J . Phys. Chem. 1992, 96, 2903-2909
(eo*/ri)(l/em- 1 ) - eo2/tmr Here e,, is the permittivity of the mixture, t is that of a polar component, r, is the radii of the radical-ions which are supposed to be equal to each other, and eo is the electron charge. On the basis of these assumptions, the change of energy of the RIP a t the radius of its dissociation, rb, in the binary mixture can be estimated as follows: Eb
eo2(l/Cm- l / t ) ( l / r j - l/rb)
(1)
For reasonable values of r b k 10 A, ri = 3 A, and e = 50, the Ebvaries from 0.25 to 0.06 eV when the bulk permittivity changes from 10 to 25. At the radius of recombination of the RIP, r,, there is the energy barrier, E,, which is caused by the changing character of interactions of radical-ions with the medium upon transition from a RIP (e.g., ion-dielectric continuum) to the exciplexes (e.g., dipole-dielectric continuum).” In polar solvents the value of E, seems not to be considerably affected by medium polarity. For acetonitrile solutions of Py/DMA polymethylene-linked systems, E, was determined experimentally3 as 0.13 eV. It is noteworthy that the physical nature of the E b barrier is quite similar to that of the E, barrier because the ion interactions, which depend on the dielectric properties of the medium, are different inside and outside the clusters. Within the cluster, the RIP can be approximately considered as quasimolecular so thats ‘pb = kb/(ka + kb) (Pa = ka/(ka + kb) (2) where cp, and cpb are the quantum yields of recombination and of dissociation, respectively, and k, and kb are their quasi-mono(1 1) Hoytink, G. J. Discuss. Faraday SOC.1968, 45, 14.
2903
molecular reaction constants. We also assume that the dissociated RIP inevitably lose spin correlation so that only one-fourth of them possess singlet character upon bulk recombination. Under steady-state conditions, this simple approach predicts the relative change of fluorescence detected to be
R
N
A(Pa((Pa
+ ‘~b/4)-’= (A(Pa/Va)(l + %/4~a)-’ (3)
where A(P, is the change of (P, caused by the applied magnetic field. Taking into account eq 2, one can derive the final formula: (Aka/ka)[(l + ka/kb)(l
+ kb/4ka)l-’
(4)
In terms of this simple model it is supposed that k, depends upon the applied external magnetic field so that the Aka/ka represents the relative change caused by the applied field. The ratio, k,/kb exp(Eb - E,)/kBT, can vary upon changing the composition of the binary mixture. Here kBis the Boltzmann’s constant and T i s the temperature. That preexponential factors of the quasi-monomolecular reaction constants are assumed to be equal to each other is natural in the framework of this phenomenological model. However, a more sophisticated approach gives the same results.s Expression 3 is a maximum in respect to the ratio k,/kb that is obtained when k,/kb = i.e., (E, - Eb) 5 1kBT. As follows from eq 1, the condition for obtaining the maximum value of R as a function of mixture composition is fulfilled when e,, is - 1 5 . The latter is consistent with the previous work of Nath and Chowdhuryg and with this study.
-
Summary Magnetic field modulation of exciplex fluorescence in binary solvents is affected by the heterogeneous structure of the binary liquid solvent. Therefore, the MFE technique can be a useful tool for the study of the structure of liquid mixtures.
Picosecond Laser Studies on the Dynamics of Compact Ion Pairs: Comparison between Homogeneous and Micellar Solution Stephan M. Hubig Center for Fast Kinetics Research, The University of Texas at Austin, Austin, Texas 78712 (Received: September 17, 1991) The dynamics of compact ion pairs generated by photoexcitation of charge-transfercomplexes between viologen and naphthalene derivativeshave been studied by laser flash photolysis. Ion pair lifetimes and charge separation efficiencies have been measured, which allows us to determine directly charge recombination and free ion dissociation rate constants. The free energy of the charge recombination reaction has been calculated from the one-electron redox potentials of electron donor and acceptor that have been measured electrochemically. Plots of charge recombination rate constants vs the free energy show the ‘Marcus-inverted” region. Ion dissociation rate constants increase with decreasing complex stability constants which have been obtained from Benesi-Hildebrand plots. The results in homogeneous (acetonitrile and butyronitrile) and heterogeneous (SDS micellar solution) environments are compared, and micellar effects on the formation of charge-transfer complexes, on electron-transfer reactions, and on solvation processes are discussed.
