8118
J. Phys. Chem. 1996, 100, 8118-8124
Conformational Dynamics of Semirigidly Bridged Electron Donor-Acceptor Systems As Revealed by Stationary and Time-Resolved Fluorescence Spectroscopies at Higher Pressures S. Schneider* and W. Ja1 ger Institut fu¨ r Physikalische and Theoretische Chemie, UniVersita¨ t Erlangen-Nu¨ rnberg, Egerlandstrasse 3, D-91058 Erlangen, Germany
X. Y. Lauteslager and J. W. Verhoeven Laboratory of Organic Chemistry, UniVersity of Amsterdam, Nieuwe Achtergracht 129, NL-1018 WS Amsterdam, The Netherlands ReceiVed: December 19, 1995X
In low polarity solvents, several electron donor-acceptor systems D-B-A with a (semi-)flexible bridge B and sufficiently strong driving force exhibit the so-called harpooning process. That is, the primarily formed charge transfer state with extended geometry (ECT) relaxes via a change of the bridge conformation to a more compact exciplex (CCT). The dependence of the rate of transformation, kfold, on solvent parameters and η was studied by pressure tuning of these quantities (1 < p < 350 MPa). For the investigated compounds WS2 and WS3, -dependent activation energies between 16 and 30 kJ/mol were derived. In contrast, viscosity seems to have no effect on the rate of folding.
1. Introduction Electron donor-acceptor systems of the type D-B-A are widely used as a powerful tool for studying photoinduced electron transfer.1 One of the most important conclusions derived from studies on systems with rigid bridges is that fast electron transfer can occur over large distances, provided the D-A couple has a large driving force.2 Furthermore, it was found that in low-polarity solvents D-B-A systems with a flexible or semiflexible bridge B can exhibit a “harpooning process” if the driving force is great enough to allow a fast electron transfer over that distance at which donor D and acceptor A are held by the bridge in an extended conformation.3-5 After charge separation the steric barrier for conformational changes of the (semi-)flexible bridge (e.g., the chair-boat interconversion of a piperidine moiety) is reduced by the attractive Coulombic interaction of the charges located at the donor and acceptor, thus making transformations possible from the extended (ECT) to the more compact (CCT) charge transfer state within the lifetime of the ECT state (see Scheme 1). The dynamics of the conformational changes are conveniently monitored by fluorescence measurements if either one or both states undergo a radiative charge recombination transition to the electronic ground state, as was the case in most of the examples studied so far. In previous publications6-8 it was shown that D-B-A systems with aniline as donor and cyanonaphthalene as electron acceptor exhibit the “harpooning” effect if connected by an aliphatic chain as prototype of a flexible bridge (WS1) or by piperidine acting as semiflexible bridge (WS2 and WS3 in Chart 1). Experimental evidence is provided by the dual emission observed around room temperature and the increase in relative intensity of the shorter wavelength fluorescence from the ECT state versus the longer wavelength fluorescence from the CCT state with decreasing solvent temperature.7 Furthermore, the emission from the ECT state was shown to occur immediately after excitation, whereas the CCT state fluorescence exhibits a rise time equal to the decay time of the ECT emission.6 * Author to whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, April 15, 1996.
S0022-3654(95)03765-8 CCC: $12.00
SCHEME 1: Energy Level Diagram and Kinetic Scheme of Formation and Decay of Extended (ECT) and Compact (CCT) Charge Transfer States
CHART 1: Structures and Abbreviations of Compounds
In the model depicted in Scheme 1, it is assumed that the conversion of the ECT species to a CCT species, shortly called folding, is an irreversible, thermally activated process. The presence of a solvent will express itself not only by changing the height of the barrier (influence of ), but also by the friction © 1996 American Chemical Society
Semirigidly Bridged Electron Donor-Acceptor Systems
J. Phys. Chem., Vol. 100, No. 20, 1996 8119
exerted on the moving parts (influence of η). In order to account for the latter, it is common to use an expression derived by Kramers9 instead of the simple Arrhenius equation.
