J . Phys. Chem. 1984, 88, 1449-1454 where S represents M C H or 2MB. Pyrene captures an electron and a hole to form a pyrene anion ( P i ) and a pyrene cation (Py+) (reactions 13 and 14). Since the pyrene anions decay by a composite first-order reaction, they decay by recombination with cationic species, such as the pyrene cation and the solvent cation (S’), in a spur. Figure 7 shows that the decay-rate constant of pyrene cations coincides with that of pyrene anions, indicating the occurrence of reaction 15. The apparent activation energy for the decay of pyrene anions at 95-89 K is 26 kcal/mol, which is much higher than the activation energy for the tunneling neutralization. Thus, the tunneling neutralization may not play an important roll in the decay of pyrene anions. Figure 7 shows that the decay-rate constants of pyrene anions can also be expressed by the following Doolittle-type equation:
kso log T
--89.35 T-80
+
3,372
where kSois expressed in units of s-l. The plots of log (k75/7‘)
1449
and log ( k , , / T ) coincide well with the curve of eq 16 for log ( k s o / q . Thus, the temperature effect on the decay-rate constant is expressed by eq 16. It is noted that Tdo(80 K) in eq 16 is consistent roughly with the glass transition temperature (8 1 K) of the MCH-2MB mixture, which was estimated by extrapolation from glass transition temperatures of pure MCH and 2MB.I’ The viscosity of the MCH-2MB mixture was reported for 103-104 K.19 The log ( k / T ) for pyrene anions does not agree with log 7-l at high temperatures.
Acknowledgment, We thank Professor Hiroyasu Nomura at Nagoya University for his fruitful discussions. This work was supported in part by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science, and Culture. Registry No. MTHF, 96-47-9; MCH, 108-87-2; ZMB, 7 8 - 7 8 - 4 ;Py, 129-00-0; Py-, 34512-41-9. ( 1 8 ) Angell, C. A.; Sare, J. M.; Sara, E. J. J . Phys. Chem. 1978,82,2622. ( 1 9 ) Salk, G. A,; Labhart, H. J . Phys. Chem. 1968, 72, 752.
Triton X-1 00 Micelles in the FerrousjThionine Photogalvanic Cell E. J. J. Groenen,* M. S. de Groot, R. de Ruiter, and N. de Wit KoninklijkelShell- Laboratorium, Amsterdam (Shell Research B. V.), 1003 A A Amsterdam, The Netherlands (Received: April 19, 1983; In Final Form: July 14, 1983)
The effect of the nonionic amphiphile Triton X- 100 on the electrical performance of the ferrous/thionine photogalvanic cell has been analyzed. The addition of Triton X-100 micelles to the aqueous acidic cell solution leads to solubilization of the dye thionine in the outer poly(oxyethy1ene) spheres of the micelles. Consequently, the solubility of thionine increases and thermal back-reactions are suppressed, whereas the diffusion of species toward the electrodes slows down. An overall efficiency increase of a factor of 5 has been reached relative to the photogalvanic cell free of micelles.
1. Introduction
In a ferrous/thionine photogalvanic cell illumination of the solution results in photochemical electron transfer from ferrous ions to thionine. Excess electrons on the thionine molecules are transferred to one electrode (the “light” electrode) and, through an external electric load, taken up by ferric ions at the other electrode (the “dark” electrode). Ideally, the system acts as a (cyclic) light-driven electricity generator. Unfortunately, in homogeneous solutions back electron transfer also takes place. This dissipation of free energy constitutes a considerable problem in the use of the ferrous/thionine photogalvanic cell. In an effort to introduce a (spatial) barrier to this back electron transfer, we have studied the addition of micelles to a ferrous/thionine cell. In recent years it has been shown that certain micelles effectively delay back electron transfer in solutions.’ In addition to a slow back-reaction, an efficient photogalvanic cell requires that incident light be absorbed close to the light electrode in order to enable the electron-rich thionine species to reach the electrode by diffusion within its lifetime. In this respect the low solubility of thionine in aqueous acid solutions (pH N 1.8) implies a serious limitation. The solubility of thionine could be improved in several ways. Firstly, it may be enhanced by substitution with ionic or polar groups to give, for example, dis ~ l f o n a t e dor ~ ,N-substituted ~ t h i o n i n e ~ . ~Unfortunately, .~ these ( 1 ) M. Gratzel, Proc. Int. Conf: Photochem. Comers. Storage Sol. Energy, 3rd, 1980, 131 (1981). and references cited therein.
