710
J . Phys. Chem. 1992, 96, 710-715
position, it can be concluded that these compounds are not stilbene-like but that the para-substituted styryl moiety acts as an integral substituent. The observed solvatochromic shift is very large for BOZ-NMe2 and BOZ-Jul, although the increases in dipole moments upon excitation predicted by PPP and CNDO/S calculations are small. This can be explained in terms of changes in local dipole moments inducing local relaxation of solvent molecules, instead of changes in overall dipole moment. A more likely alternative explanation is the existence of a highly polar fluorescent TICT state formed by single bond twisting upon excitation. In fact, CNDO/S calculations show that BOZ-NMe2 possesses a low-lying TICT state (twisted single bond connecting benzoxazinone and ethylene). The existence of two rotamers is likely to be responsible for the excitation wavelength dependence of the emission spectra in some solvents, consistent with a more or less pronounced departure of the fluorescence decay from a single exponential. If these two
rotamers lead to the same TICT state predicted by the theory, no excitation wavelength dependence of the emission spectra would be observed. Therefore, additional radiative deactivation channels (different for the two rotamers) may be the origin of the wavelength dependence. It is interesting to note that the fluorescence quantum yield of BOZNMez is high in nonpolar solvents and low in polar solvents. Therefore, this molecule appears to be of potential use as a probe of hydrophobic regions of biological samples of surfactant assemblies. Acknowledgment. We thank Dr. C. Rulliere for helpful discussions and for performing the PPP calculations. Registry No. DFSBO, 90422-12-1;BVC, 126959-78-2;BOZ-crown, 114880-42-1;BOZ-H, 137334-95-3;BOZ-NMe2, 113501-50-1;BOZ1,4-benzoxazin-2Jul, 137334-96-4;7-(N,N-dimethylamino)-3-methylone, 925 10-33-3; 9-formyljulolidine, 33985-71-6.
Electron Transfer in Linked Vlologen-Quinone Molecules: Rate Constant Enhancement with Increased Chain Length A. M. Brun,? S . M. Hubig,*.+M. A. J. Rodgem,*.*and W. H. Wades Chemistry Department, University of Texas at Austin, Austin, Texas 78712, Center for Fast Kinetics Research, University of Texas at Austin, Austin, Texas 78712, Center for Photochemical Sciences, Bowling Green State University, Bowling Green, Ohio 43403 (Received: February 28, 1991; In Final Form: September 25, 1991)
We synthesized a homologous series of molecules (MVnnQ) where a methylviologen (MV) and a aminochloronaphthoquinone (Q) are linked to each other via a flexiblechain. Using the electron pulse radiolysis technique, we have measured timeresolved spectra and rate constants for intra- and intermolecular electron transfer between donor and acceptor site of the MVnnQ molecules in water and in SDS micellar solution. For comparison, we also irradiated a solution containing a 1:l mixture of methylviologenand aminochloronaphthoquinoneand measured spectra and intermolecular ET reactions between the separated electron donor and acceptor molecules. The intramolecular electron transfer rate constants of all MVnnQ molecules were surprisingly low both in water and in aqueous SDS micellar suspensions. The intramolecular rate constants measured in water increase with increasing number of intervening bonds, leading to the conclusion that electron transfer occurs by a through-space rather than through-bond mechanism. The intramolecular rate constants virtually lose their chain length dependence in SDS suspensions where because of an extended codiguration of the micellii MVnnQ molecules through-space interaction is not favored.
Introduction The movement of an electron from one molecule (or part of one molecule) to another has been the subject of intense experimental and theoretical study in recent years.' On the experimental side important advances were made by groups who synthetically prepared new molecular systems in which donor and acceptor residues were separated from each other by rigid spacer groups, thereby removing the distractions created by diffusional uncertainties for intermolecular electron transfer (ET) reactions. Strategies such as this have enabled the characterization of long distance (i.e., noncollisional) ET reactions in liquid-phase systems. Synthetic approaches have been to covalently link the electron donor-acceptor couples at opposite ends of molecular frameworks provided by steroids,2 cyclic alkanes,3 polybicyclic alkanes? oligopeptides of p r ~ l i n ea, ~cyclic amino acid, and covalently-linked porphyrin/quinone molecules.6 Another approach has been to covalently modify a redox protein at a peripheral site with an electron-donating residue. Here, the heme moiety in, e.g., cyto*Authors to whom correspondence should be addressed. 'Center for Fast Kinetics Research, University of Texas. *Bowling Green State University. Chemistry Department, University of Texas.
