J. Phys. Chem. 1983, 87, 399-407
core is -20 A and furthermore, at the higher [Pt] the reaction observed in their time-resolved experiments is primarily the charging reaction 1 with the bare metal surface and before an appreciable amount of H2 is adsorbed. Miller and McLendonebprepared Pt-PVA colloids by the same method of Kiwi and Gratzel and with moderate centrifugation have obtained hydrodynamic radius of 360 A (asmeasured by the latter authorsg) and Pt core radius of 300 A,measured by electron microscopy. Such a large radius for the Pt core would then yield extremely low particle concentration M) and preclude any particle-particle collision during the reaction. On the other hand, for this method of preparation, Kiwi and Gratzel found 20% of the initial amount of Pt colloid before centrifugation had an hydrodynamic radius of 110 A and our calculations above indicate a core radius of -20 A. With the same preparation method Miller and McLendon should have more than 20% such small particles in their partially centrifuged samples. For 40% by weight the concentration of 20-A particles would be (for 6 pM Pt) 1.1 X lo4 M [(Pt),]. With 1/2kd= 3.4 X lo9 M-I s-l calculated above for these particles, this concentration gives a rate of particle-particle encounters of 3.8 s-l, and an even higher rate for encounters of 1.1X M 20-A particles with 0.5 X 10-l2M 3 0 0 4 particles. Miller and McLendon give a first-order rate constant for MV+ disappearance in 6 pM Pt of 0.078 s-l.
399
Our conclusion is that in our experiments (well below pHlI2)using the preparation methods of Brugger et al.1° the particle-particle interaction can reasonably explain the [PtI2dependence. Further, if the Miller and McLendon preparation is similar to that of Kiwi and Gratzel, then a number of particle-particle collisions occur during the reaction of MV+ in their experiments and our hypothesis may be applicable. Using our theory, we calculate a vs. 0.078 measured. first-order rate constant of 0.29 However, as this experiment appears to be near pH1 2, we have probably used too high a value for k l (lo1' M-( s-l), and our simple kinetic theory needs modification. If particle-particle collisions occur frequently during MV+ oxidation, then the proposed thin-cell a n a l o d b loses significance in expIaining the [Pt] dependence. However, this thin-cell reaction may be totally dominated by pairs of particles which are essentially in collision so that at any moment the number of such pairs is proportional to the collision rate, i.e., proportional to [PtI2.
Acknowledgment. We are much obliged to D. Ficht and G. Cox for their dedicated operation of the linac. Support of this research by a NATO Research Grant No. 1780 to E.P. and D.M. is gratefully acknowledged. Work at ANL is performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Science, US.DOE, under Contract No. W-31-109-ENG-38. Registry No. H2, 1333-74-0;Pt, 7440-06-4; MV+, 25239-55-8.
One-Electron Transfer Equilibria and Kinetics of N-Methylphenothiazine in Micellar Systems Claudlo Mlnero,+ Edmondo Pramauro, Ezlo Pellzzetti, Istituto di Chimica Anaiitica, Universiti di Torino, 10 125 Torino, Italy
and Dan Melsel" Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received September 20, 1982)
The kinetics and equilibria of electron transfer between N-methylphenothiazine and aquoiron(II1)or octacyanomolybdate(V) in the presence of various micellar-forming surfactants (CTAN,Triton, SDS) were investigated by using several spectrophotometric techniques. The presence of micelles strongly influences the equilibria and the kinetics of the reactions. Binding constants are determined and electrostatic and hydrophobic effects in the various micellar systems are analyzed.
Introduction Electron transfer reactions involving phenothiazine derivatives are currently under intensive investigations. The interest in this class of compounds stems from their exceptional photoredox properties' as well as from their physiological activity.2 Micellar effects on the electron transfer reactions of these compounds are of relevance to both these areas of interest. On one hand, micelles are often used as model systems to mimic cellular membranes while the interactions of the phenothiazine drugs with such membranes may affect their therapeutic properties. On the other hand, several phenothiazine derivatives have been used in micellar or vesicular designs for photochemPresent address: CISE, Segrate (Milano), Italy.
ical energy storing systems. In view of this widespread interest we report here on the effects of micelle-forming surfactants on the equilibrium and kinetics of the electron transfer reactions between N-methylphenothiazine (MPTZ) and aquoiron(II1) or octacyanomolybdate(V). Although micellar effects on electron transfer rates have been extensively studied, reports on their effects on oneelectron transfer equilibria are rare. Kinetic studies have already provided a wealth of information on the mechanistic details of the micellar effects on electron transfer reaction^.^!^ When kinetic effects are combined with redox (1) Infelta, P. P.; Gratzel, M.; Fendler, J. H. J. Am. Chem. SOC.1980, 102, 1479. Moroi, Y.; Infelta, P. P.; Gratzel, M. Ibid. 1979, 101, 573. (2) Forrest, I. S.;Cam, C. J.; Usdin, E. Adu. Biochem.Psychopharmcol.
1974, 9. Gasco, M. R.; Carlotti, M. E. Pharm. Acta Helu. 1977,52, 296.
0022-3654/83/2087-0399$01.50/00 1983 American Chemical Society
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The Journal of Physical Chemistry, Vol. 87, No. 3, 1983
equilibria studies of the same redox systems, the contributions of electrostatic and hydrophobic interactions could be e ~ a l u a t e d . ~Simultaneous determinations of both equilibrium and rate parameters of organic radicals are rather scarce. So far the only reported micellar effects on redox equilibria and rates of radicals are those of sodium dodecyl sulfate micelles effects on several quinone/semiquinone couples.* The present report extends such studies to redox equilibria between an organic radical cation and some inorganic complexes.