0022-3654/84/2088-1449$01.50/0
modified thionines turn out to show faster back electron transfer as well. Secondly, the use of a water/acetonitrile solvent mixture, instead of water, also improves the solubility of thionine, while slowing down back-reaction in solution.6 Finally, micelles are known to solubilize, preferentially, organic molecules in aqueous solutions. In connection with the above-mentioned problems, we have studied the effects of micelles on the performance of the ferrous/thionine photogalvanic cell. For reasons explained further on, we have concentrated on the nonionic amphiphile Triton X-100 as the micelle-forming agent. We investigated whether the addition of Triton X- 100 micelles has any considerable influence on the solvation and solubility of thionine, on back-reactions in solution, and on diffusion. Finally, we made an effort to explain the observed net photogalvanic effect by amalgamation of these individual factors.
2. Experimental Section The purification of thionine and the preparation of photogal( 2 ) W. J. Albery, P. N. Bartlett, J. P. Davies, A. W. Foulds, A. R. Hillman, and F. A. Souto-Bachiller, Faraday Discuss. Chem. SOC.7 0 , 341 (1980). ( 3 ) W. J. Albery, P. N. Bartlett, A. W. Foulds, F. A. Souto-Bachiller, and R. Whiteside, J . Chem. SOC.,Perkin Trans. 2, 794 (1981). ( 4 ) D. Creed, W. C. Burton, N. C. Fawcett, and M. T. Williams, Proc. Int. Con$ Photochem. Convers. Storage Sol. Energy, 3rd, 1980, 243 (1981). ( 5 ) J. C. M. Brokken-Zijp, M. J. van den Brink, P. A. J. M. Hendriks, and J. H. H. Mews, British Patent Application No. 8027812, Aug 28, 1980. ( 6 ) N. N. Lichtin; Proc. Int. Con$ Photochem. Conoers. Storage Sol. Energy, Ist, 1976, 119 (1977).
0 1984 American Chemical Society
1450 The Journal of Physical Chemistry, Vol. 88, No. 7, 1984 vanic solutions were performed as described earlier.’ Triton X-100 (Baker) was used as received. The photogalvanic cell was equipped with a transparent light electrode, which served as window, a platinum gauze counterelectrode in the dark part of the cell, and a Luggin saturated calomel reference electrode. The light electrode, made by evaporating gold onto Pyrex, had an average light transmission of about 40% between 400 and 700 nm. The area of the light electrode was 1.7 cm2;that of the dark electrode was large enough to prevent current limitation. In the photogalvanic experiment a solar simulator (900 W, Oriel) equipped with an AM1 filter was used as light source, the light intensity being varied by a series of square apertures placed in front of the optical integrator. A 460-nm cutoff filter and a water filter prevented UV and I R radiation from reaching the cell. The intensity of the light falling onto the entrance window of the cell, indicated below by I , was measured with a pyroelectric radiometer (Laser Precision Corp.). Transient spectroscopic measurements were performed on a homemade crossbeam instrument. In a perpendicular arrangement, light from a 150-W Xenon lamp induced the photochemical reaction, and a second beam monitored the absorption of thionine at 600 nm. In this way the reappearance of thionine was followed after switching off the exciting light with an electronically controlled mechanical shutter (10-90% in 5 ms).
3. Ferrous/Thionine Photogalvanic Cell and Choice of Triton x-100 Upon light absorption in the ferrous/thionine photogalvanic cell, the photoreduction of thionine (Th) by ferrous ions produces semithionine (S) and ferric ions. Semithionine rapidly disproportionates to thionine and leucothionine (L). U
S
Th
+NH,
H~+N
L
The following reaction scheme adequately summarizes the whole process, including the relevant recombination reactions (pH 53):’
+ Fe(2+) + H+ S + Fe(II1) 2s + H+&Th + L k-z
+ Fe(II1) -% Th + Fe(2+) + H+ L + Fe(II1) -% S + Fe(2+) + 2H+
S
(1)
(3)
(4)
The potential of the light electrode is determined by the dye and the iron couple and that of the dark electrode only by the iron couple because the electrode is in the nonirradiated part of the cell. light electrode
L-
k(’W
Fe(II1)
Th
dark electrode Fe(II1)
+ 3H+ + 2e
+ -
+e
We)
e
Fe(2+)
Fe(2+)
(5) (6) (7)
(7) J. C. M. Brokken-Zijp and M. S . de Groot, Chem. Phys. Lett., 76, 1 (1980).
