J. Phys. Chem. 1992,96, 3151-3166
3757
Strongly Exothermic Electron-Transfer Reaction in the Excited Singlet State of Alkylcarbazole-Polynitrofluorene and -Polynitrofluorenone Bichromophoric Systems. 1. Correlation between the Probability of Charge Separation, Photoactivity, and Picosecond Laser Photolysis Studies on the Photoinduced Charge Recombination of Ion Pair State Produced in Some Media Tapan GangulyJ Devendra K. Sharma,t Sylvain Gauthier, Denis Gravel,* and Gilles Durocher* DPpartement de Chimie, UniversitC de MontrCal, C.P. 6128, Succ. A, MontrCal, QuCbec, H3C 357 Canada (Received: November 5, 1991) The present study was undertaken to investigate the parameters controlling the rates of forward and backward electron-transfer reactions in strongly exothermic bichromophoric systems of the alkylcarbazole-polynitrofluorene and -plynitrofluorenone types. Electronicabsorption spectra of these bichromophoric systems in acetonitrile have shown the appearanceof charge-transfer bands from which the electronic matrix elements for electron transfer is evaluated (-40 meV). From the redox properties of the D-S-A couples the rates for charge separation (CS) is calculated using the semi-quantum-mechanical theory applied ) photoinduced CS of these systems vary to these nonadiabatic electron-transfer reactions. The time constants ( T ~ of~ the from 200 fs to about 20 ps, so that they are considerably longer than the solvent (acetonitrile) dielectric relaxation time T~ except that of B4,which is close to T ~ These . rates are compared to those obtained by the time-resolved absorption spectra of contact ion pairs (CIP) with picosecond laser spectroscopy. The xerographic activity is also measured for the bichromophore encased in polymeric Lexan matrices and for polysebacate and polysuccinate oligomers containing these bichromophores as pendant groups. It is shown that the square of the rate constant for charge separation (kCs2)correlates well with the xerographic gains measured in photoactivity experiments. More detailed measurements of the photoinduced charge recombination of the ion pairs formed by irradiation of these systems with the third harmonic of the YAG laser at 355 nm have shown that the first-order rate constants for the subsequent relaxation (kd) of these contact ion pairs (CIP) to the solvent-separated ion pairs (SSIP) and for the charge recombination (kCR)to the original ground state of these systems are about of the same order of magnitude (- lo8 s-l) and are nearly solvent independent. The intrinsic properties of these systems favor good electron transport in various media that can be controlled by modifying the electronic coupling and the nature of the nuclear modes coupled to the two electronic states (Franck-Condon factors). 1. Introduction
Electron-transfer (ET) research today spans the boundaries of physical, inorganic, organic, analytical, and biological chemistry.' There are so many different systems-organic and inorganic systems, colloids, photoconducting polymers, metal-liquid electrode interfaces, mimicking of photosynthesis, semiconductor-liquid electrodes, liquid-liquid interfaces and proteins-where electron transfers come into play. Rates and efficiencies of ET reactions are influenced by various structural and thermodynamic factors,14 including the driving force for reaction (thermally averaged Franck-Condon factors), orientation factors, reorganization energy of donor and acceptor, distance of separation between species, diffusional, collisional, and electrostatic factors, and solvent orientation dynamics.'gv3 These factors are of critical importance in understanding how biological systems attain high efficiencies of charge separation as well as in the design of systems for molecular electronics. Testing of the Marcus* theory has become nowadays a usual practice in the This has motivated theoretical and experimental investigations into the dependence of the E T rate on each of these factors. The driving force dependence of ET has been thoroughly investigated recently' in all applications of electron-transfer reactions since the classical and semiclassical theories predict a maximum rate at some systemdependent optimum value and lower rates at lower and higher driving force (AGO) values giving rise to the normal and inverted regions of electron transfer. Although Miller et aL5have presented results showing normal and inverted behavior in charge-shift reactions, convincing evidence for the existence of both regions in intramolecular charge separation is Moreover, it was recently shown that the dependence of the rate of charge recombination (CR) of the contact ion pair (CIP) kEg on the free On leave from: Department of Spectroscopy, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032,India. *Departmentof Chemistry and the Canadian Centre for Picosecond Laser Flash Photolysis, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec, Canada H3G 1M8. * To whom all correspondence should be addressed.
