J. Phys. Chem. 1995,99, 11959- 11966
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Electron Transfer through Vesicle Membranes: Effects of Reactant Compartmentalization and Intervesicle Migration on the Reaction Kinetics Leif Hammarstrtim" and Mats Almgren Department of Physical Chemistry, Uppsala University, Box 532, S-751 21 Uppsala, Sweden Received: March 22, 1995; In Final Form: May 22, 1995@
The kinetics of electron transfer through vesicle membranes mediated by viologen was considered in detail. In previous studies, the rate-determining step of the reaction has been found to be the disproportionation of two viologen radicals: 2C,V+ C,V2+ C,V. The effect of reactant compartmentalization was demonstrated by both experiments and simulations. Second-order fits to the kinetic data showed that disregarding compartmentalization is a good approximation for the major part of the observed reaction when the initial average occupancy number (no> 1 10. The value for the rate constant obtained from a "good" fit was unaffected by compartmentalization. Both simulations and experiments showed that when (no) 5 5 , it was not possible to obtain a satisfactory second-order fit over the same interval. Experiments showed that migration of C,V2+ between vesicles was rapid (l/k- < 1 ms), but migration of C,V+ was slow on the time scale of the experiments. The effect of viologen migration was demonstrated by simulations. The simulation results are general for compartmentalized reactions described by 2A A B, with and without the possibility of intercompartment exchange of A during the reaction.
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I. Introduction
kd
2c,v+ Spatial and dimensional confinement of reactants that undergo diffusion-controlled reactions is well-known to change the kinetics from that in homogeneous solution. Both macroscopic (diffusion equations) and microscopic (random walk) models have been used to describe the reactions.' In addition, both diffusion- and reaction-controlled reactions are affected when the reactants are distributed over small compartments, such as surfactant aggregates, polymers, colloids, etc. Namely, if the intercompartment migration of the reactants is slow, the distribution of occupancy numbers among the compartments will cause the reaction to proceed with different rates in different compartments. The effect of compartmentalizationwill become increasingly evident as the average occupancy number decreases, and the use of homogeneous kinetic models will be an increasingly poor approximation. Stochastic models have been developed to treat some types of elementary reactions in compartmentalized systems. I We have for some time studied electron transfer through the membranes of egg lecithin vesicles.2 The electron transfer was mediated by amphiphilic electron acceptors, in most cases viologens, bound at the vesicle interface. The acceptor, at one interface, was initially reduced by dithionite, an excited photosensitizer, or a reducing radical formed in pulse radiolysis. At the end of the reaction, ferricyanide as a secondary acceptor on the other side of the membrane had been reduced, and this reduction had been mediated by the amphiphilic acceptor. In the studies with viologen, the use of a secondary electron acceptor in the vesicle interior and viologen only at the outer interface allowed us to directly exclude self-exchange of electrons between viologens on opposite interfaces as the mechanism of the observed reaction, which had been proposed earlier in this and similar systems3 Neither did simple diffusion of the viologen radical (C,V+) through the membrane contribute significantly to the reaction. We proposed an alternative mechanism (Figure 1) where a rate-determining disproportionation reaction @Abstract published in Advance ACS Abstracts, July 1, 1995.