Experimental Section Reagents. N-Methylphenothiazine was obtained from Pfalz and Bauer and purified by recrystallization from Ar-saturated ethanol. The purified material had a melting point of 99 "C (lit. mp 100 "C). Iron(II1) perchlorate or nitrate (C.Erba) was used as received and standardized by complexometric titrations. A stock solution of iron(I1) perchlorate was prepared by dissolving a pure iron wire in perchloric acid and was standardized by oxidimetric titration. Iron(I1) sulfate (C.Erba) was standardized by the same procedure. Octacyanomolybdate(1V) was prepared according to the procedure described in the literature6 and the corresponding MoVderivative was obtained by electrooxidation. Sodium dodecyl sulfate (SDS) was purified by recrystallization; hexadecyltrimethylammonium nitrate (CTAN) was prepared from the corresponding bromide by passing a solution of the bromide through an ion-exchange resin and was then recrystallized; Triton X-100 (Baker) was used without further purification. All other inorganic salts were of analytical grade and their solutions were standardized according to usual titrimetric procedures. Water used throughout this study was doubly distilled. Spectrophotometric Measurements. UV-visible spectra were recorded on a Cary 219 spectrophotometer. The molar absorptivity of the cation radical, MPTZ', was determined by oxidizing MPTZ with hexachloroiridate(1V) or cerium(1V) sulfate, oxidants which ensure complete oxidation of MPTZ. Kinetic Measurements. Most of the kinetic runs were carried out on a Durrum-Gibson stopped-flow spectrophotometer. Concentrations of MPTZ were in the range of (1-6) X loW5 M, while the concentrations of the oxidants were dependent on the surfactant system. The following experimental conditions were employed: in SDS and Triton, [HC104]= 0.010 M and p = 0.10 M (NaC104),while in CTAN [HNO,] = 0.010 M and p = 0.10 M (NaNO,) or p = [HNOJ = 0.10 M. All kinetic experiments were performed at 25.0 f 0.1 O C . When possible, the concentrations of both FeIn and Fen were high enough to ensure pseudo-first-order conditions for reaction 1. Under these conditions, plots of In ( A , Fe"'
kl + MPTZ r Fe" + MPTZ' k-1
(1)
A,) (where A , and A, represent the absorbances at equilibrium and at time t , respectively) as a function of time, (3)(a) Bhalekar, A. A.; Engberts, J. B. F. N. J. Am. Chem. SOC.1978, 100, 5914. (b) Bruhn, H.; Holzwarth, J. Ber. Bunsenges. Phys. Chem. 1978,82,1006.(c) Bunton, C. A.; Cerichelli,G. Int. J.Chem. Kinet. 1980,
12,519. (d) Ponganis, K.V.; DeArujo, M. A.; Hodges, H. L. Imrg. Chem. 1980,19, 2704. (e) Meisel, D.;Matheson, M.; Rabani, J. J. Am. Chem. SOC.1978,100, 117. (f) Pelizzetti, E.;Pramauro, E. Inorg. Chem. 1980, 19, 1307. (9) Almgren, M.; Grieser, F.; Thomas, J. K. J. Phys. Chem. 1979,83,3232. (4) Pelizzetti, E.; Pramauro, E. Ber. Bunsenges. Phys. Chem. 1979,83, 996. (5)Pramauro, E.;Pelizzetti, E.; Diekmann, S.; Frahm, J. Inorg. Chem. 1982,21, 2432. (6)Furman, N. H.; Miller, C. 0. Inorg. Synth. 1950,3,160.
were linear for at least 90% of the reaction. The slopes of the plots define pseudo-first-order rate constants (kow) for the approach to equilibrium. Since kobsd= k,[Fe"'] + k-,[Fe"] a plot of kobsd/[Fen]as a function of [Fern]/ [Fen] gives the second-order rate constants kl as the slope and k-, as the intercept of this line. For reaction 2 in the presence of SDS comparable conMo(CN):-
ka
+ MPTZ
k-2
Mo(CN):-
+ MPTZ+
(2)
centrations of both reactants were used due to the rapidity of the reactions. The proper kinetic equations were adopted in order to obtain the specific rate ~onstants.~ The standard deviations of each of the rate constants were in the range 5-8%. Some of the kinetic results, in particular those that were too fast for the time resolution of the stopped-flow technique, were obtained with the pulse-radiolysis technique. Details of the ANL linac systems have been previously described and a similar strategy for preparation of the radicals was presently assumed.29 Briefly, electron pulses of 2-4-11s duration were used to produce 1-2 pM total concentration of radicals, which were detected by the conventional spectrophotometric technique. The solvated electrons, eaq-]which are produced on the radiolysis of aqueous solutions were all converted to OH radicals by reaction with N20 (all solutions in these experiments were deaerated and N 2 0 saturated). The OH radicals would then react either with Br- (0.2 M NaBr in all of these experiments) or with ethyl alcohol according to the following two pathways: OH OH(H)
+ Br-
Br-
+ CH3CH20H
Br2- + OH-
CH,CHOH
+ H 2 0 (H,)
The presence of the alcohol (0.17 M in all of these experiments) was dictated by the low solubility of MPTZ in the absence of micelles. The hydrogen atoms reacted similarly to produce the alcoholic radicals, the fate of which is unknown in these systems, although it was verified that they have no effect either on the reactions or on the stability of the other radicals or complexes of the system of interest. Note that due to the requirements of the radiolysis experiments the chemical composition of the solutions is not identical with that in the other experiments. Nevertheless, similar results were obtained from the different techniques when similar ionic strengths were employed. Solutions to be irradiated contained MPTZ and Mo(CN):- at different ratios of concentrations, thus the B r i (A, = 360 nm, e- = 1.2 X lo4M-l cm-') would react with either one of them to produce either MPTZ' or Mo(CN)*,-. The rate constant for the reaction of Br2-with MPTZ was found to be 2.3 X lo9 M-l s-l, close to the values previously obtained for similar N-alkylphenothiazines29 while the rate constant with M O ( C N ) ~is~ much slower ((1.0 f 0.2) X lo' M-' s-l). The rate of approach to equilibrium could then be followed under pseudo-firstorder conditions. Typical computer-processed results of these experiments are shown in Figure 1. In the presence of SDS M), the observed rate constant for the reaction of Br2- with MPTZ decreased monotonically (2.3 X los M-l s-l in 0.01 M SDS to 6 X lo7 M-' s-l in 0.1 M SDS), indicating that this reaction occurs with the fraction of MPTZ that is unbound to the micelles rather than at the interface. Gel Filtration Chromatography. The binding constants of MPTZ to CTAN and SDS micelles were determined by
