2 over the more than 3 orders of magnitude change in this parameter, an exponential a-bond parameter of 1.1 corresponding to a distance parameter in ( 3 ) of closer to 1.0 8,-‘ would give significantly better agreement. In the case of decalin and the other saturated hydrocarbons studied,* the lifetimes for n = 4 and 6 would on the other hand be better described by a somewhat lower value for the exponential parameter than the value of 1 .O in eq 1. We feel therefore that while eq 1 may give a reasonably good general description of the recombination kinetics in the exponential distance regime, it should be kept in mind that the exponential parameter may in fact contain solvent (or energy) dependent terms. We now turn to the deviation from the exponential distance dependence which is clearly shown by the data for the longer DMN [n]DCNE compounds for decalin and benzene in Figure 2. The deviation occurs for trans-decalin above n = 6 and for benzene above n = IO. For both solvents the recombination lifetime, 71, actually eventually decreases with increasing length of the bridge. For dioxane, however, the exponential dependence holds even up to the n = 13 compound. The net result of this is that the lifetimes actually undergo a complete reversal in order with dioxane becoming the longest and decalin the shortest for the longest bridge compound. From the above it is clear that we have a considerable and unexpected degree of complexity in the kinetics even for these well-defined molecular systems. What is perhaps even more surprising is that this complexity is found in solvents that are all nominally nonpolar with dielectric constants all within the range 2.2 f 0.1.
The fact that delayed donor fluorescence begins to the observed at the same point that the deviation from the exponential dependence of T D R on n occurs and that the decay time of this fluorescence is the same as that of the dipolar species monitored by the TRMC technique leaves little doubt as to the underlying explanation for this phenomenon: the oycurrence of charge recombination via an indirect pathway inuolving reverse electron transfer to regenerate the locally excited donor, process C, followed by decay of the excited donor to the ground state, process D: D+[n]A-
k a
D*[n]A
(C)
D*[n]A -% D[n]A (+hu) (D) Processes A through D are shown schematically in Figure 4. The reason for the Occurrence of the inverse electron-transfer pathway only at longer distances is twofold. Firstly, the rate for the direct pathway to the ground state (B) decreases exponentially with distance, thus dramatically increasing the competitive chance of any other recombination route. Secondly, the Coulombic contribution to the stability of the charge-separated state decreases with increasing distance between donor and acceptor. This brings the level of the charge-separated state, CS, increasingly closer to that of the locally excited donor state, LED, as is illustrated in Figure 5 . The barrier toward the reverse electron-transfer process therefore decreases with distance. This effect is particularly pronounced for the present nonpolar liquids for which
Warman et al.
Figure 4. A schematic representation of the processes occurring subsequent to photon absorption by the present donor-insulator-acceptor compounds with the corresponding rate coefficient symbols shown. The rate coefficient kR used in the text refers to the overall exponential decay of the charge-separatedstate determined from kinetic fits to the TRMC transients observed. 4-
3
I-
I
/////.
I
I
I
I
0
4
8
12
Sigma bonds
Figure 5. An ergodynamic representation of the changes occurring in the energy level of the charge-separatedstates of DMN[n]DCNE molecules as the number, n, of intervening u bonds increases together with the resulting changes in the electron-transfer kinetics between the chargeseparated state and the local excited donor and ground states shown on the extreme left. The diagram illustrates how indirect charge recombination via back electron transfer to regenerate the local excited donor can eventually dominate the overall decay kinetics for long distances due to the diminishing energy of Coulombic attraction between the charged centers. The actual lifetimes shown are for benzene as solvent.
Coulomb forces play an important role over large distances: the Coulomb energy is for example reduced to kBT(0.025 eV at room temperature) only at a distance of 300 8, for a medium of dielectric constant 2. If equilibration between the LED and the CS states is attained on a time scale considerably shorter than the time scale for the ultimate decay processes, then the overall decay rate will be given by (5) kRCq = ~ D + R ( k -~~ D F J + / (kcs/k-cs) ~ The derivation of ( 5 ) is given in the Appendix. Its applicability requires that the sum of the rates for the forward and reverse charge separation processes is considerably larger than for the rates of the ultimate decay process, i.e. (kcs + k& >> (kD + k D R ) . Equation 5 should provide a reasonably good approximation for benzene and dioxane up to the 12-a-bond compound and for decalin at least up to n = 8 since the kcs is known to be considerably larger than kD. Its application to other solute-solvent combinations can only be considered to be an empirical extension which may provide a semiquantitative description.