0022-365419512099-11959$09.0010
=c,v2++ c,vo kc
between two viologen radicals formed the doubly reduced, neutral viologen (C,VO). The neutral viologen diffused rapidly (t % 1 ms) through the vesicle membrane and reduced two equivalents of the ferricyanide. The disproportionation equilibrium in eq 1 is shifted far to the left, but since the neutral viologen was rapidly removed and consumed in a subsequent reaction step, the reaction was driven to completion. When the primary reductant (dithionite) was added in excess, the reoxidized viologen (C,V2+) formed in the disproportionation reaction was again reduced. Thus, the reaction ended when all viologen had transversed the membrane and been reoxidized by the ferricyanide and trapped on the inside of the vesicles. In pulse radiolysis, the viologen was only partially reduced, leaving most viologen as C,V2+. In spite of the high concentration of C,V2+ on the external interface, the reaction was not retarded, showing that the conproportionation reaction (eq 1 from right to left) was negligible. The reaction was followed by absorption spectroscopy, and the kinetic curves from the transmembrane step were fitted to a second-order model for homogeneous solutions. The fist halflife of the reaction was inversely proportional to the mole fraction of reduced viologen radical initially formed at the vesicle interface, as expected for a reaction that is of second order with respect to the surface concentration of viologen radical (eq 1). However, the compartmentalization of the viologen, with a limited number of reactants per vesicle, is expected to result in deviations from second-order kinetics, unless the exchange of reactants between the vesicles is much faster than the observed reaction. It was found, though, that fair to excellent second-order fits were obtained when the average number of reactants per vesicle at the start of the reaction was around 10 or above. In the present study, the effects of reactant compartmentalization were considered in detail. The rate-determining disproportionation reaction (eq 1) produces one dicationic viologen (Cn,,,V2+). In the stopped-flow experiments, this is rapidly reduced to Cn,,,,V+again, by the dithionite in the external water 0 1995 American Chemical Society
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11960 J. Phys. Chem., Vol. 99, No. 31, 1995
Figure 1. Proposed disproportionation mechanism for transmembrane redox mediated by the viologen (V). The figure shows the situation when viologen is initially on the outside and is reduced by an excess of reductant (Red), as in the stopped-flow experiments. Femcyanide ( F ~ ( C N ) G ~is-used ) as an electron acceptor in the vesicle interior. When both reductant and femcyanide are in excess, the reaction is driven to completion, and all viologen molecules end up as Vzt in the vesicle interior.
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phase. Therefore, the reaction corresponds to the compartmentalized reaction 2A A B, where A denotes the viologen radical and B the doubly reduced viologen that disappears in the transmembrane reaction step. There is also a possibility of a redistribution of A between the vesicles during reaction. Analytical solutions for the time dependence of the reactant concentration could not be obtained for this reaction scheme! Hence, computer simulations were made. The aim was (i) to demonstrate, by simulations, the deviations from second-order kinetics as the average initial number of reactants per vesicle, (no), decreased, (ii) to investigate, by fitting the simulated curves to second-order kinetics, the dependence of the rate constant obtained and the quality of the fit on (no) and the fit interval, (iii) to see whether the simulations could reproduce the experimental curves, (iv) to determine, by experiments, the importance of intervesicle migration of both C,V2+ and C,,V+, and (v) to determine ( n ) at the end of the reaction. The results show that disregarding compartmentalization when (no) I 10 is a good approximation for the major part of the observed reaction. Furthermore, the value of the second-order rate constant obtained in the fitting procedure agrees with that for the corresponding reaction without effects of compartmentalization.
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11. Experimental Section The egg lecithin was provided in chloroform by Lipid Products, Nutfield, UK, and was of highest purity. Cetylmethylviologen dichloride (CMVC12) was available from earlier studies.2a.b Diheptylviologen dibromide ((C7)2VBr2, Eastman Kodak) was recrystallized from butanol. Ruthenium(I1) bis(bipyridine)(4,4'-hexadecylbipyridine) dichloride was a gift from Anna Borje, Royal Institute of Technology, Stockholm, Sweden. Vesicles were prepared in 50 mM phosphate buffer, pH = 8.0, by sonication, as described before,2 resulting in [lecithin] = 1-9 mM. Femcyanide was entrapped by addition to the buffer prior to sonication (internal concentration = 0.1-0.3 M, giving 150-400 pM global concentration with 2 mM lecithin). After sonication, the femcyanide was removed from the bulk solution by gel exclusion chromatography (Sephadex G-50 Fine, Pharmacia, Uppsala, Sweden). KCl (0.15-0.6 M) was added to the buffer used in the chromatographic procedure to compensate osmotically for the removed ferricyanide. The stopped-flow experiments were performed as described beforeS2The reaction was followed by time-resolved absorption