chrome c becomes the acceptor entity.' Others have used electrostatically driven self-association to form complexes between (1) Several excellent reviews exist; some of these are: (a) Marcus, R. A,; Sutin, N. Biochim. Biophy?ys.Acta 1985, 811, 265-322. (b) Closs, G. L.; Miller, J. R. Science 1988,240, -7. (c) McLendon, G. Acc. Chem. Res. 1988, 21, 160-167. (d) Cusanovich, M. A.; Hazzard, J. T.; Meyer, T. E.; Tollin, G. J. Macrobiol. Sci.-Chem. 1989, A26(203), 433-443. (e) Newton,
M. D.; Sutin, N. Annu. Reu. Phys. Chem. 1984, 35,437-480. (f) Khairutdinov, R. F.;Brickenstein, E . U . Photochem. Photobiol. 1986, 43, 339-356. (g) Sykes, A. G . Chem. Soc. Rev. 1985, 283. (2) (a) Miller, J. R.; Calcaterra, L. T.; Closs, G. L. J. Am. Chem. SOC. 1983,105,670. (b) Clw, G. L.; Piotrowiak, P.;Maclnnis, J. M.; Fleming, G. R. J. Am. Chem. Soc. 1988, 110, 2652-2653. (c) Olivier, A. M.; Craig, D. C.; Paddon-Row, M. N.; Krwn, J.; Verhoeven, J. W. Chem. Phys. Lett. 1988, 150, 366-373. (d) Johnson, M. D.; Miller, J. R.; Green, N. S.;Closs, G. L. J. Phys. Chem. 1989, 93, 1173-1 176. (3) Warman, J. M.; De Haas, M. P.; Oevering, H.; Verhoeven, J. W.; Paddon-Row, M. N.; Olivier, A. M.; Hush, N. S . Chem. Phys. Lett. 1986, 128, 95. (4) (a) Ashikaga, K.; Ito, S.;Yamamoto, M.; Nishijima, Y .J. Am. Chem. SOC.1988, 110, 198-204. (b) Verhoeven, J. W. Appl. Chem. 1986, 58, 1285-1 290. (5) (a) Isied, S.S.;Vassilian,A.; Magnuson, R. A.; Schwarz,H. A. J. Am. Chem. Soc. 1985,107, 7432. (b) Schanze, K. S.;Sauer, K. J. Am. Chem. Soc. 1988, 110, 1180-1186. (c) Faraggi, M.; DeFelippis, M. R.; Klapper, M. H. J. Am. Chem. SOC.1989, 1 1 1 , 5141-5145.
0022-3654/92/2096-710%03.00/00 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 2, 1992 711
ET in Linked Viologen-Quinone Molecules 1.40
1.oo
0.60
0.20
I
-0.20 320
I 420
520
620
720
WAVELENGTH ( nm ) Figure 1. Time-resolved spectra of the ET reaction between methylviologen and quinone moieties of MV53Q (0 = 8 ps, A = 89 ps); the MV53Q concentration was 100 pM. Insets: (A) Kinetics trace observed at 475 nm: bleaching of the ground state of the quinone moiety due to electron transfer from a reduced M V ” moiety; [MV53Q] = 150 pM.
be spatially proximate even in a microheterogeneous environment, e.g., a surfactant micelle. The motive for constructing this molecule (MVQ) was to test whether ET from the reduced viologen entity (generated by electron pulse radiolysis) to the quinone residue was possible when the MVQ species was associated with a micellar surface. This was shown to be so, even though earlier work by us had shown that such reaction did not proceed when the redox couples were present as individual molecular species.I2 A significant result of this preliminary study was that while ET from reduced viologen to quinone certainly occurred, the intramolecular rate constant, both in aqueous micellar system and in water alone, was very low (near 1 X lo3 s-l) and orders of magnitude lower than would be anticipated from the measured intermolecular rate constant (3.8 X lo* M-’ s-l). This intriguing observation has led us to synthesize a series of molecules that we designate as MVnnQ (see formula). The MV and Q residues
(B) Kinetics trace observed a t 600 nm: decay of the reduced methylviologen moiety due to electron transfer to a quinone moiety; [MV52Q] = 150 pM. For A and B the fitted curves 1 and 2 correspond to eqs 4 and 3, and to eq 5 (see text).
a pair of redox proteins or a proteinsmall molecule group? Both covalently-linked and electrostatically-heldapproaches have been aimed at holding the donor and acceptor pair at fixed distances from one another. In these several ways, researchers have been able to test independently the influence of donoracceptor distance, driving force, and solvent reorganization energy on the ET process. Impressive agreement between the experimentalists and the theorists has resulted? the predictions of Marcuslo being particularly well borne out. Recently we reported a preliminary study in which alkylbipyridinium (viologen) and aminochloronaphthoquinone residues were covalently attached via a short (three carbon) methylene chain.” Such a linkage was thought to be relatively flexible and it was synthesized in an effort to provide an ET couple that would (6) (a) McIntosh, A. R.; Siemiarczuk, A.; Bolton, J. R.; Stillman, M. J.; Ho, T. F.; Weedon, A. C. J. Am. Chem. SOC.1983, 105, 7215-7223. (b) Wasielewski, M. R.; Niemczyk, M. P.; Svec, W. A.; Pewitt, E. B. J . Am. Chem. SOC.1985,107,5562-5563. (c) Gust, D.; Moore, T. A,; Makings, L. R.; Liddell, P. A.; Nemeth, G.A.; Moore, A. L. J . Am. Chem. Soc. 1986,108, 8028-8031. (d) Cowan, J. A.; Sanders, J. K. M.; Beddard, G. S.; Harrison, R. J. J . Chem. Soc., Chem. Commun. 