Introduction Recent studies on photoinduced electron-transfer reactions have shown that the formation and the subsequent reactions of ion pairs are the crucial steps in fluorescence quenching processes via electron transfer as well as in reaction mechanisms initiated by photoexcitation of ground-state charge-transfer (electron donoracceptor) complexes.Id It is generally accepted that in the (1) (a) Gould, I. R.;Young, R.H.; Moody, R. E.; Farid, S. J. Phys. Chem. 1991, 95, 2068. (b) Gould, I. R.; Ege, D.; Moser, J. E.; Farid, S. J . Am. Chem. SOC.1990, 112,4290. (c) Gould, I. R.; Moser, J. E.; Ege, D.; Farid, S. J . Am. Chem. SOC.1988, 110, 1991. (d) Gould, I. R.;Ege, D.; Mattes, S. L.; Farid, S.J. Am. Chem. Soc. 1987, 109, 3794. (e) Gould, I. R.;Moody, R.; Farid, S. J. Am. Chem. Soc. 1988, 110, 7242.
0022-3654/92/2096-2903$03.00/0
SCHEME I: Reaction Scheme for Photoexcitation of Charge-Transfer Complexes (A = Electron Acceptor, D = Electron Donor)
recond.ir) F T rs.,ciioiis
latter case compact or “tight” ion pairs are formed whereas in the former case solvent-separated or Yloosenion pairs are ob@ 1992 American Chemical Society
2904
The Journal of Physical Chemistry, Vol. 96, No. 7, 1992
SCHEME II: Formulas for Viologen and Naphthalene Derivatives
a X
x
= H, F, CI, Br,
CN
~erved.I*~>~ The concept of differently structured ion pairs is based on the difference in lifetimes and free ion yields measured for ion pairs produced by fluorescence quenching as compared to those produced by photoexcitation of charge-transfer complexes. In this paper we focus on the formation and decay of compact ion pairs produced by photoexcitation of charge-transfer complexes. Basically, compact ion pairs can exhibit two possible decay pathways (see Scheme I): charge recombination within the ion pair or dissociation of the ions out of the solvent cage, ultimately leading to “free” solvated ions. Whether or not the dissociation process of the contact ion pairs studied in this paper occurred via an intermediate solvent-separated ion pair will be discussed later. In order to determine the rate constants for charge recombination (k,,) and ion dissociation (kdiss) experimentally, the ion pair lifetime ( T ) and the free ion yield (0) need to be measured
where [R’] represents the molar concentration of either solvated radical ion, D” or A’- (see Scheme I), and is the molar concentration of photons absorbed by the ground-state species. Charge recombination reactions within ion pairs may occur on subnanosecond time scales depending on the redox potential difference, the distance between electron donor and acceptor, the temperature, and the solvent. In order to observe such short-lived ion pairs spectroscopically, the charge separation reaction leading to the ion pair must be completed in an even shorter time period. In dynamic fluorescence quenching experiments this goal cannot be achieved in most cases because the quenching process is at most diffusion-controlled and there are solubility limits for the highest possible quencher concentrations. For instance, assuming an average fluorescence quenching rate constant of 5 X lo9 M-’ s-l, one would need quencher concentrations greater than 2 M in order to generate ion pairs in less than 100 ps. Since such conditions are usually not achievable in fluorescence quenching experiments, the rate constants for charge recombination and ion dissociation cannot be measured directly. The only way to obtain somewhat theoretical charge recombination rate constants is by assuming a certain value for the ion dissociation rate constant and by (2) (a) Asahi, T.; Mataga, N. J . Phys. Chem. 1991,95, 1956. (b) Ojima,
S.;Miyasaka, H.; Mataga, N. J . Phys. Chem. 1990,94,7534. (c) Ojima, S.; Miyasaka, H.; Mataga, N. J. Phys. Chem. 1990, 94, 5834. (d) Ojima, S.; Miyasaka, H.; Mataga, N. J . Phys. Chem. 1990, 94, 4147. (3) Kikuchi, K.; Takahashi, Y.; Koike, K.; Wakamatsu, K.; Ikeda, H.; Miyashi, T. 2.Phys. Chem. (Munich) 1990, 167, 27. (4) (a) Haselbach, E.; Vauthey, E.; Suppan, P. Tetrahedron 1988, 44, 7335. (b) Vauthey, E.; Suppan, P.; Haselbach, E. Helu. Chim. Acta 1988,
71, 93. (5) (a) Kochi, J. K. Pure Appl. Chem. 1991,63, 255. (b) Kochi, J. K. Acta Chem. s c a d . 1990,44,409. (c) Yabe, T.; Sankararaman, S.; Kochi, J. K. J . Phys. Chem. 1991, 95, 4177. ( 6 ) (a) Rehm, D.; Weller, A. Eer. Bunsen-Ges. Chem. 1969,73, 834. (b) Rchm, D.; Weller, A. Isr. J. Chem. 1970, 8, 259. (c) Weller, A. Z . Phys. Chem. (Munich) 1982, 133, 93. (7) Mataga, N.; Shioyama, H.; Kanda, Y. J. Phys. Chem. 1987, 91, 314.