spectroscopy at 602 or 550 nm, where the viologen radical and its dimer absorb strongly, but not the other forms of viologen. When the dithionite was added, it reduced the viologen on the external interface of the membrane, and the absorbance increased. In the following transmembrane reduction step the absorption decreased again when the viologen was reoxidized by ferricyanide in the vesicle interior. The temperature was always 21 f 1 "C. The kinetic curves for the transmembrane electron transfer reaction was fitted to second-order kinetics using a SIMPLEX algorithm. In addition to the rate constant and the amplitude, the fitted equation included a parameter that defined the level of the base line, which could be fixed or floating. The detection system used a single light beam,and some stray light reached the photomultiplier. This made the detemination of the absolute absorbance somewhat uncertain, which affected the estimations of the concentration of viologen radicals at the end of the reaction. The best way to determine the absorbance at long times (A,) is probably to compare the signal during the mixing period, before viologen was reduced by dithionite, with the signal just before the run was started, which should be A, for the previous run. This would give the difference in absorbance without effects from instrumental fluctuations or drifts. However, if processes in the observation cell that did not involve viologen affected the signal at long times, or if the signal during mixing was not the correct zero level, this procedure would give somewhat erroneous results. Note that, for the typical experiments with 10 viologens per vesicle, 0.5 viologen radicals per vesicle at the end of the reaction would result in an absorbance of 50.005, which made an accurate determination of A, difficult. In the experiments with three CMV per vesicle, a higher vesicle concentration was used, and the possible remaining viologen radicals at the end would result in a higher value of A,. In these experiments the signal levels indicated that at most 0.1 radicals per vesicle remained ((n,) 5 0.1) after 200 s. In the experiments with (c7)2v there was no indication of a higher value of (n-) than 0.1; therefore, this value was assumed in all experiments. It must be pointed out that the concentration of viologen was kept low enough to ensure that the absorbance was linearly dependent on the concentration, irrespective of stray light and instrumental fluctuations. Thus, relative values of absorbance were reliable; e.g., simple reduction of methylviologen with dithionite resulted in perfectly single-exponential curves.
III. Simulations In the following section, we consider the effect of compartmentalization on the kinetics of the reaction under study. The need for simulations is demonstrated, and the simulations are described. Kinetics in Compartmentalized Systems. In the reaction presently considered, the rate-determining disproportionation (eq 1) consumes only one reactant, since the C,,,,V*+ produced is rapidly reduced again by the excess dithionite. Consequently, the reaction corresponds to the compartmentalized reaction 2A A B. The mole fraction of viologen was 10.02 in this study. Therefore, the viologen dications may be assumed to bind to the vesicles independent of each other, resulting in a Poisson distribution prior to reaction. Thus, consider the reaction 2A A B, with the reactants distributed over compartments of equal size. Assume that the reactants are Poisson distributed initially but do not migrate between the compartments during the reaction. The reaction is far from diffusion controlled, so the reduced dimensionality and size of the compartments are not important for the rate constant. The reaction rate in each compartment will then be
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Electron Transfer through Vesicle Membranes
J. Phys. Chem., Vol. 99, No. 31, 1995 11961
proportional to the number of possible pairwise encounters. The rate of change in concentration of compartments with n reactants, [Afl],is then given by d[Anl dt - kd(n(n - I)[&] - ( n -I- l)n[An+lI)
(2)
where kd is the second-order rate constant. The rate of change in the average occupancy number, (n),is then given by m
--=dt
m
PdAt = kdn(n - 1)At = n(n - 1)AO; PdAt 1, and when (n,) is allowed to be larger than zero in the fits, this compensates for the slight decrease in rate. Thus, the rate constant will be close to 1, but the total amplitude obtained in the fit will be slightly lower. When the fit interval was extended, the residuals grew worse and the rate constant increased (Figure 3, Table 1). If the zero level was fixed at the value when the reaction had terminated, the residuals were very poor, and the rate constant obtained was much larger than for the good fits. This behavior is expected since compartmentalization results in curves which exhibit positive deviations (higher (a) from homogeneous second-order kinetics as the reaction proceeds. When (no) was 1 5 , the fit over 90% of the amplitude was not good, as judged from the residual, and became increasingly worse as (no) decreased. Concomitantly, the rate constant obtained increased. In Table 2, the rate constants obtained for varying values of (no)are collected. They demonstrate clearly that the effect of compamentalization increases with decreasing