1987, 55-58. (e) Feitelson, J.; Barboy, N. J. Phys. Chem. 1986, 90, 271-274. (f) Lindsey, J. S.; Mauzerall, D. C. J. Am. Chem. SOC.1983, 105, 6528-6529. (7) (a) Isied, S . S.; Worosila, G.;Atherton, S . J. J . Am. Chem. Soc. 1982, 104,7659-7661. (b) Winkler, J. R.; Nocera, D.; Y o h m , K.; Bordignon, E.; Gray, H. B. J . Am. Chem. Soc. 1982,104,5798-5800. (c) Isied, S. S.; Kuehn, C.; Worosila, G.J. Am. Chem. SOC.1984,106, 1722-1726. (d) Meade, T. J.; Gray, H. B.; Winkler, J. R. J . Am. Chem. SOC.1989,111,4353-4356. (e) Mayo, S . L.; Ellis, W. R.; Crutchley, R. J.; Gray, H. B. Science 1986, 233, 948-952. (8) (a) Mdjourty, J.; Blough, M.; Hoffman, B. J . Am. Chem. Soc. 1983, 105, 4470-4472. (b) Liang, N.; Pielak, G.J.; Mauk, A. G.;Smith, M.; Hoffman, B. Proc. Narl. Acad. Sci. U.S.A. 1987, 84, 1249-1252. (c) Mchndon, G.;Simolo, K.; Mauk, A. G. J. Am. Chem. Soc. 1984,106,5012. (d) McLendon, G.; Miller, J. R. J. Am. Chem. SOC.1985,107,7811-7816. (e) Hazzard, J. T.; Tollin, G. Biochemisfry 1987,26, 2836. (f) Pielak, G.J.; Concar, D. W.; Moore, G.R.; Williams, R. J. P. Prorein Eng. 1987, 1, 83-88. (g) Zhou, J. S.; Granada, E. S . V.; Leontis, N. B.; Rodgers, M. A. J. J . Am. Chem. SOC.1990, 112, 5074-5080. (h) Wasieiewski, M. R.; Tiede, D. M. Febs Letr. 1986, 204, 368-372. (i) Jackman, M. P.; Sykes, A. G.;Salmon, G. A. J. Chem. SOC.,Chem. Commun. 1987, 65-66. (9) (a) Ratner, M. A. J . Phys. Chem. 1990, 94, 4877-4883. (b) Closs, G . L.; Johnson, M. D.; Miller, J. R.; Piotrowiak, P. J . Am. Chem. SOC.1989, I Z I , 3751-3753. (c) Finckh, P.; Heitele, H.; Volk, M.; Michel-Beyerle, M. E.J . Phys. Chem. 1988,92,6584-6590. (d) Oevering, H.; Paddon-Row, M. N.; Heppener, M.; Olivier, A. M.; Cotsaris, E.;Verhoeven, J. W.; Hush, N. S. J. Am. Chem. SOC.1987, 109, 3258-3269. (e) Pasman, P.; Mes, G. F.; Koper, N. W.; Verhoeven, J. W. J . Am. Chem. SOC.1985,107,5839-5843. (10) Marcus, R. A. J . Chem. Phys. 1956, 24, 966-978. ( 1 1 ) Brun, A. M.;Hubig, S. M.; Rodgers, M. A. J.; Wade, W. H. J . Phys. Chem. 1990, 94, 3869-3871.
Formula for: (A) QI; (B) Qd (n’= 2, 3); (C) MV, (n = 3, 5, 7); (D) MVnn’Q ( n = 3, 5 , 7 and n’ = 2, 3)
are identical with those in MVQ, viz, a methylalkylbipyridinium and an aminochloronaphthoquinone. The linkage consists of n (n = 3-7) and n’(n’= 2 and 3) methylene groups linked by a dimethylated quaternary nitrogen atom. Again, no rigidity in the linkage was anticipated, but the idea of making successively larger flexible chains was to obtain some evidence which would perhaps help us to understand why a downhill ET in a flexible-linked system was so slow. This report presents our data gathered in this respect and attempts an understanding, albeit qualitative, of the forces at work.
Experimental Section 1. Apparatus. Pulse radiolysis experiments were carried out with a previously described13 4-MeV Van de Graaff electron accelerator and computer-controlled kinetic spectrophotometric equipment for fast kinetic measurements. 2. Materials. Millipore ‘Reagent Grade” water was used for all experiments. Isopropyl alcohol (spectrophotometric grade) was obtained from Mallinckrodt. Methylviologen (Sigma) and sodium dodecyl sulfate (Gallard-Schlesinger, BDH) were used as received. Acetone (spectrophotometric grade) was obtained from Kodak. All solutions were buffered at pH = 7 (2 mM KH2P04 3 mM Na2HP04). To improve the solubility of MV2+nnQ,10%acetone was added to both micellar and aqueous solutions. Aqueous solutions also contained 10%isopropyl alcohol for removal of hydroxyl radicals. Each sample was bubbled or stirred and blown with nitrogen for ca. 1 h prior to measurement. 3. Electron pulse Radiolysis. Electron pulse radiolysis of deaerated aqueous solutions produces hydrated electrons, hydroxyl radicals, hydrogen atoms, molecular hydrogen, and hydrogen peroxide. In our experiments, all oxidizing species were scavenged by either isopropyl alcohol in homogeneous solution or sodium dodecyl sulfate (SDS)in micellar solution. The remaining re-
+
~
~~~
_______
(12) (a) Hubig, S. M.; Rodgers, M. A. J. J . Phys. Chem. 1990, 94, 1933. (b) Hubig, S. M.; Dionne, B. C.; Rodgers, M. A. J. J. Phys. Chem. 1986,90, 5873. (13) Foyt, D. C. Compur. Chem. 1981.2, 49.