The Journal of Physical Chemistry, Vol. 95, No. 5, 1991 1983
Charge Recombination within Molecular Assemblies
TABLE 11: Solvent Effects on the Fluorescence from the Charge-Separated State of “Fluoropr~be”~~~’~ in Decalin-Dioxane Mixtures’ vol % dioxane E,.,, eV PES, eV AW, eV
TABLE I: Lifetimes 01 the Giant Dipole States 01 DMN[n]DCNE Compounds in tram-lkcrlin, Benzene, and p-DioxaeO lifetimes, ns ~~~~
n
R,-, A
4 6 8
6.8 8.7 11.5 13.0 14.9 15.9
IO 12 13
decalin meas calc 8 45 58 12 11
7.6 52.4 58.0 13.7 10.3 10.0
benzene meas calc 1 6 32 360 740 520
0.8 6.1 45 330 740 375
dioxane meas calc 0.5 2.5 43 297 1050
0
0.08 0.61 4.5 33 244 664
’The calculated values are based on eq 8 with values of AG(m),s of +0.535,0.292, and 0 eV and values of ~ ( 0in)(1)~ of~130, 15, and 1.5
ps, respectively.
If the free energy difference between the LED state and the CS state for infinite separation of the donor and acceptor is AG( m)CS, then the free energy difference, in electronvolts, for a center-to-center distance, Rc in angstroms, will be given by AC(Rc)cs = AG(m),, - 14.4/eRc (6) where t is the dielectric constant of the medium. We can substitute then in (5)for kCS/k-CS = exp(-AG(RC)CS/kBT)
(7)
to give eq 8 for the predicted distance dependence of the decay rate under conditions where both direct and indirect recombination pathways are operative. kRq = kDR + (ko - kDR)/{l
+ exp[-(AG(a)cs
- 14.4/&)/k~q) (8)
We have calculated values of kRq for the DMN[n]DCNE compounds in trans-decalin and benzene using eq 8 with values of kD of 1 .O X IO* and 1.7 X lo8 s-l measured using the model donor compound and values of t of 2.17 and 2.28, respectively. The kDRvalues were calculated via (3) with preexponential factors of 7.7 x lo9 and 6.7 X 1Olo s-’ corresponding to the values of T(O)DR given above. The values of AG(m),,, the only remaining free parameter, required to give a reasonable fit to the experimental data were found to be 0.535and 0.292 eV for decalin and benzene, respectively. Comparisons between the experimental values of T R and the calculated values of 1/kRq are shown in Table 1. The agreement is seen to be quite good. Equation 8 therefore gives a good general description of the overall recombination rate including complications resulting from reverse electron transfer which come into play when the driving force is small. It is perhaps worth mentioning that the Occurrenceof the reverse electron-transfer pathway for charge recombination is not simply an experimental curiosity limited to the present compounds but is probably of much more general relevance. It will certainly be of importance in the design of light harvesting systems where the maximum conservation of the initially absorbed photon energy, i.e. minimal driving force, is a major concern. Recombination by reverse electron transfer is also a potential complication which should always be kept in mind when interpreting the results of studies of the driving-force dependence of the rate of long-distance electron transfer, particularly for driving forces on the order of only a few tenths of an electronvolt or less. Soluent Eflects. It has already been noted that the solvents used in the present work may all be considered to be nonpolar on the basis of their bulk dielectric constants, all of which lie within the narrow range of 2.2 f 0.1. Despite this, very large differences in the kinetics of charge recombination are found, as discussed in the previous section and as can be readily seen from the data in Figures 2 and 3. Clearly specific, microscopic interactions between the ionic centers and the solvent must be operative in benzene and dioxane presumably as a result of their higher order electric moments. The anomalous solvating power of benzene and dioxane is something which has been known for many years and is evidenced
2.4 4.8 9.1 16.7 25.9 37.5 50.0 74.1 100
benzene
3.00 2.98 2.92 2.87 2.77 2.67 2.61 2.56 2.50 2.44 2.60
0.021 0.084 0.125 0.227 0.323 0.390 0.433 0.495 0.554 0.400
0.43 0.43 0.44 0.45 0.49 0.50 0.5 1 0.5 1 0.50 0.50
aEmx is the energy corresponding to the wavelength of maximum intensity, AEs is the shift in E,,, on adding dioxane, and AWis the full width at half-maximum of the emission band.