The Journal of Physical Chemistry, Vol. 87, No. 3, 1983
N-Methylphenothiazine in Micellar Systems I
I
1
1
1 0 2 x [SDS], M
2
0.005f
i
I
If
401
4
6
2
I .o
I
3.5
I
?O
-\>a >-
IO3 x [CTAN], M
Flgwe 2. Pbts of V,/(V , - V,) vs. surfactant concentration: (0)CTAN (bottom and left scale); (A)SDS (top and right scale). I, msec
surfactant, [D] is the molar concentration of the surfactant which exceeds the critical micelle concentration, KD is the "molecular sieving" constant which is equal to the ratio
of solute concentration in the imbibed liquid to its concentration in the nonmicellar portion of the external liquid, and k 'is the proportionality constant between the solute adsorbed per unit volume of gel matrix and the equilibrium concentration of monomer solute in the liquid. Since the binding constant, KB, is related to the partition coefficient through the expression KB = ( P - 1) P,lothe slope/intercept ratio in the plots according to eq 3 provides in principal a method for determination of KB (cf. Figure 2). As can be seen in Figure 2 above the cmc's the experimental results are indeed governed by eq 3, while below the cmc the poor solubility of MPTZ renders determination of the intercept very inaccurate and prevents us from obtaining reliable results. Intersections of the lines in Figure 2 with the abscissa define the critical micellar concentrations of CTAN and SDS in the presence of solute and Sephadex G-25. The cmc's are greater than those determined for the surfactants alone. Such differences may arise from effects of the solute or the gel on the cmc's. However, although it is difficult to estimate the absolute binding constants from the ratios of slope to intercept, the ratio KBCTAN/KBSDS can be evaluated from the slopes ratio. This value is 15 f 1. Surface Tension Measurements. The bulk phase concentration at the point of the intersection of the two linear portions of the plots of y vs. log C was taken as the critical micellar concentration, in the different experimental conditions. For CTAN, in absence of added electrolytes, a value 9.0 X 10"' M was obtained, in agreement with the literature value.'l In the presence of the reactants and at the experimental ionic strengths, the cmc's are lowered to (4.0-4.5) X M (0.10 M nitrate; slightly dependent on reactant concentration). For Triton X-100, cmc = 2.2 X 10"' (in the presence of the reactants and 0.10 M perchlorate) and for SDS, cmc = 8.3 X lo4 M (at the highest Fe3+concentration and 0.10 M perchlorate) were obtained. Changes in cmc's are often caused by electrolytes and solubilizates.12 Spectral and Equilibrium Data. The molar absorptivity of MPTZ+ at 515 nm was measured to be (9.3 f 0.4) X lo3 M-' cm-'. The equilibrium quotients evaluated spectro-
(7) Frost, A. A.; Pearson, R. G. "Kinetics and Mechanisms";Wiley: New York, 1961. (8) Ackers, G. L. Adu. Protein Chem. 1970,24, 441. (9)Herries, D.G.; Bishop, W.; Richards, F. M. J . Phys. Chem. 1964, 68,1842.
(10) Berezin, I. V.;Martinek, K.; Yataimirskii,Y. A. RUSS.Chem. Reu. (Engl. Transl.) 1973, 42, 787. (11) Mukerjee, P.; Mysels, K. T. Natl. Stand. Ref. Data Ser., Natl. Bur. Stand. 1971, No. 36. (12) Rosen, M. J. "Surfactant and Interfacial Phenomena"; Wiley: New York, 1978.
Figure 1. The pulse radiolytic method of producing the radicals and kinetic measurements of the approach to equilibrium 2. (a) 1 X M MPTZ, no Mo(CN),~; (b) same as a on addition of 2 X lo-' M MO(CN),~. Both contain 0.2 M NaBr, 0.17 M EtOH, N20saturated; A = 520 nm. Solid line is least-squares best fit to formation of MPTZ' in a and to formation of MPTZ' followed by its reaction with MO(CN),~ both assuming pseudo-first-order kinetics.
gel filtration on a Sephadex G-25 column (1.6 cm diameter and 35.3 cm height; V, = 71 ~ m ~ With ) . ~Blue Dextran 2000 the void volume, Vo,and the sum of void and imbibed volume, Vo+ Vi, of the packed column were determined to be 29.5 and 65.1 cm3, respectively. Prior to each run the column was equilibrated overnight with the appropriate eluent. The runs were initiated by the addition of 0.5-1.0 mL of a solution of MPTZ in the presence of the appropriate surfactant concentration. Fractions of 0.2-0.5 mL were collected by means of an automatic fraction collector and the absorbances at 256 nm of each fraction were monitored spectrophotometrically. All runs were carried out at 22 f 1 "C. Surface Tension Measurements. A Dognon-Abribat tensiometer with platinum blade was employed. Calibration of the apparatus was checked by measuring the interfacial tension of triply distilled water. The critical micellar concentrations (cmc) were determined by plotting the surface tension against the logarithm of the surfactant concentration.
Results Binding Constants of MPTZ. It has been shown in gel filtration chromatographyg that the observed elution volumes, V,, and the partition coefficient, P, of the solute between the micellar and aqueous phase are related through eq 3, where P is the partial molar volume of the
402
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The Journal of Physical Chemistry, Vol. 87, No. 3, 1983
TABLE I: Kinetic and Equilibrium Data For Reaction 1 in the Presence and Absence of CTANa
0.8
1.o 1.3 1.6 2.0 2.5 3.2 4.0 5.0
8.0 10.0
[ H + ] = 0.01M, p = 0.10 M, Nitrate 220 130 1.7 11.4 140 0.081 9.3 140 0.066 7.1 140 0.051 6.1 130 0.047 5.0 130 0.038 4.4 120 0.036 3.3 120 0.028 120 0.017 2.0 1.5 130 0.012 140 140
[H+] =p 2 x 10-3 6X 1x
320 5.2 2.1
2.2 0.068 0.061 0.050 0.042 0.034 0.030 0.024 0.018 0.013
2.9 0.043 0.018
8 10 30 40 60 80 100
0.010
20 50
0.008
= 0.10M, Nitrate
110 120 120 100
TABLE 111: Equilibrium and Rate Constants For Reaction 2 in the Absence and Presence of SDSa
3.6 0.046 0.020
0.010
Each kinetic or equilibrium data point is an average over 6-8 different [ F e 3 + ] / [ F e z +ratios. ] Accuracy of the kinetic and spectrophotometric results is t 10%. Measured spectrophotometrically at equilibrium. a
TABLE 11: Kinetic and Equilibrium Data For Reaction 1 in the Presence and Absence of Triton X-100' [Triton
Each data point averaged over 6-8 different [ F e 3 + ] / [ F e z'1 ratios.