(no). The corresponding fits for the curves produced by the other models with (no) = 10 resulted in good residuals. The rate constants obtained were ~ 0 . 9 0for model I and 0.98-1.00 for model 111(a = 0.2-2). The similarity of the results for models I1 and I11 is expected from close correspondence of the curves in Figure 2 when (n) > 1. To summarize, the migration experiments (see above) show that model 11, or model I11 with a < 2, best represent the real reaction; i.e., the C,,,V2+ produced in each disproportionation exchanges between vesicles with unit efficiency, while the exchange of viologen radicals is slow compared to the reaction (model 111) or even negligible (model 11). The results from the fits show that the major part of the raction is well approximated by second-order kinetics when (no) 2 10. Furthermore, when the zero level ((n,)) is allowed to float in the curve fit, the value of the rate constant obtained is equal to the value for the corresponding reaction without effects of compartmentalization. Comparison of the Simulated and Experimental Curves. In Figure 3b results are shown from a second-order fit for an
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11964 J. Phys. Chem., Vol. 99, No. 31, 1995
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Time (s) Time Figure 3. Results from second-order fits to (a) a simulated curve (model 11, left row) and an (b) experimental curve ((c7)2v, right row), with (no) = 10. The lowest plot in each row shows the simulated or experimental curve (fully drawn line) together with the fit (dashed) over a long time interval, with the zero level fixed to the value at the end of the reaction (note the slight uncertainty of (n-), see Experimental Section). The residuals from those fits are shown in the upper plot of each row. The second plot from the top is the residual from the same fit interval, but with floating zero level. The lowest residual plot is from a fit over the first 90% of the amplitude and shows that the fit is good for both the simulated and the experimental curves. The scales on the vertical axes are the same for the corresponding residuals.
TABLE 1: Rate Constants and (n-) Obtained from Second-Order Fits to Simulated and Experimental Curve@ fit interval (times tin) ~~~
simulation model I1 rate constantb (n-)
(c7)2v kd ( S - ' ) ~
(n,)
kd
CMV ( s - ' Y (n-)
~
9, floating(n,) 30, floating (n,) 30, fixed (n,)
1.03 1.07 1.40
0.17 5.1 x -0.5 0.24 6.1 x 10-2 -0.25 0.52 9.5 x 0.1
0.17 0.18 0.14
0.2 -0.1
0.1
a The dependence on the fit interval and (n,) is demonstrated. Only the fits over nine times the first half-life (%90% of the amplitude) gave good residuals (see Figure 2). Please not the slight uncertainty of the values of (n,) for the experimental curves (see Experimental Section). Rate constant = (&/2 (no))-' (dimensionless), see eq 10. Secondorder rate constant in eq 1. The concentration is given as (n); hence, the dimension of k d is SKI.
TABLE 2: Rate Constants Obtained from Second-Order Fits to Simulated and Experimental Curves with Varying (no)"
(no)
simulation model I1 rate constantb.c
CMV k d ( s - ' ) d
30 20 10 5 3
1.002 1.008 1.03 1.06' 1.29
0.17 & 0.03 0.17 k 0.03 0.17 & 0.03 0.24 & 0.05' 0.25 % 0.0Y
" The fits were made over 90% of the reactio amplitude (9t1/2)with floating (n-). Rate constant = (01/2(no))-' (dimensionless), see equ 10. Average, maximum error = 3%. Second-order rate constant in eq 1 (see Table 1). e Residual plot not satisfactory. /Poor residual plot. experimental curve with (c7)2v. There is a close correspondence between the results from the simulated and experimental curves with (C7)zV (Figure 3 and Table l), but the variation of (n,) and observed rate constant, k d , with the fit interval was different for CMV (see below). The effects of decreasing (no) was experimentally examined with CMV as redox mediator. The second-order fits resulted in good residuals when (n) 2 10, and the value of kd was
constant within experimental error (Table 23. However, when (n) I5 the residuals were not good, and the values of the rate constant obtained were higher, as predicted by the fits of the simulated curves. Unfortunately, these experiments could not be repeated with (C7)2V, since the rate constant was too low to allow experiments with high accuracy over times long enough for (no) 5 5. From the similarity of the results from the second-order fits, one may assume that the experimental and simulated curves would overlap perfectly if plotted in the same diagram (with appropriate scaling of the axes), as was done in Figure 4. The axes were arbitrarily scaled to obtain the best possible overlap for the major part of the curves. It is clear that the experimental curves deviate slightly from the simulated. The curve with (C7)2V is lower than the simulated at intermediate times, while the curve with CMV is higher. As can be seen in Table 1, this causes the dependence on the fit interval of the values for kd and (n-) obtained for the CMV curves to be different from the other curves. From the values of k d in Table 1 and the estimates of C,Vf migration above, the corresponding simulations would 0.05 for CMV and a = 0.2-2 for (C7)zV. include a However, curves produced by model 111, with varying values of a,did not give a better overlap with the experimental ones, since they did not level out on this time scale. Neither was the overlap improved when the simulations used different (no) or vesicle polydispersity was included. There are several possible reasons for the difference between the models and the experiments. First, the experimental curves were very sensitive to noise and background processes at long observation times, where the signal was low. One possible background process is an increased light scattering from the vesicle solution after mixing in the stopped-flow apparatus. Since the ionic strength of the two solutions were high and differed by ~ 5 due % to the dithionite added, one would not expect a change in light scattering. Nevertheless, this was