by the unexpectedly large solvatochromic shifts produced by these solvents in the emission spectra of conjugated donor-acceptor c ~ m p o t p d s . Large ~ ~ solvatochromic shifts have also been found for certain rigid, nonconjugated DIAD molecule^'^ with fully chargelseparated excited states. In Table I1 are listed the shifts of the emission maximum, Us, of the u-bond-separated donoracceptor compound “ f l u o r o p r ~ b e ”observed ~ ~ ~ ~ ~on adding dioxane to decalin. The total shift in pure dioxane for this solute is seen to be as much as 0.56 eV. The same solute in benzene shows a shift of approximately 0.4 eV with respect to a saturated hydrocarbon. The DMN[n]DCNE compounds do not fluoresce at all in dioxane. A weak fluorescence from the CS state can however be observed in saturated hydrocarbons and for n = 4 and 6 in benzene?*IO The maximum of the emission in benzene is found to be bathochromically shifted by approximately 0.4 eV from the maximum at 2.7 eV found in saturated hydrocarbon~.~-I~ Because of the similarity of the shift for the present compounds in benzene with that found for fluoroprobe, it would seem reasonable to assume that the shifts determined for fluoroprobe in the decalin-dioxane mixtures provide a reasonably good estimate of the energy level shift of the CS state of the DMN[n]DCNE compounds in these mixtures. Because of the similarity in the bulk physical properties of dioxane and decalin, including their dielectric constants and viscosities, one can use such mixtures to finely tune the energy level of the CS state without large changes occurring concurrently in other potentially influential parameters. We have therefore carried out measurements on the charge recombination kinetics of DMN[n]DCNE with n = 6 and 12 in such mixtures in the hope of gaining a better insight into the factors controlling the strong solvent dependences observed. We consider first the results for DMN [6] DCNE for which complications resulting from reverse electron transfer can be taken to be absent in all solvents. The first, perhaps intuitively surprising finding, which has already been alluded to, is that the charge-separated state of DMN[6]DCNE is not just slightly more stable but orders of magnitude more stable in completely nonpolar saturated hydrocarbon solvents than in benzene or dioxane. This can be understood at least qualitatively in terms of general electron-transfer theory, eq 4. Thus, the Franck-Condon factor, Fab,for a transition and from state a to state b for which the energy difference is Eab for which the (Gaussian) energy dispersion parameter associated with the transition is 2u2, is given by the Fab = exp[-(E,b - L M - L s ) 2 / 2 ~ 2 ] / ( 2 ~ ~ 2 ) o . 5 (9) (1 3 ) Reichardt, C. Solvent Effects in Organic Chemistry; Verlag Chemie: New York, 1979; Chapter 6. (14) (a) Mes, G. F.; de Jong, B.; van Ramesdonk, H. J.; Verhoeven, J. W.; Warman, J. M.; de Haas, M. P.;Horsman-van den Dool, L. E. W. J. Am. Chem. Soc. 1984,106,6524. (b) Hermant, R. M.; Bakker, N. A. C.;Scherer, T.; Krijnen, B.; Verhoeven, J. W. J. Am. Chem. SOC.1990, 112, 1214. ( ! 5 ) van Ramesdonk, H. J.; Vos, M.; Verhoeven, J. W.; Mahlmann, G. R.; Tissink, N. A.; Messen, A. W. Polymer 1987, 28, 951.
Warman et al.