kfold )
{[ ( ) ]
ωa β 2ωb 1+ 2π 2ωb β
2 0.5
} ( )
- 1 exp -
EA RT
(1)
where ωa and ωb are the initial well frequency and the imaginary barrier frequency, respectively. β is the angular velocity correlation frequency, which is a measure of the solvent-solute friction, and is therefore usually taken as proportional to the macroscopic solvent viscosity. The various attempts to fit experimental data for the photoisomerization of diphenylpolyenes failed, however, and resulted in discussions about the validity of eq 1 to describe properly the effects of friction.10-12 Experiments in which the viscosity was changed by applying (high) pressure rather than by changing solvents or/and temperature revealed that the usual assumption of solvent and temperature independent activation energies is incorrect.12-14 Anderton and Kauffman15,16 proved this point quantitatively by applying a novel analysis procedure, which they named the isodielectric Kramers-Hubbard fit (IKH fit). They still use eq 1, but approximate β via the Hubbard relation17
β ) (6kBT/I)τR
(2)
where τR represents the experimentally determined rotational correlation time and I the molecular moment of inertia. Furthermore, they use combinations of different solvents (nalcohols) and temperatures that yield fixed solvent permittivities. The activation energies derived from the Arrhenius plots of the such selected rate constants of isodielectric solvents vary linearly with the dielectric constant and are lower than those derived, e.g., from isoviscous plots. The trend of increasing barrier height with decreasing solvent permittivity is explained as consequence of a polar transition state. Transferring the just described considerations to our problem of exciplex folding results in the prediction that application of the simple Arrhenius equation will most likely result in erroneous valves for EA, unless care is taken that only such rate constants are used which are measured under the condition of equal solvent viscosity and permittivity. One possible way to comply with this requirement is to change the pressure and temperature of one and the same solvent. In Figure 1a, the variation of and η with temperature and pressure is displayed for the two solvents used in this investigation, namely n-hexane and methylcyclohexane (data are based on refs 18-20). The corresponding parameters of the other solvents, which were used in the previous studies of the exciplex kinetics of compounds WS1-WS3, are also displayed for comparison (T ) 300 K). It is obvious that the changes in viscosity induced by variation of pressure are quite large and can surmount in absolute magnitude the differences observed for the usually applied lower and higher viscous nonpolar solvents at standard conditions (e.g., 2-methylbutane (η ) 0.225 cP) and n-hexadecane (η ) 3.44 cP)). The variation in dielectric constant, on the other hand, is relatively small (j20%), but similar in size to the differences observed for different nonpolar solvents (2-methylbutane (r ) 1.843) and n-hexadecane (r ) 2.051)). As mentioned above, the influence of the latter variation on the calculated activation energy was mostly ignored in earlier studies. As will be shown below, it can have significant effects if the reactive state and the transition state possess very different dipole moments. Then, even the small variations in induced by pressure changes can be used to derive the dependence of ∂EA on . The advantage of changing the
Figure 1. (a) Variation of the relative dielectric constant r with pressure and temperature (T ) 283, 293, 303, 313, and 323 K). - -, n-hexane; s, methylecyclohexane. (b) Relation between viscosity η and relative dielectric constant r at various pressures and temperatures. O, data points for n-hexane (T ) 273, 303, and 333 K) and methylcyclohexane (T ) 303 K). For comparison, other solvents at 293 K and p ) 1 bar (1, 2-methylbutane; 2, n-nonane; 3, cyclohexane; 4, n-tetradecane; 5, n-hexadecane; 6, trans-decalin; 7, cis-decalin).