712 The Journal of Physical Chemistry, Vol. 96, No. 2, 1992
Brun et al.
ducing species reacted with the substrates forming reduced methyl viologen (MV'+) and reduced quinone (Q+) in the case of separated electron donor and acceptor molecules (see eqs 1 and 2); and M V n n Q and MV2+nnQ- in the case of linked donor-acceptor molecules (seeeqs 3-5). At the substrate concentrations k +Q& MV2+ + Q'MV'+ + Q'MV2+ + Qzk*
MV'+
kb
(1)
E
(2)
v)
z
0
MV'+nnQ
kh
MV2+nnQ'-
0
(3)
+ MV2+nnQ5MV2+nnQ + MV*+nnV- (4) MV'+nnQ + MV2+nnQ'MVz+nnQ + MV2+nnQ2k*
MV'+nnQ
kF
--
-
(5)
that we employed the initial reduction proceeded to completion in 1 ps or less. The subsequent inter- and intra-ET reactions occured over tens and hundreds of microseconds.
Results Spectra. Figure 1 shows the transient absorption spectra of
MVnnQ (where n = 5 and n'= 3) taken at two delay times after electron pulse irradiation. The spectra of all the MVnnQ (where n = 3 , 5 , 7 and n' = 2,3) molecules measured showed the same characteristics as described for the MVQ mo1ecule:ll an absorption band around 400 nm, where both the reduced methylviologen moiety (MV*+nnQ)and the reduced quinone moiety (MV2+nnQ'-) absorb light, an absorption band around 600 nm, where mainly MV'+nnQ absorbs (e = 13 700 M-I cm-I)l4 and a ground-state bleaching at 475 nm, caused by the formation of semiquinone radicals MVZ+nnQ-. Electron pulse radiolysis experiments under comparable conditions with a 1:l mixture (MVZ+,+ Qd) and with the MVnnQ molecules showed the same time-resolved spectra. This correspondence between the time-resolved spectra for the separate species in 1:l ratio and for the linked MVnnQ molecules leads to the conclusion that only intra- and intermolecular electron transfer reactions between MV and Q moieties have to be considered when the linked molecules are reduced by electron pulse irradiation. Two singly reduced states can be formed by electron capture at either end of the bifunctional MVnnQ molecule, one with the electron initially localized at viologen (Mv'+nnQ) and one initially localized at quinone (MV2+nnq-). In order to determine the initial distribution of the two radicals the absorption at 600 nm (MV'+nnQ) and the bleaching (negative absorption) at 475 nm (MV2+nnQ-) were measured immediately after the pulse. A solution of methylviologen in water of the same concentration (50 and 100 pM) was used as dosimeter. Knowing the extinction coefficients of the MV" radical at 600 nm and of the molecule MVnnQ at 475 nm (t = 3200,2160,3060 M-' cm-' for QI, Q2, Q3, respectively) allowed us to determine the initial concentrations of all radicals. It was observed that the initial concentrations of the two radicals (MV+nnQ and MVz+nnQ-) were the same and equal to half of the initial concentration of M V radicals formed in the dosimeter solution. The same experiment in the case of separate molecules (MV2+, + Qd), yielded similar results, Le., equal initial concentrations of MV'+, and Q'-d. Kinetics. (A) Aqueous Solution. For kinetic evaluation of the ET reactions involving the linked species MVnnQ, the growth of the bleaching at 475 nm and the decay at 600 nm were fitted as independent first- and second-order reactions (see insets in Figure 1). The first-order reaction marked '1" in the figure was attributed to the sum of intermolecular and intramolecularelectron transfer from the reduced methyl viologen moiety to the quinone moiety as indicated by reactions 4 and 3, respectively. The in(14) Watanabe, T.; Honda, K. J . Phys. Chem. 1982, 86, 2617-2619.
I
0
50
100
150
2w
[ MV53Q ] / 10-6 M Figure 2. Plot of the observed first-order rates constants vs MV53Q concentration, in aqueous solution. The slope of the plot yields the sum of the intermolecular rate constants (kF+ kB)while the intercept yields the sum of the intramolecular ET rate constants (k, + kbi).
TABLE I: Forward Int"0lecul.r Rate Constants (Eq 3, k,) and Rate Comtmts (Eq4, kF)Observed at 600 nm in Water for MVQ and MVm'Q ka, s-' MV32Q 1.65 (h2.0) X MV33Q 1.02 (h0.3) X MV52Q 2.26 (h0.8)X MV53Q 6.06 (h0.7) X MV72Q 9.30 (h0.6) X 1.40 (h0.9) X MVQ a
lo2 lo3
lo3 lo3 10' 10'
kF, M-' S-I 1.20 (h0.02) X lo8 2.87 (h0.13) X 2.86 (h0.09) X 2.21 (h0.06) X 2.57 (h0.13) X 3.80 (h0.20) X
lo8 lo8 lo8 lo* lo8
Taken from ref 1 1.