Current is drawn by coupling the oxidation of leucothionine at the light electrode to the reduction of ferric at the dark electrode. In the ferrous/thionine cell all partners in the thermal backreactions (thionine, semithionine, leucothionine, and ferric ions predominantly present as FeS04(1+)) are positive ions. In our effort to improve the performance of the cell, we did not expect much benefit from the use of ionic amphiphiles: anionic micelles might accelerate the back-reaction by bringing together both reactants on the micellar “surface”, whereas cationic micelles would probably not have any effect unless specific solvation forces compensated for the electrostatic repulsion between the polar head groups of the amphiphiles and the dye. Indeed, two preliminary experiments seemed to support this conclusion: Whereas (i) addition of lo-’ mol.L-’ cetyltrimethylammonium bromide did not change the lifetime of leucothionine, (ii) the introduction of lo-’ mol-L-’ ferrous dodecyl sulfate caused the lifetime to be very short ( < O S s). It had also been reported recently8 that in the presence of lo-’ rno1.L-l sodium dodecyl sulfate the rate constant k4 is as high as lo6 L.mol-’.s-’ (compare 2.4 X lo2 without surfactant7). Hence, in our effort to improve the performance of the ferrous/thionine photogalvanic cell, we selected a nonionic micelle-forming agent, viz. Triton X-100. Triton X-100 consists of a poly(oxyethy1ene) chain linked to an aliphatic hydrocarbon chain via a benzene ring.
In water above the critical micelle concentration (cmc, about 2 X mol-L-’ for Triton X-loo), these amphiphilic molecules organize themselves into micelles: spherical aggregates of about 150 molecule^.^ The hydrocarbon chains extend into the interior of the micelle, whereas the hydrophilic poly(oxyethy1ene) groups protrude into the water phase. In this way nonpolar organic regions are created in water, and they are separated from the water by interphases of medium polarity. It is this heterogeneous medium that we tested as solvent for the ferrous/thionine photogalvanic cell.
4. Results and Discussion
U
Th
Groenen et al.
4.1. The Electrical Performance of the Ferrous/Thionine Cell in the Presence of Triton X-100. Figure 1 presents results for two different solutions in the same cell configuration. The two solutions were identical in concentrations of ferrous sulfate, ferric sulfate, and sulfuric acid. In addition, the ”standard” solution mol.L-’ thionine and the other lo-’ rno1.L-l contained 4.5 X Triton X-100 plus 4.6 X 10” mol-L-’ thionine (the presence of Triton X-100 allows a higher dye concentration, cf. section 4.2). At all light intensities both the open-circuit voltage V, and the short-circuit current i Ccome out considerably higher for the latter cell; for example, the power increases by a factor of 5.4 at a (day) light intensity of 35 mWcm-2. The variation of photovoltage and current as a function of the concentrations of thionine and Triton X-100 is represented in Table I. Both V,, and is, increase gradually with increasing thionine concentration. On the other hand, at a constant dye concentration the addition of Triton X-100, even up to lo-’ mol-L-’, hardly affects V,, and isc; at 3 X lo-’ mo1.L-’ a strong decrease sets in. Clearly, a correct understanding of these observations requires an analysis of the effect of Triton X-100 on several individual cell parameters such as the solubility and dimerization of thionine, the kinetics in the solution and at the electrodes, and the diffusion of the charge carriers in the solution toward the electrodes. 4.2. The Solvation of Thionine in the Presence of Triton X-100. The visible absorption spectrum of thionine in an aqueous acidic solution is shown in Figure 2, curve a. Upon addition of Triton (8) W. R. Bowen, Acta Chem. Scand., Ser. A . 35, 311 (1981). (9) K. Kalyanasundararn and J. K. Thomas in “Micellization, Solubilization and Microemulsions”,Vol. 2, K. L. Mittal, Ed., Plenum Press, New York, 1977, p 569; M. Corti and V . Degiorgio, Opt. Commun., 14, 3 5 8 (1975); H. H. Paradies, J . Phys. Chem., 84, 599 (1980).