pressure and temperature is illustrated in Figure 1b. By taking proper combinations of p and T, distinct values of and η can be realized and the activation energies derived in a correct way from an Arrhenius plot (isodielectric and isoviscous solvents). 2. Materials and Methods 2.1. Materials. Methylcyclohexane and n-hexane (spectroscopic grade) were used as purchased from Aldrich and Ferak. Solutions were typically e10-5 M and bubbled with argon for 30 min before emission measurements were performed. The synthesis and characterization of compounds WS2 and WS3 is described elsewhere.21 2.2. Experimental Techniques. The high-pressure optical cell was built following the design provided to us by Dr. D. Schwarzer from the MPI fu¨r Biophysikalische Chemie, Go¨ttingen.22 It has three sapphire windows in a 90° and 180° arrangement and can, therefore, be used for both emission and absorption experiments. The cell is surrounded tightly by copper tubes (heat exchanger) that allow a variation of the sample temperature which is controlled by a thermocouple inside the cell. The pressure is generated by a spindle press and applied to the sample cell via a transducer to separate the medium (H2O) in the pressure-generating part of the apparatus from the sample solution. Various valves allow evacuation of the cell and filling in the solution without contact with air. The cell can be used at pressures up to 400 MPa (4 kbar). No differences in recorded data were observed for measurements at increasing and decreasing pressure if one allowed enough time for the sample to
8120 J. Phys. Chem., Vol. 100, No. 20, 1996
Schneider et al.
establish complete (thermal) equilibrium after a pressure change. For absorption measurements, the cell was inserted into a Perkin Elmer Lambda 2 spectrometer (spectra are not shown). To record stationary fluorescence spectra, the emitted light was guided by fiber optics to a Chromex 0.5 m spectrograph and monitored by a Peltier-cooled CCD camera (PI; Model CCD1024EM/UV). All emission spectra are corrected for the spectral response of the system. Fluorescence decay times were determined by a home-built apparatus using the single photon timing technique. The full width at half-maximum of the instrument response function is about 400 ps when the frequencydoubled output of a synchronously pumped, cavity-dumped rhodamine 6G dye laser is used for excitation (like in the stationary experiments). The analysis of the decay curves was performed on the basis of a multiexponential decay law using the usual least-squares fit routines. Both single-curve fits and global fits were conducted. 2.3. Theoretical Procedures. The rate constant for conversion of the ECT complex into the CCT complex, kfold, can be determined from the stationary emission spectra as well as from the results of the time-resolved experiments.6,7 If one assumes that exciplex ()CCT) formation is fast and irreversible and that the rates for radiative and nonradiative transitions to the ground state (see Scheme 1) are independent of pressure and temperature in the applied range, then kfold can easily be derived from the measured decay time of the ECT state via
kfold )
1 - (kf + knr) τECT
(3) (τECT)-1
(kf + knr) is determined as limiting value of under conditions, where folding is negligible. On the basis of the model displayed in Scheme 1, the fluorescence yields for emission by the ECT and CCT complex can be expressed as
ΦECT ) kfτECT
(4a)
ΦCCT ) Φfoldkf′τCCT ) kfoldτECTkf′τCCT
(4b)
By combining eqs 4a and 4b, one gets
kfold )
ΦCCT kf 1 ΦECT kf′ τCCT
(5)
If the folding process can be described by an Arrhenius equation
( )
[ ( ) ( ) ( )] ΦCCT kf 1 + ln + ln ΦECT τCCT kf′k0
(7)
The third term in eq 7 is assumed to be constant (see above). The second term is found to be constant within experimental error in the time-resolved experiments. Therefore, EA and especially its variation with solvent permittivity can be derived from the relative fluorescence intensity of the ECT and CCT state.
( )
EA + C ) -RT ln
ΦCCT ΦECT
In order to evaluate the ratio ΦCCT/ΦECT
ΦCCT ∫ICCT(λ) dλ ) ΦECT I (λ) dλ
(9)
∫ ECT
from the recorded emission spectra, these are fitted first as a superposition of two Gaussians in the energy domain23
{[
]}
i 2 ν˜ - ν˜ max Ai 5 1 (10) I(λ) ) 2 I(ν˜ ) ) ∑ ν˜ exp σi 2σi λ and then the necessary integration is done numerically.