energy gap between the ion pair and the ground state is quite different from the bell-shaped energy gap dependence of the C R (1) (a) Marcus, R. A. Annu. Rev. Phys. Chem. 1964,15, 155. (b) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985,811,265.(c) Mataga, N.In Photochemical Energy Conversion;Norris, J. R., Meisel, D., Eds.;Elsevier: New York 1988;p 32. (d) Photoinduced Electron Transfer; Fox, M. A., Channon, M., a s . ; Elsevier: New York, 1988;parts A-D. (d) GrBtzel, M. Heterogeneous Electron Transfer; CRC Press: Boca Raton, FL, 1988. ( f ) Gust, D.;Moore, T. A. In Advances in Photochemistry; Volman, Hammond, and Neckers, Eds.; Wiley: New York, 1991; p 1. (g) Sumi, H.; Marcus, R. A. J. Chem. Phys. 1986,844894.Rips, I.; Jortner, J. J. Chem. Phys. 1987, 87,2090. Sparpaglione, M.; Mukarnel, S. J. Chem. Phys. 1988,88, 3263. (h) Fox, M. A. Photochem. Photobiol. 1990, 52, 617. (2)(a) Marcus, R. A. J. Chem. Phys. 1956,24,966,979. (b) Marcus, R. A. J. Chem. Phys. 1965,43,679. (3)(a) Bagchi, B.; Fleming, G. R. J. Phys. Chem. 1990, 94, 9. (b) Maroncelli, M.; Macinnis, J.; Fleming, G. R. Science 1989, 243, 1674. (c) Fleming, G. R.; Wolynes, P. G. Phys. Today 1990,43,36. (d) Eads, D. D.; Dismer, B. G.; Fleming, G. R.J. Chem. Phys. 1990, 93,1136. (e) Bagchi, B.; Chandra, A.; Fleming, G. R. J. Phys. Chem. 1990,94,5197.( f ) Castner, E.W., Jr.; Bagchi, B.; Maroncelli, M.; Webb, S.P.; Ruggiero, A. J.; Fleming, G. R. Ber. Bunren-Ges. Phys. Chem. 1988,92,363. (g) Barbara, P.; Jarzeba, W. In Advances in Photochemistry; Volman, D. H., Hammond, G . S., Neckers, D. C., Eds.;Wiley: New York, 1990, p 1. (h) Weaver, M. J.; McManis, G. E.; Jarzeba, W.; Barbara, P. F. J. Phys. Chem. 1990,94,1715. (i) Barbara, P. F.; Jarzeba, W. Ace. Chem. Res. 1988,21, 195. (4)Hopfield, J. J.; Onuchic, J. N.; Beratan, D. N. J. Phys. Chem. 1989, 93,6350. (5) (a) Miller, J. R.; Calcaterra, L. T.; Closs, G. C. J. Am. Chem. SOC. 1984,106,3047. (b) Closs, G. L.; Johnson, M. D.; Miller, J. R.; Rotrowiack, P. J. Am. Chem. Soc. 1989,Ill, 3751. (c) Closs, G. L.; Miller, J. R. Science 1988,240,440. (d) Closs, G. L.; Calcaterra, L. T.; Green, N. J.; Penfield, K. W.; Miller, J. R. J. Phys. Chem. 1986, 90,3673. (e) Warman, J. M.; Smit, K. J.; de Haas, M. P.; Jonker, S. A,; Paddon-Row, M. N.; Oliver, A. N.; Kroon, J.; Oevering, H.; Verhoeven, J. W. J. Phys. Chem. 1991, 95, 1979; J . Am. Chem. SOC.1990, 112, 4868. (6) (a) Mataga, N.; Kanda, Y.; Asahi, T.; Miyasaka, H.; Okada, T. Chem. Phys. 1988,127,239. (b) Mataga, N.; Nishikawa, S.;Asahi, T.; Okada, T. J. Phys. Chem. 1990,94,1443. (c) Ojima, S.; MiyaSaka, A.; Mataga, N. J. Phys. Chem. 1990,94,5834. (d) Asahi, T.;Mataga, N.; Takashani, Y.; Miyashi, T. Chem. Phys. Lett. 1990, 171,309. (e) Asahi, T.;Mataga, N. J. Phys. Chem. 1991, 95, 1956. (f) Asahi, T.;Mataga, N.; Takahashi, Y.; Miyashi, T. Chem. Phys. Lett. 1990,171,309. (9) Mataga, N.; Kanda, Y.; Okada, T. J. Phys. Chem. 1986,80,3880. (h) Mataga, N.; Shioyama, H.; Kanda, Y. J. Phys. Chem. 1987,91,314.