The Journal of Physical Chemistry, Vol. 88, No. 7, 1984 1451
Triton X-100 Micelles
-'
'1 VIS
0.5
> E
\
0
1.0
1.5
2.0 2.5
>o I O 0
50 B
0
IO
50
30
70
I/mw cm-2
Figure 1. Open-circuit voltage V, and short-circuit current i, as a function of incident light intensity I for a standard ferrous/thionine cell (0)and a Triton X-100-containing cell (0).Solution compositions: (0) [Th] = 4.5 X mo1.L-I; ( 0 ) [Th] = 4.6 X lo4 mobL-', [Triton X-1001 = IO-1 mo1.L-l; for both solutions [Fe(2+)] = 1.25 X lo-, m o l X ' , [Fe(III)] = 4.8 X mol.L-', pH 1.7, anion sulfate. The curves were calculated as outlined in section 6 from the parameter values given below. Standard potentials: Ee(Th) = 0.410 V and Ee(Fe) = 0.676 V vs. NHE. Electron-transfer rate parameters: k,(Th) = 5 X cm-s-', a,(Th) = 0.5, k,(Fe) = 3.1 X cm&, a,(Fe) = 0.23. Diffusion layer thickness 3 X cm.20 Rate constants (for the Triton X-I00 cell in parentheses): k2 = 2.4 X IO9 (5.0 X lo8) Lmol-'.s-', k-, = 1.0 X lo4 (6.6 X lo3) Lmol-k', k3 = 5.8 X lo5 (6.5 X lo4) La mol-'.s-l, and k, = 2.4 X 10, (1.6 X 10,) Lmol-'.s-'. Diffusion coefficients (for the Triton X-100 cell in parentheses): D(L) = 5.6 X 10" (1.2 X 10.") c m 2 d , D(Fe(II1)) = 5.4 X 10" (3.8 X 10") c m 2 d .
TABLE I: Variation of Open-circuit Voltage V,, and Short-circuit Current is, with Thionine and Triton X-100 Concentrations at an Incident Light Intensity of 70 mW.crn-' [Triton X-1001 = 10" mol. L[thionine],
a
[thionine] = 2.1 X mo1.L-I
-
is,,
mol*L-'
VOc, PA; mV cm'
7.0 X 2.6 X 4.6 X
165 176 180
19 47 65
[Triton X-1001,
V,,,
mo1.L-I
mV
0
5.4 X lo-' 1.0 X lo-' 3.0 X lo-' 5.0 X lo-'
178 177 172 120
isc, PA. cm-2 41b 42 44 33
16 a For all solutions: [Fe(2+)]= 1.25 X lo-' mol.L-', [Fe(III)] = 4.8 X mol.L-', pH 1.7, anion sulfate. Extrapolated from measurements at lower thionine concentrations in the absence of Triton X-100.
X- 100 above cmc, this spectrum shifts bathochromically, to curve b, which is indicative of a change in the solvation sphere of the dye. As the shift is small, it seems likely that thionine does not penetrate into the inner (hydrocarbon) core of the micelle but is solvated by the ply(oxyethy1ene)s at the micelle/water interphase. The polarity in this region resembles that in methanol,10 in agreement with the similarity of the spectrum (Figure 2, curve b) with that in pure methanol. In the micelle-containing solution the aggregation of thionine is suppressed and its solubility increased. The spectrum of a highly concentrated solution of thionine in water (Figure 2, curve c; high concentration only attainable a t p H much too high for a ferrous/thionine cell) clearly shows additional absorption bands due to dimers." These absorption bands are absent when Triton X-100 (10-1 mol-L-') is present in the solution (cf. curve b). Thus, it appears that Triton X-100 suppresses dimer formation of thionine, which would tend to improve the performance of the (10) P. Mukerjee, J. R. Cardinal, and N. R. Desai, ref 9, Vol. I,p 2 4 1 . (1 1) E. Rabinowitch and L. F. Epstein, J . Am. Chem. Soc., 63, 69 (1941).
I 400
1
1
I
500
600
700
A /nm mol.L-' thionine in Figure 2. Absorption spectra of thionine: (a) aqueous sulfuric acid (pH 1.7); (b) 4 X lo4 mo1.L-I thionine in aqueous sulfuric acid (pH 1.7) containing IO-' mol-L-' Triton X-100; (c) mo1.L-I thionine in aqueous sulfuric acid (pH 5).