termolecular electron transfer step shows first-order kinetics because the concentration of radicals produced by the electron pulse was much lower (ca. 2 pm) than the lowest MVnnQ concentration used (10 run). The secondsrder reaction marked y2win the figure showed a biomolecular rate constant of ca. lo9 M-' s-' and was attriiuted to the redox disproportionation reaction between reduced methylviologen and reduced quinone moieties (eq 5)." Combinations of the rate constants for inter- and intramolecular electron transfer, kF,kB,k,, and kbi (eqs 3 and 4) were obtained from a plot of the observed first-order rate constants (kobs)for the early part of the reaction (marked "1") versus the substrate concentration (see Figure 2):
= (kF + kd[MVnnQI + (kii + kbi) (6) According to eq 6, the sum of the intermolecular rate constants (kF k,) is obtained from the slope of plots such as in Figure 2, while the intercept yields the sum of the intramolecular rate constants (k, + kbi). For the separated molecules MV2+ and Q species, we dettrmined the bimolecular rate constant of the forward kf(2.84; 1.70; 1.79 X 109 M-' s-' for QI, Qz,and Q3,respecti~ely)'~ and the back kb (4.55; 1.44, 1.05 X lo7 M-' s-l for Q1, Qz,and Qsrespectively)'* intermolecular electron transfer. kf is virtually 2 orders of magnitude greater than kb. This is in line with the one-electron-reduction potentials (vs NHE)of the MV2+/MV'+ (-448 mV)I4 and Q / Q - (-280 mV)I6 couples. Thus, the sum kF + kB is approximately equal to kF and the sum k, + kbi is approximately equal to k,. The values of the intra- and intermolecular forward electron transfer rate constants are listed in Table I. Also reported in this table for comparison are the rate constants measured previously with the molecule MVQ. The intermolecular rate constants carry an acceptable precision (see Table I). This is not the case for the determination of kfibecause the intercept of plots kobs
+
(1 5) Brun, A. M. Unpublished results. (16) This value is an average of the peak potentials corresponding to the reduction of the quinones for the molecules MVnnQ.
The Journal of Physical Chemistry, Vol. 96, No. 2, 1992 713
ET in Linked Viologen-Quinone Molecules
I
WE/-
8
0
1.01
0
of more than single occupancy of a micelle is less than 0.15 for a ratio R = [MVnnQ]/[micelle] lower than 0.7. Thus the exponential decay (Figure 3, inset) of the viologen radicals at 600 nm for R C 0.7 is evidently showing the intramolecular electron transfer only (eq 3). As Figure 3 shows, with increasing ratios R the probability of having more than one MVnnQ molecule per micelle becomes increasingly significant causing the observed rate constants to increase due to bimolecular reactions within individual micelles (eq 4). However, the invariant nature of the rate constant vs MVnnQ concentration (Figure 3) for R < 1 shows that intramolecular reaction only is occurring at these concentration ratios.
.
-
pE 0.50.0
0.2
0.4
0.6
0.0
1.0
1.2
[ MV23Q ] / [ micelle ] Figure 3. Plot of the observed first-order rate constants vs [MV32Q]/ [micelle] ratios for [SDS] = 15 mM. Inset: first-order kinetic trace observed at 600 nm for [MV32Q]/[micelle] = 0.70. TABLE II: First-Order Rate Collstpnts Observed at 600 m in SDS for the Ratio [MVQY[dceUe]or [MVm'Qy[miceUe] Lower Than 0.7 k m i a s-'
MV32Q MV33Q MV52Q
kmiw
1.09 (*0.25)
MV53Q
1.32 1.52
MVQn
X lo' (h0.35) X lo3 (10.35) X 10'
MV72Q
s-'
1.47 (h0.43) X lo3 1.79 (k0.17) X lo3 1.10 (h0.40) X lo3
Taken from ref 11.
such as in Figure 2 is very close to zero and therefore difficult to extract precisely. Nevertheless, as Table I shows, kfiincreased with increasing chain length between the methylviologen moiety and the quinone moiety in the series MVnnQ. (B)Micellar Media. In the case of the linked species MVQ, we have already shown" that where kfiis very low (ca. lo3SI), the precision of the determination of kfi can be improved by carrying out the electron pulse radiolysis experiments in aqueous micellar solutions of sodium dodecyl sulfate (SDS). In such systems the linked molecules become associated with the micellar periphery. The Poisson distribution of substrates within the micellar ensemble suppresses the concentration-dependent term and makes the intramolecular contribution easier to determine directly. Thus, electron pulse radiolysis experimentswith MVnnQ in 15 mM SDS micellar solution gave kinetic decay curves that cleanly followed first-order kinetics as opposed to the mixed kinetics observed in water (see inset in Figure 3). We measured the first-order rate constants as a function of the ratio R = [MVnnQ]/[micelle]. R was varied by changing the substrate concentration at [SDS] = 15 mM. For R < 0.7 the observed rate constants were independent of the MVnnQ concentration and the values at this plateau (kmie)are reported in Table 11. As Figure 3 shows for R > 0.7 the observed rates constants increased with increasing R. In order to differentiate between intra- and intermolecular ET in micellar dispersions, we need to know the distribution of MVnnQ among the SDS micelles. Thus,we calculated the molar micelle concentrations f r ~ m ' ~ J * [MI = ([SDS] - cmc)/N
(7)
where the critical micelle concentration (cmc) and the aggregation number (N) were taken to be 8.1 mM" and 62,'* respectively. Based upon the fact that the PF6- salts of MVnnQ species have a very low solubility in water, and that the separate species MVZ+ as well as naphthoquinones tend to associate with the micellar aggregates, we conclude that all MVnnQ molecules are micelle-associated. According to Poisson statistics, the probability (17) Turro, N. J.; Yekta, A. J. J . Am. Chem. Soc. 1978, 100, 5951. (18) Almgren, M.; Grieser, F.; Thomas, J. K. J . Chem. Soc., Faraday Trans. 1979, 75, 1674.