0022-365419212096-3757%03.00/0 0 1992 American Chemical Society
3758 The Journal of Physical Chemistry, Vola96, No. 9, 1992 of solvent-separated ion pair @ip, indicating a different mechanism of CR in the strongly interacting IP formed by chargetransfer (CT) complex excitation from that in the more weakly interacting SSIP which can be interpreted by conventional ET theories.6e Some papers recently appeared on the theory of chargetransfer spectra" and ET reaction in frozen solution^.^ It was shown that different frozen states give rise to various curves of the survival probability of the donor, and it was concluded that in analyzing the experimental data it is important to take into consideration both distribution of the donoracceptor distance and of the solvent orientation around the reactant^.^ The past decade has seen a remarkable upsurge of interest in the dynamical role of the solvent in liquid-state chemical processe~.~B*'~ The ET in dynamically disordered polar media" and at liquid-liquid interface12has also been discussed. No doubt that the ET behavior in heterogeneous media will become an exciting field of research in the coming years. Fast charge-transfer processes in these media are of interest as potential molecular devices for long-distance signal processing and transfer.IfJ3 It was shown that push-pull bichromophoric molecular systems that undergo intramolecular charge transfer upon excitation display photocond~cting'~J~ and nonlinear optical properties.16 They may also be probes for investigating micropolarity17J8and solubilization sites and orientation in microheterogeneous media.I9 The problem of the effect of the distance of separation (R) between the donor and acceptor on the rates of forward and reverse ET is very complex in an ensemble of distributed donors and acceptors since both the electronic and nuclear factors might be influenced differently for certain distance distributions. No theory presently exists relating dynamical properties of the solvent coupled to the distance dependency of the P A system to time-dependent experimental observables. The distance dependence of the ET rates was extensively investigated by Miller et alezousing frozen (7) (a) Gould, I. R.; Ege, D.; Moser, J. E.; Farid, S. J . Am. Chem. SOC. 1990, 112, 4290. (b) Gould, I. R.; Young, R. H.; Moody, R. G.;Farid, S. J . Phys. Chem. 1991, 95, 2068. (8) Marcus, R. A. J . Phys. Chem. 1990, 94,4963. (9) Kakitani, T.; Mataga, N. J . Phys. Chem. 1988, 92, 5059. (10) (a) Hynes, J. T. In The Theory of Chemical Reactionr; Baer, M., Ed.; CRC Press: Boca Raton, FL, 1985; Vol. 4, p 171. (b) Hynes, J. T. J . Star. Phys. 1986, 42, 149. (c) Chandler, D. J . Star. Phys. 1986,42,49. (d) Carter, E. A.; Hynes, J. T. J . Chem. Phys. 1991, 94, 5961. (11) (a) Nadler, W.; Marcus, R. A. Isr. J . Chem. 1990,30, 69. (b) Rips, I.; Klafter, J.; Jortner, J. J . Phys. Chem. 1990, 94, 8557. (c) Shalev, E.; Jortner, J. Chem. Phys. Lett. 1991, 178, 31. (d) Bixon, M.; Jortner, J. J . Phys. Chem. 1991, 95, 1941. (12) Marcus, R. A. J . Phys. Chem. 1990, 94, 1050. (13) . , la) . , Lehn. M. Ansew. Chem.. I n t . Ed. E n d . 1988. 27, 107. lb) Slama-Schwok, A.; Blancfard-Desce, M.; Lehn, J. M.J . Phys. Chem. 19% 94,3894. (c) Lehn, J. M. Angew. Chem., Inr. Ed. Engl. 1990,29, 1304. (d) Balzani, V.; Scandola, F. Supramolecular Photochemistry; Honvocd, G., Ed.; Chichester, U.K., 1991; Chapter 12. (e) Carter, F. L., Siatkowski, R. E.; Woltjen, H., Eds. Molecular Electronic Deuices; North-Holland; Amsterdam (1989). (14) (a) Brisse, F.; Durocher, G.; Gauthier, S.;Gravel, D.; MarquL, R.; Vergelati, C.; Zelent, B. J . Am. Chem. Soc. 1986,108,6579. (b) &lent, B.; Messier, P.; Gravel, D.; Gauthier, S.; Durocher, G. J . Photochem. Photobiol. 1987,40, 145. (c) Zelent, B.; Messier, P.; Gauthier, S.; Gravel, D.; Durocher, G. J . Photochem. Phorobiol. 1990, 52, 165. (d) Gravel, D.; Gauthier, S.; Brisse, F.; Raymond, S.; DAmboise, M.; Messier, P.; Zelent, B.; Durocher, G. Can. J. Chem. 1990, 68, 908. (15) (a) Pearson, J. M.; Stolka, M. Poly(N-uinylcarbazole); Gordon & Breach: NY, 1981. (b) Simon, J.; Andrt, J. J. Molecular Semiconductors; Springer-Verlag: Berlin, 1985. (16) (a) Messier, J., Kajzar, F., Prasad, P., Ulrich, D., Eds. Nonlinear Optical Effects in Organic Polymers; Kluwver Academic Publisher: Dordrmht, 1989. (b) Mukamel, S.;Jing, Yan Yi Acc. Chem. Res. 1989, 22, 301. (c) Mukamel, S.Annu. Reu. Phys. Chem. 1990, 41, 647. (17) (a) BelletBte, M.; Lachapelle, M.; Durocher, G. J. Phys. Chem. 1990, 94, 5337. (b) BelletEte, M.; Durocher, G. J . Colloid Interface Sci. 1990, 134, 289. (c) BelletBte, M.; Lachapelle, M.; Durocher, G. J. Phys. Chem. 1990, 94,7642. (d) Lachapelle, M.; BelletZte, M.; Poulin, M.; Godbout, N.; Legrand, F.; Htroux, A.; Brim, F.; Durocher, G. J . Phys. Chem. 1991,95,9764. (18) (a) Schanze, K. S.;Shin, D. M.; Whitten, D. G. J. Am. Chem. SOC. 1985,107, 507. (b) Backer, C. A.; Whitten, D. G. J . Phys. Chem. 1987, 91, 865. (19) Shin, D. M.; Schanzer, K. S.; Whitten, D. G. J . Am. Chem. SOC. 1989, 1 1 1 , 8494.