J. Phys. Chem., Vol. 99, No. 31, I995 11965
Electron Transfer through Vesicle Membranes
A
C
V
0
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Time Figure 4. Results from simulations (model 11, fully drawn) and experiments (CMV, dashed; (C7)2V, dotted) with arbitrary scaling, (no) = 10. n e plot shows that the kinetics differs somewhat. The total time shown on the horizontal axis is 5 (dimensionless)for the simulations, which corresponds to ~ 2 s5for CMV and =lo0 s for (c7)2v. Inset: magnification of the earlier part of the curves.
observed under certain circumstances, such as when larger vesicles were used and the initial level of light scattering was much higher. Exponential curves were observed on the same time scale as used in the present experiments. Note that the total signal change due to that process does not have to be large to cancel the change in absorbance resulting from a small, slow decrease in (n),e.g., as produced by C,V+ migration (see Figure 2). Second, additional processes involving the viologen may have been important. Dimerization of viologen radicals on the time scale of the experiments would have changed the shape of the kinetic curves. Therefore, curves were also recorded at 550 nm, which is an isosbestic point for methylviologen radical and its dimer in water.8 There was no difference in the shape of these curves from those recorded at 602 nm, showing that dimerization was insignificant on the observed time scale. There is also a possibility that the viologen radical may diffuse through the vesicle membrane directly, on a longer time scale, even though this process was insignificant for the observed reaction when (no) 2 10. In experiments with CMV when (no) = 3, it was observed that (n,) 5 0.1 (after ~ 2 0 s). 0 If the value estimated for the CMV+ migration rate constant was correct (k- < 1 x lo-* s-l), this migration cannot explain this observation. An alternative explanation is that direct transmembrane diffusion of CMV+ may be significant on this relatively long time scale. However, since the intervesicle migration of CMV+ could not be characterized, we do not at this stage want to claim that CMV+ diffused through the membrane. In the experiments reported previously,2b using reductants formed by pulse radiolysis, these reductants recombined within 100 ps. Therefore, the C,V2+ formed in the disproportionation events could not be reduced again. Consequently, migration of C,V2+ did not infuence the reaction, which is then similar to simulation model I, but two reactants were consumed in each disproportionation event. Assuming no exchange of C,V+, all vesicles that initially contained an odd number of C,V+ would have one reactant left at the end of the reaction, and those with an even number initially would have none, resulting in (n-) e 0.5 for large (no). Since the experimental data were of lower
quality than the stopped-flow data and could not be collected over long times, it was not possible to make a detailed comparison of experimental and simulated curves in this case. An analytical solution for the time dependence of (n) has been provided for the reaction 2A B: which is applicable to the pulse radiolysis experiments under the assumptions of no C,V+ migration or compartment polydispersity. This solution has been applied to experiments on triplet-triplet annihilation in
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micelle^.^ V. Conclusions
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The effect of reactant compartmentalization on the kinetics of the second-order reaction 2A A B was theoretically considered and demonstrated by both simulations and experiments. The effects on the simulated and experimental kinetics were essentially in agreement. When the initial average occupancy number (no) 2 10, fits made over the first 90% of the signal amplitude (=9?1/2), with a floating zero level ((n-)), resulted in good residuals. For the simulated curves, the values of the rate constant obtained was identical to the value for the reaction in the corresponding system without effects of compartmentalization. This showed that disregarding compartmentalization when (no) 2 10 is a good approximation for the major part of the observed reaction. Thus, the values for the rate constant of viologen-mediated transmembrane electron transfer obtained from experimental curves in previous reports2 are expected to be unaffected by compartmentalization. Both simulations and experiments showed that when (no) 5 5, it was not possible to obtain a satisfactory second-order fit over the same interval.