Hubig calculating a recombination rate constant based on this theoretical kdissvalue and a measured free ion yield 0. In our case, kinetic measurements on the picosecond time scale are feasible because photoexcitation of charge-transfer complexes at wavelengths within the charge-transfer absorption band induces immediate ( T C 30 ps) ion pair formation.2 Moreover, the charge-separated state is the only transient state observed on the picosecond time scale after laser excitation, and no other excited states are complicating the time-resolved absorption spectra. Continuing earlier picosecond flash photolysis studies,* we discuss in this paper data on charge-transfer complexes between viologen ions (V2+)and various naphthalene (NAP) derivatives (see formulas in Scheme 11). Photoexcitation of such complexes resulted in the formation of +/+ ion pairs, [V’+-.NAP’+]. By varying the naphthalene or viologen substituents, k,, constants could be directly measured as a function of the free energy AGO of the charge recombination reaction. It has been demonstrated that k,, values depend not only on the free energy but also on the molecular dimensions of the charge-transfer complex, i.e., the electron-transfer distance.1b*c*2b In order to avoid effects caused by the size of electron donor or acceptor molecule, we changed only substituents. Ion dissociation rate constants could also be determined experimentally for each charge-transfer complex and compared with theoretical values from the l i t e r a t ~ r e . ’ ~ * ~ ~ - ~ * ~ Oxidation potentials of the substituted naphthalenes were measured by cyclic voltammetry, and complex formation constants were obtained from Benesi-Hildebrand plots.9 Most electron-transfer studies reported in the literature describe electron donoracceptor systems in homogeneous, organic solvents. However, biological charge separation and recombination processes mostly occur in or around biomembranes, and there is a lack of information about the effects of charged interfaces on electrontransfer reaction parameters. For instance, Coulombic forces are expected to affect not only charge recombination and ion dissociation processes within the compact ion pair but also subsequent reactions of the free ions in the charged interface. There is also very little known how charged interfaces control the formation of charge-transfer complexes*J&’2and the redox potentials’) of electron donors and acceptors. For this study we chose sodium dodecyl sulfate (SDS) micellar dispersions as an interface model and compared the results in homogeneous and heterogeneous milieu.
Experimental Section Chemicals. Naphthalene (99%), 1-fluoronaphthalene (99%), 1-bromonaphthalene (98%), 1-cyanonaphthalene (98%), acetonitrile (HPLC grade), and butyronitrile (99%) were purchased from Aldrich and were used as received. The chloro-substituted naphthalene (Fluka) was a mixture of 90% 1-chloronaphthalene and 10%2-chloronaphthalene. Benzyl- and methylviologen were obtained from Sigma. For the experiments in micellar solution the dichloride salts were used as received. For the measurements in acetonitrile solution the hexafluorophosphate salts were prepared by mixing the viologen dichloride salts with excess ammonium hexafluorophosphate (99.9%,Aldrich) in water, yielding a white precipitate which was washed several times with water. The hexafluorophosphate salts were readily soluble in aceto- and butyronitrile. Sodium dodecyl sulfate (“especially pure” grade) was purchased from Gallard-Schlesinger (BDH). For all micellar (0.1 M SDS) solutions Millipore (“reagent grade”) water was used. Picosecond T i R e s o l v e d Measurements. The laser source for the picosecond time-resolved kinetic measurements is a modelocked Nd:YAG laser (Quantel YG 402). Both the harmonic (e.g., 355 nm) and the residual 1064-nm light pulses are extracted from (8) Hubig, S. M. J . Lumin. 1991, 47, 137. (9) Benesi, H. A.; Hildebrand, J. H. J. Am. Chem. SOC.1949, 71, 2703. (10) (a) Hamity, M.; Lema, R. H. Can. J. Chem. 1988, 66, 1552. (b) Hamity, M.; Lema, R. H. Can. J . Chem. 1991,69, 146. ( 1 1) Masuhara, H.; Tanabe, H.; Mataga, N. Chem. Phys. Lett. 1979,63, 273. (12) Atherton, S. J.; Hubig, S. M.; Callan, T. J.; Duncanson, J. A.; Snowden, P. T.; Rodgers, M. A. J. J . Phys. Chem. 1987, 91, 3137. (13) Kaifer, A. E.; Bard, A. J. J. Phys. Chem. 1985, 89, 4876.