Ganguly et al. solution at low temperature. The theoretical description of forward ET without solvent relaxation has been satisfactorily described by Inokuti and Hirayama.2' However, more recently a satisfactory description of forward and reverse photoelectron transfer has been p r e ~ e n t e d . ~ Theoretical ~-~~ solutions were developed for uniform and random distribution of donor and acceptor molecule in solid solution, and respective equations for decay profiles of radical cation and radical pair were presented. The effect of freezing the solvent is obviously to fix donors and acceptors at random positions, but an extension of the theoretical approach for the case of liquid solution was also presented in order to take into account the diffusion of species. These theoretical models which discuss the distribution function for distances are expected to play a key role in the understanding of the photoconductivity of polymers containing pendant donor-acceptor bichromophoric units since it is well-known that the rate constants for charge separation and charge recombination are coupled to the charge mobility through the diffusion coefficient or the length of electron h0p.6J5J6-25 The development of organic photoconductive polymers was stimulated by the discovery that poly(N-vinylcarbazole) (PVK), sensitized with trinitrofluorenone (TNF), exhibits high enough levels of photoconductivity to be useful in practical applications such as electroph~tography.'~~,~~ Unfortunately, the description of photoconductivity is, in many cases, limited to the statement that the polymers are photoconductive or, at best, steady-state measurements were carried out. In other words, the description is far too qualitative at present. Moreover, the lack of detailed studies on photocondutive polymers other than PVK is noteworthy in view of the commercial importance of organic photoconductors, which are essential in the multibillion dollar, xerographic-copier, laser-printer, and duplicator industry. The interest around the carbazole system remains high nowadays because of the wealth of information accumulated in the literature and the opportunity it may provide for the rational design and optimization of high-performanceorganic based photoactive polymers.27 In that respect, intramolecular donor-acceptor bichromophoric systems where the ET reaction is known to be strongly exothermic are of crucial importance to study for at least three main reasons: (i) The inverted "Marcus" region has not yet been shown to exist in these cases.6a,b (ii) Some of these systems have recently been shown to produce highly efficient photoconducting 01igomers.l~(iii) The ion pair can be produced both by CS at encounter between the excited donor or acceptor and the ground-state acceptor or donor and by excitation of the charge-transfer complex formed by the same pair in the ground state. In this work, we will address the question of the quantitative aspects of the charge separation (CS) and charge recombination (CR) processes that take place in the bichromophoric systems B,-B5 and PI-P5 shown in Figure 1. The bichromophores are made up of two covalently linked molecular components: an alkylcarbazole derivative as the electron donor (D) and a polynitre or polycyanofluorene or -fluorenone derivative playing the role (20) (a) Miller, R. J. J . Phys. Chem. 1978, 82, 767. (b) Beitz, J. V.; Miller, J. R. J . Chem. Phys. 1979, 71, 4579. (c) Miller, J. R.; Beitz, J. V.; Huddleston, R. K. J. Am. Chem. SOC.1984, 106, 5057. (21) Inokuti, M.; Hirayama, F. J . Chem. Phys. 1965, 43, 1978. (22) (a) Lin, Y.; Dorfman, R. C.; Fayer, M. D. J . Chem. Phys. 1989,90, 159. (b) Dorfman, R. C.; Lin, Y.; Fayer, M. D. J. Phys. Chem. 1989, 93, 6388. (c) Deeg, F.; Fayer, M. D. J . Chem. Phys. 1989, 91, 2269. (d) Dorfman, R. C.; Lin, Y.; Fayer, M. D. J. Phys. Chem. 1990, 94, 8007. (e) Lin, Y.; Dorfman, R. C.; Fayer, M. D. J. Chem. Phys. 1990, 93, 3550. (f) Song, L.; Dorfman, R. C.; Swallen, S. F.; Fayer, M. D. J. Phys. Chem. 1991, 95, 3454. (23) Mikhelashvili, M. S.;Feitelson, J.; Dodu, M. D. Chem. Phys. Lett. 1990, 171, 575. (24) Sienicki, K.; Durocher, G. Chem. Phys. Lett. 1991, 176, 322. (25) Vannikov, A. V.; Grishina, A. D. Russ. Chem. Rev. 1989,58, 1169. (26) (a) Hoegl, H.; Sus, 0.;Neugebauer, W. German Patent, 1 Oct 29, 1959, 068, 115. (b) Gill, W. D. J . Appl. Phys. 1972, 43, 5033. (27) (a) Biswas, M.; Urgu, T. Makromol. Chem. Phys. 1986,26,249. (b) Domes, H.; Fisher, R.; Hoorer, D.; Strobriegl, P. Makromol. Chem. 1989, 190, 165.