photometrically were in quite good agreement with those kinetically derived. For equilibrium 1,the following values were estimated in the absence of surfactants: K 1 = 3.2 f 0.3 ([H+] = 0.01 M, p = 0.10 M, perchlorate) and K 1 = 1.9 f 0.2 ([H+] = 0.01 M, p = 0.02 M, perchlorate); K 1 = 2.2 f 0.2 ([H+] = 0.01 M, p = 0.10 M, nitrate) and K1 = 3.6 f 0.3 ([H+] = p = 0.10 M, nitrate). For equilibrium 2, K 2 = 3.0 f 0.4 ([H+] = p = 0.10 M, perchlorate) and K 2 = 0.9 f 0.2 ([H+] = p = 0.02 M, perchlorate]. Kinetics in Absence of Surfactants. Because of the low solubility of MPTZ, the kinetic runs in absence of surfactants were carried out in 10% v/v of ethanol (except in the pulse radiolysis measurements). The second-order rate constants under these conditions can be assumed to be the values in water in the absence of surfactants. Plots of kObsd/[Fe"]as a function of [Fe"']/[Fe"] are linear and yield k , = (2.4 f 0.3) X lo2 M-I s-, and k-l = (1.0 f 0.2) X lo2 M-ls-l (0.1 M perchlorate); kl = (2.2 f 0.3) X lo2 M-I and k-, = (1.3 f 0.2) x lo2 M-' s-l (nitrate, [H+]= 0.01 M); k , = (3.2 f 0.4) X lo2 M-'& and k-, = (1.1f 0.2) X lo2 M-l s-l (nitrate, [H+] = 0.10 M). For reaction 2 we obtain k 2 = (9.6 f 0.9) x lo7 M-'s-l and k2= (3.3 f 0.4) X lo7 M-'s-I in 0.2 M NaBr. Kinetics and Equilibria in Presence of Micelles. The specific rate constants and the equilibrium quotients for
[H'] = 0.02 M, Perchlorate 0.9 27 29
a Each value is an average over 5-7 ratios of [Mov]/ [ M O ' ~ ] . Spectrophotometrically measured at equilibrium. ' Measured by pulse radiolysis in 0.2 M NaBr.
TABLE IV: Kinetic and Equilibrium Data For Reaction 1 in the Absence and Presence of SDSa
8.0 X 1.0x
1.6 x 2.0
[H'] = 0.01 M, g = 0.10 M , Perchlorate 240 100 2.4 0.55 70 1.0 38 0.35 77 1.3 27 77 0.27 1.6 21 0.23 82 2.0 19 0.20 82 2.5 16 0.12 82 3.2 10 92 0.10 4.0 9.3 83 0.081 6.6 5.0 85 0.060 5.1 6.5 90 4.3 0.048 8.0
[ H + ] = 0.10M , Perchlorate 3.0 96' 330' 17 16 11.5' 7.2c 16 7.7 4.8 16 5.5 3.4 14 3.3 2.3 15 2.5 1.7 15 2.1 1.4
2.5 3.2 4.0 5.0 6.5 8.0
x x x
x
x
x x
1.0x
1.6 X 2.5 X 1.0x 6.5 X 1.0x
[HI] = 0.01M, p = 0.10 M, Perchlorate 2.4 X 10' 1.0 X 10' 2.4 9.4 X l o 3 0.88 8.3 X l o 3 10-3 1.6 x 104 1.6 x i o 4 1.00 10-3 2.0 x 105 2.2 x 105 0.91 10-3 2.7 x 105 3.0 x 105 0.90 10-3 3.4 x 105 3.5 x 105 0.97 10-3 3.8 x 105 3.6 x 105 1.05 3.0 x 105 3.3 x 105 0.91 10-3 2.9 x 105 3.0 x 105 0.97 10-3 2.6 x 105 2.5 x 105 1.04 10-3 1.8x 105 2.6 x 105 0.69 10-2 1.6 x 105 1.9 x 105 0.84 10.' 9.1 X l o 4 1.5 X l o 5 0.61 10.' 6.6 X l o 4 1.1 X l o 5 0.60 10-2 4.5 x 104 7.0 x 104 0.64 2.6 X l o 4 5.2 X 10' 0.50 10-1 1.9 x 104 3.8 x i o 4 0.50
3.2 0.87 0.98 0.85 0.93 1.03 1.01 1.02 0.99 1.05 0.95 0.92 0.76 0.62 0.58 0.62 0.60
' Each value averaged over 5-10 ratios of [Felll]/[Fell] for SDS > 5 . 0 x 10.' M. Spectrophotometrically measured under equilibrium conditions. ' The same experiments at [H+&; 0.01M and 0.02 M NaC10, yield Ky = 1 . 9 and K l , e x p t= 0.63 0.07 in 1O-'M < [SDS] < 0 . 1 M. equilibrium 1 in the presence of CTAN, Triton, and SDS and for equilibrium 2 in SDS are summarized in Tables I-IV.