Dynamics of Compact Ion Pairs
The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 2905 TABLE I: Thermodynamic Data on Charge-Transfer Complexes between Viologens and Substituted Naphthalenes Eo(NAP),b AGO: K,(MeCN),d KJSDS), complex' V eV M-' M-' MV/NAP MV/NAP-F MV/NAP-CI MV/NAP-Br BV/NAP-CN MV/NAP-CN
Figure 1. Picosecond time-resolved absorption spectroscopy apparatus: MCA, multichannel analyzer; PC, personal computer; PP, peristaltic pump; FO, fiber optics; BFO, bifurcated fiber optis; SP, spectrograph; DDA, dual diode array; C H , cuvette holder; CL, cylindrical lens; M, mirror; DM, dichroic mirror; A, aperture; HF, heat filter; UF, UV band-pass filter; IF, IR band-pass filter; DL, delay stage; CC, continuum generating cell; FL, focusing lens.
the laser and travel together to a dichroic mirror that reflects the harmonic laser pulse in a 90' angle and transmits the 1064-nm light (see Figure 1). While the harmonic light is focused onto the sample cuvette, the 1064-nm light traverses a variable delay stage before being focused onto a 10-cm cuvette containing a 5050 mixture of deuterated phosphoric acid and D20to produce a white continuum light flash of 30-ps duration. The continuum light is focused onto a diffusing frosted glass plate and recollimated and focused onto the common end of a bifurcated fiber optics bundle that splits the beam into two branches: a sample beam that probes the sample where it is excited by the harmonic laser pulse (excited state) and a reference beam that probes the sample where it is not excited (ground state). The two light beams are picked up by fiber optics on the other side of the cuvette and led to a UFS 200 spectrograph to which an image-intensified dual diode array (2 X 512 diodes) is attached. Thus, with one single continuum flash the light transmitted through the excited (I)and unexcited sample (1,) can be detected for each wavelength, and the difference absorption spectrum A = log ( I 0 / I ) can be calculated. The wavelength resolution of the system is 1 nm per diode. The diode array data are passed via a Tracor Northern 6200 multichannel analyzer to a personal computer for storage, analysis, and display. In a typical experiment about 200 spectra are averaged for one delay time. By moving the delay stage the arrival of the continuum flash can be delayed by up to 5 ns with respect to the excitation pulse, generating time-resolved spectra with a time resolution limited only by the pulse width of the laser (ca. 30 ps). Before each measurement the two diode arrays were balanced, and all data were corrected by this balance. Microsecond TmeResolved Measurements. The microsecond time-resolved kinetic measurements were performed using a Q-switched Nd:YAG laser (Quantel YG 481) with a ca. 10-ns pulse and a kinetic spectrophotometer including an Oriel 150-W xenon lamp, a computer-driven Bausch & Lomb monochromator, and a Hamamatsu R928 photomultiplier tube. The data were collected by a Biomation 8100 digitizer and stored in a personal computer for kinetic analysis. All samples were deaerated prior to laser flash photolysis by bubbling with nitrogen gas. Cyclic Voltammetry. The redox potentials were measured using a PAR 175/173/179 system combined with a Houston x-y recorder as described earlier.I4 We chose a platinum disk (0.10 mmz) as the working electrode, a platinum wire as the auxiliary electrode, and a silver wire as the quasi-reference electrode. The silver electrode potential was measured to be 0.10 V vs SCE using ferrocene as standard. The platinum electrodes were polished with 1.O- and 0.3-pm alumina before each experiment. All measure(14) Torres, W.; Fox, M. A. Chem. Mater. 1990, 2, 306.