The Journal of Physical Chemistry, Vol. 96, No. 9, 1992 3759
ET Reactions in Bichromophoric Systems
pi
D1
D2
D3
Bl
PI
B2
B 2a
B3
B4
J35
p2
p.3
P3a
p4
p5
Figure 1. Structural formulas of the compounds studied.
of electron acceptor (A). These bichromophores and oligomers should yield information on the influence on the photoactivity of these systems, of the relative distance between D-A pairs, of the relative distance between the donor and the acceptor chromophores, and of the energy gap (AGO)dependence in the CS process. The main difference between these systems and the well-known molecularly doped PVK is the possibility of varying the interbichromophoric distance along the chain and of better controlling the distance between the D-A pairs which was impossible by design in the doped PVK systems where phase separation between dopant and polymer occurs. The recombination of charge carriers will also be looked at. The geminate charge recombination (CR) will be studied quantitatively by picosecond flash photolysis since such recombination of charges within the photoconductor is well-known to be a loss process. Indeed the key process affecting the overall photogeneration efficiency is the field-induced separation of carriers, competing with geminate recombination. We will describe in this
study the picosecond dynamics accompanying the geminate recombination (or CIP relaxation) to the A-S-D ground state (bR) which is in competition with the CIP relaxation or dissociation (kd) to the solvent-separated ion pair (SSIP) as shown in Scheme I. The medium effect on these reactions will also be discussed. SCHEME I
A-S-D
,k
A--S-D+ CIP
kd
(A--S-D+)s SSIP
2. Experimental Section 2.1. Materials. The structural formulas of the compounds studied are presented in Figure 1. The synthesis and characterization of the bichromophores and oligomers have already been described in refs 14c,d and references cited therein. Purification of the solvents used has also been described before.14 All solutions for the measurements were deoxygenated by flushing with a nitrogen gas stream or by freeze-pumpthaw cycles.
Ganguly et al.
3760 The Journal of Physical Chemistry, Vol. 96, No. 9, 1992 TABLE I: Redox Potentials and Gibbs Free Energies for Charge Separation in Some CarbazoleFluorene Bichromophores' excited state E1/2°x,b E1/2r*,b E*g.olb bichromophore Bl
82 BI B4
BS
D D D D D
'A* IA* 'A* IA* IA*
V 1.28 1.24 1.20 1.24 1.05
V -1.02 -0.33 -0.72 -0.44 -0.44
eV 3.49 3.43 3.38 3.32 3.32
R, A 6.1 5.75 6.0 7.5 6.3
Rs, 8, 3.8 2.7 2.7 4.5 3.8
Rmax, 8, 8.6 9.4 9.4 11 8.3
-AGO, eV
Rs 1.29 2.01 1.60 1.72 1.93
R
RIM,
1.25 1.93 1.52 1.69 1.89
1.23 1.90 1.48 1.67 1.87
a The crystallographic center-to-center D-A distances are specified by R; maximum and shortest distances are obtained from Dreiding models bThese values are obtained in acetonitrile vs SCE.