TABLE 11: Solubility of Thionine in Aqueous Sulfuric Acid (pH 1.7) as a Function of Triton X-100 Concentration [Triton [Triton X-1001, [thionineImax, X-1001, [thionine]max, molL" mobL-' mobL-' mo1.L-l 0 7 x 10-5 10-l 5 x 10-4 3 x lo-' 10-3 10-3 7 x 109 x 10-5 photogalvanic cell because dimers are known to transform absorbed light only into heat.I2 The increased solubility of thionine in the presence of Triton X-100 is represented in Table 11: whereas it is limited to about 7 X mol-L-' in aqueous sulfuric acid, the solubility increases to mo1.L-' at a Triton X-100 concentration of 3 X 10-1 mol.L-l (pH 1.7). Additional evidence for the solvation of thionine in the outer poly(oxyethy1ene) phase of the micelles is obtained from the following experiment. Poly(ethy1ene glycol) (molecular weight 400) resembles the poly(oxyethy1ene) moiety of Triton X-100 and mixes homogeneously with water. Addition of 1 mo1.L-' poly(ethylene glycol) to an aqueous acidic solution of thionine shifts the absorption band and increases the solubility to mol.L-l, comparable to the solubility at 3 X 10-1 mo1.L-I Triton X-100. This clearly indicates that thionine becomes solvated by the poly(oxyethy1ene) chains. As far as the solubility of thionine is concerned, the specific effect of the micelles is merely to create a high local poly(oxyethy1ene) concentration at a relatively low overall amphiphile concentration. Apparently, in an aqueous acidic solution containing Triton X-100 and thionine, three forms of thionine are present: monomers in the water phase (Th"), dimers in the water phase (Th,"), and monomers in the micellar phase (Th"). It proved possible to resolve the composition of any solution by deconvolution of the visible absorption spectrum in the following way. For each wavelength the absorbance A(X) may be written as A(X) = I(c(X;Th")[Th"] + c(X;Th,W)[Th,W]+ t(X;Thm)[Thm]] (8) where 1 represents the optical path length and c(A;x) the molar extinction coefficient of species x at wavelength A. The absorption bands of monomer and dimer thionine in water, t(X;ThW)and (12) D. E. Hall, W. D. K. Clark, J. Eckert, N. N. Lichtin, and P. D. Wildes, Am. Ceram. SOC.Bull., 56, 408 (1977).
1452 The Journal of Physical Chemistry, Vol. 88, No. 7, 1984
C ( X ; T ~ , ~were ) , determined from a study of the spectrum in aqueous sulfuric acid (pH 1.7) as a function of thionine concentration.] l , I 3 Furthermore, the thionine monomer spectrum in the micellar phase, t( X;Thm),was obtained from the absorption spectrum at high Triton X-100 concentration. It was found that above 2 X lo-' mo1.L-' Triton X-100 the position and shape of the thionine spectrum become independent of both the thionine and the Triton X- 100 concentrations, indicating that all thionine molecules are present as monomers in the micelles. We have therefore taken the absorption band of 1.1 X 10" mo1.L-I thionine in an aqueous acidic solution (pH 1.7) containing 3.2 X lo-' mol..L-' Triton X-100 to represent e(X;Thm). The spectra of the three species being known, the fraction of each species in a particular solution could be determined from a fit of the visible absorption spectrum according to eq 8 . For one thionine concentration the result is shown as a function of the Triton X-100 concentration in Figure 3. At Triton X-100 concentrations above cmc a gradually increasing fraction of the thionine becomes solvated in the micelles, while ThWand Th2Wfractions decrease. If for the moment we assume one thionine molecule per Triton X-100 micelle, we may define the equilibrium constant describing the distribution of thionine over the aqueous and the micellar phases as [Thm]/[ThW]([Triton X-1001 - cmc). This ratio was found to have a value of 80 f 20 L-mol-'. The solvation of thionine being known, we have to consider the distribution of semi- and leucothionine over the aqueous and the micellar phases. We assume the solvation of these reduced forms to be similar to that for thionine, which seems reasonable in view of the pH of 1.7 employed in this study. It has been found that leucothionine may be separated from an aqueous phase by extraction with diethyl ether at a pH of 3.8.14 We have shown that this is only possible at high pH values, which suggests that deprotonation of leucothionine (which renders the dye neutral) is inv01ved.I~ However, at the p H of 1.7, at which we performed the present experiments, there is no indication that the reduced forms of thionine are more or less hydrophilic than thionine. 