1984 The Journal of Physical Chemistry, Vol. 95, No. 5, 1991
10
I
0.1 0.2
0.4
0.8
LE, ( e v ) Figure 6. Lifetime of the charge-separated state of DMN[6]DCNE in decalin-dioxane mixtures (filled circles) as a function of the increased stabilization energy, A&, of the charge-separated state. The values of AE, were interpolated from the solvatochromic shift data in Table 11. The full line was calculated by using eq 12 in the text with a value of 0.64 (eV)2 for 2u2 and a lifetime of 45 ns in pure decalin. The open point is the recombination lifetime found for this compound in benzene. In (9), LM and & are the molecular (or internal) and solvent reorganization energies, respectively. Since L M is usually taken to be solvent independent, (Eab- LM)in (9) can be replaced by the solvent-indeperident quantity Eo. Fa,,= exp[-(E, - Ls)2/2u2]/(2.rru2)o.s
(10)
For an emissive transition the fluorescence spectrum corresponding to ( I O ) is given by
[ ( E ) = I(E,,J
exp[-(Eo - Ls - E)*.4 In 2 / A p ]
(1 I )
In ( 1 I ) , E,,, = Eo - Ls is the energy at maximum fluorescence intensity and AW, = 2(2u2 In 2)0.5, is the full width at halfmaximum of the spectrum. For saturated hydrocarbons Ls is expected to be close to zero so that Eomay be identified with the emission maximum of 2.7 eV found for these apolar solvent^.'^'^ The parameters & can be identified with the shift in the emission maximum, AEs, in the solvating solvent. If the energy dispersion associated with {he transition is assumed to be solvent independent to a first approximation, then eq 12 for the ratio of the rate for recombination in the solvating solvent to that in a saturated hydrocarbon, Fs/Fo, can be derived from ( I O ) F s / F o = exp[Ls(2Eo - Ls)/2u2]
(12)
For a highly exoergic process, as for direct recombination in the present case, Eo is positive and much larger than Ls, which is usually taken to have a value of approximately 1 eV or less. Relationship 12 indicates therefore a close to exponential increase with Ls in Fs/Fo and hence in the ratio of the electron-transfer rate coefficients. In Figure 6 we have plotted semilogarithmically the lifetimes found for D M N [ 6 ] D C N E in mixtures of decalin and dioxane against the energy shift as interpolated from the data obtained using the fluoroprobe in Table 11. As can be seen, the data display a close to linear behavior in this semilogarithmic representation, confirming the close to exponential dependence of kDRon AEs as given in (1 2). The lifetime point for benzene is also plotted in Figure 6 at 0.4 eV and is seen to lie slightly higher than the data for the decalin-dioxane mixture at this energy. The line drawn through the points in Figure 6 was calculated by using expression 12 together with a value of 0.64 (eV)2 for 2u2. This value corresponds to a spectral fwhm of 1.33 eV, which is a factor of 2 larger than the A W values of approximately 0.65 (16) Redi, M.; Hopfield, J . J. J . Chem. Phys. 1980, 72, 6651. (17) Marcus, R. A.; Sutin, N . Eiochim. Biophys. Acta 1985, 811, 265.
eV actually found for the fluorescence from the C S states of the D M N [ n]D C N E c o m p o ~ n d s . ~The ~ ' ~discrepancy is even larger if the value of 2uZrequired to give a good fit to the data in Figure 6 is compared with that expected on the basis of the expression for the dispersion contained in the frequently used version of the Marcus expression,"^'* i.e. 2u2 = 4LskBT. This would predict a value of approximately 0.1 eV2 or smaller. We now turn to the more complex solvent effects found for the longer compounds where the alternative pathway of recombination via reverse electron transfer also becomes important. One of the consequences of the occurrence of the reverse reaction has been found to be that the decay kinetics become sensitive not only to solvent polarization effects but also even to the electronic polarizability of the medium. Thus, for the n = 4 and 6 compounds the recombination lifetimes of 8.3 f 0.5 and 42 f 3 ns, respectively, found in different saturated hydrocarbon solvents can be considered to be equal within the error limits of the measurements. For the D M N [ 8 ] D C N E compound however lifetimes of 17, 28, and 58 ns are found for n-hexane, cyclohexane, and trans-decalin.2 These completely apolar solvents have dielectric constants of 1.89, 2.02, and 2.17, respectively, at room temperature. This sensitivity to electronic polarizability, under conditions where the reverse electron-transfer pathway is important, is predicted by eq 8. This equation can be rearranged to give the value of the free energy change at infinite separation which would be required to explain a given reverse electron-transfer rate: AG(m)cs = -~BT In [ ( k ~ / k-~1)/(1 - k D R / k R ) ]