TABLE II: Electron Interaction Energies, Electronic Frequencies, and Calculated Rate Constants for Charge Separation in Some Carbazole-Fluorene Bichromophores
Bl B2 B1 B4
BS
Cmaa, CT
maxi
A64,
M-I cm-I
cm-' (18 180) 18 180 18 200 17760 I8 870
cm(3580) 3580 3500 3580 3400
33 2.1 32
0 0 1.7 7.4 7.4 1.2 2.8 7.8 12.3 0 0 26.5 25.3
"Polymer film thickness. Residual surface potential, after dark decay. CSlightly lower gain values have been observed for positive charging experments. G = (l/d)[(dV,/dt),,, - (dVd/df),,o]. meanings as in eq 6. Results of the measurements and calculations are given in Table VI. If one compares the trends in the relative gains between the Lexan dispersions and the oligomers, some disparities occur. B1 and PI are both poor photoconductors, and this has already been explained mainly by the poor overlap that exists between the donor and the acceptor m o i e i t i e ~ . ' ~The ~ photoactivity increases for B2 and much more for B4 and the same trend is observed in the oligomers. This result might possibly rule out the possible intervening effect of intermolecular chargetransfer interaction in Lexan binder since it was shown beforeIu that aggregation between the acceptor moieties was much stronger for B1 as compared to B2 and B4. On the other hand, the relatively high photoactivity observed in B3 and B5 completely disappears in P3 and P5 as shown in Table VI. The very fact that P3a (polysuccinate structure) sees its photoconductivity increasing compared to P3 proves without doubt that the polymer structure is one of the factor to be considered in the photocarrier transport. This might also explain the behaviors of P3 and P5. Table VI also shows a comparison with an appropriate sample of the classic PVK-TNF system. As compared to this classic sample, oligomers P2 and P4 seem promising as good photocondutors even though their actual photoconductivities are still lower since molecular weights of oligomers P2 and P4 (-6000) are much lower than that of the PVK polymer (-80000), which means fewer chain ends that can act as electron and/or hole traps in the latter.I'
4. Discussion In view of the above considerations and results, it might be qualitatively concluded that the photoactivity results observed for oligomers PI, P2, and P4 and for bichromophores BI, BZ,and B4 in Lexan are largely explainable on the basis of the spectroscopic and X-ray crystallographic results reported herein. Indeed, the marked enhancement of photoactivity of oligomer P2 and P4 over PI and of bichromophores B2 and B4 over BI is most logically attributable to the better overlap existing between the donoracceptor moieties confirmed by the X-ray in~estigation'~ and also by the chargetransfer complex formation between the donor and acceptor chromophores observed in B2 and B4 (see Table 11). Even though xerographic evaluation of photoconductivity does not provide a definitive answer to carrier generation and carrier transport separately, the derived quantities can be discussed with reference to the photophysical measurements of these systems. Indeed the gain measured in Tables V and VI is proportional to the hole carrier generation (n+e+)and to the hole mobility ( F + ) following eq 8,15where n+ is the number of hole carriers. Gan+e+p+ = kc++ (8) The carrier generation (n+e+)should be proportional to the charge separation decay rate constant (ka) of the donoracceptor couple. When the carriers are transported by the hopping mechanism, the carrier mobility ( p ) is given by eq 9,40where r
3764 The Journal of Physical Chemistry, Vol. 96, No. 9, 1992 (9)
is the distance between the hopping sites, exp(-2av) expresses the overlap of wave functions on two adjacent hopping sites, and Yph exp(-W/kT) is the probability of hopping over the potential barrier, W. If one is looking at the negative charging results as exemplified in Tables V and VI, oligomers or Lexan dispersions with the shortest donor-donor distances (r) have undoubtedly the highest mobility for an identical potential barrier (W).This would be a plausible explanation for the fact that P3, is a much better photoconductor than P3since the bichromophoric unit is identical in both polymers but the various units are much closer in the polysuccinate oligomer (P3,) compared to the polysebacate oligomer P,. As far as all other oligomers are concerned (all polysebacates), it might be expected that the mobility does not vary much from one to the other. The same assumption might also be valid for all the Lexan bichromophoric dispersions for which a correction for the distance dependence has been added in the expression for the gain in photoactivity (eq 6 ) . On the other hand, it is well-known that the rate constant for charge separation (kcs) and charge mobility ( p ) are related through the diffusion coefficient (D) p
by the
= De/kT;
D = p2kCs
relations hi^^^ p
= p2kcse/kT
where p is the length of electron hop. These relations apply only to electron transfer between single-type transport sites and the occurrence of fixed distances between them. If relations 8 and 10 do apply, a linear correlation is expected between the gain in photoactivity and the square of the rate constant for charge separation. Let us now focus our attention to the evaluation of the rate constant for charge separation in these bichromophoric systems and to the assumptions used in doing this. 4.1. Nature of the Ion Pair. Figures 3-5 and what is known on similar bichromophoric systems6 indicate that electron transfer (kcs) takes place following excitation of the acceptor moiety to form a geminate radical ion pair of which only the radical anion is accessible experimentally, the absorption of the radical cation being in a higher wavelength region (700-900 nm). At longer time delays, not only are contact ion pairs (CIP) formed but also solvent-separated ion pairs (SSIP) are produced.6 The main differences between