Discussion Electron pulse radiolysis experiments have allowed us to determine rate constants for both intramolecular and intermolecular electron transfer between MVZ+and Q moieties of the MVnnQ molecules in aqueous (Table I) and micellar (Table 11) solutions. confining our attention first to the intramolecularrate constants (kfi) in aqueous media (Table I), we note that the transfer of an electron within the molecule requires some milliseconds, or large fraction thereof, for completion. One concem in this respect was that the ET was possibly occurring within the time resolution of our electron pulse radiolysis experiments (the shortest pulse used being 50 ns) and that we are observing some slower, secondary decay events. However, the data belie this interpretation. Two radicals can be formed by electron capture at either end of the bifunctional MVnnQ molecules, one with the radical site on MV (MV'nnQ), one with it on Q (MVz+nnQ'). Immediately after electron pulse irradiation the ratio of the two radical concentrations was close to unity. This is as expected considering the similar rate constants of the reactions of MV2+with hydrated electrons (5.4 X 1O'O M-' s-')19 and of the Q moiety with hydrated electrons ((2.18-4.53) X 1O'O M-l &).I5 If a rapid electron transfer from the MV'+ moiety to Q had happened prior to our initial observation time, the concentration of MV2+nnQ'- radicals would be much higher than the concentration of MV'+nnQ radicals. In fact this was not the case and the sum of the concentrations of the two radicals was the same as the total concentrationof radicals formed in the dosimetry experiment. Therefore, no radicals were lost or converted due to a rapid electron transfer within our instrument rise time. Another concern was the free energy change and how it is affected by the presence of the micelle. In aqueous solution, the difference between the redox potentials of separated methylviologen (-448 mV)I4 and quinone (-280 mV)I6 entities was calculated to be 200 mV, Le., AGO < 0 for the ET from the reduced methylviologen to the quinone. We obtained similar redox potentials differences for the attached MVnnQ molecule^.'^ In micellar solution, the viologen moiety is assumed to be in a highly polar and ionic environment.I2 Thus the redox potential of the micellized MV moiety is expected to be similar to the one measured in water. On the other hand, the micellized quinone moiety will be dominantly in a very nonpolar environment, and the redox potential is assumed to be close to the one measured in a nonpolar solvent (DMF). From redox potentials measured in water and DMF, re~pectively,'~ we estimated a redox potential difference of 150 mV between micellized methylviologen and quinone moieties. Bard and KaiferZ0measured the micellar effect on the reductive electrochemistry of methylviologen and found a small decrease in the redox potential (40 mV) going from aqueous to micellar (SDS) solution. Therefore, AGO may be lower in SDS solution than in aqueous solution, but not to the point of causing the reaction to be endothermic. The movement of an electron from the molecular system of the donor (D) species to that of the acceptor (A) species requires some measure of electronic coupling between the two entities. This can occur through the space between the D and A residues since the amplitude of the molecular electronic wave functions fall off (19) Rodgers, M. A. J. Radio?. Phys. Chem. 1984,23, No. 1-2.245-250. (20) Kaifer, A. E.; Bard, A. J. J . Phys. Chem. 1985, 89, 4877.
714 The Journal of Physical Chemistry, Vol. 96, No. 2, 1992
exponentially with distance from their maximal values.Ic Thus the wave functions of the D and A entities have some finite overlap probability in the intervening space. This overlap, which decreases exponentiallyas the intervening distance increases, facilitates the transfer. Coupling of this kind may be augmented by electronic orbitals of the intervening medium. In this respect Closs and MillerIbprovide a graphic picture of the through-bond mechanism in which the LUMOs of intervening spacer groups act to form a conduit for D and A electronic coupling. Both through-bond and through-space mechanisms yield an exponential falloff of electron-transfer rate constants with distance but at a given distance the through-bond route is apparently more effective. We are particularly fortunate in this work in that we have been able to measure the rate parameters for both inter- and intramolecular processes for the same molecule in the same solvent system. This provides us with useful comparison values, as indicated above. For example, both reaction types have identical reactant and product states, the change in charge from (+1;0) to (+2;-1) is the same, and the solvent is the same. Thus both AGO and the reorganization energy (A) are not expected to differ between the intra- and intermolecular ET processes in the MVnnQ species. The fact that the intermolecular rate constants (kF)measured in water and listed in Table I are not significantly affected by the length of the molecular chain connecting the D and A units is in concert with the above argument. On the other hand, the values of kn listed in Table I show a marked increase as the intervening molecular chain length increases from 8 bonds (MV32Q) to 12 bonds (MV72Q). This ca. 50-fold increase in kfiis surprising and close scrutiny is of interest. For ET between D and A residues across rigid spacer links (e.g., steroid, decalin, etc.), Closs and Millerib found that the greater the number of bonds between donor (biphenylide anion radical) and acceptor (naphthalenyl) residues, the lower the ET rate constant. Thus going from 4 to 10 such intervening bonds caused a rate constant lowering of some 2000-fold, completely in accord with a through-bond ET mechanism in the rigid spacer system. The rate constant dependence on chain length in the MVnnQ series is the inverse of that observed in the rigidized systems, leading to the conclusion that ET in the flexible series is not following the through-bond movement. Another interesting facet arises when a comparison is made between the measured intermolecular and intramolecular rate constants in the MVnnQ series. The intermolecular values have no chain length variation (see above) and show a mean value of 2.5 X lo8 M-I s-l; the intramolecular parameters show a strong chain length dependence. An immediate and obvious conclusion from these facts is that the flexibility of the chain is governing interactions (to be amplified below) between the reactant pair, and that the flexibility increases as the number of intervening bonds increases, allowing the interactions to become more optimal and/or more frequent with the concomitant increase in rate constant. In order to make a comparison of the magnitude of kn and kF, it is useful to think of the MVnnQ reduced species as a reactant pair comprising one MV" donor radical and one quinone acceptor which are constrained together by a flexible tether. For the sake of the argument, consider that the tether is completely flexible such that the D and A entities can contact each other as if they were individual, unlinked species (Le., in an intermolecular sense). The purpose of the tether is simply to keep the reacting pair from diffusing away from each other. A scale model (HGS Molecular Structure Models) of MV32Q shows it to have a tiptc-tip length of 2.4 nm when fully extended. This represents the diameter of the sphere that will wholly contain MV32Q no matter what its conformation. The D and A units are mutually confined in much the same way as if individual unlinked D and A molecules were residing in the aqueous interior of a reverse micellar dispersion. In this analogy, D and A would be hydrophilic species that have zero tendency to move out of the water pool into the organic dispersion medium, but they are completely free to move around and interact within the confines imparted by the micellar interface.