1.52 1.66 1.68 1.70 2.02 2.02
2.21 2.35 2.37 2.39 2.62 2.71
2.0 0.9 0.4 0.1 0.1 0.1
2.3 2.2 2.8 2.1 1.o 1.2
MV = methylviologen, BV = benzylviologen, N A P = naphthalene, NAP-F = 1-fluoronaphthalene, NAP-CI = 1-chloronaphthalene, NAP-Br = I-bromonaphthalene, NAP-CN = 1-cyanonaphthalene. One-electron oxidation potentials of naphthalene components (vs SCE). CCalculatedas the difference between the redox potentials of electron donor and acceptor not considering contributions from Coulombic work. Equilibrium constants for complex formation in acetonitrile (MeCN) and micellar (SDS) solution.
ments were carried out in acetonitrile (Baker, doubly distilled from CaH, and stored over 3-A molecular sieves) containing 0.3 M tetraethylammonium hexafluoroborate (Southewestem Analytical Chemicals, "electrometric grade", recrystallized from ethyl acetate) as supporting electrolyte. The solutions were bubbled with nitrogen for 15 min prior to each measurement, which were conducted under nitrogen. Scan rates were 20 and 50 mV/s. Absorption Measurements. The absorption spectra were recorded with a Hitachi U3210 spectrophotometer, and the data were transferred to a personal computer for the Benesi-Hildebrand analysis.
Results Redox Potentials. In order to understand the charge-transfer absorption spectra and to calculate AGOvalues for the one-electron-transfer reactions, one needs to know the one-electron redox potentials of electron donors and acceptors. Using the cyclic voltammetry technique, we measured one-electron oxidation potentials between l .52 and 2.02 V vs SCE going from unsubstituted naphthalene to l-cyanonaphthalene in 0.02 M acetonitrile solutions (see Table I). Since naphthalene showed a nonreversible redox behavior, the values presented are peak potentials. As oneelectron reduction potentials for the electron acceptors, we took = -0.69 V15 and P !, = -0.60 VI6 vs SCE for methyl- and benzylviologen, respectively. Neglecting Coulombic work,40 we calculated the driving forces AGOfor charge recombination within the compact ion pair as the difference between electron donor and electron acceptor potentials and obtained values between 2.21 and 2.71 eV for the ion pairs described above (see Table I). On the basis of the fact that the one-electron reduction potential of methylviologen changed only by ca. 50 mV going from aqueous to SDS micellar ~olution,'~ we neglected micellar effects on the redox potentials and used the same AGOvalues in acetonitrile and SDS solutions. Charge-Tramfer Complex Formation. All solutions containing either benzyl- or methylviologen and one of the naphthalene derivatives listed above showed an absorption band (shoulder) around 400 nm where neither the viologen nor the naphthalene derivatives absorb (see Figure 2). As shown for the methylviologen-naphthalene system," the new absorption band can be attributed to the formation of a ground-state charge-transfer (electron donor-acceptor) complex. Such charge-transfer complexes were observed both in acetonitrile solutions and in 0.1 M SDS micellar dispersions. The position of the absorption maximum of the shoulder, which was determined by calculating the first derivatives of the absorption spectrum, shifted by about 20 nm going from unsubstituted to cyano-substituted naphthalene. With increasing naphthalene and/or viologen concentration the charge-transfer absorption band became stronger (see Figure 2), (15) Ito, M.; Kuwana, T. J. J. Electroanal. Chem. 1971, 32, 415. (16) Wardman, P.; Clarke, E. D.J. Chem. SOC.,Faraday Trans. I 1976, 72, 1377. (17) Jones 11, G.; Malba, V. Chem. Phys. Lett. 1985, 119, 105.
2906
Hubig
The Journal of Physical Chemistry, Vol. 96, No. 7, 1992
1.74
4-
-1
1.95
.%0
\
*
.li
.w9
*
*
-.OY***
193
1
330.
318.
400.
492.
,
1
1
w”sm Figure 2. Absorption spectra of SDS micellar solutions containing 2.3 mM methylviologen and (1) 0, (2) 4, (3) 8, (4) 12, and (5) 20 mM 1-chloronaphthalene.
and applying the Benesi-Hildebrand e q ~ a t i o nwe , ~ were able to determine complex formation equilibrium constants, Kq (see eq 2), for each system in acetonitrile as well as in SDS micellar dispersion (see Table I).
where [V2+], [NAP], and [MV2+-NAP] are the analytical concentrations of electron donor, electron acceptor, and electron (18) Rodgers, M . A. J.; Foyt, D. C.; Zimek, Z. A. Radial. Res. 1978, 75, 296. (19) Rodgers, M. A. J. Radiar. Phys. Chem. 1984, 23, 245. (20) Hubig, S. M.; Dionne, C. B.; Rodgers, M. A. J . J. Phys. Chem. 1986, 90, 5873. (21) Hubig, S. M.; Rodgers, M. A. J . J . Phys. Chem. 1990, 94, 1933. (22) Almgren, M.; Swarup, S. J. Colloid Interface Sci. 1983, 91, 256. (23) Almgren, M.; Griesser, F.;Thomas, J . K. J. Chem. SOC.,Faraday Trans. 1 1979, 75, 1674. (24) Turro, N . J.; Yekta, A. J. Am. Chem. SOC.1978, 100, 5951.