these two species is the higher electronic coupling element (HDA)in the CIP compared to the SSIP and obviously the higher solvation of the latter species compared to the former.6" In the current solvent, acetonitrile, exciplex emission originating from the CIP dissociation are rarely observed, and these bichromophoric systems are no exceptions. SSIP formation and/or geminate CIP recombination are faster processes. Figure 4 shows that within 50 ps the charge separation process is completed, and this is for the three bichromophores investigated by flash photolysis, B1,B2,and B4. With the assumption of an exponential rise in the contact ion pairs, this puts a higher limit of about 20 ps for the observed lifetime and a lower limit of 5 X 1Olo s-l for the rate of charge separation (kcs) in these bichromophoric systems in acetonitrile. It should in fact be higher than this since the time response of our flash system is 20 ps and even deconvolution of the signal did not give us coherent and reproducible results with these systems. On the other hand, as indicated in Table IV, the rate of charge recombination (kR)seem to show a systematic dependence upon -AGO in acetonitrile which is not the case fo kd. This kd value is much less than that calculated by the kinetic diffusion theory for acetonitrile solution.' This probably shows that the solvent is not playing such an important role in the relaxation of the radical ion pair in these bichromophoric systems. This is also confirmed (40) Mort, J.; Knight,
J. Nature 1981, 290, 659,
Ganguly et al. by the results obtained in lP-dioxane, which is not a normal polar solvent and is well-known to behave like a solvent with a dielectric constant of about 7.17,One can see in Table I11 that the kRvalues generally increase a little in lY4-dioxanecompared to acetonitrile contrary to what might be expected on the basis of charge recombination (CR) reactions of ion pairs produced by photoinduced electron transfer in the "inverted Marcus region" (see eq 12).'a9a For this case of ET, the CR decay of the geminate pair becomes slower in less polar solvents and the dissociation becomes also slower due to the higher activation energies necessary for dissociation:" Table IV reproduces the rate of geminate recombination measured in acetonitrile and the energy gap (AGO) for the reaction between the initial and final state as calculated from eq 5. It is obvious that the electron-transfer rate constant (kCR)increases with an increase of the freeenergy gap of the ET reaction behaving like in the "normal" region from the Marcus theory though no linear correlation is obtained between In kRand AG,Z as expected from the semiquantum-mechanicaltheory applied to nonadiabatic ET reactions (eq 12). By using this theory and the same crystallographic interchromophoric distances ( R ) ,one can calculate the nuclear factor ( K " ) for the reaction and also evaluate the electronic frequency factor (vel)and the electronic matrix element (HDA).for the charge recombination processes. The results are given in Table IV. In these calculations, fixed values of & (=0.3 eV) and Y (-1500 cm-I) were used (see discussion in part 4.2). One can see that the electronic matrix elements for the back electron transfer in B2 and B4 are very weak compared to that of B1.Moreover, these electronic factors seem to compensate for the higher values of the nuclear factor in B2 and B4 to produce overall lower charge recombination decay rates (kCR). The electronic coupling matrix elements calculated for the charge recombinations in these bichromophoric systems compare well and are even smaller than those obtained by Miller et al. in their studies of ET between donors and acceptors linked by rigid spacer groupsSa4 In those cases and others,se however, through-bond coupling (all-trans configuration of the spacer) plays an important role which is practically excluded in regards to the molecular structure of the bichromophoric systems studied here where the chromophores are linked by polymethylene bridge^.^,^^ It is also interesting to note that the dynamics of charge recombination seems to be about the same whether the bichromophore is in solution or included as a pendant group in a polymeric chain. Table I11 shows that the yield of ion dissociation is also quite high for P2in 1,Cdioxane. This is probably another factor of importance in what makes these oligomers such good photoconductors; that is, the charge recombination and dissociation are scarcely affected by the medium where the bichromophore is embedded. In other words these parameters are controlled by the intrinsic properties of the bichromophores themselves. Moreover, in all these systems studied, the geminate charge recombination process is not faster than the ion dissociation giving rise to quantum yields of ion formation in tbe range 0.3-0.9,which means that for B2 and B4 only 15% and 24% respectively of the incident photons that are absorbed and are responsible for the chargeseparated process (kCR)are wasted due to the energy-wasting return electron-transfer reaction (kCR)in acetonitrile. All these particular behaviors might be correlated to the fact that the return electron-transfer free energy changes are about the same or even lower in absolute value than the forward electron-transfer free energy changes in all the bichromophoric systems studied except for B1. These D-S-A systems are unique in that Now let us turn our attention to the theories of electron-transfer reactions in order to evaluate rates in these systems. 4.2. Analysis of Electron-Transfer Rates. Modern theor i e ~ l ~ + treat ~ * electron ~ ~ ~ ~transfer J ~ , as ~ ~a radiationless ~ transition and define the rate in a golden rule type expression in which the rate is given as the product of an electronic matrix element squared lHDAIZ and a Franck-Condon weighted density (FCWD) of states (eq 11). kcs = (2x/h)lf?DAIZFCWD