+ 14.4/cRc
(13)
For the n = 8 compound in a saturated hydrocarbon solvent we take for the rate constant for direct recombination, kDR, the value that would have been expected in the absence of the reverse electron-transfer pathway. This is 2.6 X lo6 s-I (TDR = 390 ns) based on the extrapolation of eq 3 with vDR = 7.7 X IO9 s-'. The values of AG(m), required to yield the lifetimes for the different saturated hydrocarbons given above by using the known centerto-center distance for the n = 8 compound of 11.8 A4 and the known dielectric constants are found to be 0.671,0.603, and 0.534 for n-hexane, cyclohexane, and trans-decalin, respectively. The gradual decrease in AG( m)CSwith increasing dielectric constant of the saturated hydrocarbon is as expected because of the increase in the polarization energy of the ionic centers. For two ionic centers of average radius r the polarization energy is given by Pcs = 14.4(1 - I / c ) / ~ (14) From the 0-0 transition energy of the D M N donor of 3.78 eV and the oxidation and reduction potentials of the donor and D C N E acceptor of 1 .I and -1.75 eV, respectively, in acetonitrile the value of AG(m)cs for this highly polar solvent, c = 37, is found to be -0.93 eV. The values of AG(m)cs for the saturated hydrocarbons should therefore be given by hG(m)cs =-0.93 + 1 4 . 4 ( l / t - 1/37)/r (15) A value of the average ionic radius of 4.4 8, yields AG(m), values of 0.7 I , 0.60, and 0.49 for n-hexane, cyclohexane, and trans-de-
calin. These values show the same trend and are in general agreement with the values determined from the kinetic data. As remarked previously, the effect of the indirect recombination pathway is to eventually invert the order of the lifetimes. Thus, for D M N [ IZIDCNE the lifetime in decalin is 1 1 ns, Le. almost completely controlled by the indirect recombination pathway, while in dioxane it is 265 ns and due almost exclusively to direct charge recombination. The value of AG(Rc)cs for D M N [ I21DCNE in decalin is calculated, via (6) with AG(m), = 0.534 eV, to be 0.090 eV, i.e. slightly endoergic. For dioxane, on the other hand, charge separation should still be reasonably exoergic with a AG(R& value on the order of -0.47 eV on the basis of AEs = 0.56 eV for pure dioxane. It seemed of interest to attempt to investigate the transition region between these two extremes in some detail. To this end ( I 8) Marcus, R. A. J . Chem. Phys. 1956, 24, 966.
Charge Recombination within Molecular Assemblies
The Journal of Physical Chemistry, Vol. 95, No. 5, 1991
1985
TABLE III: Recombination Lifetimes, iR= l / k ~ and , Quantum of Charge Separation for DMN[n]DCNE with n = 6 and Yields, &Q, 12 in Decalin-Dioxane Mixtures n 6
vol % dioxane 0
7 14 21 32 100
12
0 5.1 9.6 14.8 19.4 23.9 28.6 33.3 41.2 49.2 54.4 66.7 73.2 76.9 81.1 83.3 89.3 90.9 94.9
AE.," eV 0.000 0.100 0.195 0.270 0.355 0.560 0.000 0.075 0.141 0.205 0.260 0.302 0.345 0.372 0.412 0.437 0.452 0.480 0.495 0.503 0.513 0.517 0.525 0.530 0.538 0.555 0.555
EL 0.2
10
0.4
0.6
AE, (ev) Figure 7. Lifetime of the charge-separatedstate of DMN[12]DCNE in decalin-dioxane mixtures (filled circles) plotted as a function of the increased stabilization energy, AEs, of the charge-separated state. The values of AEs were interpolated from the solvatochromic shift data in Table 11. The full line was calculated via eqs 16-18. The dashed line was calculated by using the same equations but AEs/2 in place of AEs. The lifetime found in pure benzene is shown as the open circle.