3. Results and Discussion
EA kfold ) k0 exp (6) RT with constant preexponential factor k0 (no influence of solvent viscosity), then the activation energy EA can be determined via EA ) -RT ln
Figure 2. Stationary emission spectra recorded for WS3 as a function of pressure (s, 1 bar, - -, 3500 bar; pressure increment between consecutive curves is 500 bar). (a) n-Hexane (303 K); (b) methylcyclohexane (303 K).
(8)
3.1. Stationary Emission Spectra. In Figure 2, stationary emission spectra of WS3 in methylcyclohexane and n-hexane recorded at 300 K (λex ) 300 nm) as a function of solvent pressure are shown. Because the collection efficiency varies with pressure (dependence on refractive index), all recorded traces are scaled such that the red emission maxima (CCT) coincide in height. Due to this normalization procedure, it is easily seen that the relative intensity of the emission from the ECT state increases with pressure. This counterintuitive situation that the contribution of emission from an extended conformation increases at higher pressure is seen in both solvents, although it is less pronounced in n-hexane than in methylcyclohexane. Because it is also less pronounced in WS2 than in WS3, we restricted our analysis of stationary spectra to that of WS3. The fit parameters (cf. eq 10) of the recorded spectra (Table 1) confirm the apparent conclusion that the maximum of the
Semirigidly Bridged Electron Donor-Acceptor Systems TABLE 1: Variation of Fluorescence Maxima ν˜ max and Bandwidth ∆ν˜ of ECT and CCT State Emission and Ratio of Both Yields, ΦCCT/ΦECT, as a Function of Solvent Permittivity (Er) or Poalrity (∆f) p ΦCCT/ νmaxECT νmaxCCT ∆νECT ∆νCCT (MPa) r30°C ΦECT ∆Ea (cm-1) (cm-1) (cm-1) (cm-1) ∆f30°C 0.1 50 100 150 200 250 300 350
2.002 2.052 2.095 2.131 2.153 2.177 2.200 2.222
49.4 42.5 35.2 28.2 22.9 19.9 16.6 13.1
0.1 50 100 150 200 250 300 350
1.871 1.942 1.988 2.024 2.055 2.079 2.099 2.116
49.3 53.5 51.4 43.0 41.4 33.7 35.4 29.4
WS3 in Methylcyclohexane 4.20 26 364 21 236 1992 4.29 26 219 21 195 1875 4.40 26 089 21 249 1991 4.54 25 893 21 272 1989 4.66 25 833 21 295 2112 4.75 25 700 21 295 4643 4.86 25 589 21 345 2111 5.00 25 504 21 386 2343 WS3 in n-Hexane 4.20 26 717 21 155 4.15 26 504 21 186 4.17 26 364 21 173 4.28 26 240 21 182 4.30 26 226 21 182 4.43 26 103 21 182 4.40 26 096 21 177 4.51 25 974 21 204
1996 2230 1874 2111 1876 2109 1870 1994
4530 4531 4530 4646 4643 4643 4760 4867
0.1001 0.1031 0.1055 0.1075 0.1087 0.1100 0.1111 0.1122
4526 4531 4530 4529 4529 4529 4532 4644
0.0918 0.0964 0.0993 0.1014 0.1032 0.1046 0.1057 0.1067
CCT emission is essentially independent of the pressure and, concomitantly, from the solvent permittivity. What cannot immediately be seen by inspection of Figure 2 is, however, that the maximum of the ECT emission shifts strongly bathochromic at higher pressures. If one uses the solute and solvent parameters to construct a Lippert-Mataga plot,24,25 one gets a larger slope than that found in the previous analysis which comprises both nonpolar and polar solvents.6 (The calculated dipole moment of the emitting ECT state is 36 versus 28 D in ref 6 for an effective radius F ) 5.7 Å.) Eventually, this difference is caused in part by the fact that in the previously study a somewhat different line shape function was applied in the spectral analysis. The essential conclusions are, however, independent of the assumed spectral distribution function. Included in Table 1 is also the ratio ΦCCT/ΦECT as derived from the emission spectra recorded at different pressures and the calculated values for EA - C. They clearly demonstrate the dependence of EA on permittivity. An absolute determination of EA is not possible because of the lack of knowledge of several parameters, especially k0. In order to facilitate the comparison of the obtained variation of EA versus with the results from time-resolved measurements, C is chosen such that the average calculated EA values of both techniques become equal. This approximation is meaningful because the course of EA versus received by both techniques is nearly identical (see Figure 5). 