Discussion Reaction Rates i n the Absence of Surfactants. It was previously reported13that the electron transfer rate constants for a series of N-alkylphenothiazines and Fe"'/Fe" show a dependence on the free energy of the reaction, which follows the Marcus theory.14 The presently obtained kl and It-, are very close to the expected values, thus the intrinsic parameters of the MPTZ/MPTZ+ couple can be assumed to be the same as for the other N-alkylphenothiazine^.'^ Equilibria and Reaction Rates in the Presence of Cationic Micelles. The changes of the equilibrium constant, K,, as a function of CTAN concentration is as expected for a situation where Fe3+,Fe2+,and MPTZ+ are almost entirely in the aqueous phase and MPTZ is partially bound to the micelles. The observed equilibrium (13) Pelizzetti, E.; Mentasti, E. Inorg. Chem. 1979, 18, 583. (14) Marcus, R. A. Annu. Reu. Phys. Chem. 1964, 15, 155.
The Journal of Physical Chemistry, Vol. 87, No. 3, 7983
N-Methylphenothiazlne in Micellar Systems
200
403
1
o.2
r
I
I
1
I
4
2 4 103x [ C T A N ] , M
I
0
IO3 x [ C T A N ] , M
q/e,FG
Flgure 3. Plot of vs. CTAN concentration (equilibrium constants spectrophotometrically obtained).
Scheme I
constant @$ :, is then related to the equilibrium constant in the absence of the surfactant, through eq 4, where
e,
PTAN 1,espt
t
Figure 4. Plot according to eq 6a for the kinetic data of reaction 1 In the presence of CTAN.
A satisfactory linearity is obtained on plotting l / ( k y k?,):; as a function of 1/[D], as expected from eq 6. However, the intercept in such a plot yields a value which is very close to l/ky. Thus, the rate constant for MPTZ which is solubilized in the micelle to react with Fe3+at the interface, i.e., kyTAN,is much smaller than ky. Equation 6 can therefore be rewritten as
or, since G T A N [ D>> ] 1, eq 5 can be simplified to
T m n i
= 1
+ GTAN[D]
b W
(4)
GTAN represents the association constant for MPTZ with CTAN and [D] the concentration of surfactant which exceeds the cmc. The value of the association constant is obtained b lotting as a function of [D] (Fig(2.8 f 0.5) X lo4 M-' (nitrate, [H+] = 0.01 ure 3), %"= M; &" spectrophotometrically evaluated). In nitrate, a = (2.5 f 0.6) X lo4 M-I. [H+] = 0.10 M, The kinetic runs have been performed at large excess of [Fe3+]and [Fez+]over [MPTZ]. As can be seen in Table I, k-, is virtually independent of CTAN concentration, and its value is close to that evaluated in the absence of surfactant. This observation serves as further support that there is no interaction between MPTZ+ and the cationic micelles. The kinetic behavior can be analyzed according to Scheme I for micellar i n h i b i t i ~ n .Since ~ ~ it was shown that the rate of entrance and exit of solubilizates in and out of the micelles occurs in the microseconds time scale, it is clear that the MPTZ equilibration between the aqueous and micellar subphases is achieved much faster than the rate of approach to equilibrium of reaction 1. This model leads, therefore, to the following equation for the total forward reaction: kf + kyTANGTAN[D] kCTAN = (5) 1,expt 1 + GTAN[D] where ky and k P A Nrepresent the rate constants in the aqueous and cationic micellar pseudophase, respectively. Equation 5 is usually written in the reciprocal form15 1 -l + 1 (6) ky kf - kFTAN (kf - kyTAN)GTm[D]
q/@,zxT
aTAN
kyzxT
(15) Menger, F. M.; Protnoy, C. E. J.Am. Chem. SOC.1967,89,4698.
KCTAN 1,expt
i
'"I I = kCTAN + ___ -
1
GTAN [D1
From a plot according to eq 6a, a value of GTAN = (2.6 f 0.5) X lo4 M-l, close to those previously reported, is obtained. On the other hand, a plot according to eq 6b does not provide a reliable estimate of kyTAN(see Figure 4).
It is worthwhile to note that the reaction rate between Fe3+in the bulk and MPTZ associated with the cationic micelles is decreased by more than three orders of magnitude in respect to its rate in aqueous solution. This strong inhibition can be attributed to the electrostatic repulsion between Fe3+and the positively charged micellar surface. The kinetic results at [H+] = 0.10 M are also in agreement with the above scheme. Kinetics and Equilibria in Nonionic Micelles. As in the previously described systems, the kinetic runs were performed at large excess of [Fe3+]and [Fe2+]over [MPTZ]. The observed rate constant for the backward reaction does not change significantly with surfactant concentration (see Table 11)and its value is close to that obtained in aqueous solution (perchlorate medium), Le., k-, = 82 f 7 M-ls-l in the Triton solution. This is a rather interesting observation since it indicates that the interaction between the radical-cation MPTZ+ in the CTAN micelles is not merely an interfacial electrostatic repulsion. Apparently, the solubility of MPTZ+ in water considerably exceeds its solubility in the less polar micellar pseudophase. Nevertheless, the decrease in the binding constant of MPTZ to Triton X-100 as compared to that of CTAN (see below) indicates that both electrostatic and hydrophobic interactions contribute to the interactions of the parent molecule and its radical cation with the micelles. As a consequence of the lack of an effect of the micelle concentration on k-l, a similar analysis to the one described
404
The Journal of Physical Chemistry, Vol. 87, No. 3, 1983
Minero et ai.
Scheme I1
h 4
/
l
I
8
IO'x [Triton], M
Flgure 5. Plot according to eq 4 for reaction 1 in the presence of Triton.