4.3. The Homogeneous Kinetics in the Presence of Triton X-100. As indicated in the Introduction, we assumed that, owing to the preferred solvation of thionine in the micellar phase and ferric in the water phase, a delay of the back-reactions might result from the spatial separation of the reaction partners. In order to verify this assumption, the rate of the back-reactions was measured in the presence of Triton X-100. Previous work in our laboratory' had shown that analysis of the reappearance of thionine with time, after switching off the exciting light, permits the determination of k-2, k3, and k4 (if k2 is known). We now applied the same procedure to solutions containing 10-'-3 X IO-' mol-L-' Triton X-100, i.e. solutions in which thionine is (mainly) present as Thm. Rate constants are summarized in Table 111. In comparison with the micelle-free aqueous sulfuric acid solution, both back-reactions 3 and 4 are slower. The semithionine/ferric reaction is delayed by 1 order of magnitude, while for the leucothionine/ferric reaction a factor of 2 is found. 4.4. The Electrode Reactions in the Presence of Triton X-100. Separate measurements on the Fe(III)/Fe(2+) and Th/L couple showed that the standard redox potentials, Ee, do not change upon addition of Triton X-100, except for a possible slight decrease (lo-' mol.L-'. In general, the Fe(III)/Fe(2+) electron-transfer rate changes upon addition of Triton- 100, as we have amply verified for platinum, carbon, and tin dioxide electrodes. When we realize the surfactant nature of Triton X-100, this is not surprising because the rate of the Fe(III)/Fe(2+) electron transfer is known to depend strongly on the nature of the electode surface." However, we preferred (13) (14) (1 5) (16) (1961). (17)
J. Lavorel, J. Phys. Chem., 61, 1600 (1957). K . 6. Mathai and E. Rabinowitch, J . Phys. Chem., 66, 663 (1962). D. Reinalda, personal communication. C. G. Hatchard and C. A. Parker, Trans. Faraday Soc., 57, 1093
M. D. Archer, M. I. C. Ferreira, W. J. Albery, and A. R. Hillman, J . ElecrroanaL G e m . Interfacial Electrochem. 111, 295 (1980); D. E. Hall, P. D. Wildes, and N. N. Lichtin, J . Electrochem. Soc., 125, 1365 (1978); E. J. J. Groenen, M . S . de Groot, and R. de Ruiter, to be submitted for publication.
Groenen et ai.
0.5-
-
0 CMC
I
0
LO^ [TRITON r-roo]
Figure 3. Distribution of thionine over different forms as a function of Triton X-100 concentration in an aqueous sulfuric acid solution, (pH 1.7) containing 1.43 X mo1.L'' thionine in all. TABLE 111: Rate Constants for the Homogeneous Reactions as a Function of Triton X-100 Concentration
0 10-1 3 x 10-1
2.4a OSOb 0.21b
*
1.0' 0.66 0.42
5.8c 0.65 0.34
2.4' 1.6 1.1
From ref 16. Calculated from k , in the absence of Triton X-100, assuming reaction 2 to be diffusion controlled ( k , Dapp(Th)). From ref 7.
'
-
to eliminate this effect here, to allow a clear recognition of the homogeneous effects of Triton X-100. Therefore, in the present study we used gold on Pyrex as the light electrode, for which k(Fe) turned out to be insensitive to the addition of Triton X-100. The Th/L electron transfer is fast, irrespective of the electrode material, and does not change in the presence of Triton X-100. The electrochemical parameters characterizing the electron transfers at the gold film electrode were found to be the following: k,(Th) = 5 X loT3c m d , a,(Th) = 0.5 (from cyclic voltammetry) and k,(Fe) = 3.1 X cms-I, a,(Fe) = 0.23 (from differential pulse voltammetry), where k, represents the value of k at E = Ee and a,(a,) the anodic (cathodic) transfer coefficient (cf. eq 5 and 6).21 4.5. Diffusion in the Presence of Triton X-100. The diffusion of ferrous and ferric ions was studied electrochemically by using a platinum rotating disk electrode. At the sulfate concentrations used in the present study, D(Fe2+) and D(Fe"') were found to be equal within 5%. The variation of the ferrous (ferric) diffusion coefficient with the Triton X-100 concentration is represented in Figure 4, curve a. A slight decrease in the diffusion coefficient occurs around the cmc, but no serious transport limitation is found up to a Triton X-100 concentration of 0.15 mo1.L-I. At still higher concentrations there is a sudden decrease in the diffusion coefficient coinciding with a strong increase in the viscosity of the solution (cf. Figure 4, curve c). Probably, the description of the solution in terms of spherical aggregates of Triton X-100 in water then no longer applies. We also studied the diffusion of thionine in the presence of Triton X- 100 electrochemically using differential pulse voltammetry. The description of the transport of charge by the dye toward an electrode is complicated because two potential charge carriers are present, which have quite different diffusion coefficients: (i) thionine in the water phase with D(ThW)= 5.6 X lo6 crn*Bs-' (determined in the absence of Triton X-100 from the limiting current at a platinum rotating disk electrode) and (ii) thionine in the Triton X-100 micelles with a much lower diffusion cm2.s-l (taken equal to the coefficient D(Thm) = 3.5 X diffusion coefficient of the Triton X- 100 r n i ~ e l l e s ~ ~ ' ~ ) .