1
40‘0.
1
1
1
eio.
1
1
B#).
TIME (PICO-SEC’S)
‘1;I T
4.
9.08-
In SDS micellar solution both the viologen and the naphthalene species were assumed to be solubilized in the micellar pseudophase only, the latter because of its hydrophobic character and the former because of its Coulombic attraction to the negatively charged SDS micelle surface.1s-21 Thus, in order to determine the equilibrium constant for complex formation between micellized viologen and naphthalene molecules, “local” concentrations of the complex partners within the micellar pseudophase need to be considered rather than analytical concentrations.1° Taking R = 18.1 A as micellar radius2*for 0.08 M SDS solutions, we calculated the volume of one mole of SDS micelles to be V, = 4/3?rR3NA = 15 L mol-’ (NA= 6.0225 X loz3mol-I). Assuming an aggregation number (N) of 6223and a critical micelle concentration (cmc) of about 8 mM,24the molar concentration of micelles in a 0.08 M SDS solution was calculated to be [mic] = (0.08 - cmc)/N = 1.2 X mol L-I. Thus, a 0.08 M micellar solution contains about 1.8 vol 5% micelles, and “local” concentrations of micellized species can be calculated by dividing the analytical concentrations by 0.018. Therefore, in micellar solution the complex formation equilibrium constants, KBH,resulting from Benesi-Hildebrand plots that are based on analytical concentrations, need to be corrected by a factor of 0.018 in order to obtain the true equilibrium constants, K,, which are listed in Table I and are based on “local” concentrations:
1
‘ -ed.o ’ do. ‘
414.
1
-.20e-
WAVELPIGTH
Figure 3. (a, top) Picosecond time-resolved decay trace of the MV” radical observed at 605 nm after photoexcitation of the methylviologen1-chloronaphthalene charge-transfer complex in SDS micellar solution. (b, bottom) Spectrum at 30 ps after excitation.
TABLE 11: Laser Flash Photolvsis Date comdex” MV/NAP MV/NAP-F MV/NAP-CI MV/NAP-Br BV/NAP-CN MV/NAP-CN
r9bps in MeCN in SDS 28 29 40 40 63 71
57 90 170 190 500 480
oc in MeCN
in SDS
0.016
0.004 0.003 0.004 0.034 0.025 0.023
0.025 0.026 0.035
0.080 0.090
“For explanations of symbols see Table I. bIon pair lifetimes in acetonitrile (MeCN) and micellar (SDS) solution. CFree ion yields (see eq 1) in acetonitrile (MeCN) and micellar (SDS) solution.
donor-acceptor complex, respectively. Picosecond Time-Resolved Laser Flash Photolysis. A typical picosecond time-resolved transient absorption spectrum obtained upon excitation of a viologen-naphthalene charge-transfer complex at 355 nm is shown in Figure 3b. The spectrum recorded immediately after excitation ( t = 30 ps) shows the absorption bands of the reduced viologen species (V)peaking around 400 and 600 nmZ5whereas the absorption band of the oxidized naphthalene species (NAP’+, A,, = 685 nmX) is hidden underneath the much stronger viologen radical cation absorption band. The absorption (25) Venturi, M.; Mulazzani, Q.G.; Hoffman. M. Z. Radiat. Phys. Chem. 1984, 23, 229. (26) Gschwind, R.; Haselbach, E. Helo. Chim.Acta 1979, 62, 941.