50
t-
40
c
1 4
I
I
8
IO2 x [SDS], M
,I
Flgure 7. Plot according to eq 6a for reaction of 2 in SDS.
aDs
binding constants of MPTZ and MPTZ+, and PBP, respectively, through eq 7. As can be seen in Table 111, I
-/
is independent of the concentration of SDS for [SDd] L 8 X M. This indicates that both a ? s [ D ] and than 1 and thus eq 7 can be = G?'/@BDS. From Table I11 one 5 f 1 ([Hi] = 0.1 M) and 30 f 3 ([H+]= 0.02 M). It should be noted that the ratio P B D S also represents the decrease in the reduction potential of the MPTZ/MPTZ+ couple on micellization. As has previously been s h o ~ n , Eo(oxlrd),a ~g = Eoox/rd - (RT/F)In (KB+/KB)and thus at the lower ionic strength (0.02 M) the last term will contribute 85 mV while at p = 0.1 M the last term would contribute 40 mV to the redox potential. These values are substantially smaller than the surface potentials at the corresponding ionic strengths (110 and 80 mV, respectively28).It seems, therefore, that the change in the binding constant of MPTZ' as compared to MPTZ reflects not only the increase in the electrostatic interaction but also some decrease in its hydrophobic interaction with the micellar subphase. Furthermore, from the el filtration = experiments mentioned above, we obtain €@AN 15 and since in the previous section we derive = 2.5 X lo4 M-l, we can estimate = 1.7 X lo3 M-' and therefore GqS = 8.5 X lo3 M-I in [H+] = 0.1 M or 5.1 x lo4 M-' in [H+] = 0.02 M.18 These values may be compared with the binding constant of the N-methylphenazonium radical to SDS micelles.21 The inhibition of the rate of reaction 2 may be treated according to Scheme I1 in a manner similar to the one described above for reaction 1. Equations 5-6b are then @,:"t
1.0
0.5
D] , M-'
Flgure 6. Plot according to eq 6 b for system 1 in the presence of Triton.
in the previous section can be applied to the equilibrium and kinetic data in the Triton system. Analysis according to eq 4 would then yield = (6.4 f 0.6) X lo3 M-' (see Figure 5).16 The kinetic results conform with the predicted linearity of eq 6. However, similar to the CTAN case, the intercept in this system is also very close to l/ky,making it impossible to accurately estimate kT. If it is tentatively assumed that a [ D ] >> 1, a reasonable assumption particularly at high surfactant concentration, eq 6b provides a rough estimate of kT = 1.5 f 0.8 M-' s-l (see Figure 6). Thus, the micellar association to a noncharged surfactant inhibits the electron transfer reaction rate constant by at least two orders of magnitude. Equilibria and Kinetics in Anionic Micelles. In view of the low solubility of MPTZ in water, it is quite certain that it will interact with SDS micelles. The results described above for CTAN and Triton micelles substantiate this assumption. Furthermore, due to the interfacial negative charge and probably some hydrophobic interactions, MPTZ+ is also expected to interact with the SDS micellar phase. On the other hand, due to the high repulsive interaction, both oxidation states of the complex, M O ( C N ) ~ ~would / ~ - , be excluded from the micellar phase. Scheme I1 would then describe the system for reaction 2. Under these assumptions, the experimentally observed is related to the equilibrium constant of reaction 2, @:!p, equilibrium constant in the aqueous solution, and the
e,
(16) A binding constant of 2 X lo3 M-' was estimated for phenothiazine.' The additional methyl group increases the binding constant as expected for an additional carbon atom.I7
aDS K.,.h. aDS
(17) Tanford, C. 'The Hydrophobic Effect";Wiley: New York, 1973. (18) The binding constant of phenothiazine with SDS was estimated to be ca. 1 X 103 M-l? The present value for MPTZ is in good agreement with the increase expected for a methyl group.17Jg (19) Pramauro, E.; Pelizzetti, E. Anal. Chim. Acta 1981, 126, 253. (20) Pelizzetti, E.; Mentasti, E.; Pramauro, E. Inorg. Chem. 1978, 17, 1688. (21) Evans, C. A.; Bolton, J. R. J. Am. Chem. SOC.1977, 99, 4502.
The Journal of Physical Chemktty, Vol. 87, No. 3, 7983
N-Methylphenothlazlne in Micellar Systems
u J
t
t
water increases more than the relative rate increase of the forward reaction and thus the decrease in the equilibrium constant. A similar effect of SDS on the electron transfer reaction of the system O S L $ + / ~ + / F ~ ~(where +/~+ L = 4,4'-dimethyL2,2'-bipyridine) has been previously ob~ e r v e d .A~ similar analysis would thus be applied to the present results. Since all the reactants in the present system strongly associate with the SDS micelles, and since the rate constants in the micellar system are two orders of magnitude or more bigger than they are in water, we can safely assume that the reaction occurs primarily in the Stern layer of the micellar-water interface. The interesting point to examine quantitatively now is, therefore, whether the enhanced rates are only an effect of increased local concentrations of the reactants in the interfacial region caused by the electrostatic interactions of the counterions Fe3+J2+with the surface potential. It should be noted that since r-l is bigger than rl, contrary to expectations based solely on electrostatic considerations, for Fe3+vs. Fe2+ions, other interactions should also be considered. To evaluate the contribution of the electrostatic interactions we express the observed rate constants in the following form:
I
I
1~16~
I x If2
I x 10-
[SDSl,M
Figure 8. Plot of log r , (e)and log r-l (A)as a function of SDS concentration for reaction 1. The ratlos rl/& (0, right) and r-&t (A, left) are also shown. The f- factors have been calculated by assuming a 5-A shell, P = -85 mV, aggregation number 100, and micellar radius 22 A.502332'
applicable to both the forward and backward reactions with trivial modifications. Plots of l/k!g:pt vs. [SDS] according to eq 6a then yield k$BDs/kr = 5.4 X lo4 s (see Figure 7). From the above-determined pBDs one then derives kr = 3.2 X los M-' 8. Again, k!DS is too small to be reliably determined. Since the electron transfer reaction between a series of ZV-alkylphenothiazines and Fe3+/2+or Fe(CN)6g//' has been observed to follow the Marcus theory,l3,l4the value of ka could be predicted by using the simple self-exchange relation for the cross electron transfer rate: kY =
( ~ M P T & M ~ ) ' / ~
405
(8)
where -k and kM,, are the self-exchange rate constants of MPTZ/MPTZ+ and MO(CN)~"/*, respectively. Using the values -k = 3.5 X 108 M-' 6'(ref 13) and kMo = 1.1 X lo8 M-' s-l (ref 20) and the presently measured we can estimate k r = 3.3 X lo8 M-' s-l. Thus, the two independently calculated values of k r agree quite well with one another while they both are somewhat higher than the experimentally determined value (Table 111). The equilibrium constant as well as the rate constant for the forward and back reaction 1were also measured in the presence of SDS. Table IV summarizes these results. Both rate constants dramatically increase on addition of SDS, reach a maximum close to the cmc, and then decrease with increasing [SDS]. The equilibrium constant, however, decreases somewhat on addition of SDS and then monotonically continues to decrease when [SDS] increases. The dependence of both rate constants on [SDS] is typical for a case when both reactants (of both forward and backward reactions) interact with the micellar subphase.10.22 The increase of the reaction rate constants relative to that in water, defined as r1 = k ~ ~ ~ pand t / r-l k ~ = k!!Ftx t/k?l, are plotted in Figure 8 as a function of [SDSj. From Table IV and Figure 8, it is evident that the rate of the backward reaction in SDS relative to that in
m,
(22) Fendler, J. H.;Fendler, E. J. 'Catalysis in Micellar and Macromolecular Systems"; Academic Press: New York, 1975.