Brun et al. The fully extended length of 2.4 nm for the MVnnQ entity corresponds to a volume of 7.24 nm3,and every reduced viologen moiety has a quinone acceptor immediately available for reaction within that volume element. This corresponds to an "effective" acceptor concentration of ca. 0.25 M in the vicinity of reduced viologen. The intermolecular rate constant for MV32Q (Table I) is 1.2 X lo8 M-' s-I, whence the anticipated "effective" rate constant for the kinetically first-order intramolecular process is 3 X lo7 s-l, This anticipated value is some 5 orders of magnitude higher than the measured value of kn (Table I). Similar conclusions can be drawn for the other members of MVnnQ listed in Table I. Thus,on the reasonable premise that the thermodynamic factors governing the electron transfer are independent of whether the two entities encounter via an intermolecular or intramolecular route, and assuming an infinitely flexible linker, then the expectation would be that the rates of the two types of reaction, adjusted for concentration as above, ought to be comparable. A discrepancy of 5 orders of magnitude probably means that the link is only of limited flexibility. So, the absolute values of the rate parameters in Table I and the increase of kfiwith increasing chain length taken together lead to the conclusion that the intramolecular electron transfer reaction rate constant is a consequence of reactive interactions that occur as the partially flexible chain undergoes its contortions. In support of this concept we turn to the data collected in Table 11. Here we see that when the MVnnQ species are associated with SDS micelles, the intramolecular rate constants virtually lose their chain length dependence. At the micellar interface a reduced MVnnQ entity will tend to have the hydrophobic naphthoquinone segment associated with lipoid regions, and the cationic viologen segment within the more polar regions, e.g., within the Stem layer. Such an arrangement is expected to provide an energy barrier to free rotation and preferred conformations will almost certainly arise. This effect will tend to diminish the inferred electronic coupling through closer approach. While such a rationalition, albeit vague, offers an explanation of the observed facts, it says nothing concerning why a through-bond mechanism is apparently not operating here. The literature provides several examples of one-electron-transfer reactions between donor and acceptor residues that are separated by rigid spacer systems such as steroids? cyclic alkane^,^ and olig~prolines.~ In many cases the intramolecular rate constants decreased exponentiallywith the number of inserted bonds which is consistent with the through-bond mechanism. Such a dependence is also equally consistent with a through-space mechanism but all indications are that under such conditions the through-bond interactions are much more favorable. There are few other studies of ET within molecules having flexible spacers. Thus Isied and Vassilian*' studied ET between Ru" and Co"' ammine complexes linked by isonicotamide coupled with either a single amino acid or a dipeptide. They found that adding one glycine or phenylaniline residue lowered the rate constant by 3 orders of magnitude, adding a second lowered it by about another order of magnitude. This second addition lowered the activation enthalpies and increased (negatively) the activation entropies. Again hied and coworkerssbfound a factor of 5 or 10 enhancement in kintrawhen flexible phenylalanine or glycine replaced rigid proline in a dipeptide linking Os" and ColI1 ammine complexes. This latter evidence suggests that a through-space coupling can be an important contributor if through-bond couplings are weak. Very recently Zhao et a1.22 studied photoindud ET between eosine and methylviologen residues coupled by bridges of 3-6 methylene links. They found the highest rate constant (0.56 X lo8 s-l) for n = 4. This work was conducted in MeOH and strong intergroup couplings existed for n = 4 as shown by NMR in DMSO. These literature studies are sparse and the observations are difficult to cast into a clear (21) Isied, S. S.; Vassilian, A. J . Am. Chem. Soc. 1984,106, 1726-1732. (22) Zhao, 24.; Shen, T.; Xu, H-J. J . Phorochem. Phorobiol. A: Chem. 1990.52, 47-53.
J. Phys. Chem. 1992,96,715-726 pattern. In our case it would appear that the through-bond forces are of negligible intensity and through-space interactions are dominant. An explanation that occurs to us derives from the fact of the flexibility of our spacer system. Cave et al.23have calculated the electronic matrix element for the electron transfer between a pair of porphyrins. They find that the mutual orientation of the donor and acceptor states has severe consequences on the magnitude of the coupling which reduces to zero in some orientations. In their review article Class and Millerlbput forward a pictorial description of how coupling between the LUMO's of donor and acceptor is achieved via the L U M O s of the spacer groups. Extending the conclusions of Cave et al.23the magnitude of such couplings will be affected by the orientations of the intervening bonds. In a rigid system the interbond alignments are presumably optimal whereas in flexible spacers such as ours the molecules will visit a multitude of conformations only some of which will be capable of providing effective LUMO coupling. In this way through-bond interactions may be diminished. In summary, we conclude that the intramolecular electron transfer between reduced viologen radicals and a quinone occurs with an efficiency that increases as the number of intervening bonds increases. This is antisense to what is required for any (23) (a) Cave, R. J.; Siders, P.; Marcus, R. A. J. Phys. Chem. 1988, 90, 1436-1444. (b) Siders, P.; Cave, R. J.; Marcus, R. A. J . Chem. Phys. 1984, 81, 5613-5624.