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Acknowledgment. This work was supported by The Swedish Natural Science Research Council. Appendix. Intervesicle Migration of Viologen Radicals In this appendix, experiments for studying migration of CMV+ and (C7)2V+ are described, and some experimental and interpretational problems are discussed.
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11966 J. Phys. Chem., Vol. 99, No. 31, 1995
In the experiments, vesicle solutions ([lecithin] = 1.5 mM, [KCl] = 0.2-0.6 M, 50 mM phosphate buffer, pH = 8.0) were mixed in equal proportions in the stopped-flow apparatus. One of the vesicle solutions contained dithionite and reduced viologen on the outer interface, while the other contained intemal ferricyanide. The reaction was followed by observing the decrease in absorbance from the viologen radicals, presumably as they migrated to the vesicles with ferricyanide and reacted according to Figure 1. However, although deoxygenized, the solution without dithionite inevitably contained some residual oxygen which reoxidized a fraction of the viologen very rapidly upon mixing of the solutions. Due to the rapid migration of C,V2+, the viologen was therefore redistributed between the vesicles to an uncontrollable extent before it was reduced again by the dithionite. To avoid oxygen entering the samples, the experiment was repeated with dithionite added to both solutions before mixing. The observed absorbance from the viologen radical decayed in what initially appeared as a first-order process, but then the absorbance change leveled out and eventually stopped before all radicals had disappeared, for reasons discussed below. The curves showed a slight, initial increase in rate as more vesicles with ferricyanide were populated. Experiments were also made with solutions where all vesicles contained extemal viologen but only one-half of them contained ferricyanide. When mixed with dithionite solutions in the stopped flow, that half of the viologen located on vesicles with ferricyanide reacted in the usual transmembrane electron transfer reaction. The kinetic curves were initially identical to curves from experiments where all vesicles contained ferricyanide, but the absorbance from the viologen radicals continued to decrease slowly even at longer times, due to migration of the radicals from vesicles without ferricyanide. With 45 CMV+ per vesicle, 50-55% of the total concentration of viologen had reacted within 20 s, at which time less than 1% of the second-order transmembrane reaction remained (kd = 0.2 s-l, see Table 1). Correspondingly, for 45 (C7)2V+ per vesicle, 80-85% of the viologen had reacted after 70 s (kd = 0.05 s-l), indicating a net migration of 60-70% of the viologen initially on vesicles without ferricyanide. These experiments suggest that the intervesicle migration of CMV' was slow on the observed time scale of transmembrane electron transfer (20 s) but that the migration of (C7)2V+ was significant on the corresponding time scale (70 s). However, the interpretation of the migration experiments is not straightforward, as is evident when the reaction events leading to the observed signal are considered. According to the discussion above, the migration is expected to be a firstorder processes, with rate constant k-. In the present migration experiments the observed reaction involved the transmembrane electron transfer reaction in vesicles with ferricyanide. The observed reaction should thus have been retarded when the transmembrane reaction was not fast compared to migration. This retardation would have been most significant in the beginning of the reaction, before the reactive vesicles were sufficiently populated with C,V+, and at low values of (n),when many of the migration events would only have lead to single population of a previously empty vesicle. Furthermore, as the transmembrane electron transfer reaction proceeded, all disproportionation events on reactive vesicles produced C,V2+ that would have exchanged between vesicles
with a probability close to unity, as discussed in the text. In the migration experiments, about one-half of these exchanges were expected to move the viologen back to a nonreactive vesicle, which would have retarded the observed reaction. An additional complicating factor was that the exit and entrance processes may have been affected by Coloumbic forces at high values of (n), and (n) would have been different for the reactive and nonreactive vesicle populations. It is also possible that C,V2+ produced by disproportionation events on nonreactive vesicles could separate from the geminate C,Vo by migration, which would not be a first-order process. This would not necessarily lead to accumulation of C,Vo, since this may be reoxidized to C,V+ in processes that are to slow to interfere with the normally observed transmembrane electron transfer reaction. A further problem is that dithionite leaks through the vesicle membranes.2c Although this process is slow, it will eventually reduce all ferricyanide in the interior of the vesicles. Although the concentration of ferricyanide in the vesicle interior was high (0.5 M), dithionite leakage occurred on the same time scale as the observed migration. This is probably the reason why the reaction was terminated after %lo3s, before all viologen radicals had disappeared. Indeed, absorption spectroscopy showed that the ferricyanide concentration was low at the end of the reaction. In conclusion, the intervesicle migration rates of the viologen radicals could not be determined by the present experiments, but an estimate of the time scale and significance of the migration process was obtained.