lifetimes were measured in decalindioxane mixtures as was done for the DMN[6]DCNE compound previously, with however remarkably different results as is shown in Figure 7 where the lifetimes are plotted against the energy shift, AEs. As can be seen, as the driving force for charge separation, -AG(Rc)cs, increases with increasing dioxane concentration the lifetime also increases, initially gradually, from a value close to the unquenched lifetime of the locally excited donor of IO ns, but then more steeply. A maximum in the lifetime is reached at a AEs value of slightly less than 0.5 eV after which it decreases with further increase in the driving force (dioxane content). It is perhaps worth reemphasizing that the total overall change in the dielectric constant of the medium in going from pure decalin to pure dioxane is in fact only from 2.17 to 2121. These results serve therefore to illustrate once again the extremely sensitive and complex behavior of long-distance recombination kinetics particularly for conditions of small driving force even for molecules with well-defined and rigid geometries. We have attempted to describe at least semiquantitatively the form of the data in Figure 7 in the following way: We begin with the basic equation derived in the previous section for the effective overall rate of recombination under conditions of low driving force k~ = kDR
+ (kD - ~ D R ) / (+I exP[-@(Rc)Cs/kB~1
(16)
For the direct recombination rate, ~ D Rin, the mixture we take the same dependence on AEs to apply as was found for the n = 6 compound, i.e. eq 12 with 2aZ = 0.64 eVZand Eo = 2.7 eV, and normalize this to the rate found in pure dioxane, for which direct recombination is the controlling pathway. kDR= 4.9
X
IO4 exp[AEs(5.4 - AEs)/0.64]
(17)
For the free energy difference between the LED and the CS states, AG(Rc)cs, we take the value for pure decalin of +0.09 eV, calculated on the basis of AG(-)cs = 0.53 eV and Rc = 14.9 A, and adjust this by the solvent shift, AEs, interpolated from the values in Table 11. AC(Rc)cs = 0.09 - PES (18) For the unquenched LED lifetime we take the values measured for the model donor compound of 10 and 7.5 ns for pure decalin and dioxane, respectively. For mixtures of the two liquids we have assumed a linear interpolation on the basis of volume fraction between these extreme values. The values of the recombination lifetimes, iR = 1 /kR, calculated on the basis of the above are shown as the full line in Figure 7 .
100 100
ns 45 19 11 7 4 0.5
bm6
11
0.14 0.24 0.35 0.41 0.46 0.48 0.50 0.5 1 0.56 0.52 0.69 0.77 1.04 0.84 1.12 0.88 0.72 0.90 0.7 1 0.76 0.81
iR,
14 16 29 45 83 198 233 317 275 525 523 508 606 440 47 1 385 284 324 270 258
1 1
1 1 1 1
Interpolated from the solvent-shiftdata for "fluoroprobe" given in Table 11. bFor n = 6 assumed = I on the basis of the very rapid charge separation rate; for n = 12 determined from the absolute magnitude of the TRMC signal taking a dipole moment of the CS state of 78 D.
While there could be said to be a qualitative resemblance to the experimental results, in particular with regard to the occurrence of a maximum at an intermediate concentration, there can certainly be no talk of a quantitative fit. The only way to improve the quantitative agreement is to moderate the decrease in the rate of the reverse electron-transfer reaction as AEs increases. This can be achieved for example by using instead of A& in (1 8) AEs/b with 6 > 1 on a purely empirical basis. The dashed line in Figure 7, which gives a reasonably good fit to the experimental data, was in fact calculated by using 6 = 2. It is to be hoped that the availability of detailed data on the charge recombination process under close to thermoneutral conditions will provide a stimulus for theoretical studies in this regime. Perhaps these will justify this use of a smaller value than AEs. The fact that any dipolar transient is observed at all for the DMN [ 121DCNE compound in pure decalin is perhaps surprising in view of the estimate of a negative driving force of 0.09 eV for the charge separation process. However, in the case of the n = 8 compound (Rc = 11.5 A) in cyclohexane, for which the driving force is also close to zero, the charge separation lifetime has been directly measured and found to be 48 PS.*-~*" This is only slightly more than twice the lifetime found for much more polar media with relatively large driving forces. It would seem therefore that the activation barrier toward long-distance charge separation remains extremely low even for solute-solvent combinations for which it is certain that the driving force is within a tenth of an electronvolt of zero. It is possible to determine an absolute value of the quantum yield of the charge-separated state, &s, from fits to the TRMC signals based on the known irradiation parameters9 and the measured dipole moment of 78 D' for DMN+[1 ZIDCNE-. These values are listed in Table 111. As can be seen, $cs increases with increasing dioxane concentration from a low of 0.14 for pure decalin to approximately 0.8 for pure dioxane. Under conditions where the reverse electron-transfer process is negligible, as in pure dioxane, the effective quantum yield is