715
mechanism (e.g., through bond or through space) that has a diminishing interaction with donor-acceptor distance. Such an effect can be understood if the intervening chain has a degree of flexibility that allows conformations to occur that place D and A residues in conjunctions that allow close through-space (i.e., collisional) interactions. The longer the chain, the more such interactions are favored, i.e., flexibility increases with chain length. However, our simple calculations on what intramolecular rates would be expected show that the probability of these close encounters occurring between D and A pairs is very small. Acknowledgment. The electron pulse radiolysis experiments were carried out at the Center for Fast Kinetics Research, which is supported jointly by the Biotechnology Program of the Division of Research Resources of NIH (RR 00886)and by the University of Texas at Austin. Partial support for this work came from NIH grant G M 31603 (to M.A.J.R.). We are very grateful to B. K. Naumann for his expert technical assistance in operating the electron accelerator. We thank Mark Meier and Tom Mallouk from the Chemistry Department, University of Texas at Austin, for their advices with the synthesis of the molecule MVQ, and A. J. Bard and G. Denuault from the Chemistry Department, University of Texas at Austin, for assistance in the electrochemical measurements. Supplementary Material Available: Synthesis of the molecules MVQ and MVnnQ ( n = 3, 5 , 7 and n' = 2, 3) (12 pages). Ordering information is given on any current masthead page.
Sodium/Sulfur Chemical Behavior in Fuel-Rich and -Lean Flames Keith Schofield* and Martin Steinberg Department of Chemistry, University of California. Santa Barbara, California 931 06 (Received: February 28, 1991)
An experimental and analytical program examining sodium/sulfur chemistry has been conducted in a series of fuel-rich and -lean H2/02/N2flames, with and without added sulfur, and covering a wide range of temperatures and stoichiometries. Fluorescence measurements of OH and Na downstream profiles and sodium line reversal temperatures provided a broad data base for kinetic modeling. Analysis indicated NaS02to be the only significant sodium/sulfur product formed in the lean flames. Even so,its concentrationsremain an extremely small fraction of the total sodium. The more important perturbation of the distribution of sodium over its molecular forms results from the catalytic effect of sulfur on the flame radical concentration levels rather than from the formation of additional species. A bond dissociation energy of Doo(Na-S02) = 197 20 kJ mol-' is derived assuming a nonplanar structure or 210 f 20 kJ mol-' if the molecule is planar. NaOS is dominant in the rich flames, coupled with small contributions from NaS02, NaSH, NaS, and NaS2. Together, these can constitute from about 10 to 20% of the total flame sodium and do represent in this case an enhancement of molecular formation. Preliminary data in fuel-rich C2H2/02/N2flames are consistent with this model. This further illustrates the general insensitivityof alkali-metal chemistry to fuel type. When coupled to other available data, the low levels of NaS02 estimated for the present fuel-lean flames tend to suggest that Na$04 formation in the gas phase appears to be unlikely under most practical conditions. However, this still cannot be rigorously ruled out for all situations and requires further study to resolve the critical dependences that control high-temperature Na2S04corrosion.
Introduction Sodium sulfate was identified 45 years ago as a serious corrmive agent in the ash deposits on power plant boiler tubes.' Subsequently, the surprising corrosive character of sodium sulfate also was noted in deposits on oxidation resistant alloys in combustion driven gas t~rbines.2~Whether it is formed through homogeneous gas-phase chemistry in the combustion gases or is produced heterogeneously on the surfaces has remained an unanswered question. There is no chemical kinetic information for modeling (1) Reid, W. T.; Corey, R.C.; Cross, B. J. Trans. ASME 1945, 67, 279. Corey, R. C.; Cross, 9. J.; Reid, W. T. Trans. ASME 1945, 67, 289. (2) Simons, E. L.; Browning, G. V.; Liebhafsky, H. A. Corrosion 1955, 11, 505. (3) de Crescente, M. A.; Bornstein, N . S. Corrosion 1968, 24, 127.
this aspect of the problem. Consequently, past efforts to analyze the gas/surface interactions have been forced to invoke limiting conditions of frozen chemistry or chemical equilibrium for the sodium/sulfur system.4~~ Although an extensive literature has developed concerning sodium sulfate in combustion systems, only a few efforts have been made to understand the underlying sodium/sulfur flame chemistry. Fenimore6 reported a decrease of Na with the addition of SO2 (4) Fryburg, G. C.; Miller, R. A.; Stearns, C. A.; Kohl, F. J. High Temperature Metal Halide Chemistry. The Electrochemical Society Softbound Proceedings, Hildenbrand, D. L., Cubicciotti, D. D., Eds.; Princeton, NJ; 1978; Vol. 78-1, p 468; (also NASA TM-73794, 1977). (5) Rosner, D. E.; Chen, B.-K.; Fryburg, G. C.; Kohl, F. J. Combust. Sci. Technol. 1979, 20, 87. (6) Fenimore, C. P. Symp. (Int.) Combust. [Proc.] 1973, 14, 955.
0022-3654/92/2096-I 15$03.00/0 0 1992 American Chemical Societv