The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 2907
Dynamics of Compact Ion Pairs spectrum indicates the formation of an ion pair, the lifetime of which could be determined by analyzing the decay kinetics of the reduced viologen component. A typical kinetic trace showing the decay of the viologen absorption band at 605 nm is displayed in Figure 3a, and ion pair lifetimes for acetonitrile and 0.1 M SDS micellar solutions are listed in Table 11. The lifetimes 5 40 ps were corrected by using the approximation T~~~ = (robs2rlase:)1/2.41The ion pair lifetimes of the naphthalene and the chloronaphthalene complexes were also measured in butyronitrile. Interestingly, the lifetimes were the same as in acetonitrile in spite of the difference in the dielectric constant. For all charge-transfer complexes mentioned above we obtained monoexponential decay curves such as in Figure 3a, but the kinetic traces did not decay back to the prepulse baseline. The raised baseline indicated that a longer-lived species was formed which decayed on a microsecond time scale (vide infra). Microsecond Time-Resolved Laser Flash Photolysis. The time-resolved spectra observed on the microsecond time scale showed the same absorption bands as the picosecond time-resolved spectra, i.e., the absorption bands of the reduced viologen component (V'+). The longer-lived absorption bands were assigned to the solvated radical ion. There were two pieces of information to extract from the microsecond flash photolysis experiments: the initial amount of solvated radical ions produced and the decay kinetics. In order to determine the initial amount of solvated viologen radical ions, [V'+l0 (see eq 4), we extrapolated the decay traces observed at 605 nm back to time t = 0 ( 4 6 0 5 ) in eq 4). The was number of photons absorbed during the laser flash (labs) obtained by measuring the triplet absorption at 525 nm of a benzophenone solution with the same absorbance at 355 nm as the charge-transfer complex solution. Since the extinction coefficients of the transient species were well-known (eao5 = 14000 M-' cm-l for reduced methylviol~gen,~~ €605 = 15 000 M-' cm-' for reduced benzylviologen,2s and €525 = 7640 M-l cm-' for the benzophenone triplet state29),the yield of free solvated ions could be determined according to eq 4:
a = - [v"10 labs
A(605) --A(525)
%25 €605
(4)
The free ion yields CP for acetonitrile and SDS micellar solutions are given in Table 11. For all measurements very low concentrations of viologens and naphthalene derivatives were chosen in order to avoid dimerization of the naphthalene or the viologen species. The free ion yields obtained were reproducible within 5%. The microsecond time-resolved kinetic traces followed different rate laws comparing experiments in acetonitrile and SDS micellar solutions. In acetonitrile, the concentrations of the solvated ions decayed according to second-order kinetics which was expected for bimolecular ion-ion recombination reactions. Bimolecular rate constants between 1 X 1O'O and 3 X lolo M-' s-' were extracted for all viologen-naphthalene ion recombination reactions. We did not find any correlation between the bimolecular recombination rate constants and AGOof the recombination reaction. In SDS micellar solutions we observed biexponential decay traces for all ion-ion recombination reactions. The fast component could be fitted as a first-order reaction, and an averaged rate constant of (4 f 1) X lo6 s-l was obtained for all complexes studied. The slow component followed second-order kinetics, leading to rate constants between 2.7 X lo9 M-' s-I for the methylviologen/cyanonaphthalenecomplex and 1.1 X lolo M-' s-' for the methylviologen/naphthalene complex. Determination of Charge Recombination and Ion Dissociation Rate Constants. According to eq 1, rate constants for charge recombination within the ion pair (krs) and ion dissociation out (27) Watanabe, T.; Honda, K. J . Phys. Chem. 1982, 86, 2617. (28) Convin, A. H.; Arellano, R. R.; Chiwis, A. B. Biochim. Biophys. Acta 1968, 162, 533. (29) Hurley, J. K.; Sinai, N.; Linschitz, B. Photochem. Photobiol. 1983, 38, 9.
TABLE 111: Rate Constants for Charge Recombination (k,) and Ion Dissociation (kdiu)in Acetonitrile (MeCN) and Micellar (SDS) Solution
k,,, complex' MV/NAP MV/NAP-F MV/NAP-CI MV/NAP-Br BV/NAP-CN MV/NAP-CN a
AG,,beV 2.21 2.35 2.37 2.39 2.62 2.71
l o L os-l
MeCN 3.5 3.4 2.4 2.4 1.5 1.3
SDS 1.7 1.1 0.6 0.5 0.2 0.2
kdiss, lo* S-' MeCN SDS 5.6 0.68 8.7 0.28 6.3 0.24 8.8 1.80 13.0 0.50 12.0 0.58
For explanations of symbols see Table I. bCalculated as described
for Table I.