(11)
The rate constant of electron transfer under nonadiabatic
The Journal of Physical Chemistry, Vol. 96, No. 9, 1992 3765
E T Reactions in Bichromophoric Systems
TABLE VII: Reorganization Energies and Nuclear Factors for Cbarne Sewration in Some CarbazoleFluoreoe Bichromophores
bichromoDhore B1 B2 B3 B4
excited state involved -
D D D D D
&7
eV 0.65 0.58 0.63 0.89 0.69
‘A*
IA* IA* IA* ‘A*
L,: eV
0.3 0.3 0.3 0.3 0.3
um..6 3 6 4 3 5
10’~. 33 0.43 9.0 18 1.6
B5 “These A (=& + A ) values compared quite well with those obtained from the relation i& = 4A + AGo.lb bThis is the vibrational level contributing the most to the nuclear factors in these highly exothermic charge separation systems in the Marcus inverted region. conditions can be written, using the semiclassical treatment approximation, in the general form of *
kcs = ( ? r / h 2 ~ k T ) 1 / 2 1 H D A 1 2 ~ ( e - S S uexp{-[(AGO //u!) u-0
+ A, +
~ h v ) ~ / 4 A , k r(12) ]) where
S = A,/hv The summation term in eq 12 is called the nuclear factor (K,,) that contains the Franck-Condon factors, and the remaining terms form the so-called electronic frequency factor (v,,). The Franck-Condon term contains the dependence on the reaction exothermicity (-AGO). The rearranged modes related to the solvent reorganization energy (A,) are treated classically and defmed by MarcusZand Hush3%in the dielectric continuum model of two spherical reactants by
in which e is the transferred electronic charge, to is the permittivity of free space, topand 6, are the solvent refractive index (optical dielectric constant) and the solvent dielectric constant, rDand rA are the radii of the oxidized donor and the reduced acceptor, respectively, and R is their center-to-center separation. The vibrational modes associated with A,, in eqs 12 and 13 are treated quantum mechanically, and it is assumed that the frequency of these modes can be represented by a single average frequency v. We have chosen fixed values for X, and v of 0.3 eV and 1500 cm-l, respectively, in all calculations we did on these bichromophoric systems. These values are characteristic values for aromatic donor-acceptor Equation 11 reproduces the essential elements of the classical theory, including the prediction of a decrease in rate with increasing exothermicity (the Marcus inverted region), for reactions that are more exothermic than the sum of A, and A,, (the total reorganizational energy). From the Gibbs free energies calculated for the donoracceptor center-to-center distances ( R ) given in Table I, the electronic matrix elements (HDA) obtained from the CT spectra in Table I1 and the reorganizational energies (A, and A,) shown in Table VII, the electronic frequency factors (vel),the nuclear factors (K,), and the rate of charge separation have been evaluated and are shown in Table 11. In all A, calculations, the radii of donors and acceptors have been kept fixed at 4 A. Even with these approximations, one can see that the calculated A values fit well with those obtained from the classical correlation that exists between the chargetransfer band frequency, the reorganization energy (A), and the driving force of the ET reaction (AGo)lb (see bottom of Table VII). Equation 12 shows that the overall electron-transfer rate constant results from a summation of the rate constants of electron transfer from the donor to different vibrational levels of the acceptor. Table VI1 shows the vibrational level that contributes for the most part to the nuclear factor in each bichromophoric system. As can be seen, the Franck-Condon factors ( K , ) increase when the energy gap decreases (lower u values). This theory of
20 0.6
1.1
I.6
2.1
log G Figure 7. log-log plot of the square of the rates of charge separation as a function of the xerographic responses in a Lexan matrix.
+
ET predicts that since -AGO > X, A,, the inverted Marcus region is attained so that the nuclear factor ( K , ) should increase when -AGO decreases. This is exactly what we have if one looks at the values for K, in Table VI1 and compares them to the values of -AGO in Table I. But since the electronic factors are not identical in these systems and very low at least for B,, the kcs value for Bl does not fit the inverted Marcus region predicted by eq 12. It has to be pointed out here that the kcs values reported in Table I1 and evaluated from eq 12 are strictly valid for excitation in the charge-transfer band since the electronic matrix elements have been obtained from the C T spectra (eq 2). For excitation in the acceptor moiety, the electronic matrix elements might only be lower if not equivalent following a possible relaxation of the donor-to-acceptor distance distribution function. This would have the effect of increasing the C S lifetimes (&-I) from the values in Table I1 up to the minimum value (20 ps) that can be observed experimentally. But since the maximum distance between the D-A pairs in these bichromophores is limited to 10 A, one can easily see from eqs 2 and 12 that for B3for instance, the maximum value of (kcs-l) is 1.5 ps, which is much lower than the time resolution of our instrumentation. On the other hand, the charge recombination kinetics has shown only single time-invariant rates, which is in contrast of the complex decay kinetics expected for a large distribution of donor-to-acceptor distances. For these reasons, the assumption has been made here that the HDA matrix elements for the charge-transfer interaction and for the “through-space” interaction between the excited acceptor and the ground-state donor are equivalent. Finally, one has to make sure in using eq 12 that the electron-transfer reaction studied is really nonadiabatic. The nonadiabaticity of an electron-transfer process can be evaluated through parameter A defined by eq 15,Ibv4lwhere 7 / is the longitudinal solvent relaxation time equal to 0.2 ps in acetonitrile. For A