1986 The Journal of Physical Chemistry, Vol. 95, No. 5, 1991
given simply by the ratio kcs/(kcs + k D ) . The value of 0.8 corresponds therefore to a lifetime toward charge separation for DMN[12]DCNE of 1.9 ns on the basis of the natural donor lifetime of 7.5 ns. This is similar to the values of 1.4 and 2.7 ns determined for T~~ for DMN[lZ]DCNE in benzene and diethyl ether by picosecond donor fluorescence quenching measurements.] When the reverse electron-transfer process plays an important role in the overall kinetics, the concept of a quantum yield for charge separation is unclear. For example, under conditions of rapid equilibration between the LED and CS states, the fraction of molecules in the CS state at equilibrium will be simply 1/( 1 kcs/kcs). The quantum yield is therefore probably more a reflection of the equilibrium concentration of the CS state than the competitive decay modes of the LED state. It is clear that charge separation in pure decalin must take ca. 10 ns or possibly considerably longer. Because the charge separation time is probably longer than the unquenched lifetime of the excited donor, the equilibrium approximation can in fact not be applied. A full numerical kinetic analysis of the data is in fact necessary in order to unravel the individual kinetic components. We hope to present a more detailed analysis in a future publication. ( c ) Donor-Acceptor Variations. As shown in Figure 3, the results on charge recombination obtained with the DMN[n]DCNE compounds have been augmented by measurements on a series of compounds with a DMN donor but with a different, 1,2-bis(methoxycarbony1)ethylene (DMCE), acceptor. The lifetimes of the CS states of these compounds, together with values of the lifetime toward charge separation, determined from fluorescence quenching experiments, are listed in Table IV. No data are included for the DMCE acceptor compounds in saturated hydrocarbons. This is because of their photoinstability in these solvents for reasons as yet unknown. There are two basic differences between these DMCE molecules and the DCNE compounds which might be expected to influence the kinetics of charge separation and recombination; (a) the mystem of the acceptor is twisted by 90' yith respect to the donor *-system, and (b) the driving force for separation is expected to be larger by 0.1-0.2 eV because of the higher reduction potential of the ester (-1.6 eV compared with -1.75 eV for DCNE). On taking into account slight changes in the 0-0 transition energy and oxidation potential of the donor for the ester compounds, the value of AG(m)cs in acetonitrile is in fact found to be -1.1 5 eV in place of -0.93 eV for the DMN[n]DCNE compounds. The effect of these changes on the charge separation dynamics is in fact rather small. The data suggest a slight decrease in the rate of charge separation for the ester compounds despite the larger driving force. From the plots of the charge recombination ,lifetime in Figure 3 and in particular the comparison with the DCNE compounds in benzene, it is clear that a general decrease in the lifetime toward direct recombination by approximately a factor of 2 has resulted from changing the acceptor. This decrease in T~~ is somewhat less than might have been expected on the basis of the close to 0.2-eV decrease in energy of the CS state. For example, if we use eq 12 with 202 = 0.64, a decrease in exoergicity of charge recombination would be predicted to result in an increase in the rate of charge recombination by a factor of approximately 5 . It would seem therefore that, as for the charge separation process, charge recombination for the ester compounds is somewhat slower than would be expected on the basis of the changes in energy levels of the states alone. As can be seen from the data in Figure 3, the effect of the larger driving force for the ester compounds is to increase the range of separation distance over which the exponential dependence as given by ( I ) is obeyed. This has as a result that, while the recombination times for the shorter compounds are less than for the DCNE acceptor, for the longest compound the lifetime is greater. A few experiments have been carried out on assemblies containing the DCNE acceptor but with dimethoxybenzene (DMB) as donor in place of dimethoxynaphthalene. The results are listed in Table IV. In all cases the lifetime of the DMB compound is longer and for n = 4 in benzene and n = 8 in dioxane by quite
+
Warman et al. TABLE IV: Recombination Times, rRin nanoseconds, of tbe Charge-Separated States of Miscellaneous, Rigid, Donor-Insulator-Acceptor Compounds in Different Solvents Determined by TRMC; Values of the Charge Separation Time, rCSin picoseconds, Deduced from the Quenching of the Local Donor Fluorescence in Nonpolar and Moderately Polar Solvents solute' Db[n,xIcAd solventC i Rns , T ~ ps ~ ,
DMN[6,b]DCNE DMN[8,b]DCNE DMN[7]DMCE DMN[81DMCE
DMN[8,2E]DMCE DMN[ 1 IIDMCE DMN[12,2E]DMCE DMN[ 12,4E]DMCE
DMB[4]DCNE DMB[I]DCNE
Chx
JL
Ben
5
EtA Chx Ben EtA
49 68
Ben
I
DBE Ben Dox DBE EtA Ben DBE EtA Ben Dox Ben
Dox Ben Ben
Chx Ben Dox DBE EtA
C?
33 2.5 34