of the ion pair (kdiss)could be determined taking the measured free ion yields Q, and ion pair lifetimes T from Table 11. All rate comtants for acetonitrile solutions and SDS micellar dispersions are listed in Table 111. Discussion In order to study the dynamics of ion pairs in homogeneous and heterogeneous environments, we have performed laser flash photolysis experiments on ground-state charge-transfer complexes. First, we focus on the formation of charge-transfer complexes in homogeneous and micellar solution. Since only one complex partner, i.e. V2+, carries charges, the complex stability in homogeneous solution is not controlled by Coulombic forces, as it has been shown for porphyrin-azaaromatic hydrocarbon complexe~,~O but by the ion pair character of the complex which depends on the electron donor and acceptor strength^.^' The low Kq values listed in Table I are due to the fact that a-donors and a-acceptors were used to form the charge-transfer complexes. The complex stability in acetonitrile decreased by a factor of 20 going from unsubstituted naphthalene to cyanonaphthalene, the latter being a much weaker electron donor due to the electron-withdrawing cyano substituents (Hammett u value = 0.66). However, there is another possible interpretation of the data, Le., in terms of electron-transfer distances. It is very likely that with increasing size of the naphthalene substituent the distance between electron donor and acceptor within the complex increases, which reduces the complex stability. In micellar environment we did not observe any trend in the complex stability which varied only by a factor of 2. Obviously, Coulombic and hydrophobic forces affecting the location of the viologen and the naphthalene component, respectively, control the complex stability more than electron donor strength. Interestingly, although the Kq values are not much higher than in acetonitrile, the complex formation is clearly enhanced because of very high local concentrations of the complex partners within the micelle, which shift the complex formation equilibrium (see eq 2a) toward the right side. Photoexcitation of the viologen-naphthalene charge-transfer complexes within the charge-transfer absorption band (q, = 355 nm) leads first to the formation of compact ion pairs consisting of a reduced viologen ion (V*+)and an oxidized naphthalene ion (NAP'+). The question of whether after completion of a laser pulse we were studying the decay kinetics of the initial compact ion pairs or the kinetics of solvent-separated ion pairs formed within the 30-ps laser pulse cannot be answered with experimental proof. Using 3.75 and 4.75 A as radii for the naphthalene and the viologen molecule, respectively, we calculate diffusion coefficients of 1.6 X and 1.3 X cm2/s for the two ion pair partners. Therefore, according to Einstein's equation, the naphthalene and the viologen ion could move apart about 4 8, within the 30-ps time period of the laser pulse, which would provide enough room for solvent molecules to align between the two ions. However, if this were the case, it would be very difficult to rationalize why two positively charged solvent-separated ions should form an ion pair that recombines in less than a nanosecond, instead (30) Brun, A. M.; Harriman, A.; Hubig, S. M. J . Phys. Chem. 1992, 96,
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However, if we consider the data points being part of a bell-shaped Marcus plot as suggested by Farid et al.,’ then the steeper curve observed for micellar solutions can be seen as the bottom part of 24.00-the bell whereas the acetonitrile data points seem to be rather close tT4 8 to the flat top of the bell, indicating a significant shift of the 06 0 bell-shaped curve along the AGOaxis. Such a shift could be caused 0‘O 23.00-Y by a change in the solvent reorganization going from o9 C acetonitrile to micellar media, or by a shift of the lAGol values 12 22.00-due to medium-dependent Coulombic effects. The two data points measured in aqueous solutions are very close to those obtained 15~06 in micellar systems, which indicates that the solvent reorganization 21 .oo energy of micellized ion pairs is very similar to the one of ion pairs in pure aqueous solution or, in other words, the micellized ion pairs are located close to aqueous regions of the micelle. 20.00I The fact that lifetimes measured in acetonitrile and butyronitrile 2.0 2.5 3.0 did not differ at all, in spite of the polarity difference between If% Lev1 the two solvents, is surprising. Mataga et a1.%observed a decrease Figure 4. Plots of charge recombination rate constants vs free energy of in k , by 30% comparing the charge recombination rate constants the electron-transfer reaction in water (e),acetonitrile (O),and SDS of the TCNB-toluene ion pair in acetonitrile and butyronitrile. micellar solution (e): 1 , 8 = M V / N A P 2, 10 = MV/NAP-F; 3, 1 1 = In all experiments that showed such a solvent effect, the ion pair MV/NAP-C1; 4, 12 = MV/NAP-Br; 5, 15 = BV/NAF-CN; 6 , 1 6 = MV/NAP-CN; 7, 9 = MV/NAP-SO