The Journal of Physical Chemistry, Vol. 88, No. 7, 1984 1453
Triton X-100 Micelles
i"
IO3
'K' DECREASE
St
I
I O 2'
Th INCREASE
i
' D' DECREPSE
i n
I
I
I
r
Fe
--
0
I
I
-4
-3
ctMc
o
i
t
I I I -2 -I 0 Log [TRITON x-too]
STAN D ARD
Figure 4. Diffusion coefficientsDaPp(Th),D(Fe2+),and D(Fe(II1))and the kinematic viscosity q as a function of Triton X-100 concentration.
FERROUS / T HlON I NE CELL
Diffusion coefficients are deduced from electrochemical measurements on aqueous sulfuric acid solutions (pH 1.7) containing 4 X mo1.L-' thionine ( O ) , 5 X rno1.L-l Fe(2+) (o),or 5 X mo1.L-I Fe(II1)
(.I To simplify the calculation of the electrical response of the photogalvanic cell (section 4.6), we want to describe the transport of charge by thionine as if it were carried by only one (imaginary) species. We therefore interpret the change of the differential pulse voltammetric current in the presence of Triton X-100 in terms of an apparent diffusion coefficient D,,,(Th): Da,,(Th)1/2 = (ip/ipW)D(ThW)1/2
s
(9)
where ip(ipw)represents the peak current of the differential pulse voltammogram wrresponding to thionine reduction in the presence (absence) of Triton X-100. The square root of the diffusion coefficients occurs in eq 9 because of the assumption of semiinfinite linear diffusion to a planar electrode. The resultant values for the apparent diffusion coefficient of thionine as a function of the concentration of Triton X-100 are given in Figure 4, curve b. A continuous decrease in D,,,(Th) is found for Triton X-100 concentrations higher than mol-L-'. This decrease is not unexpected in view of the changing solution composition: as shown before, the higher the Triton X-100 concentration, the more thionine will be present as Thm,which is the species with the lower diffusion coefficient. However, quantitatively the value of D,,,(Th) cannot be simply related to the bulk composition. The contribution of ThWand Th" to the current is determined by their diffusion coefficients and by the rate of interchange of ThWand Th". The more severe concentration polarization for Thmcauses the transformation of Th" into Th", thereby enhancing the contribution of Th" to the current. This is clearly illustrated by the value of D,,,(Th) at lo-' mol.L-' Triton X-100. Although only about 10% of thionine is present as Th", the value of D,,,(Th) is still 3 times that of D(Thm). Indeed, the faster diffusing species transports a relatively larger part of the charge than expected on the basis of the bulk composition. For the photogalvanic cell, the following conclusion may be drawn. At lo-' mo1.L-' Triton X-100, a suitable concentration in the ferrous/thionine cell, the diffusion coefficient of ferric is reduced to about 70% and that of thionine to about 20% of its (18) N. Shinozuka and S. Hayano in "Solution Chemistry of Surfactants," Vol. 2, Plenum Press, New York, 1979, p 599.