3.2. Time-Resolved Measurements. Inspection of the stationary emission spectra already reveals that below about 450 nm there is a strong overlap of the fluorescence from the ECT and CCT state. Due to the higher yield from the CCT state, it is practically impossible to find an observation wavelength at which the ECT fluorescence dominates the decay curve. The amplitude of the fast decaying component (which represents the decay of the ECT state) is actually fairly small with the effect that the precision of the derived fit parameters is in general not as good as with detection wavelength 500 nm. There, the emission is nearly exclusively that of the CCT state and, therefore, exhibits a rising and decaying component with equal amplitudes. As will be discussed below in detail, we find that the lifetime of the CCT state is essentially independent of pressure, whereas that of the ECT state varies considerably. With respect to the fitting procedure, this implies that the decay rates of both states can approach each other or in other words, that
J. Phys. Chem., Vol. 100, No. 20, 1996 8121 the rates for population and depopulation of the CCT state become similar or even equal. In the latter case, the decay law would no longer be a biexponential, but rather of the form t exp(-kt). The least-squares-fit procedure has a tendency to lift this (near) degeneracy and produce under this condition falsified decay constants. We largely circumvented this problem by applying a global analysis in which the decay time of the CCT state was set equal independent of the actual pressure. In Figure 3, this is indicated by the horizontal line representing the inverse global lifetime of the CCT state, whereas the data points refer to the total decay rates of the ECT state at the indicated pressure and temperature. Altogether, Figure 3 contains the results of 64 measurements on WS2 and WS3 (2 solvents × 4 temperatures × 8 pressures). Figure 3 demonstrates nicely the decrease in lifetime of the ECT state with increasing temperature, but constant pressure, due to thermal activation of the folding process. The increase in lifetime at higher pressures (and constant temperature) could be caused by the higher viscosity, if friction during the folding process is of importance (eq 1). Alternatively, one could refer to transition state theory, according to which the (reaction) rate constant is expressed as
kR )
(
)
kBT ∆Gq exp h RT
(
(11a)
)
kBT ∆Uq p∆Vq ∆Sq (11b) exp + h RT RT R For T ) constant the variation of ln(kR) with pressure yields kR )
RT d(ln kR) ) -∆Vq dp + T
∂∆Sq ∂∆Uq dp dp ∂p ∂p
(12)
∂∆Sq ∂∆Uq ∂ dp dp (12b) ∂p ∂ ∂p In many electron transfer reactions p∆Vq is so large that it dominates the right-hand side of eq 11b (see, for example, ref 24a). It can be caused by intramolecular volume changes ∆Viq and/or changes of the size of the solvent cage ∆Vsq, e.g., due to electrostriction. If one estimates ∆Viq for the folding process by applying molecular models with usual van der Waals radii, one finds ∆Viq < 0.5 Å3. The volume change caused by electrostriction varies from -6.6 Å3 at 0.1 MPa to -1.5 Å3 at 350 MPa when estimated according to ref 24b with ∆µ2/r3 ) 22.5 kJ/mol. The resulting value for p(∆Viq + ∆Vsq) is very small (