kf,:Spt = kYfFe3tfcat kSlqeSIpt = k!Bez+f t,'
(94 (9b)
where fieat and fiezt represent the increase in the rate constants, ky or kY1, due to electrostatic interactions of the corresponding ions with the micelles. These terms were calculated as the ratios between the estimated concentration at the micellar surface and the concentration of the ion if dissolved in the actual volume of the aqueous phase only. The concentration of the ions at the micellar surface is calculated according to the model of Frahm and Diekm a n B and as outlined by Pramauro et al.5 The terms fmt and fLat include all other catalytic contributions to the observed rate constant which cannot be attributed to the electrostatic binding of Fe3+/2+to the SDS micelles. When this approach was applied to the complexation reaction of Ni2+ with 2,2'-bipyridine or pyridine-2-azo-p-dim e t h ~ l a n i l i n eit, ~was ~ concluded that the increase in reaction rate observed in the presence of anionic micelles is exclusively due to the increase in the concentration of the Ni2+ions at the micellar surface. In Figure 8 the ratios rl/fie3+ and r-l/feFsezt are plotted vs. [SDS]. As can be seen in this figure, they differ significantly from 1 and the following values can be derived: fcat = 2.0 f 0.3 and f'cat = 25 f 10 (at [SDS] > 1 X M). These factors are slightly dependent on SDS concentration, probably due to changes in micellar parameters. Another distinctive feature can be noted in the present system when compared with the previously investigated equilibrium of O S L ~ ~ + / ~ + - F ~While ~ + / ~in+ the . present system both ratios, rl/feFS,S+ and r-l/pFBez+,are larger than 1, this ratio for the forward reaction is less than 1in the Os2+ reactionas In both systems, however, the nonelectrostatic contribution to the acceleration of the backward reaction is larger than to the forward reaction (turning to inhibition of the forward Os2+reaction). Concerning the equilibrium constant, if it is expressed = as ratio of the forward and reverse rate constants, (kyflestfcat) (kll;fe,",ztf',,) can be derived. It follows that by plotting ( lDs/fl) vs. ( f B F 3 + / f i e 2 + ) one can obtain the value of fcat/fIcat which expresses the variation due to micellar
eDs
(23) Frahm, J.; Diekmann, S. J.Colloid. Interface Sci. 1979, 70,440. (24) Diekmann, S.; Frahm, J. J.Chem. Soc., Faraday Trans. I 1979, 75,2199.
406
Minero et al.
The Journal of Physical Chemistry, Vol. 87,No. 3, 1983
TABLE V: Summary of Micellar Effects o n Electron Transfer Rates and Equilibria' reaction
B
A
a
a
MPTZ
b
MPTZ
C
MPTZ
d
MPTZ
e
osL;+
f
DQ
g h
+ + + + +
C
D
micelle
location of the reaction
Fe3+
f
MPTZ'
+
Fez+
cationic
bulk
Fe3+
f
MPTZ'
+
Fez+
nonionic
Fe3+
2
MPTZ'
+
Fea+
anionic
bulk (little in interface) interface
Mo(CN),3-
2
MPTZ'
+
Mo(CN);-
anionic
bulk
Fe3+
2
0s~33+
+
Fea+
anionic
interface
+ +
AQS
anionic
Mo(CN),)-
anionic
bulk and interface interface
Fe3+
anionic
bulk
AQS-
i?
DQ-
Ru(bpy),3+
+ +
Mo(CN),4-
2
Ru(bpy):+
IrC1,Z-
+
Fez+
f
1~c1,~- +
In addition t o the abbreviations used in the text the following apply: L = 4,4'-dimethyl-Z,Z'-bipyridine; DQ = duroquin-
Scheme I11 association (excludingthe electrostatic contribution of Fe3+ and Fez+);this value is ca. 0.07-0.12 (slightly dependent on ionic strength) (the same parameter for O S L ~ + /was ~+ found to be ca. 8 X 103).5 At least two kinds of explanations might be invoked to rationalize this observation. The first explanation would invoke some specific interaction of the counterions with V P T Z ~+ I r e 3 ~ ) ~ * fMpTZ+, Le2* the micelles which is bigger for Fe2+than for Fe3+. This k- Y might be either a complexation reaction with the sulfate where 2 is the ionic charge and \k the surface potential of head groups or an hydrophobic interaction. None of these the micelle. is a very attractive explanation in view of the higher staAt p = 0.10 M, using \E = -75 to -85 mV,%the ratio for bility constants that Fe3+usually exhibits over Fe2+and the electrostatic contribution of Fe2+ and Fe3+ to the in view of the pure electrostatic interaction that other binding constant should be 0.04-0.06, in good agreement divalent cations usually experience, e.g., in the case of with the experimental result and at p = 0.02, if \E is asNi2+.24The other explanation would invoke an increase sumed to be -100 to -120 mV,28 the ratio should be in the intrinsic rate constant for the electron transfer re0.01-0.02. action in the less polar medium of the micellar interface. It is worthwhile to note that, if the partition coefficient Indeed, in this respect it is worthwhile to note that the for MPTZ+ could simply be expressed as the product of electron self-exchange rate constant for MPTZ/MPTZ+ a hydrophobic and an electrostatic contribution, no change (and for PTZ/PTZ+)in acetonitrile is bigger by an order in the equilibrium constant should be observed in the of magnitude than that in water.25 On the other hand, presence of SDS. This means that the hydrophobic conthe rate constant for the electron transfer reaction between tribution is influenced by the electrostatic part. In parphenothiazine and Fe3+decreases with increasing alcohol ticular by comparing the data for eq 2 at different ionic content in a series of alcohol-water mixtures.26 strengths, it may be observed that the increase in the In the conventional analysis of micellar