References and Notes (1) Some recent references include: (a) Tachiya, M. In Kinetics of Nonhomogeneous Processes: Freeman, G. R., Ed.; Wiley: New York, 1987; p 575. (b) van der Auweraer, M.; De Schryver, F. C. In Inversed Micelles:
Studies in Physical and Theoretical Chemistry, Vol. 65; Pileni, M., Ed.: Elsevier: Amsterdam, 1990; p 70. (c) Rothenberger, G.: Infelta, P. P. In Kinetics and Katalysis in Microheterogeneous Systems; Surfactant Science Series, Vol. 38; Gratzel, M., Kalynanasundaram, K. Ed.: Marcel Dekker: New York, 1990; p 49. (d) Almgren, M. In Kinetics and Katalysis in Microheterogeneous Systems; Surfactant Science Series, Vol. 38; Gratzel, M., Kalyanasundaram, K., Eds.; Marcel Dekker: New York, 1990: p 63. (e) Almgen, M. Adv. Colloid Interface Sci. 1992, 41, 9. (2) (a) Hammarstrom, L.; Almgren, M.; Norrby, T. J . Phys. Chem. 1992, 96, 5017. cb) Hammarstrom, L.; Almgren, M.; Lind, J.; MerCnyi, G.: Norrby, T.: Akermark, B. J . Phys. Chem. 1993, 97, 10083. (c) Hammarstrom, L.: Berglund, H.; Almgren, M. J . Phys. Chem. 1994, 98, 9588. (d) Hammarstrom, L.; Almgren, M. in Proceedings of the 2nd International Conference on Solar Energy Storage and Applied Photochemistry, Cairo, 6-11 Jan 1993; published in Proc. Indian Acad. Sci. (Chem. Sci.) 1993, 105, 539. (3) For recent reviews on transmembrane electron transfer in vesicles, see: (a) Robinson, J. N.; Cole-Hamilton, D. J. Chem. SOC. Rev. 1991, 20, 49. (b) Lymar, S. V.: Parmon, V. N.; Zamaraev, K. I. Photoinduced Electron Transfer Ill; Topics in Current Chemistry, Vol. 159: SpringerVerlag: Berlin, 1991; pp 1-66. (c) Hurst, J. K. In Kinetics and Catalysis in Microheterogeneous Systems; Surfactant Science Series, Vol. 38; Gratzel, M., Kalyanasundaram, K., Eds.; Marcel Dekker: New York, 1990; p 183. (d) Gratzel, M. Heterogeneous Photochemical Electron Transfer: CRC Press: Boca Raton, 1989. (4) McQuame, D. A. Adv. Chem. Phys. 1969,15, 149. (5) (a) Almgren, M. J . Am. Chem. SOC.1980, 102,7882. (b) Almgren, M.: Swarup, S. Chem. Phys. Lipids 1982, 31, 13. ( 6 ) Kuhn, E. R.: Hurst, J. K. J . Phys. Chem. 1993, 97, 1712. (7) See e.g.: Lange, Y . In Handbook of Lipid Research; Small, D. M., Ed.; Plenum: New York, 1986, p 523. (8) Kosower, E. M.; Cotter, J. L. J . Am. Chem. SOC. 1964, 86, 5524. (9) Rothenberger, G.; Infelta, P. P.; Gratzel, M. J. Phys. Chem. 1981, 85, 1850. JP9508 12V