I
FER ROUS / THIONINE/ TRITON X-1103 CELL
Figure 5. Model calculations of V, and iscat u = 2 (corresponding to a light intensity of 56 mW.cm'2). The solid lines on the left side correspond to the Triton-free cell in Figure 1, and the one on the right side corresponds to the Triton-containingcell in Figure 1. In between, results are given for hypothetical cells, in which only the dye concentration was increased or the dye concentration was increased in combination with adaptation of the rate constants to the Triton X-100 situation. Parameter values are given in Figure 1.
value in pure water. This means that especially the necessary transport of leucothionine to the light electrode becomes seriously hampered (D(L) assumed equal to D(Th)). 4.6. Model Calculations of the Photovoltage and Current. In our laboratory a model has been formulated for the ferrous/ thionine photogalvanic cell that permits the computation of the current/voltage characteristic at any solution composition and light intensity, if the rate parameters describing the solution and electrode reactions as well as the diffusion coefficients are In the present work we applied the model to analyze kn0wn.'~3~~ the changes that occur upon addition of Triton X-100 to the cell. To this end we first computed the open-circuit voltage V,, and short-circuit current is, as a function of light intensity for the cells discussed in section 4.1 (cf. Figure 1). In the model V,, and is, are calculated as a function of a parameter u, which is proportional to the incident light intensity I and the fraction of excited thionine converted to semithionine (reaction 1). The measured value of V, for the cell free of Triton X-100 at 35 mW.cm-2 was used to match the experimental I vs. the theoretical u scale. Subsequently, the whole V, and is, curves as a function of light intensity for the Triton X-100-free cell could be calculated. The computed curves shown in Figure 1 indicate that agreement between experiment and theory is satisfactory. The experiments described in sections 4.2-4.5 provided us with all the parameter values necessary for computations on the cell containing lo-' mol-L-' Triton X- 100: the (monomer) dye concentration, the homogeneous rate constants, and the diffusion coefficients. It appears from Figure 1 that, in this case, too, the calculations reproduce the (19) J. C. M. Brokken-Zijp, M. S . de Groot, and P. A. J. M. Hendriks, Chem. Phys. Lett., 81, 129 (1981). (20) M. S . de Groot, P. A. J. M. Hendriks, and J. C. M. Brokken-Zijp, Chem. Phys. Lett., 97, 521 (1983). (21) The rate constant k, is related to the standard exchange current density via = nFk,, where n is the number of electrons transferred and F is Faraday's constant.
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The Journal of Physical Chemistry, Vol. 88, No. 7, 1984
experiment very well. It is noteworthy that no change of the u / I calibration was needed, indicating that the initial photoreduction (reaction 1) is about as efficient in the presence as in the absence of Triton X- 100. When we accept that the model calculations reproduce the photoeffects well, it is instructive to repeat the computations starting from the standard cell and to introduce the various effects of Triton X-100 one by one. The resulting scheme, represented in Figure 5, shows in succession the advantage of the higher thionine concentration and the slower back-reactions and the disadvantage of the delayed mass transport. The decrease in voltage and current due to the slower diffusion actually obliterates the beneficial effect of the retardation of the back-reactions. In the final result for the Triton X-100-containing cell, one only recovers the advantage of the higher thionine concentration. Therefore, addition of Triton X-100 to the ferrous/thionine cell while keeping the thionine concentration constant hardly affects the electrical output of the cell. This result explains the variation of the cell power with the thionine and Triton X-100 concentrations
Additions and Corrections as described in section 4.1 (cf. Table I). 5. Conclusions The present study has shown that addition of nonionic Triton X- 100 micelles to an aqueous acidic ferrous/thionine cell leads to solubilization of the dye thionine in the outer poly(oxyethy1ene) spheres of the micelles. This results in a considerable increase in the solubility of thionine and, owing to the spatial separation of semi- and leucothionine from ferric ions, a significant delay of the energy dissipating back-reactions. Both effects add significantly to the efficiency of the cell. On the other hand, addition of Triton X-100 impairs diffusion. The inclusion of leucothionine in the micelles causes a retardation of its diffusion toward the light electrode. In fact, the slower mass transport more or less neutralizes the benefit of the longer lifetime of the charge carriers. The overall effect of Triton X-100 is favorable, to the extent that in practical cases an improvement in efficiency of a factor of 5 has been obtained. Registry No. Triton X-100, 9002-93-1.
ADDITIONS AND CORRECTIONS 1983, Volume 87 Helmut Haberlandt* and Friedrich Ritschl Quantum Chemical Investigation of Support-Metal Interactions and Their Influence on Chemisorption. Page 3250. The diagram shown in Figure 5 gives the electronic energy level schemes with an H atom chemisorbed to the models Aa, Ab, and Ac. It should be replaced by the following diagram which illustrates the situation described in the figure caption: Nigd-Nigd a.b.
Figure 5.
=