catalysis, the binding constant for MPTZ+ in going from p = 0.10 M to equilibrium quotient for reaction 1 can be analyzed in p = 0.02 M is very close to what is expected on the basis terms of the various binding constants according to of the electrostatic contribution; then the charge decreases Scheme 111. the hydrophobic contribution by a factor of ca. 5 in the Scheme I11 then yields eq 10. Since for [SDS] 2 overall binding constant of MPTZ+ with anionic micelles. (1 + a q S [ D ] ) ( 1+ a @ + [ D ] ) (10) Conclusion Dl)(l + a%'3+[DI) Table V qualitatively summarizes those one-electron M, the value of @,Spt does not chan e significantly (Table transfer reactions for which the micellar effects on both IV), it can be assumed that the K$s[D] terms are much kinetic and equilibrium parameters were measured. It is bigger than 1. E uation 10 then simplifies to @;&,Jfl interesting to compare first the effects of the various in= (G?s/K","s)(&$@y3+). From the values deterteractions on the location of the reaction. Exclusion of one mined above for BDs/@ one can then deduce reactant from one of the subphases could divert the reA$DL*+/@$i3=+0.04 (at [H+] = 0.10 M) and 0.01 (at [H+] action primarily to the other phase. Whether the reaction = 0.01 M and 0.02 M NaC104). occurs at the interface or the bulk will be determined by The electrostatic contribution to the micellar binding the relative contributions of these interactions (e.g., recan be estimated from10n27 action g vs. h in Table v). The only reaction in Table V which has an appreciable contribution from both subPes = e-29/25.69 (at 25.0 "C) (11) phases to its rate is reaction f.
-
(25)Kowert, B. A.;Marcoux, L.; Bard, A. J. J. Am. Chem. SOC.1972, 94,5538. Sorensen, S.P.; Bruning, W. H. Ibid. 1973, 95,2445. (26)Pelizzetti, E.;Pramauro, E. Trans. Met. Chem. 1981, 6,334. (27)Davies, J. T.In "Surface Phenomena in Chemistry and Biology"; Danielli,J. F.; Pankhurst, K. G. A,; Riddiford, A. C., Ed.; Pergamon Press: Oxford, 1958.
'p
(28)Fernandez, M. S.;Fromherz, P. J. Phys. Chem. 1977, 81, 1755. Stigter, D. J. Colloid. Interface Sci. 1967, 23, 379. (29)Pelizzetti, E.;Meisel, D.; Mulac, W.; Neta, P. J . Am. Chem. SOC. 1979, 101, 6954.
(30) Pelizzetti, E.; Pramauro, E. Inorg. Chem. 1979, 18, 882.
The Journal of Physical Chemistry, Vol. 87, No. 3, 1983 407
N-Methylphenothiazine in Micellar Systems
catalytic effect forward
interaction of the reactant/product with the micelle back
A
B
C
D
ref
inhibition
no effect
hydrophobic
electrost repl
inhibition
no effect
hydrophobic
hydrophobic and electrost accel inhibition
hydrophobic and electrost accel inhibition
hydrophobic
hydrophobic excl electrost attr
hydrophobic
electrost repl
electrost accel and hydrophobic inhibition hardly any
electrost and hydrophobic accel hardly any
electrost and hydrophobic attr hydrophobic
electrost attr
hydrophobic and electrost attr electrost repl
electrost repl
30
electrost attr
5
inhibition inhibition one; AQS = anthraquinonesulfonate.
electrost repl
electrost repl and electrost repl hydrophobic excl hydrophobic excl hydrophobic excl electrost and electrost attr hydrophobic attr electrost and electrost repl hydrophobic attr electrost and electrost attr hydrophobic attr electrost repl and hydrophobic attr
electrost repl and hydrophobic attr
b b
b b 5 3g
This work.
A large amount of effort in this study was devoted to quantitatively determine the relative contribution of electrostatic interactions (concentration effect) and of hydrophobic interactions. However, it becomes clear from the present study, as well as from a previous s t ~ d ythat ,~ the electrostatic interactions affect the hydrophobic ones thus making the distinction between the two somewhat artificial. Furthermore, it is most interesting to note that, although the contribution from electrostatic and hydrophobic interactions could quantitati,vely be determined, their individual effect on the reaction rate cannot be predicted at present. Thus, while for reaction c both the forward and backward rates are hydrophobically accelerated, the forward rate of reaction e is hydrophobically inhibited (note that the rate of the back-reaction e is hydrophobically accelerated). Perhaps a better understanding of the factors controlling electron transfer rates at the interface would allow a more definitive prediction of these changes in rates. Thus in reaction e the decrease in the equilibrium constant in SDS micelles5could account
for the hydrophobic inhibition of the forward rate. On the other hand, in reaction c the change in free energy of the reaction could not account for the rate change. Probably for this reaction the exchange rate (eq 8) of the MPTZ/ MPTZ+couple is strongly increased by the solvent polarity changes at the interface. Indeed more than an order of magnitude increase in the MPTZ/MPTZ+ exchange rate was observed on decreasing the polarity from water to a~etonitrile.~~
Acknowledgment. E.Pe. and D.M. gratefully acknowledge NATO Grant No. 1780. Part of this work was performed as the thesis of C.M. at the University of Torino. Work at Argonne National Laboratory is performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Science, U.S. DOE, under Contract No. W-31-109-ENG-38. Registry No. Fe3+,2007452-6; MO(CN)~&, 17845-99-7;MPTZ, 1207-72-3; CTAN, 37114-85-5; SDS, 151-21-3; Triton X-100, 9002-93-1.
